--- /dev/null
+# suppress compiler/linker output\r
+*.[oa]\r
+Debug/\r
+Release/\r
+\r
+# special MS Visual Studio section\r
+# ignore non-compressed browse file (holds information for ClassView, IntelliSense and WizardBar)\r
+*.ncb\r
+# ignore user specific settings\r
+*.user\r
+*.suo\r
+\r
+# ignore stuff generated by "make manual" and "make poster"\r
+*.aux\r
+*.dvi\r
+*.idx\r
+*.lof\r
+*.log\r
+*.out\r
+*.toc\r
+*.ilg\r
+*.ind\r
+*.pdf\r
--- /dev/null
+LibTomMath is licensed under DUAL licensing terms.
+
+Choose and use the license of your needs.
+
+[LICENSE #1]
+
+LibTomMath is public domain. As should all quality software be.
+
+Tom St Denis
+
+[/LICENSE #1]
+
+[LICENSE #2]
+
+ DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE
+ Version 2, December 2004
+
+ Copyright (C) 2004 Sam Hocevar <sam@hocevar.net>
+
+ Everyone is permitted to copy and distribute verbatim or modified
+ copies of this license document, and changing it is allowed as long
+ as the name is changed.
+
+ DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE
+ TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
+
+ 0. You just DO WHAT THE FUCK YOU WANT TO.
+
+[/LICENSE #2]
--- /dev/null
+\documentclass[synpaper]{book}
+\usepackage{hyperref}
+\usepackage{makeidx}
+\usepackage{amssymb}
+\usepackage{color}
+\usepackage{alltt}
+\usepackage{graphicx}
+\usepackage{layout}
+\def\union{\cup}
+\def\intersect{\cap}
+\def\getsrandom{\stackrel{\rm R}{\gets}}
+\def\cross{\times}
+\def\cat{\hspace{0.5em} \| \hspace{0.5em}}
+\def\catn{$\|$}
+\def\divides{\hspace{0.3em} | \hspace{0.3em}}
+\def\nequiv{\not\equiv}
+\def\approx{\raisebox{0.2ex}{\mbox{\small $\sim$}}}
+\def\lcm{{\rm lcm}}
+\def\gcd{{\rm gcd}}
+\def\log{{\rm log}}
+\def\ord{{\rm ord}}
+\def\abs{{\mathit abs}}
+\def\rep{{\mathit rep}}
+\def\mod{{\mathit\ mod\ }}
+\renewcommand{\pmod}[1]{\ ({\rm mod\ }{#1})}
+\newcommand{\floor}[1]{\left\lfloor{#1}\right\rfloor}
+\newcommand{\ceil}[1]{\left\lceil{#1}\right\rceil}
+\def\Or{{\rm\ or\ }}
+\def\And{{\rm\ and\ }}
+\def\iff{\hspace{1em}\Longleftrightarrow\hspace{1em}}
+\def\implies{\Rightarrow}
+\def\undefined{{\rm ``undefined"}}
+\def\Proof{\vspace{1ex}\noindent {\bf Proof:}\hspace{1em}}
+\let\oldphi\phi
+\def\phi{\varphi}
+\def\Pr{{\rm Pr}}
+\newcommand{\str}[1]{{\mathbf{#1}}}
+\def\F{{\mathbb F}}
+\def\N{{\mathbb N}}
+\def\Z{{\mathbb Z}}
+\def\R{{\mathbb R}}
+\def\C{{\mathbb C}}
+\def\Q{{\mathbb Q}}
+\definecolor{DGray}{gray}{0.5}
+\newcommand{\emailaddr}[1]{\mbox{$<${#1}$>$}}
+\def\twiddle{\raisebox{0.3ex}{\mbox{\tiny $\sim$}}}
+\def\gap{\vspace{0.5ex}}
+\makeindex
+\begin{document}
+\frontmatter
+\pagestyle{empty}
+\title{LibTomMath User Manual \\ v0.42.0}
+\author{Tom St Denis \\ tomstdenis@gmail.com}
+\maketitle
+This text, the library and the accompanying textbook are all hereby placed in the public domain. This book has been
+formatted for B5 [176x250] paper using the \LaTeX{} {\em book} macro package.
+
+\vspace{10cm}
+
+\begin{flushright}Open Source. Open Academia. Open Minds.
+
+\mbox{ }
+
+Tom St Denis,
+
+Ontario, Canada
+\end{flushright}
+
+\tableofcontents
+\listoffigures
+\mainmatter
+\pagestyle{headings}
+\chapter{Introduction}
+\section{What is LibTomMath?}
+LibTomMath is a library of source code which provides a series of efficient and carefully written functions for manipulating
+large integer numbers. It was written in portable ISO C source code so that it will build on any platform with a conforming
+C compiler.
+
+In a nutshell the library was written from scratch with verbose comments to help instruct computer science students how
+to implement ``bignum'' math. However, the resulting code has proven to be very useful. It has been used by numerous
+universities, commercial and open source software developers. It has been used on a variety of platforms ranging from
+Linux and Windows based x86 to ARM based Gameboys and PPC based MacOS machines.
+
+\section{License}
+As of the v0.25 the library source code has been placed in the public domain with every new release. As of the v0.28
+release the textbook ``Implementing Multiple Precision Arithmetic'' has been placed in the public domain with every new
+release as well. This textbook is meant to compliment the project by providing a more solid walkthrough of the development
+algorithms used in the library.
+
+Since both\footnote{Note that the MPI files under mtest/ are copyrighted by Michael Fromberger. They are not required to use LibTomMath.} are in the
+public domain everyone is entitled to do with them as they see fit.
+
+\section{Building LibTomMath}
+
+LibTomMath is meant to be very ``GCC friendly'' as it comes with a makefile well suited for GCC. However, the library will
+also build in MSVC, Borland C out of the box. For any other ISO C compiler a makefile will have to be made by the end
+developer.
+
+\subsection{Static Libraries}
+To build as a static library for GCC issue the following
+\begin{alltt}
+make
+\end{alltt}
+
+command. This will build the library and archive the object files in ``libtommath.a''. Now you link against
+that and include ``tommath.h'' within your programs. Alternatively to build with MSVC issue the following
+\begin{alltt}
+nmake -f makefile.msvc
+\end{alltt}
+
+This will build the library and archive the object files in ``tommath.lib''. This has been tested with MSVC
+version 6.00 with service pack 5.
+
+\subsection{Shared Libraries}
+To build as a shared library for GCC issue the following
+\begin{alltt}
+make -f makefile.shared
+\end{alltt}
+This requires the ``libtool'' package (common on most Linux/BSD systems). It will build LibTomMath as both shared
+and static then install (by default) into /usr/lib as well as install the header files in /usr/include. The shared
+library (resource) will be called ``libtommath.la'' while the static library called ``libtommath.a''. Generally
+you use libtool to link your application against the shared object.
+
+There is limited support for making a ``DLL'' in windows via the ``makefile.cygwin\_dll'' makefile. It requires
+Cygwin to work with since it requires the auto-export/import functionality. The resulting DLL and import library
+``libtommath.dll.a'' can be used to link LibTomMath dynamically to any Windows program using Cygwin.
+
+\subsection{Testing}
+To build the library and the test harness type
+
+\begin{alltt}
+make test
+\end{alltt}
+
+This will build the library, ``test'' and ``mtest/mtest''. The ``test'' program will accept test vectors and verify the
+results. ``mtest/mtest'' will generate test vectors using the MPI library by Michael Fromberger\footnote{A copy of MPI
+is included in the package}. Simply pipe mtest into test using
+
+\begin{alltt}
+mtest/mtest | test
+\end{alltt}
+
+If you do not have a ``/dev/urandom'' style RNG source you will have to write your own PRNG and simply pipe that into
+mtest. For example, if your PRNG program is called ``myprng'' simply invoke
+
+\begin{alltt}
+myprng | mtest/mtest | test
+\end{alltt}
+
+This will output a row of numbers that are increasing. Each column is a different test (such as addition, multiplication, etc)
+that is being performed. The numbers represent how many times the test was invoked. If an error is detected the program
+will exit with a dump of the relevent numbers it was working with.
+
+\section{Build Configuration}
+LibTomMath can configured at build time in three phases we shall call ``depends'', ``tweaks'' and ``trims''.
+Each phase changes how the library is built and they are applied one after another respectively.
+
+To make the system more powerful you can tweak the build process. Classes are defined in the file
+``tommath\_superclass.h''. By default, the symbol ``LTM\_ALL'' shall be defined which simply
+instructs the system to build all of the functions. This is how LibTomMath used to be packaged. This will give you
+access to every function LibTomMath offers.
+
+However, there are cases where such a build is not optional. For instance, you want to perform RSA operations. You
+don't need the vast majority of the library to perform these operations. Aside from LTM\_ALL there is
+another pre--defined class ``SC\_RSA\_1'' which works in conjunction with the RSA from LibTomCrypt. Additional
+classes can be defined base on the need of the user.
+
+\subsection{Build Depends}
+In the file tommath\_class.h you will see a large list of C ``defines'' followed by a series of ``ifdefs''
+which further define symbols. All of the symbols (technically they're macros $\ldots$) represent a given C source
+file. For instance, BN\_MP\_ADD\_C represents the file ``bn\_mp\_add.c''. When a define has been enabled the
+function in the respective file will be compiled and linked into the library. Accordingly when the define
+is absent the file will not be compiled and not contribute any size to the library.
+
+You will also note that the header tommath\_class.h is actually recursively included (it includes itself twice).
+This is to help resolve as many dependencies as possible. In the last pass the symbol LTM\_LAST will be defined.
+This is useful for ``trims''.
+
+\subsection{Build Tweaks}
+A tweak is an algorithm ``alternative''. For example, to provide tradeoffs (usually between size and space).
+They can be enabled at any pass of the configuration phase.
+
+\begin{small}
+\begin{center}
+\begin{tabular}{|l|l|}
+\hline \textbf{Define} & \textbf{Purpose} \\
+\hline BN\_MP\_DIV\_SMALL & Enables a slower, smaller and equally \\
+ & functional mp\_div() function \\
+\hline
+\end{tabular}
+\end{center}
+\end{small}
+
+\subsection{Build Trims}
+A trim is a manner of removing functionality from a function that is not required. For instance, to perform
+RSA cryptography you only require exponentiation with odd moduli so even moduli support can be safely removed.
+Build trims are meant to be defined on the last pass of the configuration which means they are to be defined
+only if LTM\_LAST has been defined.
+
+\subsubsection{Moduli Related}
+\begin{small}
+\begin{center}
+\begin{tabular}{|l|l|}
+\hline \textbf{Restriction} & \textbf{Undefine} \\
+\hline Exponentiation with odd moduli only & BN\_S\_MP\_EXPTMOD\_C \\
+ & BN\_MP\_REDUCE\_C \\
+ & BN\_MP\_REDUCE\_SETUP\_C \\
+ & BN\_S\_MP\_MUL\_HIGH\_DIGS\_C \\
+ & BN\_FAST\_S\_MP\_MUL\_HIGH\_DIGS\_C \\
+\hline Exponentiation with random odd moduli & (The above plus the following) \\
+ & BN\_MP\_REDUCE\_2K\_C \\
+ & BN\_MP\_REDUCE\_2K\_SETUP\_C \\
+ & BN\_MP\_REDUCE\_IS\_2K\_C \\
+ & BN\_MP\_DR\_IS\_MODULUS\_C \\
+ & BN\_MP\_DR\_REDUCE\_C \\
+ & BN\_MP\_DR\_SETUP\_C \\
+\hline Modular inverse odd moduli only & BN\_MP\_INVMOD\_SLOW\_C \\
+\hline Modular inverse (both, smaller/slower) & BN\_FAST\_MP\_INVMOD\_C \\
+\hline
+\end{tabular}
+\end{center}
+\end{small}
+
+\subsubsection{Operand Size Related}
+\begin{small}
+\begin{center}
+\begin{tabular}{|l|l|}
+\hline \textbf{Restriction} & \textbf{Undefine} \\
+\hline Moduli $\le 2560$ bits & BN\_MP\_MONTGOMERY\_REDUCE\_C \\
+ & BN\_S\_MP\_MUL\_DIGS\_C \\
+ & BN\_S\_MP\_MUL\_HIGH\_DIGS\_C \\
+ & BN\_S\_MP\_SQR\_C \\
+\hline Polynomial Schmolynomial & BN\_MP\_KARATSUBA\_MUL\_C \\
+ & BN\_MP\_KARATSUBA\_SQR\_C \\
+ & BN\_MP\_TOOM\_MUL\_C \\
+ & BN\_MP\_TOOM\_SQR\_C \\
+
+\hline
+\end{tabular}
+\end{center}
+\end{small}
+
+
+\section{Purpose of LibTomMath}
+Unlike GNU MP (GMP) Library, LIP, OpenSSL or various other commercial kits (Miracl), LibTomMath was not written with
+bleeding edge performance in mind. First and foremost LibTomMath was written to be entirely open. Not only is the
+source code public domain (unlike various other GPL/etc licensed code), not only is the code freely downloadable but the
+source code is also accessible for computer science students attempting to learn ``BigNum'' or multiple precision
+arithmetic techniques.
+
+LibTomMath was written to be an instructive collection of source code. This is why there are many comments, only one
+function per source file and often I use a ``middle-road'' approach where I don't cut corners for an extra 2\% speed
+increase.
+
+Source code alone cannot really teach how the algorithms work which is why I also wrote a textbook that accompanies
+the library (beat that!).
+
+So you may be thinking ``should I use LibTomMath?'' and the answer is a definite maybe. Let me tabulate what I think
+are the pros and cons of LibTomMath by comparing it to the math routines from GnuPG\footnote{GnuPG v1.2.3 versus LibTomMath v0.28}.
+
+\newpage\begin{figure}[here]
+\begin{small}
+\begin{center}
+\begin{tabular}{|l|c|c|l|}
+\hline \textbf{Criteria} & \textbf{Pro} & \textbf{Con} & \textbf{Notes} \\
+\hline Few lines of code per file & X & & GnuPG $ = 300.9$, LibTomMath $ = 71.97$ \\
+\hline Commented function prototypes & X && GnuPG function names are cryptic. \\
+\hline Speed && X & LibTomMath is slower. \\
+\hline Totally free & X & & GPL has unfavourable restrictions.\\
+\hline Large function base & X & & GnuPG is barebones. \\
+\hline Five modular reduction algorithms & X & & Faster modular exponentiation for a variety of moduli. \\
+\hline Portable & X & & GnuPG requires configuration to build. \\
+\hline
+\end{tabular}
+\end{center}
+\end{small}
+\caption{LibTomMath Valuation}
+\end{figure}
+
+It may seem odd to compare LibTomMath to GnuPG since the math in GnuPG is only a small portion of the entire application.
+However, LibTomMath was written with cryptography in mind. It provides essentially all of the functions a cryptosystem
+would require when working with large integers.
+
+So it may feel tempting to just rip the math code out of GnuPG (or GnuMP where it was taken from originally) in your
+own application but I think there are reasons not to. While LibTomMath is slower than libraries such as GnuMP it is
+not normally significantly slower. On x86 machines the difference is normally a factor of two when performing modular
+exponentiations. It depends largely on the processor, compiler and the moduli being used.
+
+Essentially the only time you wouldn't use LibTomMath is when blazing speed is the primary concern. However,
+on the other side of the coin LibTomMath offers you a totally free (public domain) well structured math library
+that is very flexible, complete and performs well in resource contrained environments. Fast RSA for example can
+be performed with as little as 8KB of ram for data (again depending on build options).
+
+\chapter{Getting Started with LibTomMath}
+\section{Building Programs}
+In order to use LibTomMath you must include ``tommath.h'' and link against the appropriate library file (typically
+libtommath.a). There is no library initialization required and the entire library is thread safe.
+
+\section{Return Codes}
+There are three possible return codes a function may return.
+
+\index{MP\_OKAY}\index{MP\_YES}\index{MP\_NO}\index{MP\_VAL}\index{MP\_MEM}
+\begin{figure}[here!]
+\begin{center}
+\begin{small}
+\begin{tabular}{|l|l|}
+\hline \textbf{Code} & \textbf{Meaning} \\
+\hline MP\_OKAY & The function succeeded. \\
+\hline MP\_VAL & The function input was invalid. \\
+\hline MP\_MEM & Heap memory exhausted. \\
+\hline &\\
+\hline MP\_YES & Response is yes. \\
+\hline MP\_NO & Response is no. \\
+\hline
+\end{tabular}
+\end{small}
+\end{center}
+\caption{Return Codes}
+\end{figure}
+
+The last two codes listed are not actually ``return'ed'' by a function. They are placed in an integer (the caller must
+provide the address of an integer it can store to) which the caller can access. To convert one of the three return codes
+to a string use the following function.
+
+\index{mp\_error\_to\_string}
+\begin{alltt}
+char *mp_error_to_string(int code);
+\end{alltt}
+
+This will return a pointer to a string which describes the given error code. It will not work for the return codes
+MP\_YES and MP\_NO.
+
+\section{Data Types}
+The basic ``multiple precision integer'' type is known as the ``mp\_int'' within LibTomMath. This data type is used to
+organize all of the data required to manipulate the integer it represents. Within LibTomMath it has been prototyped
+as the following.
+
+\index{mp\_int}
+\begin{alltt}
+typedef struct \{
+ int used, alloc, sign;
+ mp_digit *dp;
+\} mp_int;
+\end{alltt}
+
+Where ``mp\_digit'' is a data type that represents individual digits of the integer. By default, an mp\_digit is the
+ISO C ``unsigned long'' data type and each digit is $28-$bits long. The mp\_digit type can be configured to suit other
+platforms by defining the appropriate macros.
+
+All LTM functions that use the mp\_int type will expect a pointer to mp\_int structure. You must allocate memory to
+hold the structure itself by yourself (whether off stack or heap it doesn't matter). The very first thing that must be
+done to use an mp\_int is that it must be initialized.
+
+\section{Function Organization}
+
+The arithmetic functions of the library are all organized to have the same style prototype. That is source operands
+are passed on the left and the destination is on the right. For instance,
+
+\begin{alltt}
+mp_add(&a, &b, &c); /* c = a + b */
+mp_mul(&a, &a, &c); /* c = a * a */
+mp_div(&a, &b, &c, &d); /* c = [a/b], d = a mod b */
+\end{alltt}
+
+Another feature of the way the functions have been implemented is that source operands can be destination operands as well.
+For instance,
+
+\begin{alltt}
+mp_add(&a, &b, &b); /* b = a + b */
+mp_div(&a, &b, &a, &c); /* a = [a/b], c = a mod b */
+\end{alltt}
+
+This allows operands to be re-used which can make programming simpler.
+
+\section{Initialization}
+\subsection{Single Initialization}
+A single mp\_int can be initialized with the ``mp\_init'' function.
+
+\index{mp\_init}
+\begin{alltt}
+int mp_init (mp_int * a);
+\end{alltt}
+
+This function expects a pointer to an mp\_int structure and will initialize the members of the structure so the mp\_int
+represents the default integer which is zero. If the functions returns MP\_OKAY then the mp\_int is ready to be used
+by the other LibTomMath functions.
+
+\begin{small} \begin{alltt}
+int main(void)
+\{
+ mp_int number;
+ int result;
+
+ if ((result = mp_init(&number)) != MP_OKAY) \{
+ printf("Error initializing the number. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* use the number */
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt} \end{small}
+
+\subsection{Single Free}
+When you are finished with an mp\_int it is ideal to return the heap it used back to the system. The following function
+provides this functionality.
+
+\index{mp\_clear}
+\begin{alltt}
+void mp_clear (mp_int * a);
+\end{alltt}
+
+The function expects a pointer to a previously initialized mp\_int structure and frees the heap it uses. It sets the
+pointer\footnote{The ``dp'' member.} within the mp\_int to \textbf{NULL} which is used to prevent double free situations.
+Is is legal to call mp\_clear() twice on the same mp\_int in a row.
+
+\begin{small} \begin{alltt}
+int main(void)
+\{
+ mp_int number;
+ int result;
+
+ if ((result = mp_init(&number)) != MP_OKAY) \{
+ printf("Error initializing the number. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* use the number */
+
+ /* We're done with it. */
+ mp_clear(&number);
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt} \end{small}
+
+\subsection{Multiple Initializations}
+Certain algorithms require more than one large integer. In these instances it is ideal to initialize all of the mp\_int
+variables in an ``all or nothing'' fashion. That is, they are either all initialized successfully or they are all
+not initialized.
+
+The mp\_init\_multi() function provides this functionality.
+
+\index{mp\_init\_multi} \index{mp\_clear\_multi}
+\begin{alltt}
+int mp_init_multi(mp_int *mp, ...);
+\end{alltt}
+
+It accepts a \textbf{NULL} terminated list of pointers to mp\_int structures. It will attempt to initialize them all
+at once. If the function returns MP\_OKAY then all of the mp\_int variables are ready to use, otherwise none of them
+are available for use. A complementary mp\_clear\_multi() function allows multiple mp\_int variables to be free'd
+from the heap at the same time.
+
+\begin{small} \begin{alltt}
+int main(void)
+\{
+ mp_int num1, num2, num3;
+ int result;
+
+ if ((result = mp_init_multi(&num1,
+ &num2,
+ &num3, NULL)) != MP\_OKAY) \{
+ printf("Error initializing the numbers. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* use the numbers */
+
+ /* We're done with them. */
+ mp_clear_multi(&num1, &num2, &num3, NULL);
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt} \end{small}
+
+\subsection{Other Initializers}
+To initialized and make a copy of an mp\_int the mp\_init\_copy() function has been provided.
+
+\index{mp\_init\_copy}
+\begin{alltt}
+int mp_init_copy (mp_int * a, mp_int * b);
+\end{alltt}
+
+This function will initialize $a$ and make it a copy of $b$ if all goes well.
+
+\begin{small} \begin{alltt}
+int main(void)
+\{
+ mp_int num1, num2;
+ int result;
+
+ /* initialize and do work on num1 ... */
+
+ /* We want a copy of num1 in num2 now */
+ if ((result = mp_init_copy(&num2, &num1)) != MP_OKAY) \{
+ printf("Error initializing the copy. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* now num2 is ready and contains a copy of num1 */
+
+ /* We're done with them. */
+ mp_clear_multi(&num1, &num2, NULL);
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt} \end{small}
+
+Another less common initializer is mp\_init\_size() which allows the user to initialize an mp\_int with a given
+default number of digits. By default, all initializers allocate \textbf{MP\_PREC} digits. This function lets
+you override this behaviour.
+
+\index{mp\_init\_size}
+\begin{alltt}
+int mp_init_size (mp_int * a, int size);
+\end{alltt}
+
+The $size$ parameter must be greater than zero. If the function succeeds the mp\_int $a$ will be initialized
+to have $size$ digits (which are all initially zero).
+
+\begin{small} \begin{alltt}
+int main(void)
+\{
+ mp_int number;
+ int result;
+
+ /* we need a 60-digit number */
+ if ((result = mp_init_size(&number, 60)) != MP_OKAY) \{
+ printf("Error initializing the number. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* use the number */
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt} \end{small}
+
+\section{Maintenance Functions}
+
+\subsection{Reducing Memory Usage}
+When an mp\_int is in a state where it won't be changed again\footnote{A Diffie-Hellman modulus for instance.} excess
+digits can be removed to return memory to the heap with the mp\_shrink() function.
+
+\index{mp\_shrink}
+\begin{alltt}
+int mp_shrink (mp_int * a);
+\end{alltt}
+
+This will remove excess digits of the mp\_int $a$. If the operation fails the mp\_int should be intact without the
+excess digits being removed. Note that you can use a shrunk mp\_int in further computations, however, such operations
+will require heap operations which can be slow. It is not ideal to shrink mp\_int variables that you will further
+modify in the system (unless you are seriously low on memory).
+
+\begin{small} \begin{alltt}
+int main(void)
+\{
+ mp_int number;
+ int result;
+
+ if ((result = mp_init(&number)) != MP_OKAY) \{
+ printf("Error initializing the number. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* use the number [e.g. pre-computation] */
+
+ /* We're done with it for now. */
+ if ((result = mp_shrink(&number)) != MP_OKAY) \{
+ printf("Error shrinking the number. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* use it .... */
+
+
+ /* we're done with it. */
+ mp_clear(&number);
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt} \end{small}
+
+\subsection{Adding additional digits}
+
+Within the mp\_int structure are two parameters which control the limitations of the array of digits that represent
+the integer the mp\_int is meant to equal. The \textit{used} parameter dictates how many digits are significant, that is,
+contribute to the value of the mp\_int. The \textit{alloc} parameter dictates how many digits are currently available in
+the array. If you need to perform an operation that requires more digits you will have to mp\_grow() the mp\_int to
+your desired size.
+
+\index{mp\_grow}
+\begin{alltt}
+int mp_grow (mp_int * a, int size);
+\end{alltt}
+
+This will grow the array of digits of $a$ to $size$. If the \textit{alloc} parameter is already bigger than
+$size$ the function will not do anything.
+
+\begin{small} \begin{alltt}
+int main(void)
+\{
+ mp_int number;
+ int result;
+
+ if ((result = mp_init(&number)) != MP_OKAY) \{
+ printf("Error initializing the number. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* use the number */
+
+ /* We need to add 20 digits to the number */
+ if ((result = mp_grow(&number, number.alloc + 20)) != MP_OKAY) \{
+ printf("Error growing the number. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+
+ /* use the number */
+
+ /* we're done with it. */
+ mp_clear(&number);
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt} \end{small}
+
+\chapter{Basic Operations}
+\section{Small Constants}
+Setting mp\_ints to small constants is a relatively common operation. To accomodate these instances there are two
+small constant assignment functions. The first function is used to set a single digit constant while the second sets
+an ISO C style ``unsigned long'' constant. The reason for both functions is efficiency. Setting a single digit is quick but the
+domain of a digit can change (it's always at least $0 \ldots 127$).
+
+\subsection{Single Digit}
+
+Setting a single digit can be accomplished with the following function.
+
+\index{mp\_set}
+\begin{alltt}
+void mp_set (mp_int * a, mp_digit b);
+\end{alltt}
+
+This will zero the contents of $a$ and make it represent an integer equal to the value of $b$. Note that this
+function has a return type of \textbf{void}. It cannot cause an error so it is safe to assume the function
+succeeded.
+
+\begin{small} \begin{alltt}
+int main(void)
+\{
+ mp_int number;
+ int result;
+
+ if ((result = mp_init(&number)) != MP_OKAY) \{
+ printf("Error initializing the number. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* set the number to 5 */
+ mp_set(&number, 5);
+
+ /* we're done with it. */
+ mp_clear(&number);
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt} \end{small}
+
+\subsection{Long Constants}
+
+To set a constant that is the size of an ISO C ``unsigned long'' and larger than a single digit the following function
+can be used.
+
+\index{mp\_set\_int}
+\begin{alltt}
+int mp_set_int (mp_int * a, unsigned long b);
+\end{alltt}
+
+This will assign the value of the 32-bit variable $b$ to the mp\_int $a$. Unlike mp\_set() this function will always
+accept a 32-bit input regardless of the size of a single digit. However, since the value may span several digits
+this function can fail if it runs out of heap memory.
+
+To get the ``unsigned long'' copy of an mp\_int the following function can be used.
+
+\index{mp\_get\_int}
+\begin{alltt}
+unsigned long mp_get_int (mp_int * a);
+\end{alltt}
+
+This will return the 32 least significant bits of the mp\_int $a$.
+
+\begin{small} \begin{alltt}
+int main(void)
+\{
+ mp_int number;
+ int result;
+
+ if ((result = mp_init(&number)) != MP_OKAY) \{
+ printf("Error initializing the number. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* set the number to 654321 (note this is bigger than 127) */
+ if ((result = mp_set_int(&number, 654321)) != MP_OKAY) \{
+ printf("Error setting the value of the number. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ printf("number == \%lu", mp_get_int(&number));
+
+ /* we're done with it. */
+ mp_clear(&number);
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt} \end{small}
+
+This should output the following if the program succeeds.
+
+\begin{alltt}
+number == 654321
+\end{alltt}
+
+\subsection{Initialize and Setting Constants}
+To both initialize and set small constants the following two functions are available.
+\index{mp\_init\_set} \index{mp\_init\_set\_int}
+\begin{alltt}
+int mp_init_set (mp_int * a, mp_digit b);
+int mp_init_set_int (mp_int * a, unsigned long b);
+\end{alltt}
+
+Both functions work like the previous counterparts except they first mp\_init $a$ before setting the values.
+
+\begin{alltt}
+int main(void)
+\{
+ mp_int number1, number2;
+ int result;
+
+ /* initialize and set a single digit */
+ if ((result = mp_init_set(&number1, 100)) != MP_OKAY) \{
+ printf("Error setting number1: \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* initialize and set a long */
+ if ((result = mp_init_set_int(&number2, 1023)) != MP_OKAY) \{
+ printf("Error setting number2: \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* display */
+ printf("Number1, Number2 == \%lu, \%lu",
+ mp_get_int(&number1), mp_get_int(&number2));
+
+ /* clear */
+ mp_clear_multi(&number1, &number2, NULL);
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt}
+
+If this program succeeds it shall output.
+\begin{alltt}
+Number1, Number2 == 100, 1023
+\end{alltt}
+
+\section{Comparisons}
+
+Comparisons in LibTomMath are always performed in a ``left to right'' fashion. There are three possible return codes
+for any comparison.
+
+\index{MP\_GT} \index{MP\_EQ} \index{MP\_LT}
+\begin{figure}[here]
+\begin{center}
+\begin{tabular}{|c|c|}
+\hline \textbf{Result Code} & \textbf{Meaning} \\
+\hline MP\_GT & $a > b$ \\
+\hline MP\_EQ & $a = b$ \\
+\hline MP\_LT & $a < b$ \\
+\hline
+\end{tabular}
+\end{center}
+\caption{Comparison Codes for $a, b$}
+\label{fig:CMP}
+\end{figure}
+
+In figure \ref{fig:CMP} two integers $a$ and $b$ are being compared. In this case $a$ is said to be ``to the left'' of
+$b$.
+
+\subsection{Unsigned comparison}
+
+An unsigned comparison considers only the digits themselves and not the associated \textit{sign} flag of the
+mp\_int structures. This is analogous to an absolute comparison. The function mp\_cmp\_mag() will compare two
+mp\_int variables based on their digits only.
+
+\index{mp\_cmp\_mag}
+\begin{alltt}
+int mp_cmp_mag(mp_int * a, mp_int * b);
+\end{alltt}
+This will compare $a$ to $b$ placing $a$ to the left of $b$. This function cannot fail and will return one of the
+three compare codes listed in figure \ref{fig:CMP}.
+
+\begin{small} \begin{alltt}
+int main(void)
+\{
+ mp_int number1, number2;
+ int result;
+
+ if ((result = mp_init_multi(&number1, &number2, NULL)) != MP_OKAY) \{
+ printf("Error initializing the numbers. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* set the number1 to 5 */
+ mp_set(&number1, 5);
+
+ /* set the number2 to -6 */
+ mp_set(&number2, 6);
+ if ((result = mp_neg(&number2, &number2)) != MP_OKAY) \{
+ printf("Error negating number2. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ switch(mp_cmp_mag(&number1, &number2)) \{
+ case MP_GT: printf("|number1| > |number2|"); break;
+ case MP_EQ: printf("|number1| = |number2|"); break;
+ case MP_LT: printf("|number1| < |number2|"); break;
+ \}
+
+ /* we're done with it. */
+ mp_clear_multi(&number1, &number2, NULL);
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt} \end{small}
+
+If this program\footnote{This function uses the mp\_neg() function which is discussed in section \ref{sec:NEG}.} completes
+successfully it should print the following.
+
+\begin{alltt}
+|number1| < |number2|
+\end{alltt}
+
+This is because $\vert -6 \vert = 6$ and obviously $5 < 6$.
+
+\subsection{Signed comparison}
+
+To compare two mp\_int variables based on their signed value the mp\_cmp() function is provided.
+
+\index{mp\_cmp}
+\begin{alltt}
+int mp_cmp(mp_int * a, mp_int * b);
+\end{alltt}
+
+This will compare $a$ to the left of $b$. It will first compare the signs of the two mp\_int variables. If they
+differ it will return immediately based on their signs. If the signs are equal then it will compare the digits
+individually. This function will return one of the compare conditions codes listed in figure \ref{fig:CMP}.
+
+\begin{small} \begin{alltt}
+int main(void)
+\{
+ mp_int number1, number2;
+ int result;
+
+ if ((result = mp_init_multi(&number1, &number2, NULL)) != MP_OKAY) \{
+ printf("Error initializing the numbers. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* set the number1 to 5 */
+ mp_set(&number1, 5);
+
+ /* set the number2 to -6 */
+ mp_set(&number2, 6);
+ if ((result = mp_neg(&number2, &number2)) != MP_OKAY) \{
+ printf("Error negating number2. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ switch(mp_cmp(&number1, &number2)) \{
+ case MP_GT: printf("number1 > number2"); break;
+ case MP_EQ: printf("number1 = number2"); break;
+ case MP_LT: printf("number1 < number2"); break;
+ \}
+
+ /* we're done with it. */
+ mp_clear_multi(&number1, &number2, NULL);
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt} \end{small}
+
+If this program\footnote{This function uses the mp\_neg() function which is discussed in section \ref{sec:NEG}.} completes
+successfully it should print the following.
+
+\begin{alltt}
+number1 > number2
+\end{alltt}
+
+\subsection{Single Digit}
+
+To compare a single digit against an mp\_int the following function has been provided.
+
+\index{mp\_cmp\_d}
+\begin{alltt}
+int mp_cmp_d(mp_int * a, mp_digit b);
+\end{alltt}
+
+This will compare $a$ to the left of $b$ using a signed comparison. Note that it will always treat $b$ as
+positive. This function is rather handy when you have to compare against small values such as $1$ (which often
+comes up in cryptography). The function cannot fail and will return one of the tree compare condition codes
+listed in figure \ref{fig:CMP}.
+
+
+\begin{small} \begin{alltt}
+int main(void)
+\{
+ mp_int number;
+ int result;
+
+ if ((result = mp_init(&number)) != MP_OKAY) \{
+ printf("Error initializing the number. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* set the number to 5 */
+ mp_set(&number, 5);
+
+ switch(mp_cmp_d(&number, 7)) \{
+ case MP_GT: printf("number > 7"); break;
+ case MP_EQ: printf("number = 7"); break;
+ case MP_LT: printf("number < 7"); break;
+ \}
+
+ /* we're done with it. */
+ mp_clear(&number);
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt} \end{small}
+
+If this program functions properly it will print out the following.
+
+\begin{alltt}
+number < 7
+\end{alltt}
+
+\section{Logical Operations}
+
+Logical operations are operations that can be performed either with simple shifts or boolean operators such as
+AND, XOR and OR directly. These operations are very quick.
+
+\subsection{Multiplication by two}
+
+Multiplications and divisions by any power of two can be performed with quick logical shifts either left or
+right depending on the operation.
+
+When multiplying or dividing by two a special case routine can be used which are as follows.
+\index{mp\_mul\_2} \index{mp\_div\_2}
+\begin{alltt}
+int mp_mul_2(mp_int * a, mp_int * b);
+int mp_div_2(mp_int * a, mp_int * b);
+\end{alltt}
+
+The former will assign twice $a$ to $b$ while the latter will assign half $a$ to $b$. These functions are fast
+since the shift counts and maskes are hardcoded into the routines.
+
+\begin{small} \begin{alltt}
+int main(void)
+\{
+ mp_int number;
+ int result;
+
+ if ((result = mp_init(&number)) != MP_OKAY) \{
+ printf("Error initializing the number. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* set the number to 5 */
+ mp_set(&number, 5);
+
+ /* multiply by two */
+ if ((result = mp\_mul\_2(&number, &number)) != MP_OKAY) \{
+ printf("Error multiplying the number. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+ switch(mp_cmp_d(&number, 7)) \{
+ case MP_GT: printf("2*number > 7"); break;
+ case MP_EQ: printf("2*number = 7"); break;
+ case MP_LT: printf("2*number < 7"); break;
+ \}
+
+ /* now divide by two */
+ if ((result = mp\_div\_2(&number, &number)) != MP_OKAY) \{
+ printf("Error dividing the number. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+ switch(mp_cmp_d(&number, 7)) \{
+ case MP_GT: printf("2*number/2 > 7"); break;
+ case MP_EQ: printf("2*number/2 = 7"); break;
+ case MP_LT: printf("2*number/2 < 7"); break;
+ \}
+
+ /* we're done with it. */
+ mp_clear(&number);
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt} \end{small}
+
+If this program is successful it will print out the following text.
+
+\begin{alltt}
+2*number > 7
+2*number/2 < 7
+\end{alltt}
+
+Since $10 > 7$ and $5 < 7$. To multiply by a power of two the following function can be used.
+
+\index{mp\_mul\_2d}
+\begin{alltt}
+int mp_mul_2d(mp_int * a, int b, mp_int * c);
+\end{alltt}
+
+This will multiply $a$ by $2^b$ and store the result in ``c''. If the value of $b$ is less than or equal to
+zero the function will copy $a$ to ``c'' without performing any further actions.
+
+To divide by a power of two use the following.
+
+\index{mp\_div\_2d}
+\begin{alltt}
+int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d);
+\end{alltt}
+Which will divide $a$ by $2^b$, store the quotient in ``c'' and the remainder in ``d'. If $b \le 0$ then the
+function simply copies $a$ over to ``c'' and zeroes $d$. The variable $d$ may be passed as a \textbf{NULL}
+value to signal that the remainder is not desired.
+
+\subsection{Polynomial Basis Operations}
+
+Strictly speaking the organization of the integers within the mp\_int structures is what is known as a
+``polynomial basis''. This simply means a field element is stored by divisions of a radix. For example, if
+$f(x) = \sum_{i=0}^{k} y_ix^k$ for any vector $\vec y$ then the array of digits in $\vec y$ are said to be
+the polynomial basis representation of $z$ if $f(\beta) = z$ for a given radix $\beta$.
+
+To multiply by the polynomial $g(x) = x$ all you have todo is shift the digits of the basis left one place. The
+following function provides this operation.
+
+\index{mp\_lshd}
+\begin{alltt}
+int mp_lshd (mp_int * a, int b);
+\end{alltt}
+
+This will multiply $a$ in place by $x^b$ which is equivalent to shifting the digits left $b$ places and inserting zeroes
+in the least significant digits. Similarly to divide by a power of $x$ the following function is provided.
+
+\index{mp\_rshd}
+\begin{alltt}
+void mp_rshd (mp_int * a, int b)
+\end{alltt}
+This will divide $a$ in place by $x^b$ and discard the remainder. This function cannot fail as it performs the operations
+in place and no new digits are required to complete it.
+
+\subsection{AND, OR and XOR Operations}
+
+While AND, OR and XOR operations are not typical ``bignum functions'' they can be useful in several instances. The
+three functions are prototyped as follows.
+
+\index{mp\_or} \index{mp\_and} \index{mp\_xor}
+\begin{alltt}
+int mp_or (mp_int * a, mp_int * b, mp_int * c);
+int mp_and (mp_int * a, mp_int * b, mp_int * c);
+int mp_xor (mp_int * a, mp_int * b, mp_int * c);
+\end{alltt}
+
+Which compute $c = a \odot b$ where $\odot$ is one of OR, AND or XOR.
+
+\section{Addition and Subtraction}
+
+To compute an addition or subtraction the following two functions can be used.
+
+\index{mp\_add} \index{mp\_sub}
+\begin{alltt}
+int mp_add (mp_int * a, mp_int * b, mp_int * c);
+int mp_sub (mp_int * a, mp_int * b, mp_int * c)
+\end{alltt}
+
+Which perform $c = a \odot b$ where $\odot$ is one of signed addition or subtraction. The operations are fully sign
+aware.
+
+\section{Sign Manipulation}
+\subsection{Negation}
+\label{sec:NEG}
+Simple integer negation can be performed with the following.
+
+\index{mp\_neg}
+\begin{alltt}
+int mp_neg (mp_int * a, mp_int * b);
+\end{alltt}
+
+Which assigns $-a$ to $b$.
+
+\subsection{Absolute}
+Simple integer absolutes can be performed with the following.
+
+\index{mp\_neg}
+\begin{alltt}
+int mp_abs (mp_int * a, mp_int * b);
+\end{alltt}
+
+Which assigns $\vert a \vert$ to $b$.
+
+\section{Integer Division and Remainder}
+To perform a complete and general integer division with remainder use the following function.
+
+\index{mp\_div}
+\begin{alltt}
+int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d);
+\end{alltt}
+
+This divides $a$ by $b$ and stores the quotient in $c$ and $d$. The signed quotient is computed such that
+$bc + d = a$. Note that either of $c$ or $d$ can be set to \textbf{NULL} if their value is not required. If
+$b$ is zero the function returns \textbf{MP\_VAL}.
+
+
+\chapter{Multiplication and Squaring}
+\section{Multiplication}
+A full signed integer multiplication can be performed with the following.
+\index{mp\_mul}
+\begin{alltt}
+int mp_mul (mp_int * a, mp_int * b, mp_int * c);
+\end{alltt}
+Which assigns the full signed product $ab$ to $c$. This function actually breaks into one of four cases which are
+specific multiplication routines optimized for given parameters. First there are the Toom-Cook multiplications which
+should only be used with very large inputs. This is followed by the Karatsuba multiplications which are for moderate
+sized inputs. Then followed by the Comba and baseline multipliers.
+
+Fortunately for the developer you don't really need to know this unless you really want to fine tune the system. mp\_mul()
+will determine on its own\footnote{Some tweaking may be required.} what routine to use automatically when it is called.
+
+\begin{alltt}
+int main(void)
+\{
+ mp_int number1, number2;
+ int result;
+
+ /* Initialize the numbers */
+ if ((result = mp_init_multi(&number1,
+ &number2, NULL)) != MP_OKAY) \{
+ printf("Error initializing the numbers. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* set the terms */
+ if ((result = mp_set_int(&number, 257)) != MP_OKAY) \{
+ printf("Error setting number1. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ if ((result = mp_set_int(&number2, 1023)) != MP_OKAY) \{
+ printf("Error setting number2. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* multiply them */
+ if ((result = mp_mul(&number1, &number2,
+ &number1)) != MP_OKAY) \{
+ printf("Error multiplying terms. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* display */
+ printf("number1 * number2 == \%lu", mp_get_int(&number1));
+
+ /* free terms and return */
+ mp_clear_multi(&number1, &number2, NULL);
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt}
+
+If this program succeeds it shall output the following.
+
+\begin{alltt}
+number1 * number2 == 262911
+\end{alltt}
+
+\section{Squaring}
+Since squaring can be performed faster than multiplication it is performed it's own function instead of just using
+mp\_mul().
+
+\index{mp\_sqr}
+\begin{alltt}
+int mp_sqr (mp_int * a, mp_int * b);
+\end{alltt}
+
+Will square $a$ and store it in $b$. Like the case of multiplication there are four different squaring
+algorithms all which can be called from mp\_sqr(). It is ideal to use mp\_sqr over mp\_mul when squaring terms because
+of the speed difference.
+
+\section{Tuning Polynomial Basis Routines}
+
+Both of the Toom-Cook and Karatsuba multiplication algorithms are faster than the traditional $O(n^2)$ approach that
+the Comba and baseline algorithms use. At $O(n^{1.464973})$ and $O(n^{1.584962})$ running times respectively they require
+considerably less work. For example, a 10000-digit multiplication would take roughly 724,000 single precision
+multiplications with Toom-Cook or 100,000,000 single precision multiplications with the standard Comba (a factor
+of 138).
+
+So why not always use Karatsuba or Toom-Cook? The simple answer is that they have so much overhead that they're not
+actually faster than Comba until you hit distinct ``cutoff'' points. For Karatsuba with the default configuration,
+GCC 3.3.1 and an Athlon XP processor the cutoff point is roughly 110 digits (about 70 for the Intel P4). That is, at
+110 digits Karatsuba and Comba multiplications just about break even and for 110+ digits Karatsuba is faster.
+
+Toom-Cook has incredible overhead and is probably only useful for very large inputs. So far no known cutoff points
+exist and for the most part I just set the cutoff points very high to make sure they're not called.
+
+A demo program in the ``etc/'' directory of the project called ``tune.c'' can be used to find the cutoff points. This
+can be built with GCC as follows
+
+\begin{alltt}
+make XXX
+\end{alltt}
+Where ``XXX'' is one of the following entries from the table \ref{fig:tuning}.
+
+\begin{figure}[here]
+\begin{center}
+\begin{small}
+\begin{tabular}{|l|l|}
+\hline \textbf{Value of XXX} & \textbf{Meaning} \\
+\hline tune & Builds portable tuning application \\
+\hline tune86 & Builds x86 (pentium and up) program for COFF \\
+\hline tune86c & Builds x86 program for Cygwin \\
+\hline tune86l & Builds x86 program for Linux (ELF format) \\
+\hline
+\end{tabular}
+\end{small}
+\end{center}
+\caption{Build Names for Tuning Programs}
+\label{fig:tuning}
+\end{figure}
+
+When the program is running it will output a series of measurements for different cutoff points. It will first find
+good Karatsuba squaring and multiplication points. Then it proceeds to find Toom-Cook points. Note that the Toom-Cook
+tuning takes a very long time as the cutoff points are likely to be very high.
+
+\chapter{Modular Reduction}
+
+Modular reduction is process of taking the remainder of one quantity divided by another. Expressed
+as (\ref{eqn:mod}) the modular reduction is equivalent to the remainder of $b$ divided by $c$.
+
+\begin{equation}
+a \equiv b \mbox{ (mod }c\mbox{)}
+\label{eqn:mod}
+\end{equation}
+
+Of particular interest to cryptography are reductions where $b$ is limited to the range $0 \le b < c^2$ since particularly
+fast reduction algorithms can be written for the limited range.
+
+Note that one of the four optimized reduction algorithms are automatically chosen in the modular exponentiation
+algorithm mp\_exptmod when an appropriate modulus is detected.
+
+\section{Straight Division}
+In order to effect an arbitrary modular reduction the following algorithm is provided.
+
+\index{mp\_mod}
+\begin{alltt}
+int mp_mod(mp_int *a, mp_int *b, mp_int *c);
+\end{alltt}
+
+This reduces $a$ modulo $b$ and stores the result in $c$. The sign of $c$ shall agree with the sign
+of $b$. This algorithm accepts an input $a$ of any range and is not limited by $0 \le a < b^2$.
+
+\section{Barrett Reduction}
+
+Barrett reduction is a generic optimized reduction algorithm that requires pre--computation to achieve
+a decent speedup over straight division. First a $\mu$ value must be precomputed with the following function.
+
+\index{mp\_reduce\_setup}
+\begin{alltt}
+int mp_reduce_setup(mp_int *a, mp_int *b);
+\end{alltt}
+
+Given a modulus in $b$ this produces the required $\mu$ value in $a$. For any given modulus this only has to
+be computed once. Modular reduction can now be performed with the following.
+
+\index{mp\_reduce}
+\begin{alltt}
+int mp_reduce(mp_int *a, mp_int *b, mp_int *c);
+\end{alltt}
+
+This will reduce $a$ in place modulo $b$ with the precomputed $\mu$ value in $c$. $a$ must be in the range
+$0 \le a < b^2$.
+
+\begin{alltt}
+int main(void)
+\{
+ mp_int a, b, c, mu;
+ int result;
+
+ /* initialize a,b to desired values, mp_init mu,
+ * c and set c to 1...we want to compute a^3 mod b
+ */
+
+ /* get mu value */
+ if ((result = mp_reduce_setup(&mu, b)) != MP_OKAY) \{
+ printf("Error getting mu. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* square a to get c = a^2 */
+ if ((result = mp_sqr(&a, &c)) != MP_OKAY) \{
+ printf("Error squaring. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* now reduce `c' modulo b */
+ if ((result = mp_reduce(&c, &b, &mu)) != MP_OKAY) \{
+ printf("Error reducing. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* multiply a to get c = a^3 */
+ if ((result = mp_mul(&a, &c, &c)) != MP_OKAY) \{
+ printf("Error reducing. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* now reduce `c' modulo b */
+ if ((result = mp_reduce(&c, &b, &mu)) != MP_OKAY) \{
+ printf("Error reducing. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* c now equals a^3 mod b */
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt}
+
+This program will calculate $a^3 \mbox{ mod }b$ if all the functions succeed.
+
+\section{Montgomery Reduction}
+
+Montgomery is a specialized reduction algorithm for any odd moduli. Like Barrett reduction a pre--computation
+step is required. This is accomplished with the following.
+
+\index{mp\_montgomery\_setup}
+\begin{alltt}
+int mp_montgomery_setup(mp_int *a, mp_digit *mp);
+\end{alltt}
+
+For the given odd moduli $a$ the precomputation value is placed in $mp$. The reduction is computed with the
+following.
+
+\index{mp\_montgomery\_reduce}
+\begin{alltt}
+int mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
+\end{alltt}
+This reduces $a$ in place modulo $m$ with the pre--computed value $mp$. $a$ must be in the range
+$0 \le a < b^2$.
+
+Montgomery reduction is faster than Barrett reduction for moduli smaller than the ``comba'' limit. With the default
+setup for instance, the limit is $127$ digits ($3556$--bits). Note that this function is not limited to
+$127$ digits just that it falls back to a baseline algorithm after that point.
+
+An important observation is that this reduction does not return $a \mbox{ mod }m$ but $aR^{-1} \mbox{ mod }m$
+where $R = \beta^n$, $n$ is the n number of digits in $m$ and $\beta$ is radix used (default is $2^{28}$).
+
+To quickly calculate $R$ the following function was provided.
+
+\index{mp\_montgomery\_calc\_normalization}
+\begin{alltt}
+int mp_montgomery_calc_normalization(mp_int *a, mp_int *b);
+\end{alltt}
+Which calculates $a = R$ for the odd moduli $b$ without using multiplication or division.
+
+The normal modus operandi for Montgomery reductions is to normalize the integers before entering the system. For
+example, to calculate $a^3 \mbox { mod }b$ using Montgomery reduction the value of $a$ can be normalized by
+multiplying it by $R$. Consider the following code snippet.
+
+\begin{alltt}
+int main(void)
+\{
+ mp_int a, b, c, R;
+ mp_digit mp;
+ int result;
+
+ /* initialize a,b to desired values,
+ * mp_init R, c and set c to 1....
+ */
+
+ /* get normalization */
+ if ((result = mp_montgomery_calc_normalization(&R, b)) != MP_OKAY) \{
+ printf("Error getting norm. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* get mp value */
+ if ((result = mp_montgomery_setup(&c, &mp)) != MP_OKAY) \{
+ printf("Error setting up montgomery. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* normalize `a' so now a is equal to aR */
+ if ((result = mp_mulmod(&a, &R, &b, &a)) != MP_OKAY) \{
+ printf("Error computing aR. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* square a to get c = a^2R^2 */
+ if ((result = mp_sqr(&a, &c)) != MP_OKAY) \{
+ printf("Error squaring. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* now reduce `c' back down to c = a^2R^2 * R^-1 == a^2R */
+ if ((result = mp_montgomery_reduce(&c, &b, mp)) != MP_OKAY) \{
+ printf("Error reducing. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* multiply a to get c = a^3R^2 */
+ if ((result = mp_mul(&a, &c, &c)) != MP_OKAY) \{
+ printf("Error reducing. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* now reduce `c' back down to c = a^3R^2 * R^-1 == a^3R */
+ if ((result = mp_montgomery_reduce(&c, &b, mp)) != MP_OKAY) \{
+ printf("Error reducing. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* now reduce (again) `c' back down to c = a^3R * R^-1 == a^3 */
+ if ((result = mp_montgomery_reduce(&c, &b, mp)) != MP_OKAY) \{
+ printf("Error reducing. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* c now equals a^3 mod b */
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt}
+
+This particular example does not look too efficient but it demonstrates the point of the algorithm. By
+normalizing the inputs the reduced results are always of the form $aR$ for some variable $a$. This allows
+a single final reduction to correct for the normalization and the fast reduction used within the algorithm.
+
+For more details consider examining the file \textit{bn\_mp\_exptmod\_fast.c}.
+
+\section{Restricted Dimminished Radix}
+
+``Dimminished Radix'' reduction refers to reduction with respect to moduli that are ameniable to simple
+digit shifting and small multiplications. In this case the ``restricted'' variant refers to moduli of the
+form $\beta^k - p$ for some $k \ge 0$ and $0 < p < \beta$ where $\beta$ is the radix (default to $2^{28}$).
+
+As in the case of Montgomery reduction there is a pre--computation phase required for a given modulus.
+
+\index{mp\_dr\_setup}
+\begin{alltt}
+void mp_dr_setup(mp_int *a, mp_digit *d);
+\end{alltt}
+
+This computes the value required for the modulus $a$ and stores it in $d$. This function cannot fail
+and does not return any error codes. After the pre--computation a reduction can be performed with the
+following.
+
+\index{mp\_dr\_reduce}
+\begin{alltt}
+int mp_dr_reduce(mp_int *a, mp_int *b, mp_digit mp);
+\end{alltt}
+
+This reduces $a$ in place modulo $b$ with the pre--computed value $mp$. $b$ must be of a restricted
+dimminished radix form and $a$ must be in the range $0 \le a < b^2$. Dimminished radix reductions are
+much faster than both Barrett and Montgomery reductions as they have a much lower asymtotic running time.
+
+Since the moduli are restricted this algorithm is not particularly useful for something like Rabin, RSA or
+BBS cryptographic purposes. This reduction algorithm is useful for Diffie-Hellman and ECC where fixed
+primes are acceptable.
+
+Note that unlike Montgomery reduction there is no normalization process. The result of this function is
+equal to the correct residue.
+
+\section{Unrestricted Dimminshed Radix}
+
+Unrestricted reductions work much like the restricted counterparts except in this case the moduli is of the
+form $2^k - p$ for $0 < p < \beta$. In this sense the unrestricted reductions are more flexible as they
+can be applied to a wider range of numbers.
+
+\index{mp\_reduce\_2k\_setup}
+\begin{alltt}
+int mp_reduce_2k_setup(mp_int *a, mp_digit *d);
+\end{alltt}
+
+This will compute the required $d$ value for the given moduli $a$.
+
+\index{mp\_reduce\_2k}
+\begin{alltt}
+int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d);
+\end{alltt}
+
+This will reduce $a$ in place modulo $n$ with the pre--computed value $d$. From my experience this routine is
+slower than mp\_dr\_reduce but faster for most moduli sizes than the Montgomery reduction.
+
+\chapter{Exponentiation}
+\section{Single Digit Exponentiation}
+\index{mp\_expt\_d}
+\begin{alltt}
+int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
+\end{alltt}
+This computes $c = a^b$ using a simple binary left-to-right algorithm. It is faster than repeated multiplications by
+$a$ for all values of $b$ greater than three.
+
+\section{Modular Exponentiation}
+\index{mp\_exptmod}
+\begin{alltt}
+int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
+\end{alltt}
+This computes $Y \equiv G^X \mbox{ (mod }P\mbox{)}$ using a variable width sliding window algorithm. This function
+will automatically detect the fastest modular reduction technique to use during the operation. For negative values of
+$X$ the operation is performed as $Y \equiv (G^{-1} \mbox{ mod }P)^{\vert X \vert} \mbox{ (mod }P\mbox{)}$ provided that
+$gcd(G, P) = 1$.
+
+This function is actually a shell around the two internal exponentiation functions. This routine will automatically
+detect when Barrett, Montgomery, Restricted and Unrestricted Dimminished Radix based exponentiation can be used. Generally
+moduli of the a ``restricted dimminished radix'' form lead to the fastest modular exponentiations. Followed by Montgomery
+and the other two algorithms.
+
+\section{Root Finding}
+\index{mp\_n\_root}
+\begin{alltt}
+int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
+\end{alltt}
+This computes $c = a^{1/b}$ such that $c^b \le a$ and $(c+1)^b > a$. The implementation of this function is not
+ideal for values of $b$ greater than three. It will work but become very slow. So unless you are working with very small
+numbers (less than 1000 bits) I'd avoid $b > 3$ situations. Will return a positive root only for even roots and return
+a root with the sign of the input for odd roots. For example, performing $4^{1/2}$ will return $2$ whereas $(-8)^{1/3}$
+will return $-2$.
+
+This algorithm uses the ``Newton Approximation'' method and will converge on the correct root fairly quickly. Since
+the algorithm requires raising $a$ to the power of $b$ it is not ideal to attempt to find roots for large
+values of $b$. If particularly large roots are required then a factor method could be used instead. For example,
+$a^{1/16}$ is equivalent to $\left (a^{1/4} \right)^{1/4}$ or simply
+$\left ( \left ( \left ( a^{1/2} \right )^{1/2} \right )^{1/2} \right )^{1/2}$
+
+\chapter{Prime Numbers}
+\section{Trial Division}
+\index{mp\_prime\_is\_divisible}
+\begin{alltt}
+int mp_prime_is_divisible (mp_int * a, int *result)
+\end{alltt}
+This will attempt to evenly divide $a$ by a list of primes\footnote{Default is the first 256 primes.} and store the
+outcome in ``result''. That is if $result = 0$ then $a$ is not divisible by the primes, otherwise it is. Note that
+if the function does not return \textbf{MP\_OKAY} the value in ``result'' should be considered undefined\footnote{Currently
+the default is to set it to zero first.}.
+
+\section{Fermat Test}
+\index{mp\_prime\_fermat}
+\begin{alltt}
+int mp_prime_fermat (mp_int * a, mp_int * b, int *result)
+\end{alltt}
+Performs a Fermat primality test to the base $b$. That is it computes $b^a \mbox{ mod }a$ and tests whether the value is
+equal to $b$ or not. If the values are equal then $a$ is probably prime and $result$ is set to one. Otherwise $result$
+is set to zero.
+
+\section{Miller-Rabin Test}
+\index{mp\_prime\_miller\_rabin}
+\begin{alltt}
+int mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)
+\end{alltt}
+Performs a Miller-Rabin test to the base $b$ of $a$. This test is much stronger than the Fermat test and is very hard to
+fool (besides with Carmichael numbers). If $a$ passes the test (therefore is probably prime) $result$ is set to one.
+Otherwise $result$ is set to zero.
+
+Note that is suggested that you use the Miller-Rabin test instead of the Fermat test since all of the failures of
+Miller-Rabin are a subset of the failures of the Fermat test.
+
+\subsection{Required Number of Tests}
+Generally to ensure a number is very likely to be prime you have to perform the Miller-Rabin with at least a half-dozen
+or so unique bases. However, it has been proven that the probability of failure goes down as the size of the input goes up.
+This is why a simple function has been provided to help out.
+
+\index{mp\_prime\_rabin\_miller\_trials}
+\begin{alltt}
+int mp_prime_rabin_miller_trials(int size)
+\end{alltt}
+This returns the number of trials required for a $2^{-96}$ (or lower) probability of failure for a given ``size'' expressed
+in bits. This comes in handy specially since larger numbers are slower to test. For example, a 512-bit number would
+require ten tests whereas a 1024-bit number would only require four tests.
+
+You should always still perform a trial division before a Miller-Rabin test though.
+
+\section{Primality Testing}
+\index{mp\_prime\_is\_prime}
+\begin{alltt}
+int mp_prime_is_prime (mp_int * a, int t, int *result)
+\end{alltt}
+This will perform a trial division followed by $t$ rounds of Miller-Rabin tests on $a$ and store the result in $result$.
+If $a$ passes all of the tests $result$ is set to one, otherwise it is set to zero. Note that $t$ is bounded by
+$1 \le t < PRIME\_SIZE$ where $PRIME\_SIZE$ is the number of primes in the prime number table (by default this is $256$).
+
+\section{Next Prime}
+\index{mp\_prime\_next\_prime}
+\begin{alltt}
+int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
+\end{alltt}
+This finds the next prime after $a$ that passes mp\_prime\_is\_prime() with $t$ tests. Set $bbs\_style$ to one if you
+want only the next prime congruent to $3 \mbox{ mod } 4$, otherwise set it to zero to find any next prime.
+
+\section{Random Primes}
+\index{mp\_prime\_random}
+\begin{alltt}
+int mp_prime_random(mp_int *a, int t, int size, int bbs,
+ ltm_prime_callback cb, void *dat)
+\end{alltt}
+This will find a prime greater than $256^{size}$ which can be ``bbs\_style'' or not depending on $bbs$ and must pass
+$t$ rounds of tests. The ``ltm\_prime\_callback'' is a typedef for
+
+\begin{alltt}
+typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat);
+\end{alltt}
+
+Which is a function that must read $len$ bytes (and return the amount stored) into $dst$. The $dat$ variable is simply
+copied from the original input. It can be used to pass RNG context data to the callback. The function
+mp\_prime\_random() is more suitable for generating primes which must be secret (as in the case of RSA) since there
+is no skew on the least significant bits.
+
+\textit{Note:} As of v0.30 of the LibTomMath library this function has been deprecated. It is still available
+but users are encouraged to use the new mp\_prime\_random\_ex() function instead.
+
+\subsection{Extended Generation}
+\index{mp\_prime\_random\_ex}
+\begin{alltt}
+int mp_prime_random_ex(mp_int *a, int t,
+ int size, int flags,
+ ltm_prime_callback cb, void *dat);
+\end{alltt}
+This will generate a prime in $a$ using $t$ tests of the primality testing algorithms. The variable $size$
+specifies the bit length of the prime desired. The variable $flags$ specifies one of several options available
+(see fig. \ref{fig:primeopts}) which can be OR'ed together. The callback parameters are used as in
+mp\_prime\_random().
+
+\begin{figure}[here]
+\begin{center}
+\begin{small}
+\begin{tabular}{|r|l|}
+\hline \textbf{Flag} & \textbf{Meaning} \\
+\hline LTM\_PRIME\_BBS & Make the prime congruent to $3$ modulo $4$ \\
+\hline LTM\_PRIME\_SAFE & Make a prime $p$ such that $(p - 1)/2$ is also prime. \\
+ & This option implies LTM\_PRIME\_BBS as well. \\
+\hline LTM\_PRIME\_2MSB\_OFF & Makes sure that the bit adjacent to the most significant bit \\
+ & Is forced to zero. \\
+\hline LTM\_PRIME\_2MSB\_ON & Makes sure that the bit adjacent to the most significant bit \\
+ & Is forced to one. \\
+\hline
+\end{tabular}
+\end{small}
+\end{center}
+\caption{Primality Generation Options}
+\label{fig:primeopts}
+\end{figure}
+
+\chapter{Input and Output}
+\section{ASCII Conversions}
+\subsection{To ASCII}
+\index{mp\_toradix}
+\begin{alltt}
+int mp_toradix (mp_int * a, char *str, int radix);
+\end{alltt}
+This still store $a$ in ``str'' as a base-``radix'' string of ASCII chars. This function appends a NUL character
+to terminate the string. Valid values of ``radix'' line in the range $[2, 64]$. To determine the size (exact) required
+by the conversion before storing any data use the following function.
+
+\index{mp\_radix\_size}
+\begin{alltt}
+int mp_radix_size (mp_int * a, int radix, int *size)
+\end{alltt}
+This stores in ``size'' the number of characters (including space for the NUL terminator) required. Upon error this
+function returns an error code and ``size'' will be zero.
+
+\subsection{From ASCII}
+\index{mp\_read\_radix}
+\begin{alltt}
+int mp_read_radix (mp_int * a, char *str, int radix);
+\end{alltt}
+This will read the base-``radix'' NUL terminated string from ``str'' into $a$. It will stop reading when it reads a
+character it does not recognize (which happens to include th NUL char... imagine that...). A single leading $-$ sign
+can be used to denote a negative number.
+
+\section{Binary Conversions}
+
+Converting an mp\_int to and from binary is another keen idea.
+
+\index{mp\_unsigned\_bin\_size}
+\begin{alltt}
+int mp_unsigned_bin_size(mp_int *a);
+\end{alltt}
+
+This will return the number of bytes (octets) required to store the unsigned copy of the integer $a$.
+
+\index{mp\_to\_unsigned\_bin}
+\begin{alltt}
+int mp_to_unsigned_bin(mp_int *a, unsigned char *b);
+\end{alltt}
+This will store $a$ into the buffer $b$ in big--endian format. Fortunately this is exactly what DER (or is it ASN?)
+requires. It does not store the sign of the integer.
+
+\index{mp\_read\_unsigned\_bin}
+\begin{alltt}
+int mp_read_unsigned_bin(mp_int *a, unsigned char *b, int c);
+\end{alltt}
+This will read in an unsigned big--endian array of bytes (octets) from $b$ of length $c$ into $a$. The resulting
+integer $a$ will always be positive.
+
+For those who acknowledge the existence of negative numbers (heretic!) there are ``signed'' versions of the
+previous functions.
+
+\begin{alltt}
+int mp_signed_bin_size(mp_int *a);
+int mp_read_signed_bin(mp_int *a, unsigned char *b, int c);
+int mp_to_signed_bin(mp_int *a, unsigned char *b);
+\end{alltt}
+They operate essentially the same as the unsigned copies except they prefix the data with zero or non--zero
+byte depending on the sign. If the sign is zpos (e.g. not negative) the prefix is zero, otherwise the prefix
+is non--zero.
+
+\chapter{Algebraic Functions}
+\section{Extended Euclidean Algorithm}
+\index{mp\_exteuclid}
+\begin{alltt}
+int mp_exteuclid(mp_int *a, mp_int *b,
+ mp_int *U1, mp_int *U2, mp_int *U3);
+\end{alltt}
+
+This finds the triple U1/U2/U3 using the Extended Euclidean algorithm such that the following equation holds.
+
+\begin{equation}
+a \cdot U1 + b \cdot U2 = U3
+\end{equation}
+
+Any of the U1/U2/U3 paramters can be set to \textbf{NULL} if they are not desired.
+
+\section{Greatest Common Divisor}
+\index{mp\_gcd}
+\begin{alltt}
+int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
+\end{alltt}
+This will compute the greatest common divisor of $a$ and $b$ and store it in $c$.
+
+\section{Least Common Multiple}
+\index{mp\_lcm}
+\begin{alltt}
+int mp_lcm (mp_int * a, mp_int * b, mp_int * c)
+\end{alltt}
+This will compute the least common multiple of $a$ and $b$ and store it in $c$.
+
+\section{Jacobi Symbol}
+\index{mp\_jacobi}
+\begin{alltt}
+int mp_jacobi (mp_int * a, mp_int * p, int *c)
+\end{alltt}
+This will compute the Jacobi symbol for $a$ with respect to $p$. If $p$ is prime this essentially computes the Legendre
+symbol. The result is stored in $c$ and can take on one of three values $\lbrace -1, 0, 1 \rbrace$. If $p$ is prime
+then the result will be $-1$ when $a$ is not a quadratic residue modulo $p$. The result will be $0$ if $a$ divides $p$
+and the result will be $1$ if $a$ is a quadratic residue modulo $p$.
+
+\section{Modular Inverse}
+\index{mp\_invmod}
+\begin{alltt}
+int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
+\end{alltt}
+Computes the multiplicative inverse of $a$ modulo $b$ and stores the result in $c$ such that $ac \equiv 1 \mbox{ (mod }b\mbox{)}$.
+
+\section{Single Digit Functions}
+
+For those using small numbers (\textit{snicker snicker}) there are several ``helper'' functions
+
+\index{mp\_add\_d} \index{mp\_sub\_d} \index{mp\_mul\_d} \index{mp\_div\_d} \index{mp\_mod\_d}
+\begin{alltt}
+int mp_add_d(mp_int *a, mp_digit b, mp_int *c);
+int mp_sub_d(mp_int *a, mp_digit b, mp_int *c);
+int mp_mul_d(mp_int *a, mp_digit b, mp_int *c);
+int mp_div_d(mp_int *a, mp_digit b, mp_int *c, mp_digit *d);
+int mp_mod_d(mp_int *a, mp_digit b, mp_digit *c);
+\end{alltt}
+
+These work like the full mp\_int capable variants except the second parameter $b$ is a mp\_digit. These
+functions fairly handy if you have to work with relatively small numbers since you will not have to allocate
+an entire mp\_int to store a number like $1$ or $2$.
+
+\input{bn.ind}
+
+\end{document}
--- /dev/null
+#include <tommath.h>
+#ifdef BN_ERROR_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+static const struct {
+ int code;
+ const char *msg;
+} msgs[] = {
+ { MP_OKAY, "Successful" },
+ { MP_MEM, "Out of heap" },
+ { MP_VAL, "Value out of range" }
+};
+
+/* return a char * string for a given code */
+const char *mp_error_to_string(int code)
+{
+ int x;
+
+ /* scan the lookup table for the given message */
+ for (x = 0; x < (int)(sizeof(msgs) / sizeof(msgs[0])); x++) {
+ if (msgs[x].code == code) {
+ return msgs[x].msg;
+ }
+ }
+
+ /* generic reply for invalid code */
+ return "Invalid error code";
+}
+
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_FAST_MP_INVMOD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* computes the modular inverse via binary extended euclidean algorithm,
+ * that is c = 1/a mod b
+ *
+ * Based on slow invmod except this is optimized for the case where b is
+ * odd as per HAC Note 14.64 on pp. 610
+ */
+int fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
+{
+ mp_int x, y, u, v, B, D;
+ int res, neg;
+
+ /* 2. [modified] b must be odd */
+ if (mp_iseven (b) == 1) {
+ return MP_VAL;
+ }
+
+ /* init all our temps */
+ if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) {
+ return res;
+ }
+
+ /* x == modulus, y == value to invert */
+ if ((res = mp_copy (b, &x)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ /* we need y = |a| */
+ if ((res = mp_mod (a, b, &y)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
+ if ((res = mp_copy (&x, &u)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if ((res = mp_copy (&y, &v)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ mp_set (&D, 1);
+
+top:
+ /* 4. while u is even do */
+ while (mp_iseven (&u) == 1) {
+ /* 4.1 u = u/2 */
+ if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ /* 4.2 if B is odd then */
+ if (mp_isodd (&B) == 1) {
+ if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+ /* B = B/2 */
+ if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* 5. while v is even do */
+ while (mp_iseven (&v) == 1) {
+ /* 5.1 v = v/2 */
+ if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ /* 5.2 if D is odd then */
+ if (mp_isodd (&D) == 1) {
+ /* D = (D-x)/2 */
+ if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+ /* D = D/2 */
+ if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* 6. if u >= v then */
+ if (mp_cmp (&u, &v) != MP_LT) {
+ /* u = u - v, B = B - D */
+ if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ } else {
+ /* v - v - u, D = D - B */
+ if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* if not zero goto step 4 */
+ if (mp_iszero (&u) == 0) {
+ goto top;
+ }
+
+ /* now a = C, b = D, gcd == g*v */
+
+ /* if v != 1 then there is no inverse */
+ if (mp_cmp_d (&v, 1) != MP_EQ) {
+ res = MP_VAL;
+ goto LBL_ERR;
+ }
+
+ /* b is now the inverse */
+ neg = a->sign;
+ while (D.sign == MP_NEG) {
+ if ((res = mp_add (&D, b, &D)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+ mp_exch (&D, c);
+ c->sign = neg;
+ res = MP_OKAY;
+
+LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
+ return res;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* computes xR**-1 == x (mod N) via Montgomery Reduction
+ *
+ * This is an optimized implementation of montgomery_reduce
+ * which uses the comba method to quickly calculate the columns of the
+ * reduction.
+ *
+ * Based on Algorithm 14.32 on pp.601 of HAC.
+*/
+int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
+{
+ int ix, res, olduse;
+ mp_word W[MP_WARRAY];
+
+ /* get old used count */
+ olduse = x->used;
+
+ /* grow a as required */
+ if (x->alloc < n->used + 1) {
+ if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* first we have to get the digits of the input into
+ * an array of double precision words W[...]
+ */
+ {
+ register mp_word *_W;
+ register mp_digit *tmpx;
+
+ /* alias for the W[] array */
+ _W = W;
+
+ /* alias for the digits of x*/
+ tmpx = x->dp;
+
+ /* copy the digits of a into W[0..a->used-1] */
+ for (ix = 0; ix < x->used; ix++) {
+ *_W++ = *tmpx++;
+ }
+
+ /* zero the high words of W[a->used..m->used*2] */
+ for (; ix < n->used * 2 + 1; ix++) {
+ *_W++ = 0;
+ }
+ }
+
+ /* now we proceed to zero successive digits
+ * from the least significant upwards
+ */
+ for (ix = 0; ix < n->used; ix++) {
+ /* mu = ai * m' mod b
+ *
+ * We avoid a double precision multiplication (which isn't required)
+ * by casting the value down to a mp_digit. Note this requires
+ * that W[ix-1] have the carry cleared (see after the inner loop)
+ */
+ register mp_digit mu;
+ mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);
+
+ /* a = a + mu * m * b**i
+ *
+ * This is computed in place and on the fly. The multiplication
+ * by b**i is handled by offseting which columns the results
+ * are added to.
+ *
+ * Note the comba method normally doesn't handle carries in the
+ * inner loop In this case we fix the carry from the previous
+ * column since the Montgomery reduction requires digits of the
+ * result (so far) [see above] to work. This is
+ * handled by fixing up one carry after the inner loop. The
+ * carry fixups are done in order so after these loops the
+ * first m->used words of W[] have the carries fixed
+ */
+ {
+ register int iy;
+ register mp_digit *tmpn;
+ register mp_word *_W;
+
+ /* alias for the digits of the modulus */
+ tmpn = n->dp;
+
+ /* Alias for the columns set by an offset of ix */
+ _W = W + ix;
+
+ /* inner loop */
+ for (iy = 0; iy < n->used; iy++) {
+ *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++);
+ }
+ }
+
+ /* now fix carry for next digit, W[ix+1] */
+ W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
+ }
+
+ /* now we have to propagate the carries and
+ * shift the words downward [all those least
+ * significant digits we zeroed].
+ */
+ {
+ register mp_digit *tmpx;
+ register mp_word *_W, *_W1;
+
+ /* nox fix rest of carries */
+
+ /* alias for current word */
+ _W1 = W + ix;
+
+ /* alias for next word, where the carry goes */
+ _W = W + ++ix;
+
+ for (; ix <= n->used * 2 + 1; ix++) {
+ *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
+ }
+
+ /* copy out, A = A/b**n
+ *
+ * The result is A/b**n but instead of converting from an
+ * array of mp_word to mp_digit than calling mp_rshd
+ * we just copy them in the right order
+ */
+
+ /* alias for destination word */
+ tmpx = x->dp;
+
+ /* alias for shifted double precision result */
+ _W = W + n->used;
+
+ for (ix = 0; ix < n->used + 1; ix++) {
+ *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
+ }
+
+ /* zero oldused digits, if the input a was larger than
+ * m->used+1 we'll have to clear the digits
+ */
+ for (; ix < olduse; ix++) {
+ *tmpx++ = 0;
+ }
+ }
+
+ /* set the max used and clamp */
+ x->used = n->used + 1;
+ mp_clamp (x);
+
+ /* if A >= m then A = A - m */
+ if (mp_cmp_mag (x, n) != MP_LT) {
+ return s_mp_sub (x, n, x);
+ }
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_FAST_S_MP_MUL_DIGS_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* Fast (comba) multiplier
+ *
+ * This is the fast column-array [comba] multiplier. It is
+ * designed to compute the columns of the product first
+ * then handle the carries afterwards. This has the effect
+ * of making the nested loops that compute the columns very
+ * simple and schedulable on super-scalar processors.
+ *
+ * This has been modified to produce a variable number of
+ * digits of output so if say only a half-product is required
+ * you don't have to compute the upper half (a feature
+ * required for fast Barrett reduction).
+ *
+ * Based on Algorithm 14.12 on pp.595 of HAC.
+ *
+ */
+int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
+{
+ int olduse, res, pa, ix, iz;
+ mp_digit W[MP_WARRAY];
+ register mp_word _W;
+
+ /* grow the destination as required */
+ if (c->alloc < digs) {
+ if ((res = mp_grow (c, digs)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* number of output digits to produce */
+ pa = MIN(digs, a->used + b->used);
+
+ /* clear the carry */
+ _W = 0;
+ for (ix = 0; ix < pa; ix++) {
+ int tx, ty;
+ int iy;
+ mp_digit *tmpx, *tmpy;
+
+ /* get offsets into the two bignums */
+ ty = MIN(b->used-1, ix);
+ tx = ix - ty;
+
+ /* setup temp aliases */
+ tmpx = a->dp + tx;
+ tmpy = b->dp + ty;
+
+ /* this is the number of times the loop will iterrate, essentially
+ while (tx++ < a->used && ty-- >= 0) { ... }
+ */
+ iy = MIN(a->used-tx, ty+1);
+
+ /* execute loop */
+ for (iz = 0; iz < iy; ++iz) {
+ _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
+
+ }
+
+ /* store term */
+ W[ix] = ((mp_digit)_W) & MP_MASK;
+
+ /* make next carry */
+ _W = _W >> ((mp_word)DIGIT_BIT);
+ }
+
+ /* setup dest */
+ olduse = c->used;
+ c->used = pa;
+
+ {
+ register mp_digit *tmpc;
+ tmpc = c->dp;
+ for (ix = 0; ix < pa+1; ix++) {
+ /* now extract the previous digit [below the carry] */
+ *tmpc++ = W[ix];
+ }
+
+ /* clear unused digits [that existed in the old copy of c] */
+ for (; ix < olduse; ix++) {
+ *tmpc++ = 0;
+ }
+ }
+ mp_clamp (c);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* this is a modified version of fast_s_mul_digs that only produces
+ * output digits *above* digs. See the comments for fast_s_mul_digs
+ * to see how it works.
+ *
+ * This is used in the Barrett reduction since for one of the multiplications
+ * only the higher digits were needed. This essentially halves the work.
+ *
+ * Based on Algorithm 14.12 on pp.595 of HAC.
+ */
+int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
+{
+ int olduse, res, pa, ix, iz;
+ mp_digit W[MP_WARRAY];
+ mp_word _W;
+
+ /* grow the destination as required */
+ pa = a->used + b->used;
+ if (c->alloc < pa) {
+ if ((res = mp_grow (c, pa)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* number of output digits to produce */
+ pa = a->used + b->used;
+ _W = 0;
+ for (ix = digs; ix < pa; ix++) {
+ int tx, ty, iy;
+ mp_digit *tmpx, *tmpy;
+
+ /* get offsets into the two bignums */
+ ty = MIN(b->used-1, ix);
+ tx = ix - ty;
+
+ /* setup temp aliases */
+ tmpx = a->dp + tx;
+ tmpy = b->dp + ty;
+
+ /* this is the number of times the loop will iterrate, essentially its
+ while (tx++ < a->used && ty-- >= 0) { ... }
+ */
+ iy = MIN(a->used-tx, ty+1);
+
+ /* execute loop */
+ for (iz = 0; iz < iy; iz++) {
+ _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
+ }
+
+ /* store term */
+ W[ix] = ((mp_digit)_W) & MP_MASK;
+
+ /* make next carry */
+ _W = _W >> ((mp_word)DIGIT_BIT);
+ }
+
+ /* setup dest */
+ olduse = c->used;
+ c->used = pa;
+
+ {
+ register mp_digit *tmpc;
+
+ tmpc = c->dp + digs;
+ for (ix = digs; ix < pa; ix++) {
+ /* now extract the previous digit [below the carry] */
+ *tmpc++ = W[ix];
+ }
+
+ /* clear unused digits [that existed in the old copy of c] */
+ for (; ix < olduse; ix++) {
+ *tmpc++ = 0;
+ }
+ }
+ mp_clamp (c);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_FAST_S_MP_SQR_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* the jist of squaring...
+ * you do like mult except the offset of the tmpx [one that
+ * starts closer to zero] can't equal the offset of tmpy.
+ * So basically you set up iy like before then you min it with
+ * (ty-tx) so that it never happens. You double all those
+ * you add in the inner loop
+
+After that loop you do the squares and add them in.
+*/
+
+int fast_s_mp_sqr (mp_int * a, mp_int * b)
+{
+ int olduse, res, pa, ix, iz;
+ mp_digit W[MP_WARRAY], *tmpx;
+ mp_word W1;
+
+ /* grow the destination as required */
+ pa = a->used + a->used;
+ if (b->alloc < pa) {
+ if ((res = mp_grow (b, pa)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* number of output digits to produce */
+ W1 = 0;
+ for (ix = 0; ix < pa; ix++) {
+ int tx, ty, iy;
+ mp_word _W;
+ mp_digit *tmpy;
+
+ /* clear counter */
+ _W = 0;
+
+ /* get offsets into the two bignums */
+ ty = MIN(a->used-1, ix);
+ tx = ix - ty;
+
+ /* setup temp aliases */
+ tmpx = a->dp + tx;
+ tmpy = a->dp + ty;
+
+ /* this is the number of times the loop will iterrate, essentially
+ while (tx++ < a->used && ty-- >= 0) { ... }
+ */
+ iy = MIN(a->used-tx, ty+1);
+
+ /* now for squaring tx can never equal ty
+ * we halve the distance since they approach at a rate of 2x
+ * and we have to round because odd cases need to be executed
+ */
+ iy = MIN(iy, (ty-tx+1)>>1);
+
+ /* execute loop */
+ for (iz = 0; iz < iy; iz++) {
+ _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
+ }
+
+ /* double the inner product and add carry */
+ _W = _W + _W + W1;
+
+ /* even columns have the square term in them */
+ if ((ix&1) == 0) {
+ _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]);
+ }
+
+ /* store it */
+ W[ix] = (mp_digit)(_W & MP_MASK);
+
+ /* make next carry */
+ W1 = _W >> ((mp_word)DIGIT_BIT);
+ }
+
+ /* setup dest */
+ olduse = b->used;
+ b->used = a->used+a->used;
+
+ {
+ mp_digit *tmpb;
+ tmpb = b->dp;
+ for (ix = 0; ix < pa; ix++) {
+ *tmpb++ = W[ix] & MP_MASK;
+ }
+
+ /* clear unused digits [that existed in the old copy of c] */
+ for (; ix < olduse; ix++) {
+ *tmpb++ = 0;
+ }
+ }
+ mp_clamp (b);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_2EXPT_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* computes a = 2**b
+ *
+ * Simple algorithm which zeroes the int, grows it then just sets one bit
+ * as required.
+ */
+int
+mp_2expt (mp_int * a, int b)
+{
+ int res;
+
+ /* zero a as per default */
+ mp_zero (a);
+
+ /* grow a to accomodate the single bit */
+ if ((res = mp_grow (a, b / DIGIT_BIT + 1)) != MP_OKAY) {
+ return res;
+ }
+
+ /* set the used count of where the bit will go */
+ a->used = b / DIGIT_BIT + 1;
+
+ /* put the single bit in its place */
+ a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT);
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_ABS_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* b = |a|
+ *
+ * Simple function copies the input and fixes the sign to positive
+ */
+int
+mp_abs (mp_int * a, mp_int * b)
+{
+ int res;
+
+ /* copy a to b */
+ if (a != b) {
+ if ((res = mp_copy (a, b)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* force the sign of b to positive */
+ b->sign = MP_ZPOS;
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_ADD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* high level addition (handles signs) */
+int mp_add (mp_int * a, mp_int * b, mp_int * c)
+{
+ int sa, sb, res;
+
+ /* get sign of both inputs */
+ sa = a->sign;
+ sb = b->sign;
+
+ /* handle two cases, not four */
+ if (sa == sb) {
+ /* both positive or both negative */
+ /* add their magnitudes, copy the sign */
+ c->sign = sa;
+ res = s_mp_add (a, b, c);
+ } else {
+ /* one positive, the other negative */
+ /* subtract the one with the greater magnitude from */
+ /* the one of the lesser magnitude. The result gets */
+ /* the sign of the one with the greater magnitude. */
+ if (mp_cmp_mag (a, b) == MP_LT) {
+ c->sign = sb;
+ res = s_mp_sub (b, a, c);
+ } else {
+ c->sign = sa;
+ res = s_mp_sub (a, b, c);
+ }
+ }
+ return res;
+}
+
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_ADD_D_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* single digit addition */
+int
+mp_add_d (mp_int * a, mp_digit b, mp_int * c)
+{
+ int res, ix, oldused;
+ mp_digit *tmpa, *tmpc, mu;
+
+ /* grow c as required */
+ if (c->alloc < a->used + 1) {
+ if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* if a is negative and |a| >= b, call c = |a| - b */
+ if (a->sign == MP_NEG && (a->used > 1 || a->dp[0] >= b)) {
+ /* temporarily fix sign of a */
+ a->sign = MP_ZPOS;
+
+ /* c = |a| - b */
+ res = mp_sub_d(a, b, c);
+
+ /* fix sign */
+ a->sign = c->sign = MP_NEG;
+
+ /* clamp */
+ mp_clamp(c);
+
+ return res;
+ }
+
+ /* old number of used digits in c */
+ oldused = c->used;
+
+ /* sign always positive */
+ c->sign = MP_ZPOS;
+
+ /* source alias */
+ tmpa = a->dp;
+
+ /* destination alias */
+ tmpc = c->dp;
+
+ /* if a is positive */
+ if (a->sign == MP_ZPOS) {
+ /* add digit, after this we're propagating
+ * the carry.
+ */
+ *tmpc = *tmpa++ + b;
+ mu = *tmpc >> DIGIT_BIT;
+ *tmpc++ &= MP_MASK;
+
+ /* now handle rest of the digits */
+ for (ix = 1; ix < a->used; ix++) {
+ *tmpc = *tmpa++ + mu;
+ mu = *tmpc >> DIGIT_BIT;
+ *tmpc++ &= MP_MASK;
+ }
+ /* set final carry */
+ ix++;
+ *tmpc++ = mu;
+
+ /* setup size */
+ c->used = a->used + 1;
+ } else {
+ /* a was negative and |a| < b */
+ c->used = 1;
+
+ /* the result is a single digit */
+ if (a->used == 1) {
+ *tmpc++ = b - a->dp[0];
+ } else {
+ *tmpc++ = b;
+ }
+
+ /* setup count so the clearing of oldused
+ * can fall through correctly
+ */
+ ix = 1;
+ }
+
+ /* now zero to oldused */
+ while (ix++ < oldused) {
+ *tmpc++ = 0;
+ }
+ mp_clamp(c);
+
+ return MP_OKAY;
+}
+
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_ADDMOD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* d = a + b (mod c) */
+int
+mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
+{
+ int res;
+ mp_int t;
+
+ if ((res = mp_init (&t)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_add (a, b, &t)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+ res = mp_mod (&t, c, d);
+ mp_clear (&t);
+ return res;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_AND_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* AND two ints together */
+int
+mp_and (mp_int * a, mp_int * b, mp_int * c)
+{
+ int res, ix, px;
+ mp_int t, *x;
+
+ if (a->used > b->used) {
+ if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
+ return res;
+ }
+ px = b->used;
+ x = b;
+ } else {
+ if ((res = mp_init_copy (&t, b)) != MP_OKAY) {
+ return res;
+ }
+ px = a->used;
+ x = a;
+ }
+
+ for (ix = 0; ix < px; ix++) {
+ t.dp[ix] &= x->dp[ix];
+ }
+
+ /* zero digits above the last from the smallest mp_int */
+ for (; ix < t.used; ix++) {
+ t.dp[ix] = 0;
+ }
+
+ mp_clamp (&t);
+ mp_exch (c, &t);
+ mp_clear (&t);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_CLAMP_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* trim unused digits
+ *
+ * This is used to ensure that leading zero digits are
+ * trimed and the leading "used" digit will be non-zero
+ * Typically very fast. Also fixes the sign if there
+ * are no more leading digits
+ */
+void
+mp_clamp (mp_int * a)
+{
+ /* decrease used while the most significant digit is
+ * zero.
+ */
+ while (a->used > 0 && a->dp[a->used - 1] == 0) {
+ --(a->used);
+ }
+
+ /* reset the sign flag if used == 0 */
+ if (a->used == 0) {
+ a->sign = MP_ZPOS;
+ }
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_CLEAR_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* clear one (frees) */
+void
+mp_clear (mp_int * a)
+{
+ int i;
+
+ /* only do anything if a hasn't been freed previously */
+ if (a->dp != NULL) {
+ /* first zero the digits */
+ for (i = 0; i < a->used; i++) {
+ a->dp[i] = 0;
+ }
+
+ /* free ram */
+ XFREE(a->dp);
+
+ /* reset members to make debugging easier */
+ a->dp = NULL;
+ a->alloc = a->used = 0;
+ a->sign = MP_ZPOS;
+ }
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_CLEAR_MULTI_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+#include <stdarg.h>
+
+void mp_clear_multi(mp_int *mp, ...)
+{
+ mp_int* next_mp = mp;
+ va_list args;
+ va_start(args, mp);
+ while (next_mp != NULL) {
+ mp_clear(next_mp);
+ next_mp = va_arg(args, mp_int*);
+ }
+ va_end(args);
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_CMP_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* compare two ints (signed)*/
+int
+mp_cmp (mp_int * a, mp_int * b)
+{
+ /* compare based on sign */
+ if (a->sign != b->sign) {
+ if (a->sign == MP_NEG) {
+ return MP_LT;
+ } else {
+ return MP_GT;
+ }
+ }
+
+ /* compare digits */
+ if (a->sign == MP_NEG) {
+ /* if negative compare opposite direction */
+ return mp_cmp_mag(b, a);
+ } else {
+ return mp_cmp_mag(a, b);
+ }
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_CMP_D_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* compare a digit */
+int mp_cmp_d(mp_int * a, mp_digit b)
+{
+ /* compare based on sign */
+ if (a->sign == MP_NEG) {
+ return MP_LT;
+ }
+
+ /* compare based on magnitude */
+ if (a->used > 1) {
+ return MP_GT;
+ }
+
+ /* compare the only digit of a to b */
+ if (a->dp[0] > b) {
+ return MP_GT;
+ } else if (a->dp[0] < b) {
+ return MP_LT;
+ } else {
+ return MP_EQ;
+ }
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_CMP_MAG_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* compare maginitude of two ints (unsigned) */
+int mp_cmp_mag (mp_int * a, mp_int * b)
+{
+ int n;
+ mp_digit *tmpa, *tmpb;
+
+ /* compare based on # of non-zero digits */
+ if (a->used > b->used) {
+ return MP_GT;
+ }
+
+ if (a->used < b->used) {
+ return MP_LT;
+ }
+
+ /* alias for a */
+ tmpa = a->dp + (a->used - 1);
+
+ /* alias for b */
+ tmpb = b->dp + (a->used - 1);
+
+ /* compare based on digits */
+ for (n = 0; n < a->used; ++n, --tmpa, --tmpb) {
+ if (*tmpa > *tmpb) {
+ return MP_GT;
+ }
+
+ if (*tmpa < *tmpb) {
+ return MP_LT;
+ }
+ }
+ return MP_EQ;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_CNT_LSB_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+static const int lnz[16] = {
+ 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
+};
+
+/* Counts the number of lsbs which are zero before the first zero bit */
+int mp_cnt_lsb(mp_int *a)
+{
+ int x;
+ mp_digit q, qq;
+
+ /* easy out */
+ if (mp_iszero(a) == 1) {
+ return 0;
+ }
+
+ /* scan lower digits until non-zero */
+ for (x = 0; x < a->used && a->dp[x] == 0; x++);
+ q = a->dp[x];
+ x *= DIGIT_BIT;
+
+ /* now scan this digit until a 1 is found */
+ if ((q & 1) == 0) {
+ do {
+ qq = q & 15;
+ x += lnz[qq];
+ q >>= 4;
+ } while (qq == 0);
+ }
+ return x;
+}
+
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_COPY_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* copy, b = a */
+int
+mp_copy (mp_int * a, mp_int * b)
+{
+ int res, n;
+
+ /* if dst == src do nothing */
+ if (a == b) {
+ return MP_OKAY;
+ }
+
+ /* grow dest */
+ if (b->alloc < a->used) {
+ if ((res = mp_grow (b, a->used)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* zero b and copy the parameters over */
+ {
+ register mp_digit *tmpa, *tmpb;
+
+ /* pointer aliases */
+
+ /* source */
+ tmpa = a->dp;
+
+ /* destination */
+ tmpb = b->dp;
+
+ /* copy all the digits */
+ for (n = 0; n < a->used; n++) {
+ *tmpb++ = *tmpa++;
+ }
+
+ /* clear high digits */
+ for (; n < b->used; n++) {
+ *tmpb++ = 0;
+ }
+ }
+
+ /* copy used count and sign */
+ b->used = a->used;
+ b->sign = a->sign;
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_COUNT_BITS_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* returns the number of bits in an int */
+int
+mp_count_bits (mp_int * a)
+{
+ int r;
+ mp_digit q;
+
+ /* shortcut */
+ if (a->used == 0) {
+ return 0;
+ }
+
+ /* get number of digits and add that */
+ r = (a->used - 1) * DIGIT_BIT;
+
+ /* take the last digit and count the bits in it */
+ q = a->dp[a->used - 1];
+ while (q > ((mp_digit) 0)) {
+ ++r;
+ q >>= ((mp_digit) 1);
+ }
+ return r;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_DIV_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+#ifdef BN_MP_DIV_SMALL
+
+/* slower bit-bang division... also smaller */
+int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
+{
+ mp_int ta, tb, tq, q;
+ int res, n, n2;
+
+ /* is divisor zero ? */
+ if (mp_iszero (b) == 1) {
+ return MP_VAL;
+ }
+
+ /* if a < b then q=0, r = a */
+ if (mp_cmp_mag (a, b) == MP_LT) {
+ if (d != NULL) {
+ res = mp_copy (a, d);
+ } else {
+ res = MP_OKAY;
+ }
+ if (c != NULL) {
+ mp_zero (c);
+ }
+ return res;
+ }
+
+ /* init our temps */
+ if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) {
+ return res;
+ }
+
+
+ mp_set(&tq, 1);
+ n = mp_count_bits(a) - mp_count_bits(b);
+ if (((res = mp_abs(a, &ta)) != MP_OKAY) ||
+ ((res = mp_abs(b, &tb)) != MP_OKAY) ||
+ ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
+ ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
+ goto LBL_ERR;
+ }
+
+ while (n-- >= 0) {
+ if (mp_cmp(&tb, &ta) != MP_GT) {
+ if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
+ ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) {
+ goto LBL_ERR;
+ }
+ }
+ if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
+ ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* now q == quotient and ta == remainder */
+ n = a->sign;
+ n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG);
+ if (c != NULL) {
+ mp_exch(c, &q);
+ c->sign = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2;
+ }
+ if (d != NULL) {
+ mp_exch(d, &ta);
+ d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n;
+ }
+LBL_ERR:
+ mp_clear_multi(&ta, &tb, &tq, &q, NULL);
+ return res;
+}
+
+#else
+
+/* integer signed division.
+ * c*b + d == a [e.g. a/b, c=quotient, d=remainder]
+ * HAC pp.598 Algorithm 14.20
+ *
+ * Note that the description in HAC is horribly
+ * incomplete. For example, it doesn't consider
+ * the case where digits are removed from 'x' in
+ * the inner loop. It also doesn't consider the
+ * case that y has fewer than three digits, etc..
+ *
+ * The overall algorithm is as described as
+ * 14.20 from HAC but fixed to treat these cases.
+*/
+int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
+{
+ mp_int q, x, y, t1, t2;
+ int res, n, t, i, norm, neg;
+
+ /* is divisor zero ? */
+ if (mp_iszero (b) == 1) {
+ return MP_VAL;
+ }
+
+ /* if a < b then q=0, r = a */
+ if (mp_cmp_mag (a, b) == MP_LT) {
+ if (d != NULL) {
+ res = mp_copy (a, d);
+ } else {
+ res = MP_OKAY;
+ }
+ if (c != NULL) {
+ mp_zero (c);
+ }
+ return res;
+ }
+
+ if ((res = mp_init_size (&q, a->used + 2)) != MP_OKAY) {
+ return res;
+ }
+ q.used = a->used + 2;
+
+ if ((res = mp_init (&t1)) != MP_OKAY) {
+ goto LBL_Q;
+ }
+
+ if ((res = mp_init (&t2)) != MP_OKAY) {
+ goto LBL_T1;
+ }
+
+ if ((res = mp_init_copy (&x, a)) != MP_OKAY) {
+ goto LBL_T2;
+ }
+
+ if ((res = mp_init_copy (&y, b)) != MP_OKAY) {
+ goto LBL_X;
+ }
+
+ /* fix the sign */
+ neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
+ x.sign = y.sign = MP_ZPOS;
+
+ /* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
+ norm = mp_count_bits(&y) % DIGIT_BIT;
+ if (norm < (int)(DIGIT_BIT-1)) {
+ norm = (DIGIT_BIT-1) - norm;
+ if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+ if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+ } else {
+ norm = 0;
+ }
+
+ /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
+ n = x.used - 1;
+ t = y.used - 1;
+
+ /* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */
+ if ((res = mp_lshd (&y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */
+ goto LBL_Y;
+ }
+
+ while (mp_cmp (&x, &y) != MP_LT) {
+ ++(q.dp[n - t]);
+ if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+ }
+
+ /* reset y by shifting it back down */
+ mp_rshd (&y, n - t);
+
+ /* step 3. for i from n down to (t + 1) */
+ for (i = n; i >= (t + 1); i--) {
+ if (i > x.used) {
+ continue;
+ }
+
+ /* step 3.1 if xi == yt then set q{i-t-1} to b-1,
+ * otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */
+ if (x.dp[i] == y.dp[t]) {
+ q.dp[i - t - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1);
+ } else {
+ mp_word tmp;
+ tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT);
+ tmp |= ((mp_word) x.dp[i - 1]);
+ tmp /= ((mp_word) y.dp[t]);
+ if (tmp > (mp_word) MP_MASK)
+ tmp = MP_MASK;
+ q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK));
+ }
+
+ /* while (q{i-t-1} * (yt * b + y{t-1})) >
+ xi * b**2 + xi-1 * b + xi-2
+
+ do q{i-t-1} -= 1;
+ */
+ q.dp[i - t - 1] = (q.dp[i - t - 1] + 1) & MP_MASK;
+ do {
+ q.dp[i - t - 1] = (q.dp[i - t - 1] - 1) & MP_MASK;
+
+ /* find left hand */
+ mp_zero (&t1);
+ t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1];
+ t1.dp[1] = y.dp[t];
+ t1.used = 2;
+ if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+
+ /* find right hand */
+ t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2];
+ t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1];
+ t2.dp[2] = x.dp[i];
+ t2.used = 3;
+ } while (mp_cmp_mag(&t1, &t2) == MP_GT);
+
+ /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
+ if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+
+ if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+
+ if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+
+ /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
+ if (x.sign == MP_NEG) {
+ if ((res = mp_copy (&y, &t1)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+ if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+ if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+
+ q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK;
+ }
+ }
+
+ /* now q is the quotient and x is the remainder
+ * [which we have to normalize]
+ */
+
+ /* get sign before writing to c */
+ x.sign = x.used == 0 ? MP_ZPOS : a->sign;
+
+ if (c != NULL) {
+ mp_clamp (&q);
+ mp_exch (&q, c);
+ c->sign = neg;
+ }
+
+ if (d != NULL) {
+ mp_div_2d (&x, norm, &x, NULL);
+ mp_exch (&x, d);
+ }
+
+ res = MP_OKAY;
+
+LBL_Y:mp_clear (&y);
+LBL_X:mp_clear (&x);
+LBL_T2:mp_clear (&t2);
+LBL_T1:mp_clear (&t1);
+LBL_Q:mp_clear (&q);
+ return res;
+}
+
+#endif
+
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_DIV_2_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* b = a/2 */
+int mp_div_2(mp_int * a, mp_int * b)
+{
+ int x, res, oldused;
+
+ /* copy */
+ if (b->alloc < a->used) {
+ if ((res = mp_grow (b, a->used)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ oldused = b->used;
+ b->used = a->used;
+ {
+ register mp_digit r, rr, *tmpa, *tmpb;
+
+ /* source alias */
+ tmpa = a->dp + b->used - 1;
+
+ /* dest alias */
+ tmpb = b->dp + b->used - 1;
+
+ /* carry */
+ r = 0;
+ for (x = b->used - 1; x >= 0; x--) {
+ /* get the carry for the next iteration */
+ rr = *tmpa & 1;
+
+ /* shift the current digit, add in carry and store */
+ *tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1));
+
+ /* forward carry to next iteration */
+ r = rr;
+ }
+
+ /* zero excess digits */
+ tmpb = b->dp + b->used;
+ for (x = b->used; x < oldused; x++) {
+ *tmpb++ = 0;
+ }
+ }
+ b->sign = a->sign;
+ mp_clamp (b);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_DIV_2D_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* shift right by a certain bit count (store quotient in c, optional remainder in d) */
+int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
+{
+ mp_digit D, r, rr;
+ int x, res;
+ mp_int t;
+
+
+ /* if the shift count is <= 0 then we do no work */
+ if (b <= 0) {
+ res = mp_copy (a, c);
+ if (d != NULL) {
+ mp_zero (d);
+ }
+ return res;
+ }
+
+ if ((res = mp_init (&t)) != MP_OKAY) {
+ return res;
+ }
+
+ /* get the remainder */
+ if (d != NULL) {
+ if ((res = mp_mod_2d (a, b, &t)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+ }
+
+ /* copy */
+ if ((res = mp_copy (a, c)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+
+ /* shift by as many digits in the bit count */
+ if (b >= (int)DIGIT_BIT) {
+ mp_rshd (c, b / DIGIT_BIT);
+ }
+
+ /* shift any bit count < DIGIT_BIT */
+ D = (mp_digit) (b % DIGIT_BIT);
+ if (D != 0) {
+ register mp_digit *tmpc, mask, shift;
+
+ /* mask */
+ mask = (((mp_digit)1) << D) - 1;
+
+ /* shift for lsb */
+ shift = DIGIT_BIT - D;
+
+ /* alias */
+ tmpc = c->dp + (c->used - 1);
+
+ /* carry */
+ r = 0;
+ for (x = c->used - 1; x >= 0; x--) {
+ /* get the lower bits of this word in a temp */
+ rr = *tmpc & mask;
+
+ /* shift the current word and mix in the carry bits from the previous word */
+ *tmpc = (*tmpc >> D) | (r << shift);
+ --tmpc;
+
+ /* set the carry to the carry bits of the current word found above */
+ r = rr;
+ }
+ }
+ mp_clamp (c);
+ if (d != NULL) {
+ mp_exch (&t, d);
+ }
+ mp_clear (&t);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_DIV_3_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* divide by three (based on routine from MPI and the GMP manual) */
+int
+mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
+{
+ mp_int q;
+ mp_word w, t;
+ mp_digit b;
+ int res, ix;
+
+ /* b = 2**DIGIT_BIT / 3 */
+ b = (((mp_word)1) << ((mp_word)DIGIT_BIT)) / ((mp_word)3);
+
+ if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
+ return res;
+ }
+
+ q.used = a->used;
+ q.sign = a->sign;
+ w = 0;
+ for (ix = a->used - 1; ix >= 0; ix--) {
+ w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
+
+ if (w >= 3) {
+ /* multiply w by [1/3] */
+ t = (w * ((mp_word)b)) >> ((mp_word)DIGIT_BIT);
+
+ /* now subtract 3 * [w/3] from w, to get the remainder */
+ w -= t+t+t;
+
+ /* fixup the remainder as required since
+ * the optimization is not exact.
+ */
+ while (w >= 3) {
+ t += 1;
+ w -= 3;
+ }
+ } else {
+ t = 0;
+ }
+ q.dp[ix] = (mp_digit)t;
+ }
+
+ /* [optional] store the remainder */
+ if (d != NULL) {
+ *d = (mp_digit)w;
+ }
+
+ /* [optional] store the quotient */
+ if (c != NULL) {
+ mp_clamp(&q);
+ mp_exch(&q, c);
+ }
+ mp_clear(&q);
+
+ return res;
+}
+
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_DIV_D_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+static int s_is_power_of_two(mp_digit b, int *p)
+{
+ int x;
+
+ /* fast return if no power of two */
+ if ((b==0) || (b & (b-1))) {
+ return 0;
+ }
+
+ for (x = 0; x < DIGIT_BIT; x++) {
+ if (b == (((mp_digit)1)<<x)) {
+ *p = x;
+ return 1;
+ }
+ }
+ return 0;
+}
+
+/* single digit division (based on routine from MPI) */
+int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
+{
+ mp_int q;
+ mp_word w;
+ mp_digit t;
+ int res, ix;
+
+ /* cannot divide by zero */
+ if (b == 0) {
+ return MP_VAL;
+ }
+
+ /* quick outs */
+ if (b == 1 || mp_iszero(a) == 1) {
+ if (d != NULL) {
+ *d = 0;
+ }
+ if (c != NULL) {
+ return mp_copy(a, c);
+ }
+ return MP_OKAY;
+ }
+
+ /* power of two ? */
+ if (s_is_power_of_two(b, &ix) == 1) {
+ if (d != NULL) {
+ *d = a->dp[0] & ((((mp_digit)1)<<ix) - 1);
+ }
+ if (c != NULL) {
+ return mp_div_2d(a, ix, c, NULL);
+ }
+ return MP_OKAY;
+ }
+
+#ifdef BN_MP_DIV_3_C
+ /* three? */
+ if (b == 3) {
+ return mp_div_3(a, c, d);
+ }
+#endif
+
+ /* no easy answer [c'est la vie]. Just division */
+ if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
+ return res;
+ }
+
+ q.used = a->used;
+ q.sign = a->sign;
+ w = 0;
+ for (ix = a->used - 1; ix >= 0; ix--) {
+ w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
+
+ if (w >= b) {
+ t = (mp_digit)(w / b);
+ w -= ((mp_word)t) * ((mp_word)b);
+ } else {
+ t = 0;
+ }
+ q.dp[ix] = (mp_digit)t;
+ }
+
+ if (d != NULL) {
+ *d = (mp_digit)w;
+ }
+
+ if (c != NULL) {
+ mp_clamp(&q);
+ mp_exch(&q, c);
+ }
+ mp_clear(&q);
+
+ return res;
+}
+
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_DR_IS_MODULUS_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* determines if a number is a valid DR modulus */
+int mp_dr_is_modulus(mp_int *a)
+{
+ int ix;
+
+ /* must be at least two digits */
+ if (a->used < 2) {
+ return 0;
+ }
+
+ /* must be of the form b**k - a [a <= b] so all
+ * but the first digit must be equal to -1 (mod b).
+ */
+ for (ix = 1; ix < a->used; ix++) {
+ if (a->dp[ix] != MP_MASK) {
+ return 0;
+ }
+ }
+ return 1;
+}
+
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_DR_REDUCE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* reduce "x" in place modulo "n" using the Diminished Radix algorithm.
+ *
+ * Based on algorithm from the paper
+ *
+ * "Generating Efficient Primes for Discrete Log Cryptosystems"
+ * Chae Hoon Lim, Pil Joong Lee,
+ * POSTECH Information Research Laboratories
+ *
+ * The modulus must be of a special format [see manual]
+ *
+ * Has been modified to use algorithm 7.10 from the LTM book instead
+ *
+ * Input x must be in the range 0 <= x <= (n-1)**2
+ */
+int
+mp_dr_reduce (mp_int * x, mp_int * n, mp_digit k)
+{
+ int err, i, m;
+ mp_word r;
+ mp_digit mu, *tmpx1, *tmpx2;
+
+ /* m = digits in modulus */
+ m = n->used;
+
+ /* ensure that "x" has at least 2m digits */
+ if (x->alloc < m + m) {
+ if ((err = mp_grow (x, m + m)) != MP_OKAY) {
+ return err;
+ }
+ }
+
+/* top of loop, this is where the code resumes if
+ * another reduction pass is required.
+ */
+top:
+ /* aliases for digits */
+ /* alias for lower half of x */
+ tmpx1 = x->dp;
+
+ /* alias for upper half of x, or x/B**m */
+ tmpx2 = x->dp + m;
+
+ /* set carry to zero */
+ mu = 0;
+
+ /* compute (x mod B**m) + k * [x/B**m] inline and inplace */
+ for (i = 0; i < m; i++) {
+ r = ((mp_word)*tmpx2++) * ((mp_word)k) + *tmpx1 + mu;
+ *tmpx1++ = (mp_digit)(r & MP_MASK);
+ mu = (mp_digit)(r >> ((mp_word)DIGIT_BIT));
+ }
+
+ /* set final carry */
+ *tmpx1++ = mu;
+
+ /* zero words above m */
+ for (i = m + 1; i < x->used; i++) {
+ *tmpx1++ = 0;
+ }
+
+ /* clamp, sub and return */
+ mp_clamp (x);
+
+ /* if x >= n then subtract and reduce again
+ * Each successive "recursion" makes the input smaller and smaller.
+ */
+ if (mp_cmp_mag (x, n) != MP_LT) {
+ s_mp_sub(x, n, x);
+ goto top;
+ }
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_DR_SETUP_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* determines the setup value */
+void mp_dr_setup(mp_int *a, mp_digit *d)
+{
+ /* the casts are required if DIGIT_BIT is one less than
+ * the number of bits in a mp_digit [e.g. DIGIT_BIT==31]
+ */
+ *d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) -
+ ((mp_word)a->dp[0]));
+}
+
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_EXCH_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* swap the elements of two integers, for cases where you can't simply swap the
+ * mp_int pointers around
+ */
+void
+mp_exch (mp_int * a, mp_int * b)
+{
+ mp_int t;
+
+ t = *a;
+ *a = *b;
+ *b = t;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_EXPT_D_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* calculate c = a**b using a square-multiply algorithm */
+int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
+{
+ int res;
+ mp_int g;
+
+ if ((res = mp_init_copy (&g, a)) != MP_OKAY) {
+ return res;
+ }
+
+ /* set initial result */
+ mp_set (c, 1);
+
+ while (b > 0) {
+ /* if the bit is set multiply */
+ if (b & 1) {
+ if ((res = mp_mul (c, &g, c)) != MP_OKAY) {
+ mp_clear (&g);
+ return res;
+ }
+ }
+
+ /* square */
+ if (b > 1 && (res = mp_sqr (&g, &g)) != MP_OKAY) {
+ mp_clear (&g);
+ return res;
+ }
+
+ /* shift to next bit */
+ b >>= 1;
+ }
+
+ mp_clear (&g);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_EXPTMOD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+
+/* this is a shell function that calls either the normal or Montgomery
+ * exptmod functions. Originally the call to the montgomery code was
+ * embedded in the normal function but that wasted alot of stack space
+ * for nothing (since 99% of the time the Montgomery code would be called)
+ */
+int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
+{
+ int dr;
+
+ /* modulus P must be positive */
+ if (P->sign == MP_NEG) {
+ return MP_VAL;
+ }
+
+ /* if exponent X is negative we have to recurse */
+ if (X->sign == MP_NEG) {
+#ifdef BN_MP_INVMOD_C
+ mp_int tmpG, tmpX;
+ int err;
+
+ /* first compute 1/G mod P */
+ if ((err = mp_init(&tmpG)) != MP_OKAY) {
+ return err;
+ }
+ if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) {
+ mp_clear(&tmpG);
+ return err;
+ }
+
+ /* now get |X| */
+ if ((err = mp_init(&tmpX)) != MP_OKAY) {
+ mp_clear(&tmpG);
+ return err;
+ }
+ if ((err = mp_abs(X, &tmpX)) != MP_OKAY) {
+ mp_clear_multi(&tmpG, &tmpX, NULL);
+ return err;
+ }
+
+ /* and now compute (1/G)**|X| instead of G**X [X < 0] */
+ err = mp_exptmod(&tmpG, &tmpX, P, Y);
+ mp_clear_multi(&tmpG, &tmpX, NULL);
+ return err;
+#else
+ /* no invmod */
+ return MP_VAL;
+#endif
+ }
+
+/* modified diminished radix reduction */
+#if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C) && defined(BN_S_MP_EXPTMOD_C)
+ if (mp_reduce_is_2k_l(P) == MP_YES) {
+ return s_mp_exptmod(G, X, P, Y, 1);
+ }
+#endif
+
+#ifdef BN_MP_DR_IS_MODULUS_C
+ /* is it a DR modulus? */
+ dr = mp_dr_is_modulus(P);
+#else
+ /* default to no */
+ dr = 0;
+#endif
+
+#ifdef BN_MP_REDUCE_IS_2K_C
+ /* if not, is it a unrestricted DR modulus? */
+ if (dr == 0) {
+ dr = mp_reduce_is_2k(P) << 1;
+ }
+#endif
+
+ /* if the modulus is odd or dr != 0 use the montgomery method */
+#ifdef BN_MP_EXPTMOD_FAST_C
+ if (mp_isodd (P) == 1 || dr != 0) {
+ return mp_exptmod_fast (G, X, P, Y, dr);
+ } else {
+#endif
+#ifdef BN_S_MP_EXPTMOD_C
+ /* otherwise use the generic Barrett reduction technique */
+ return s_mp_exptmod (G, X, P, Y, 0);
+#else
+ /* no exptmod for evens */
+ return MP_VAL;
+#endif
+#ifdef BN_MP_EXPTMOD_FAST_C
+ }
+#endif
+}
+
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_EXPTMOD_FAST_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
+ *
+ * Uses a left-to-right k-ary sliding window to compute the modular exponentiation.
+ * The value of k changes based on the size of the exponent.
+ *
+ * Uses Montgomery or Diminished Radix reduction [whichever appropriate]
+ */
+
+#ifdef MP_LOW_MEM
+ #define TAB_SIZE 32
+#else
+ #define TAB_SIZE 256
+#endif
+
+int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
+{
+ mp_int M[TAB_SIZE], res;
+ mp_digit buf, mp;
+ int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
+
+ /* use a pointer to the reduction algorithm. This allows us to use
+ * one of many reduction algorithms without modding the guts of
+ * the code with if statements everywhere.
+ */
+ int (*redux)(mp_int*,mp_int*,mp_digit);
+
+ /* find window size */
+ x = mp_count_bits (X);
+ if (x <= 7) {
+ winsize = 2;
+ } else if (x <= 36) {
+ winsize = 3;
+ } else if (x <= 140) {
+ winsize = 4;
+ } else if (x <= 450) {
+ winsize = 5;
+ } else if (x <= 1303) {
+ winsize = 6;
+ } else if (x <= 3529) {
+ winsize = 7;
+ } else {
+ winsize = 8;
+ }
+
+#ifdef MP_LOW_MEM
+ if (winsize > 5) {
+ winsize = 5;
+ }
+#endif
+
+ /* init M array */
+ /* init first cell */
+ if ((err = mp_init(&M[1])) != MP_OKAY) {
+ return err;
+ }
+
+ /* now init the second half of the array */
+ for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
+ if ((err = mp_init(&M[x])) != MP_OKAY) {
+ for (y = 1<<(winsize-1); y < x; y++) {
+ mp_clear (&M[y]);
+ }
+ mp_clear(&M[1]);
+ return err;
+ }
+ }
+
+ /* determine and setup reduction code */
+ if (redmode == 0) {
+#ifdef BN_MP_MONTGOMERY_SETUP_C
+ /* now setup montgomery */
+ if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) {
+ goto LBL_M;
+ }
+#else
+ err = MP_VAL;
+ goto LBL_M;
+#endif
+
+ /* automatically pick the comba one if available (saves quite a few calls/ifs) */
+#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
+ if (((P->used * 2 + 1) < MP_WARRAY) &&
+ P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
+ redux = fast_mp_montgomery_reduce;
+ } else
+#endif
+ {
+#ifdef BN_MP_MONTGOMERY_REDUCE_C
+ /* use slower baseline Montgomery method */
+ redux = mp_montgomery_reduce;
+#else
+ err = MP_VAL;
+ goto LBL_M;
+#endif
+ }
+ } else if (redmode == 1) {
+#if defined(BN_MP_DR_SETUP_C) && defined(BN_MP_DR_REDUCE_C)
+ /* setup DR reduction for moduli of the form B**k - b */
+ mp_dr_setup(P, &mp);
+ redux = mp_dr_reduce;
+#else
+ err = MP_VAL;
+ goto LBL_M;
+#endif
+ } else {
+#if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C)
+ /* setup DR reduction for moduli of the form 2**k - b */
+ if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
+ goto LBL_M;
+ }
+ redux = mp_reduce_2k;
+#else
+ err = MP_VAL;
+ goto LBL_M;
+#endif
+ }
+
+ /* setup result */
+ if ((err = mp_init (&res)) != MP_OKAY) {
+ goto LBL_M;
+ }
+
+ /* create M table
+ *
+
+ *
+ * The first half of the table is not computed though accept for M[0] and M[1]
+ */
+
+ if (redmode == 0) {
+#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+ /* now we need R mod m */
+ if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+#else
+ err = MP_VAL;
+ goto LBL_RES;
+#endif
+
+ /* now set M[1] to G * R mod m */
+ if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ } else {
+ mp_set(&res, 1);
+ if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+
+ /* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */
+ if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
+ goto LBL_RES;
+ }
+
+ for (x = 0; x < (winsize - 1); x++) {
+ if ((err = mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+
+ /* create upper table */
+ for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
+ if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&M[x], P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+
+ /* set initial mode and bit cnt */
+ mode = 0;
+ bitcnt = 1;
+ buf = 0;
+ digidx = X->used - 1;
+ bitcpy = 0;
+ bitbuf = 0;
+
+ for (;;) {
+ /* grab next digit as required */
+ if (--bitcnt == 0) {
+ /* if digidx == -1 we are out of digits so break */
+ if (digidx == -1) {
+ break;
+ }
+ /* read next digit and reset bitcnt */
+ buf = X->dp[digidx--];
+ bitcnt = (int)DIGIT_BIT;
+ }
+
+ /* grab the next msb from the exponent */
+ y = (mp_digit)(buf >> (DIGIT_BIT - 1)) & 1;
+ buf <<= (mp_digit)1;
+
+ /* if the bit is zero and mode == 0 then we ignore it
+ * These represent the leading zero bits before the first 1 bit
+ * in the exponent. Technically this opt is not required but it
+ * does lower the # of trivial squaring/reductions used
+ */
+ if (mode == 0 && y == 0) {
+ continue;
+ }
+
+ /* if the bit is zero and mode == 1 then we square */
+ if (mode == 1 && y == 0) {
+ if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ continue;
+ }
+
+ /* else we add it to the window */
+ bitbuf |= (y << (winsize - ++bitcpy));
+ mode = 2;
+
+ if (bitcpy == winsize) {
+ /* ok window is filled so square as required and multiply */
+ /* square first */
+ for (x = 0; x < winsize; x++) {
+ if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+
+ /* then multiply */
+ if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+
+ /* empty window and reset */
+ bitcpy = 0;
+ bitbuf = 0;
+ mode = 1;
+ }
+ }
+
+ /* if bits remain then square/multiply */
+ if (mode == 2 && bitcpy > 0) {
+ /* square then multiply if the bit is set */
+ for (x = 0; x < bitcpy; x++) {
+ if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+
+ /* get next bit of the window */
+ bitbuf <<= 1;
+ if ((bitbuf & (1 << winsize)) != 0) {
+ /* then multiply */
+ if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+ }
+ }
+
+ if (redmode == 0) {
+ /* fixup result if Montgomery reduction is used
+ * recall that any value in a Montgomery system is
+ * actually multiplied by R mod n. So we have
+ * to reduce one more time to cancel out the factor
+ * of R.
+ */
+ if ((err = redux(&res, P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+
+ /* swap res with Y */
+ mp_exch (&res, Y);
+ err = MP_OKAY;
+LBL_RES:mp_clear (&res);
+LBL_M:
+ mp_clear(&M[1]);
+ for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
+ mp_clear (&M[x]);
+ }
+ return err;
+}
+#endif
+
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_EXTEUCLID_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* Extended euclidean algorithm of (a, b) produces
+ a*u1 + b*u2 = u3
+ */
+int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3)
+{
+ mp_int u1,u2,u3,v1,v2,v3,t1,t2,t3,q,tmp;
+ int err;
+
+ if ((err = mp_init_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL)) != MP_OKAY) {
+ return err;
+ }
+
+ /* initialize, (u1,u2,u3) = (1,0,a) */
+ mp_set(&u1, 1);
+ if ((err = mp_copy(a, &u3)) != MP_OKAY) { goto _ERR; }
+
+ /* initialize, (v1,v2,v3) = (0,1,b) */
+ mp_set(&v2, 1);
+ if ((err = mp_copy(b, &v3)) != MP_OKAY) { goto _ERR; }
+
+ /* loop while v3 != 0 */
+ while (mp_iszero(&v3) == MP_NO) {
+ /* q = u3/v3 */
+ if ((err = mp_div(&u3, &v3, &q, NULL)) != MP_OKAY) { goto _ERR; }
+
+ /* (t1,t2,t3) = (u1,u2,u3) - (v1,v2,v3)q */
+ if ((err = mp_mul(&v1, &q, &tmp)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_sub(&u1, &tmp, &t1)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_mul(&v2, &q, &tmp)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_sub(&u2, &tmp, &t2)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_mul(&v3, &q, &tmp)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_sub(&u3, &tmp, &t3)) != MP_OKAY) { goto _ERR; }
+
+ /* (u1,u2,u3) = (v1,v2,v3) */
+ if ((err = mp_copy(&v1, &u1)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_copy(&v2, &u2)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_copy(&v3, &u3)) != MP_OKAY) { goto _ERR; }
+
+ /* (v1,v2,v3) = (t1,t2,t3) */
+ if ((err = mp_copy(&t1, &v1)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_copy(&t2, &v2)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_copy(&t3, &v3)) != MP_OKAY) { goto _ERR; }
+ }
+
+ /* make sure U3 >= 0 */
+ if (u3.sign == MP_NEG) {
+ mp_neg(&u1, &u1);
+ mp_neg(&u2, &u2);
+ mp_neg(&u3, &u3);
+ }
+
+ /* copy result out */
+ if (U1 != NULL) { mp_exch(U1, &u1); }
+ if (U2 != NULL) { mp_exch(U2, &u2); }
+ if (U3 != NULL) { mp_exch(U3, &u3); }
+
+ err = MP_OKAY;
+_ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL);
+ return err;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_FREAD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* read a bigint from a file stream in ASCII */
+int mp_fread(mp_int *a, int radix, FILE *stream)
+{
+ int err, ch, neg, y;
+
+ /* clear a */
+ mp_zero(a);
+
+ /* if first digit is - then set negative */
+ ch = fgetc(stream);
+ if (ch == '-') {
+ neg = MP_NEG;
+ ch = fgetc(stream);
+ } else {
+ neg = MP_ZPOS;
+ }
+
+ for (;;) {
+ /* find y in the radix map */
+ for (y = 0; y < radix; y++) {
+ if (mp_s_rmap[y] == ch) {
+ break;
+ }
+ }
+ if (y == radix) {
+ break;
+ }
+
+ /* shift up and add */
+ if ((err = mp_mul_d(a, radix, a)) != MP_OKAY) {
+ return err;
+ }
+ if ((err = mp_add_d(a, y, a)) != MP_OKAY) {
+ return err;
+ }
+
+ ch = fgetc(stream);
+ }
+ if (mp_cmp_d(a, 0) != MP_EQ) {
+ a->sign = neg;
+ }
+
+ return MP_OKAY;
+}
+
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_FWRITE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+int mp_fwrite(mp_int *a, int radix, FILE *stream)
+{
+ char *buf;
+ int err, len, x;
+
+ if ((err = mp_radix_size(a, radix, &len)) != MP_OKAY) {
+ return err;
+ }
+
+ buf = OPT_CAST(char) XMALLOC (len);
+ if (buf == NULL) {
+ return MP_MEM;
+ }
+
+ if ((err = mp_toradix(a, buf, radix)) != MP_OKAY) {
+ XFREE (buf);
+ return err;
+ }
+
+ for (x = 0; x < len; x++) {
+ if (fputc(buf[x], stream) == EOF) {
+ XFREE (buf);
+ return MP_VAL;
+ }
+ }
+
+ XFREE (buf);
+ return MP_OKAY;
+}
+
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_GCD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* Greatest Common Divisor using the binary method */
+int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
+{
+ mp_int u, v;
+ int k, u_lsb, v_lsb, res;
+
+ /* either zero than gcd is the largest */
+ if (mp_iszero (a) == MP_YES) {
+ return mp_abs (b, c);
+ }
+ if (mp_iszero (b) == MP_YES) {
+ return mp_abs (a, c);
+ }
+
+ /* get copies of a and b we can modify */
+ if ((res = mp_init_copy (&u, a)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_init_copy (&v, b)) != MP_OKAY) {
+ goto LBL_U;
+ }
+
+ /* must be positive for the remainder of the algorithm */
+ u.sign = v.sign = MP_ZPOS;
+
+ /* B1. Find the common power of two for u and v */
+ u_lsb = mp_cnt_lsb(&u);
+ v_lsb = mp_cnt_lsb(&v);
+ k = MIN(u_lsb, v_lsb);
+
+ if (k > 0) {
+ /* divide the power of two out */
+ if ((res = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) {
+ goto LBL_V;
+ }
+
+ if ((res = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) {
+ goto LBL_V;
+ }
+ }
+
+ /* divide any remaining factors of two out */
+ if (u_lsb != k) {
+ if ((res = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) {
+ goto LBL_V;
+ }
+ }
+
+ if (v_lsb != k) {
+ if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) {
+ goto LBL_V;
+ }
+ }
+
+ while (mp_iszero(&v) == 0) {
+ /* make sure v is the largest */
+ if (mp_cmp_mag(&u, &v) == MP_GT) {
+ /* swap u and v to make sure v is >= u */
+ mp_exch(&u, &v);
+ }
+
+ /* subtract smallest from largest */
+ if ((res = s_mp_sub(&v, &u, &v)) != MP_OKAY) {
+ goto LBL_V;
+ }
+
+ /* Divide out all factors of two */
+ if ((res = mp_div_2d(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) {
+ goto LBL_V;
+ }
+ }
+
+ /* multiply by 2**k which we divided out at the beginning */
+ if ((res = mp_mul_2d (&u, k, c)) != MP_OKAY) {
+ goto LBL_V;
+ }
+ c->sign = MP_ZPOS;
+ res = MP_OKAY;
+LBL_V:mp_clear (&u);
+LBL_U:mp_clear (&v);
+ return res;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_GET_INT_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* get the lower 32-bits of an mp_int */
+unsigned long mp_get_int(mp_int * a)
+{
+ int i;
+ unsigned long res;
+
+ if (a->used == 0) {
+ return 0;
+ }
+
+ /* get number of digits of the lsb we have to read */
+ i = MIN(a->used,(int)((sizeof(unsigned long)*CHAR_BIT+DIGIT_BIT-1)/DIGIT_BIT))-1;
+
+ /* get most significant digit of result */
+ res = DIGIT(a,i);
+
+ while (--i >= 0) {
+ res = (res << DIGIT_BIT) | DIGIT(a,i);
+ }
+
+ /* force result to 32-bits always so it is consistent on non 32-bit platforms */
+ return res & 0xFFFFFFFFUL;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_GROW_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* grow as required */
+int mp_grow (mp_int * a, int size)
+{
+ int i;
+ mp_digit *tmp;
+
+ /* if the alloc size is smaller alloc more ram */
+ if (a->alloc < size) {
+ /* ensure there are always at least MP_PREC digits extra on top */
+ size += (MP_PREC * 2) - (size % MP_PREC);
+
+ /* reallocate the array a->dp
+ *
+ * We store the return in a temporary variable
+ * in case the operation failed we don't want
+ * to overwrite the dp member of a.
+ */
+ tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * size);
+ if (tmp == NULL) {
+ /* reallocation failed but "a" is still valid [can be freed] */
+ return MP_MEM;
+ }
+
+ /* reallocation succeeded so set a->dp */
+ a->dp = tmp;
+
+ /* zero excess digits */
+ i = a->alloc;
+ a->alloc = size;
+ for (; i < a->alloc; i++) {
+ a->dp[i] = 0;
+ }
+ }
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_INIT_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* init a new mp_int */
+int mp_init (mp_int * a)
+{
+ int i;
+
+ /* allocate memory required and clear it */
+ a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * MP_PREC);
+ if (a->dp == NULL) {
+ return MP_MEM;
+ }
+
+ /* set the digits to zero */
+ for (i = 0; i < MP_PREC; i++) {
+ a->dp[i] = 0;
+ }
+
+ /* set the used to zero, allocated digits to the default precision
+ * and sign to positive */
+ a->used = 0;
+ a->alloc = MP_PREC;
+ a->sign = MP_ZPOS;
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_INIT_COPY_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* creates "a" then copies b into it */
+int mp_init_copy (mp_int * a, mp_int * b)
+{
+ int res;
+
+ if ((res = mp_init (a)) != MP_OKAY) {
+ return res;
+ }
+ return mp_copy (b, a);
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_INIT_MULTI_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+#include <stdarg.h>
+
+int mp_init_multi(mp_int *mp, ...)
+{
+ mp_err res = MP_OKAY; /* Assume ok until proven otherwise */
+ int n = 0; /* Number of ok inits */
+ mp_int* cur_arg = mp;
+ va_list args;
+
+ va_start(args, mp); /* init args to next argument from caller */
+ while (cur_arg != NULL) {
+ if (mp_init(cur_arg) != MP_OKAY) {
+ /* Oops - error! Back-track and mp_clear what we already
+ succeeded in init-ing, then return error.
+ */
+ va_list clean_args;
+
+ /* end the current list */
+ va_end(args);
+
+ /* now start cleaning up */
+ cur_arg = mp;
+ va_start(clean_args, mp);
+ while (n--) {
+ mp_clear(cur_arg);
+ cur_arg = va_arg(clean_args, mp_int*);
+ }
+ va_end(clean_args);
+ res = MP_MEM;
+ break;
+ }
+ n++;
+ cur_arg = va_arg(args, mp_int*);
+ }
+ va_end(args);
+ return res; /* Assumed ok, if error flagged above. */
+}
+
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_INIT_SET_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* initialize and set a digit */
+int mp_init_set (mp_int * a, mp_digit b)
+{
+ int err;
+ if ((err = mp_init(a)) != MP_OKAY) {
+ return err;
+ }
+ mp_set(a, b);
+ return err;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_INIT_SET_INT_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* initialize and set a digit */
+int mp_init_set_int (mp_int * a, unsigned long b)
+{
+ int err;
+ if ((err = mp_init(a)) != MP_OKAY) {
+ return err;
+ }
+ return mp_set_int(a, b);
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_INIT_SIZE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* init an mp_init for a given size */
+int mp_init_size (mp_int * a, int size)
+{
+ int x;
+
+ /* pad size so there are always extra digits */
+ size += (MP_PREC * 2) - (size % MP_PREC);
+
+ /* alloc mem */
+ a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size);
+ if (a->dp == NULL) {
+ return MP_MEM;
+ }
+
+ /* set the members */
+ a->used = 0;
+ a->alloc = size;
+ a->sign = MP_ZPOS;
+
+ /* zero the digits */
+ for (x = 0; x < size; x++) {
+ a->dp[x] = 0;
+ }
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_INVMOD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* hac 14.61, pp608 */
+int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
+{
+ /* b cannot be negative */
+ if (b->sign == MP_NEG || mp_iszero(b) == 1) {
+ return MP_VAL;
+ }
+
+#ifdef BN_FAST_MP_INVMOD_C
+ /* if the modulus is odd we can use a faster routine instead */
+ if (mp_isodd (b) == 1) {
+ return fast_mp_invmod (a, b, c);
+ }
+#endif
+
+#ifdef BN_MP_INVMOD_SLOW_C
+ return mp_invmod_slow(a, b, c);
+#endif
+
+ return MP_VAL;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_INVMOD_SLOW_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* hac 14.61, pp608 */
+int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
+{
+ mp_int x, y, u, v, A, B, C, D;
+ int res;
+
+ /* b cannot be negative */
+ if (b->sign == MP_NEG || mp_iszero(b) == 1) {
+ return MP_VAL;
+ }
+
+ /* init temps */
+ if ((res = mp_init_multi(&x, &y, &u, &v,
+ &A, &B, &C, &D, NULL)) != MP_OKAY) {
+ return res;
+ }
+
+ /* x = a, y = b */
+ if ((res = mp_mod(a, b, &x)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if ((res = mp_copy (b, &y)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ /* 2. [modified] if x,y are both even then return an error! */
+ if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
+ res = MP_VAL;
+ goto LBL_ERR;
+ }
+
+ /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
+ if ((res = mp_copy (&x, &u)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if ((res = mp_copy (&y, &v)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ mp_set (&A, 1);
+ mp_set (&D, 1);
+
+top:
+ /* 4. while u is even do */
+ while (mp_iseven (&u) == 1) {
+ /* 4.1 u = u/2 */
+ if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ /* 4.2 if A or B is odd then */
+ if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) {
+ /* A = (A+y)/2, B = (B-x)/2 */
+ if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+ /* A = A/2, B = B/2 */
+ if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* 5. while v is even do */
+ while (mp_iseven (&v) == 1) {
+ /* 5.1 v = v/2 */
+ if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ /* 5.2 if C or D is odd then */
+ if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) {
+ /* C = (C+y)/2, D = (D-x)/2 */
+ if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+ /* C = C/2, D = D/2 */
+ if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* 6. if u >= v then */
+ if (mp_cmp (&u, &v) != MP_LT) {
+ /* u = u - v, A = A - C, B = B - D */
+ if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ } else {
+ /* v - v - u, C = C - A, D = D - B */
+ if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* if not zero goto step 4 */
+ if (mp_iszero (&u) == 0)
+ goto top;
+
+ /* now a = C, b = D, gcd == g*v */
+
+ /* if v != 1 then there is no inverse */
+ if (mp_cmp_d (&v, 1) != MP_EQ) {
+ res = MP_VAL;
+ goto LBL_ERR;
+ }
+
+ /* if its too low */
+ while (mp_cmp_d(&C, 0) == MP_LT) {
+ if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* too big */
+ while (mp_cmp_mag(&C, b) != MP_LT) {
+ if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* C is now the inverse */
+ mp_exch (&C, c);
+ res = MP_OKAY;
+LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
+ return res;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_IS_SQUARE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* Check if remainders are possible squares - fast exclude non-squares */
+static const char rem_128[128] = {
+ 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
+ 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
+ 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
+ 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
+ 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
+ 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
+ 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
+ 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1
+};
+
+static const char rem_105[105] = {
+ 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,
+ 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1,
+ 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1,
+ 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1,
+ 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,
+ 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1,
+ 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1
+};
+
+/* Store non-zero to ret if arg is square, and zero if not */
+int mp_is_square(mp_int *arg,int *ret)
+{
+ int res;
+ mp_digit c;
+ mp_int t;
+ unsigned long r;
+
+ /* Default to Non-square :) */
+ *ret = MP_NO;
+
+ if (arg->sign == MP_NEG) {
+ return MP_VAL;
+ }
+
+ /* digits used? (TSD) */
+ if (arg->used == 0) {
+ return MP_OKAY;
+ }
+
+ /* First check mod 128 (suppose that DIGIT_BIT is at least 7) */
+ if (rem_128[127 & DIGIT(arg,0)] == 1) {
+ return MP_OKAY;
+ }
+
+ /* Next check mod 105 (3*5*7) */
+ if ((res = mp_mod_d(arg,105,&c)) != MP_OKAY) {
+ return res;
+ }
+ if (rem_105[c] == 1) {
+ return MP_OKAY;
+ }
+
+
+ if ((res = mp_init_set_int(&t,11L*13L*17L*19L*23L*29L*31L)) != MP_OKAY) {
+ return res;
+ }
+ if ((res = mp_mod(arg,&t,&t)) != MP_OKAY) {
+ goto ERR;
+ }
+ r = mp_get_int(&t);
+ /* Check for other prime modules, note it's not an ERROR but we must
+ * free "t" so the easiest way is to goto ERR. We know that res
+ * is already equal to MP_OKAY from the mp_mod call
+ */
+ if ( (1L<<(r%11)) & 0x5C4L ) goto ERR;
+ if ( (1L<<(r%13)) & 0x9E4L ) goto ERR;
+ if ( (1L<<(r%17)) & 0x5CE8L ) goto ERR;
+ if ( (1L<<(r%19)) & 0x4F50CL ) goto ERR;
+ if ( (1L<<(r%23)) & 0x7ACCA0L ) goto ERR;
+ if ( (1L<<(r%29)) & 0xC2EDD0CL ) goto ERR;
+ if ( (1L<<(r%31)) & 0x6DE2B848L ) goto ERR;
+
+ /* Final check - is sqr(sqrt(arg)) == arg ? */
+ if ((res = mp_sqrt(arg,&t)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sqr(&t,&t)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ *ret = (mp_cmp_mag(&t,arg) == MP_EQ) ? MP_YES : MP_NO;
+ERR:mp_clear(&t);
+ return res;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_JACOBI_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* computes the jacobi c = (a | n) (or Legendre if n is prime)
+ * HAC pp. 73 Algorithm 2.149
+ */
+int mp_jacobi (mp_int * a, mp_int * p, int *c)
+{
+ mp_int a1, p1;
+ int k, s, r, res;
+ mp_digit residue;
+
+ /* if p <= 0 return MP_VAL */
+ if (mp_cmp_d(p, 0) != MP_GT) {
+ return MP_VAL;
+ }
+
+ /* step 1. if a == 0, return 0 */
+ if (mp_iszero (a) == 1) {
+ *c = 0;
+ return MP_OKAY;
+ }
+
+ /* step 2. if a == 1, return 1 */
+ if (mp_cmp_d (a, 1) == MP_EQ) {
+ *c = 1;
+ return MP_OKAY;
+ }
+
+ /* default */
+ s = 0;
+
+ /* step 3. write a = a1 * 2**k */
+ if ((res = mp_init_copy (&a1, a)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_init (&p1)) != MP_OKAY) {
+ goto LBL_A1;
+ }
+
+ /* divide out larger power of two */
+ k = mp_cnt_lsb(&a1);
+ if ((res = mp_div_2d(&a1, k, &a1, NULL)) != MP_OKAY) {
+ goto LBL_P1;
+ }
+
+ /* step 4. if e is even set s=1 */
+ if ((k & 1) == 0) {
+ s = 1;
+ } else {
+ /* else set s=1 if p = 1/7 (mod 8) or s=-1 if p = 3/5 (mod 8) */
+ residue = p->dp[0] & 7;
+
+ if (residue == 1 || residue == 7) {
+ s = 1;
+ } else if (residue == 3 || residue == 5) {
+ s = -1;
+ }
+ }
+
+ /* step 5. if p == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */
+ if ( ((p->dp[0] & 3) == 3) && ((a1.dp[0] & 3) == 3)) {
+ s = -s;
+ }
+
+ /* if a1 == 1 we're done */
+ if (mp_cmp_d (&a1, 1) == MP_EQ) {
+ *c = s;
+ } else {
+ /* n1 = n mod a1 */
+ if ((res = mp_mod (p, &a1, &p1)) != MP_OKAY) {
+ goto LBL_P1;
+ }
+ if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) {
+ goto LBL_P1;
+ }
+ *c = s * r;
+ }
+
+ /* done */
+ res = MP_OKAY;
+LBL_P1:mp_clear (&p1);
+LBL_A1:mp_clear (&a1);
+ return res;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_KARATSUBA_MUL_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* c = |a| * |b| using Karatsuba Multiplication using
+ * three half size multiplications
+ *
+ * Let B represent the radix [e.g. 2**DIGIT_BIT] and
+ * let n represent half of the number of digits in
+ * the min(a,b)
+ *
+ * a = a1 * B**n + a0
+ * b = b1 * B**n + b0
+ *
+ * Then, a * b =>
+ a1b1 * B**2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B + a0b0
+ *
+ * Note that a1b1 and a0b0 are used twice and only need to be
+ * computed once. So in total three half size (half # of
+ * digit) multiplications are performed, a0b0, a1b1 and
+ * (a1+b1)(a0+b0)
+ *
+ * Note that a multiplication of half the digits requires
+ * 1/4th the number of single precision multiplications so in
+ * total after one call 25% of the single precision multiplications
+ * are saved. Note also that the call to mp_mul can end up back
+ * in this function if the a0, a1, b0, or b1 are above the threshold.
+ * This is known as divide-and-conquer and leads to the famous
+ * O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than
+ * the standard O(N**2) that the baseline/comba methods use.
+ * Generally though the overhead of this method doesn't pay off
+ * until a certain size (N ~ 80) is reached.
+ */
+int mp_karatsuba_mul (mp_int * a, mp_int * b, mp_int * c)
+{
+ mp_int x0, x1, y0, y1, t1, x0y0, x1y1;
+ int B, err;
+
+ /* default the return code to an error */
+ err = MP_MEM;
+
+ /* min # of digits */
+ B = MIN (a->used, b->used);
+
+ /* now divide in two */
+ B = B >> 1;
+
+ /* init copy all the temps */
+ if (mp_init_size (&x0, B) != MP_OKAY)
+ goto ERR;
+ if (mp_init_size (&x1, a->used - B) != MP_OKAY)
+ goto X0;
+ if (mp_init_size (&y0, B) != MP_OKAY)
+ goto X1;
+ if (mp_init_size (&y1, b->used - B) != MP_OKAY)
+ goto Y0;
+
+ /* init temps */
+ if (mp_init_size (&t1, B * 2) != MP_OKAY)
+ goto Y1;
+ if (mp_init_size (&x0y0, B * 2) != MP_OKAY)
+ goto T1;
+ if (mp_init_size (&x1y1, B * 2) != MP_OKAY)
+ goto X0Y0;
+
+ /* now shift the digits */
+ x0.used = y0.used = B;
+ x1.used = a->used - B;
+ y1.used = b->used - B;
+
+ {
+ register int x;
+ register mp_digit *tmpa, *tmpb, *tmpx, *tmpy;
+
+ /* we copy the digits directly instead of using higher level functions
+ * since we also need to shift the digits
+ */
+ tmpa = a->dp;
+ tmpb = b->dp;
+
+ tmpx = x0.dp;
+ tmpy = y0.dp;
+ for (x = 0; x < B; x++) {
+ *tmpx++ = *tmpa++;
+ *tmpy++ = *tmpb++;
+ }
+
+ tmpx = x1.dp;
+ for (x = B; x < a->used; x++) {
+ *tmpx++ = *tmpa++;
+ }
+
+ tmpy = y1.dp;
+ for (x = B; x < b->used; x++) {
+ *tmpy++ = *tmpb++;
+ }
+ }
+
+ /* only need to clamp the lower words since by definition the
+ * upper words x1/y1 must have a known number of digits
+ */
+ mp_clamp (&x0);
+ mp_clamp (&y0);
+
+ /* now calc the products x0y0 and x1y1 */
+ /* after this x0 is no longer required, free temp [x0==t2]! */
+ if (mp_mul (&x0, &y0, &x0y0) != MP_OKAY)
+ goto X1Y1; /* x0y0 = x0*y0 */
+ if (mp_mul (&x1, &y1, &x1y1) != MP_OKAY)
+ goto X1Y1; /* x1y1 = x1*y1 */
+
+ /* now calc x1+x0 and y1+y0 */
+ if (s_mp_add (&x1, &x0, &t1) != MP_OKAY)
+ goto X1Y1; /* t1 = x1 - x0 */
+ if (s_mp_add (&y1, &y0, &x0) != MP_OKAY)
+ goto X1Y1; /* t2 = y1 - y0 */
+ if (mp_mul (&t1, &x0, &t1) != MP_OKAY)
+ goto X1Y1; /* t1 = (x1 + x0) * (y1 + y0) */
+
+ /* add x0y0 */
+ if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY)
+ goto X1Y1; /* t2 = x0y0 + x1y1 */
+ if (s_mp_sub (&t1, &x0, &t1) != MP_OKAY)
+ goto X1Y1; /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */
+
+ /* shift by B */
+ if (mp_lshd (&t1, B) != MP_OKAY)
+ goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */
+ if (mp_lshd (&x1y1, B * 2) != MP_OKAY)
+ goto X1Y1; /* x1y1 = x1y1 << 2*B */
+
+ if (mp_add (&x0y0, &t1, &t1) != MP_OKAY)
+ goto X1Y1; /* t1 = x0y0 + t1 */
+ if (mp_add (&t1, &x1y1, c) != MP_OKAY)
+ goto X1Y1; /* t1 = x0y0 + t1 + x1y1 */
+
+ /* Algorithm succeeded set the return code to MP_OKAY */
+ err = MP_OKAY;
+
+X1Y1:mp_clear (&x1y1);
+X0Y0:mp_clear (&x0y0);
+T1:mp_clear (&t1);
+Y1:mp_clear (&y1);
+Y0:mp_clear (&y0);
+X1:mp_clear (&x1);
+X0:mp_clear (&x0);
+ERR:
+ return err;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_KARATSUBA_SQR_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* Karatsuba squaring, computes b = a*a using three
+ * half size squarings
+ *
+ * See comments of karatsuba_mul for details. It
+ * is essentially the same algorithm but merely
+ * tuned to perform recursive squarings.
+ */
+int mp_karatsuba_sqr (mp_int * a, mp_int * b)
+{
+ mp_int x0, x1, t1, t2, x0x0, x1x1;
+ int B, err;
+
+ err = MP_MEM;
+
+ /* min # of digits */
+ B = a->used;
+
+ /* now divide in two */
+ B = B >> 1;
+
+ /* init copy all the temps */
+ if (mp_init_size (&x0, B) != MP_OKAY)
+ goto ERR;
+ if (mp_init_size (&x1, a->used - B) != MP_OKAY)
+ goto X0;
+
+ /* init temps */
+ if (mp_init_size (&t1, a->used * 2) != MP_OKAY)
+ goto X1;
+ if (mp_init_size (&t2, a->used * 2) != MP_OKAY)
+ goto T1;
+ if (mp_init_size (&x0x0, B * 2) != MP_OKAY)
+ goto T2;
+ if (mp_init_size (&x1x1, (a->used - B) * 2) != MP_OKAY)
+ goto X0X0;
+
+ {
+ register int x;
+ register mp_digit *dst, *src;
+
+ src = a->dp;
+
+ /* now shift the digits */
+ dst = x0.dp;
+ for (x = 0; x < B; x++) {
+ *dst++ = *src++;
+ }
+
+ dst = x1.dp;
+ for (x = B; x < a->used; x++) {
+ *dst++ = *src++;
+ }
+ }
+
+ x0.used = B;
+ x1.used = a->used - B;
+
+ mp_clamp (&x0);
+
+ /* now calc the products x0*x0 and x1*x1 */
+ if (mp_sqr (&x0, &x0x0) != MP_OKAY)
+ goto X1X1; /* x0x0 = x0*x0 */
+ if (mp_sqr (&x1, &x1x1) != MP_OKAY)
+ goto X1X1; /* x1x1 = x1*x1 */
+
+ /* now calc (x1+x0)**2 */
+ if (s_mp_add (&x1, &x0, &t1) != MP_OKAY)
+ goto X1X1; /* t1 = x1 - x0 */
+ if (mp_sqr (&t1, &t1) != MP_OKAY)
+ goto X1X1; /* t1 = (x1 - x0) * (x1 - x0) */
+
+ /* add x0y0 */
+ if (s_mp_add (&x0x0, &x1x1, &t2) != MP_OKAY)
+ goto X1X1; /* t2 = x0x0 + x1x1 */
+ if (s_mp_sub (&t1, &t2, &t1) != MP_OKAY)
+ goto X1X1; /* t1 = (x1+x0)**2 - (x0x0 + x1x1) */
+
+ /* shift by B */
+ if (mp_lshd (&t1, B) != MP_OKAY)
+ goto X1X1; /* t1 = (x0x0 + x1x1 - (x1-x0)*(x1-x0))<<B */
+ if (mp_lshd (&x1x1, B * 2) != MP_OKAY)
+ goto X1X1; /* x1x1 = x1x1 << 2*B */
+
+ if (mp_add (&x0x0, &t1, &t1) != MP_OKAY)
+ goto X1X1; /* t1 = x0x0 + t1 */
+ if (mp_add (&t1, &x1x1, b) != MP_OKAY)
+ goto X1X1; /* t1 = x0x0 + t1 + x1x1 */
+
+ err = MP_OKAY;
+
+X1X1:mp_clear (&x1x1);
+X0X0:mp_clear (&x0x0);
+T2:mp_clear (&t2);
+T1:mp_clear (&t1);
+X1:mp_clear (&x1);
+X0:mp_clear (&x0);
+ERR:
+ return err;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_LCM_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* computes least common multiple as |a*b|/(a, b) */
+int mp_lcm (mp_int * a, mp_int * b, mp_int * c)
+{
+ int res;
+ mp_int t1, t2;
+
+
+ if ((res = mp_init_multi (&t1, &t2, NULL)) != MP_OKAY) {
+ return res;
+ }
+
+ /* t1 = get the GCD of the two inputs */
+ if ((res = mp_gcd (a, b, &t1)) != MP_OKAY) {
+ goto LBL_T;
+ }
+
+ /* divide the smallest by the GCD */
+ if (mp_cmp_mag(a, b) == MP_LT) {
+ /* store quotient in t2 such that t2 * b is the LCM */
+ if ((res = mp_div(a, &t1, &t2, NULL)) != MP_OKAY) {
+ goto LBL_T;
+ }
+ res = mp_mul(b, &t2, c);
+ } else {
+ /* store quotient in t2 such that t2 * a is the LCM */
+ if ((res = mp_div(b, &t1, &t2, NULL)) != MP_OKAY) {
+ goto LBL_T;
+ }
+ res = mp_mul(a, &t2, c);
+ }
+
+ /* fix the sign to positive */
+ c->sign = MP_ZPOS;
+
+LBL_T:
+ mp_clear_multi (&t1, &t2, NULL);
+ return res;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_LSHD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* shift left a certain amount of digits */
+int mp_lshd (mp_int * a, int b)
+{
+ int x, res;
+
+ /* if its less than zero return */
+ if (b <= 0) {
+ return MP_OKAY;
+ }
+
+ /* grow to fit the new digits */
+ if (a->alloc < a->used + b) {
+ if ((res = mp_grow (a, a->used + b)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ {
+ register mp_digit *top, *bottom;
+
+ /* increment the used by the shift amount then copy upwards */
+ a->used += b;
+
+ /* top */
+ top = a->dp + a->used - 1;
+
+ /* base */
+ bottom = a->dp + a->used - 1 - b;
+
+ /* much like mp_rshd this is implemented using a sliding window
+ * except the window goes the otherway around. Copying from
+ * the bottom to the top. see bn_mp_rshd.c for more info.
+ */
+ for (x = a->used - 1; x >= b; x--) {
+ *top-- = *bottom--;
+ }
+
+ /* zero the lower digits */
+ top = a->dp;
+ for (x = 0; x < b; x++) {
+ *top++ = 0;
+ }
+ }
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_MOD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* c = a mod b, 0 <= c < b if b > 0, b < c <= 0 if b < 0 */
+int
+mp_mod (mp_int * a, mp_int * b, mp_int * c)
+{
+ mp_int t;
+ int res;
+
+ if ((res = mp_init (&t)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_div (a, b, NULL, &t)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+
+ if (mp_iszero(&t) || t.sign == b->sign) {
+ res = MP_OKAY;
+ mp_exch (&t, c);
+ } else {
+ res = mp_add (b, &t, c);
+ }
+
+ mp_clear (&t);
+ return res;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_MOD_2D_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* calc a value mod 2**b */
+int
+mp_mod_2d (mp_int * a, int b, mp_int * c)
+{
+ int x, res;
+
+ /* if b is <= 0 then zero the int */
+ if (b <= 0) {
+ mp_zero (c);
+ return MP_OKAY;
+ }
+
+ /* if the modulus is larger than the value than return */
+ if (b >= (int) (a->used * DIGIT_BIT)) {
+ res = mp_copy (a, c);
+ return res;
+ }
+
+ /* copy */
+ if ((res = mp_copy (a, c)) != MP_OKAY) {
+ return res;
+ }
+
+ /* zero digits above the last digit of the modulus */
+ for (x = (b / DIGIT_BIT) + ((b % DIGIT_BIT) == 0 ? 0 : 1); x < c->used; x++) {
+ c->dp[x] = 0;
+ }
+ /* clear the digit that is not completely outside/inside the modulus */
+ c->dp[b / DIGIT_BIT] &=
+ (mp_digit) ((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digit) 1));
+ mp_clamp (c);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_MOD_D_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+int
+mp_mod_d (mp_int * a, mp_digit b, mp_digit * c)
+{
+ return mp_div_d(a, b, NULL, c);
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/*
+ * shifts with subtractions when the result is greater than b.
+ *
+ * The method is slightly modified to shift B unconditionally upto just under
+ * the leading bit of b. This saves alot of multiple precision shifting.
+ */
+int mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
+{
+ int x, bits, res;
+
+ /* how many bits of last digit does b use */
+ bits = mp_count_bits (b) % DIGIT_BIT;
+
+ if (b->used > 1) {
+ if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) {
+ return res;
+ }
+ } else {
+ mp_set(a, 1);
+ bits = 1;
+ }
+
+
+ /* now compute C = A * B mod b */
+ for (x = bits - 1; x < (int)DIGIT_BIT; x++) {
+ if ((res = mp_mul_2 (a, a)) != MP_OKAY) {
+ return res;
+ }
+ if (mp_cmp_mag (a, b) != MP_LT) {
+ if ((res = s_mp_sub (a, b, a)) != MP_OKAY) {
+ return res;
+ }
+ }
+ }
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_MONTGOMERY_REDUCE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* computes xR**-1 == x (mod N) via Montgomery Reduction */
+int
+mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
+{
+ int ix, res, digs;
+ mp_digit mu;
+
+ /* can the fast reduction [comba] method be used?
+ *
+ * Note that unlike in mul you're safely allowed *less*
+ * than the available columns [255 per default] since carries
+ * are fixed up in the inner loop.
+ */
+ digs = n->used * 2 + 1;
+ if ((digs < MP_WARRAY) &&
+ n->used <
+ (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
+ return fast_mp_montgomery_reduce (x, n, rho);
+ }
+
+ /* grow the input as required */
+ if (x->alloc < digs) {
+ if ((res = mp_grow (x, digs)) != MP_OKAY) {
+ return res;
+ }
+ }
+ x->used = digs;
+
+ for (ix = 0; ix < n->used; ix++) {
+ /* mu = ai * rho mod b
+ *
+ * The value of rho must be precalculated via
+ * montgomery_setup() such that
+ * it equals -1/n0 mod b this allows the
+ * following inner loop to reduce the
+ * input one digit at a time
+ */
+ mu = (mp_digit) (((mp_word)x->dp[ix]) * ((mp_word)rho) & MP_MASK);
+
+ /* a = a + mu * m * b**i */
+ {
+ register int iy;
+ register mp_digit *tmpn, *tmpx, u;
+ register mp_word r;
+
+ /* alias for digits of the modulus */
+ tmpn = n->dp;
+
+ /* alias for the digits of x [the input] */
+ tmpx = x->dp + ix;
+
+ /* set the carry to zero */
+ u = 0;
+
+ /* Multiply and add in place */
+ for (iy = 0; iy < n->used; iy++) {
+ /* compute product and sum */
+ r = ((mp_word)mu) * ((mp_word)*tmpn++) +
+ ((mp_word) u) + ((mp_word) * tmpx);
+
+ /* get carry */
+ u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
+
+ /* fix digit */
+ *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
+ }
+ /* At this point the ix'th digit of x should be zero */
+
+
+ /* propagate carries upwards as required*/
+ while (u) {
+ *tmpx += u;
+ u = *tmpx >> DIGIT_BIT;
+ *tmpx++ &= MP_MASK;
+ }
+ }
+ }
+
+ /* at this point the n.used'th least
+ * significant digits of x are all zero
+ * which means we can shift x to the
+ * right by n.used digits and the
+ * residue is unchanged.
+ */
+
+ /* x = x/b**n.used */
+ mp_clamp(x);
+ mp_rshd (x, n->used);
+
+ /* if x >= n then x = x - n */
+ if (mp_cmp_mag (x, n) != MP_LT) {
+ return s_mp_sub (x, n, x);
+ }
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_MONTGOMERY_SETUP_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* setups the montgomery reduction stuff */
+int
+mp_montgomery_setup (mp_int * n, mp_digit * rho)
+{
+ mp_digit x, b;
+
+/* fast inversion mod 2**k
+ *
+ * Based on the fact that
+ *
+ * XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n)
+ * => 2*X*A - X*X*A*A = 1
+ * => 2*(1) - (1) = 1
+ */
+ b = n->dp[0];
+
+ if ((b & 1) == 0) {
+ return MP_VAL;
+ }
+
+ x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
+ x *= 2 - b * x; /* here x*a==1 mod 2**8 */
+#if !defined(MP_8BIT)
+ x *= 2 - b * x; /* here x*a==1 mod 2**16 */
+#endif
+#if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT))
+ x *= 2 - b * x; /* here x*a==1 mod 2**32 */
+#endif
+#ifdef MP_64BIT
+ x *= 2 - b * x; /* here x*a==1 mod 2**64 */
+#endif
+
+ /* rho = -1/m mod b */
+ *rho = (unsigned long)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_MUL_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* high level multiplication (handles sign) */
+int mp_mul (mp_int * a, mp_int * b, mp_int * c)
+{
+ int res, neg;
+ neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
+
+ /* use Toom-Cook? */
+#ifdef BN_MP_TOOM_MUL_C
+ if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) {
+ res = mp_toom_mul(a, b, c);
+ } else
+#endif
+#ifdef BN_MP_KARATSUBA_MUL_C
+ /* use Karatsuba? */
+ if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
+ res = mp_karatsuba_mul (a, b, c);
+ } else
+#endif
+ {
+ /* can we use the fast multiplier?
+ *
+ * The fast multiplier can be used if the output will
+ * have less than MP_WARRAY digits and the number of
+ * digits won't affect carry propagation
+ */
+ int digs = a->used + b->used + 1;
+
+#ifdef BN_FAST_S_MP_MUL_DIGS_C
+ if ((digs < MP_WARRAY) &&
+ MIN(a->used, b->used) <=
+ (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
+ res = fast_s_mp_mul_digs (a, b, c, digs);
+ } else
+#endif
+#ifdef BN_S_MP_MUL_DIGS_C
+ res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */
+#else
+ res = MP_VAL;
+#endif
+
+ }
+ c->sign = (c->used > 0) ? neg : MP_ZPOS;
+ return res;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_MUL_2_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* b = a*2 */
+int mp_mul_2(mp_int * a, mp_int * b)
+{
+ int x, res, oldused;
+
+ /* grow to accomodate result */
+ if (b->alloc < a->used + 1) {
+ if ((res = mp_grow (b, a->used + 1)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ oldused = b->used;
+ b->used = a->used;
+
+ {
+ register mp_digit r, rr, *tmpa, *tmpb;
+
+ /* alias for source */
+ tmpa = a->dp;
+
+ /* alias for dest */
+ tmpb = b->dp;
+
+ /* carry */
+ r = 0;
+ for (x = 0; x < a->used; x++) {
+
+ /* get what will be the *next* carry bit from the
+ * MSB of the current digit
+ */
+ rr = *tmpa >> ((mp_digit)(DIGIT_BIT - 1));
+
+ /* now shift up this digit, add in the carry [from the previous] */
+ *tmpb++ = ((*tmpa++ << ((mp_digit)1)) | r) & MP_MASK;
+
+ /* copy the carry that would be from the source
+ * digit into the next iteration
+ */
+ r = rr;
+ }
+
+ /* new leading digit? */
+ if (r != 0) {
+ /* add a MSB which is always 1 at this point */
+ *tmpb = 1;
+ ++(b->used);
+ }
+
+ /* now zero any excess digits on the destination
+ * that we didn't write to
+ */
+ tmpb = b->dp + b->used;
+ for (x = b->used; x < oldused; x++) {
+ *tmpb++ = 0;
+ }
+ }
+ b->sign = a->sign;
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_MUL_2D_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* shift left by a certain bit count */
+int mp_mul_2d (mp_int * a, int b, mp_int * c)
+{
+ mp_digit d;
+ int res;
+
+ /* copy */
+ if (a != c) {
+ if ((res = mp_copy (a, c)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ if (c->alloc < (int)(c->used + b/DIGIT_BIT + 1)) {
+ if ((res = mp_grow (c, c->used + b / DIGIT_BIT + 1)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* shift by as many digits in the bit count */
+ if (b >= (int)DIGIT_BIT) {
+ if ((res = mp_lshd (c, b / DIGIT_BIT)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* shift any bit count < DIGIT_BIT */
+ d = (mp_digit) (b % DIGIT_BIT);
+ if (d != 0) {
+ register mp_digit *tmpc, shift, mask, r, rr;
+ register int x;
+
+ /* bitmask for carries */
+ mask = (((mp_digit)1) << d) - 1;
+
+ /* shift for msbs */
+ shift = DIGIT_BIT - d;
+
+ /* alias */
+ tmpc = c->dp;
+
+ /* carry */
+ r = 0;
+ for (x = 0; x < c->used; x++) {
+ /* get the higher bits of the current word */
+ rr = (*tmpc >> shift) & mask;
+
+ /* shift the current word and OR in the carry */
+ *tmpc = ((*tmpc << d) | r) & MP_MASK;
+ ++tmpc;
+
+ /* set the carry to the carry bits of the current word */
+ r = rr;
+ }
+
+ /* set final carry */
+ if (r != 0) {
+ c->dp[(c->used)++] = r;
+ }
+ }
+ mp_clamp (c);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_MUL_D_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* multiply by a digit */
+int
+mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
+{
+ mp_digit u, *tmpa, *tmpc;
+ mp_word r;
+ int ix, res, olduse;
+
+ /* make sure c is big enough to hold a*b */
+ if (c->alloc < a->used + 1) {
+ if ((res = mp_grow (c, a->used + 1)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* get the original destinations used count */
+ olduse = c->used;
+
+ /* set the sign */
+ c->sign = a->sign;
+
+ /* alias for a->dp [source] */
+ tmpa = a->dp;
+
+ /* alias for c->dp [dest] */
+ tmpc = c->dp;
+
+ /* zero carry */
+ u = 0;
+
+ /* compute columns */
+ for (ix = 0; ix < a->used; ix++) {
+ /* compute product and carry sum for this term */
+ r = ((mp_word) u) + ((mp_word)*tmpa++) * ((mp_word)b);
+
+ /* mask off higher bits to get a single digit */
+ *tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK));
+
+ /* send carry into next iteration */
+ u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
+ }
+
+ /* store final carry [if any] and increment ix offset */
+ *tmpc++ = u;
+ ++ix;
+
+ /* now zero digits above the top */
+ while (ix++ < olduse) {
+ *tmpc++ = 0;
+ }
+
+ /* set used count */
+ c->used = a->used + 1;
+ mp_clamp(c);
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_MULMOD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* d = a * b (mod c) */
+int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
+{
+ int res;
+ mp_int t;
+
+ if ((res = mp_init (&t)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_mul (a, b, &t)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+ res = mp_mod (&t, c, d);
+ mp_clear (&t);
+ return res;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_N_ROOT_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* find the n'th root of an integer
+ *
+ * Result found such that (c)**b <= a and (c+1)**b > a
+ *
+ * This algorithm uses Newton's approximation
+ * x[i+1] = x[i] - f(x[i])/f'(x[i])
+ * which will find the root in log(N) time where
+ * each step involves a fair bit. This is not meant to
+ * find huge roots [square and cube, etc].
+ */
+int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
+{
+ mp_int t1, t2, t3;
+ int res, neg;
+
+ /* input must be positive if b is even */
+ if ((b & 1) == 0 && a->sign == MP_NEG) {
+ return MP_VAL;
+ }
+
+ if ((res = mp_init (&t1)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_init (&t2)) != MP_OKAY) {
+ goto LBL_T1;
+ }
+
+ if ((res = mp_init (&t3)) != MP_OKAY) {
+ goto LBL_T2;
+ }
+
+ /* if a is negative fudge the sign but keep track */
+ neg = a->sign;
+ a->sign = MP_ZPOS;
+
+ /* t2 = 2 */
+ mp_set (&t2, 2);
+
+ do {
+ /* t1 = t2 */
+ if ((res = mp_copy (&t2, &t1)) != MP_OKAY) {
+ goto LBL_T3;
+ }
+
+ /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
+
+ /* t3 = t1**(b-1) */
+ if ((res = mp_expt_d (&t1, b - 1, &t3)) != MP_OKAY) {
+ goto LBL_T3;
+ }
+
+ /* numerator */
+ /* t2 = t1**b */
+ if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) {
+ goto LBL_T3;
+ }
+
+ /* t2 = t1**b - a */
+ if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) {
+ goto LBL_T3;
+ }
+
+ /* denominator */
+ /* t3 = t1**(b-1) * b */
+ if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) {
+ goto LBL_T3;
+ }
+
+ /* t3 = (t1**b - a)/(b * t1**(b-1)) */
+ if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) {
+ goto LBL_T3;
+ }
+
+ if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) {
+ goto LBL_T3;
+ }
+ } while (mp_cmp (&t1, &t2) != MP_EQ);
+
+ /* result can be off by a few so check */
+ for (;;) {
+ if ((res = mp_expt_d (&t1, b, &t2)) != MP_OKAY) {
+ goto LBL_T3;
+ }
+
+ if (mp_cmp (&t2, a) == MP_GT) {
+ if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) {
+ goto LBL_T3;
+ }
+ } else {
+ break;
+ }
+ }
+
+ /* reset the sign of a first */
+ a->sign = neg;
+
+ /* set the result */
+ mp_exch (&t1, c);
+
+ /* set the sign of the result */
+ c->sign = neg;
+
+ res = MP_OKAY;
+
+LBL_T3:mp_clear (&t3);
+LBL_T2:mp_clear (&t2);
+LBL_T1:mp_clear (&t1);
+ return res;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_NEG_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* b = -a */
+int mp_neg (mp_int * a, mp_int * b)
+{
+ int res;
+ if (a != b) {
+ if ((res = mp_copy (a, b)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ if (mp_iszero(b) != MP_YES) {
+ b->sign = (a->sign == MP_ZPOS) ? MP_NEG : MP_ZPOS;
+ } else {
+ b->sign = MP_ZPOS;
+ }
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_OR_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* OR two ints together */
+int mp_or (mp_int * a, mp_int * b, mp_int * c)
+{
+ int res, ix, px;
+ mp_int t, *x;
+
+ if (a->used > b->used) {
+ if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
+ return res;
+ }
+ px = b->used;
+ x = b;
+ } else {
+ if ((res = mp_init_copy (&t, b)) != MP_OKAY) {
+ return res;
+ }
+ px = a->used;
+ x = a;
+ }
+
+ for (ix = 0; ix < px; ix++) {
+ t.dp[ix] |= x->dp[ix];
+ }
+ mp_clamp (&t);
+ mp_exch (c, &t);
+ mp_clear (&t);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_PRIME_FERMAT_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* performs one Fermat test.
+ *
+ * If "a" were prime then b**a == b (mod a) since the order of
+ * the multiplicative sub-group would be phi(a) = a-1. That means
+ * it would be the same as b**(a mod (a-1)) == b**1 == b (mod a).
+ *
+ * Sets result to 1 if the congruence holds, or zero otherwise.
+ */
+int mp_prime_fermat (mp_int * a, mp_int * b, int *result)
+{
+ mp_int t;
+ int err;
+
+ /* default to composite */
+ *result = MP_NO;
+
+ /* ensure b > 1 */
+ if (mp_cmp_d(b, 1) != MP_GT) {
+ return MP_VAL;
+ }
+
+ /* init t */
+ if ((err = mp_init (&t)) != MP_OKAY) {
+ return err;
+ }
+
+ /* compute t = b**a mod a */
+ if ((err = mp_exptmod (b, a, a, &t)) != MP_OKAY) {
+ goto LBL_T;
+ }
+
+ /* is it equal to b? */
+ if (mp_cmp (&t, b) == MP_EQ) {
+ *result = MP_YES;
+ }
+
+ err = MP_OKAY;
+LBL_T:mp_clear (&t);
+ return err;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_PRIME_IS_DIVISIBLE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* determines if an integers is divisible by one
+ * of the first PRIME_SIZE primes or not
+ *
+ * sets result to 0 if not, 1 if yes
+ */
+int mp_prime_is_divisible (mp_int * a, int *result)
+{
+ int err, ix;
+ mp_digit res;
+
+ /* default to not */
+ *result = MP_NO;
+
+ for (ix = 0; ix < PRIME_SIZE; ix++) {
+ /* what is a mod LBL_prime_tab[ix] */
+ if ((err = mp_mod_d (a, ltm_prime_tab[ix], &res)) != MP_OKAY) {
+ return err;
+ }
+
+ /* is the residue zero? */
+ if (res == 0) {
+ *result = MP_YES;
+ return MP_OKAY;
+ }
+ }
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_PRIME_IS_PRIME_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* performs a variable number of rounds of Miller-Rabin
+ *
+ * Probability of error after t rounds is no more than
+
+ *
+ * Sets result to 1 if probably prime, 0 otherwise
+ */
+int mp_prime_is_prime (mp_int * a, int t, int *result)
+{
+ mp_int b;
+ int ix, err, res;
+
+ /* default to no */
+ *result = MP_NO;
+
+ /* valid value of t? */
+ if (t <= 0 || t > PRIME_SIZE) {
+ return MP_VAL;
+ }
+
+ /* is the input equal to one of the primes in the table? */
+ for (ix = 0; ix < PRIME_SIZE; ix++) {
+ if (mp_cmp_d(a, ltm_prime_tab[ix]) == MP_EQ) {
+ *result = 1;
+ return MP_OKAY;
+ }
+ }
+
+ /* first perform trial division */
+ if ((err = mp_prime_is_divisible (a, &res)) != MP_OKAY) {
+ return err;
+ }
+
+ /* return if it was trivially divisible */
+ if (res == MP_YES) {
+ return MP_OKAY;
+ }
+
+ /* now perform the miller-rabin rounds */
+ if ((err = mp_init (&b)) != MP_OKAY) {
+ return err;
+ }
+
+ for (ix = 0; ix < t; ix++) {
+ /* set the prime */
+ mp_set (&b, ltm_prime_tab[ix]);
+
+ if ((err = mp_prime_miller_rabin (a, &b, &res)) != MP_OKAY) {
+ goto LBL_B;
+ }
+
+ if (res == MP_NO) {
+ goto LBL_B;
+ }
+ }
+
+ /* passed the test */
+ *result = MP_YES;
+LBL_B:mp_clear (&b);
+ return err;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_PRIME_MILLER_RABIN_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* Miller-Rabin test of "a" to the base of "b" as described in
+ * HAC pp. 139 Algorithm 4.24
+ *
+ * Sets result to 0 if definitely composite or 1 if probably prime.
+ * Randomly the chance of error is no more than 1/4 and often
+ * very much lower.
+ */
+int mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)
+{
+ mp_int n1, y, r;
+ int s, j, err;
+
+ /* default */
+ *result = MP_NO;
+
+ /* ensure b > 1 */
+ if (mp_cmp_d(b, 1) != MP_GT) {
+ return MP_VAL;
+ }
+
+ /* get n1 = a - 1 */
+ if ((err = mp_init_copy (&n1, a)) != MP_OKAY) {
+ return err;
+ }
+ if ((err = mp_sub_d (&n1, 1, &n1)) != MP_OKAY) {
+ goto LBL_N1;
+ }
+
+ /* set 2**s * r = n1 */
+ if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) {
+ goto LBL_N1;
+ }
+
+ /* count the number of least significant bits
+ * which are zero
+ */
+ s = mp_cnt_lsb(&r);
+
+ /* now divide n - 1 by 2**s */
+ if ((err = mp_div_2d (&r, s, &r, NULL)) != MP_OKAY) {
+ goto LBL_R;
+ }
+
+ /* compute y = b**r mod a */
+ if ((err = mp_init (&y)) != MP_OKAY) {
+ goto LBL_R;
+ }
+ if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+
+ /* if y != 1 and y != n1 do */
+ if (mp_cmp_d (&y, 1) != MP_EQ && mp_cmp (&y, &n1) != MP_EQ) {
+ j = 1;
+ /* while j <= s-1 and y != n1 */
+ while ((j <= (s - 1)) && mp_cmp (&y, &n1) != MP_EQ) {
+ if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+
+ /* if y == 1 then composite */
+ if (mp_cmp_d (&y, 1) == MP_EQ) {
+ goto LBL_Y;
+ }
+
+ ++j;
+ }
+
+ /* if y != n1 then composite */
+ if (mp_cmp (&y, &n1) != MP_EQ) {
+ goto LBL_Y;
+ }
+ }
+
+ /* probably prime now */
+ *result = MP_YES;
+LBL_Y:mp_clear (&y);
+LBL_R:mp_clear (&r);
+LBL_N1:mp_clear (&n1);
+ return err;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_PRIME_NEXT_PRIME_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* finds the next prime after the number "a" using "t" trials
+ * of Miller-Rabin.
+ *
+ * bbs_style = 1 means the prime must be congruent to 3 mod 4
+ */
+int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
+{
+ int err, res, x, y;
+ mp_digit res_tab[PRIME_SIZE], step, kstep;
+ mp_int b;
+
+ /* ensure t is valid */
+ if (t <= 0 || t > PRIME_SIZE) {
+ return MP_VAL;
+ }
+
+ /* force positive */
+ a->sign = MP_ZPOS;
+
+ /* simple algo if a is less than the largest prime in the table */
+ if (mp_cmp_d(a, ltm_prime_tab[PRIME_SIZE-1]) == MP_LT) {
+ /* find which prime it is bigger than */
+ for (x = PRIME_SIZE - 2; x >= 0; x--) {
+ if (mp_cmp_d(a, ltm_prime_tab[x]) != MP_LT) {
+ if (bbs_style == 1) {
+ /* ok we found a prime smaller or
+ * equal [so the next is larger]
+ *
+ * however, the prime must be
+ * congruent to 3 mod 4
+ */
+ if ((ltm_prime_tab[x + 1] & 3) != 3) {
+ /* scan upwards for a prime congruent to 3 mod 4 */
+ for (y = x + 1; y < PRIME_SIZE; y++) {
+ if ((ltm_prime_tab[y] & 3) == 3) {
+ mp_set(a, ltm_prime_tab[y]);
+ return MP_OKAY;
+ }
+ }
+ }
+ } else {
+ mp_set(a, ltm_prime_tab[x + 1]);
+ return MP_OKAY;
+ }
+ }
+ }
+ /* at this point a maybe 1 */
+ if (mp_cmp_d(a, 1) == MP_EQ) {
+ mp_set(a, 2);
+ return MP_OKAY;
+ }
+ /* fall through to the sieve */
+ }
+
+ /* generate a prime congruent to 3 mod 4 or 1/3 mod 4? */
+ if (bbs_style == 1) {
+ kstep = 4;
+ } else {
+ kstep = 2;
+ }
+
+ /* at this point we will use a combination of a sieve and Miller-Rabin */
+
+ if (bbs_style == 1) {
+ /* if a mod 4 != 3 subtract the correct value to make it so */
+ if ((a->dp[0] & 3) != 3) {
+ if ((err = mp_sub_d(a, (a->dp[0] & 3) + 1, a)) != MP_OKAY) { return err; };
+ }
+ } else {
+ if (mp_iseven(a) == 1) {
+ /* force odd */
+ if ((err = mp_sub_d(a, 1, a)) != MP_OKAY) {
+ return err;
+ }
+ }
+ }
+
+ /* generate the restable */
+ for (x = 1; x < PRIME_SIZE; x++) {
+ if ((err = mp_mod_d(a, ltm_prime_tab[x], res_tab + x)) != MP_OKAY) {
+ return err;
+ }
+ }
+
+ /* init temp used for Miller-Rabin Testing */
+ if ((err = mp_init(&b)) != MP_OKAY) {
+ return err;
+ }
+
+ for (;;) {
+ /* skip to the next non-trivially divisible candidate */
+ step = 0;
+ do {
+ /* y == 1 if any residue was zero [e.g. cannot be prime] */
+ y = 0;
+
+ /* increase step to next candidate */
+ step += kstep;
+
+ /* compute the new residue without using division */
+ for (x = 1; x < PRIME_SIZE; x++) {
+ /* add the step to each residue */
+ res_tab[x] += kstep;
+
+ /* subtract the modulus [instead of using division] */
+ if (res_tab[x] >= ltm_prime_tab[x]) {
+ res_tab[x] -= ltm_prime_tab[x];
+ }
+
+ /* set flag if zero */
+ if (res_tab[x] == 0) {
+ y = 1;
+ }
+ }
+ } while (y == 1 && step < ((((mp_digit)1)<<DIGIT_BIT) - kstep));
+
+ /* add the step */
+ if ((err = mp_add_d(a, step, a)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ /* if didn't pass sieve and step == MAX then skip test */
+ if (y == 1 && step >= ((((mp_digit)1)<<DIGIT_BIT) - kstep)) {
+ continue;
+ }
+
+ /* is this prime? */
+ for (x = 0; x < t; x++) {
+ mp_set(&b, ltm_prime_tab[x]);
+ if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if (res == MP_NO) {
+ break;
+ }
+ }
+
+ if (res == MP_YES) {
+ break;
+ }
+ }
+
+ err = MP_OKAY;
+LBL_ERR:
+ mp_clear(&b);
+ return err;
+}
+
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_PRIME_RABIN_MILLER_TRIALS_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+
+static const struct {
+ int k, t;
+} sizes[] = {
+{ 128, 28 },
+{ 256, 16 },
+{ 384, 10 },
+{ 512, 7 },
+{ 640, 6 },
+{ 768, 5 },
+{ 896, 4 },
+{ 1024, 4 }
+};
+
+/* returns # of RM trials required for a given bit size */
+int mp_prime_rabin_miller_trials(int size)
+{
+ int x;
+
+ for (x = 0; x < (int)(sizeof(sizes)/(sizeof(sizes[0]))); x++) {
+ if (sizes[x].k == size) {
+ return sizes[x].t;
+ } else if (sizes[x].k > size) {
+ return (x == 0) ? sizes[0].t : sizes[x - 1].t;
+ }
+ }
+ return sizes[x-1].t + 1;
+}
+
+
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_PRIME_RANDOM_EX_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* makes a truly random prime of a given size (bits),
+ *
+ * Flags are as follows:
+ *
+ * LTM_PRIME_BBS - make prime congruent to 3 mod 4
+ * LTM_PRIME_SAFE - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS)
+ * LTM_PRIME_2MSB_ON - make the 2nd highest bit one
+ *
+ * You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can
+ * have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself
+ * so it can be NULL
+ *
+ */
+
+/* This is possibly the mother of all prime generation functions, muahahahahaha! */
+int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat)
+{
+ unsigned char *tmp, maskAND, maskOR_msb, maskOR_lsb;
+ int res, err, bsize, maskOR_msb_offset;
+
+ /* sanity check the input */
+ if (size <= 1 || t <= 0) {
+ return MP_VAL;
+ }
+
+ /* LTM_PRIME_SAFE implies LTM_PRIME_BBS */
+ if (flags & LTM_PRIME_SAFE) {
+ flags |= LTM_PRIME_BBS;
+ }
+
+ /* calc the byte size */
+ bsize = (size>>3) + ((size&7)?1:0);
+
+ /* we need a buffer of bsize bytes */
+ tmp = OPT_CAST(unsigned char) XMALLOC(bsize);
+ if (tmp == NULL) {
+ return MP_MEM;
+ }
+
+ /* calc the maskAND value for the MSbyte*/
+ maskAND = ((size&7) == 0) ? 0xFF : (0xFF >> (8 - (size & 7)));
+
+ /* calc the maskOR_msb */
+ maskOR_msb = 0;
+ maskOR_msb_offset = ((size & 7) == 1) ? 1 : 0;
+ if (flags & LTM_PRIME_2MSB_ON) {
+ maskOR_msb |= 0x80 >> ((9 - size) & 7);
+ }
+
+ /* get the maskOR_lsb */
+ maskOR_lsb = 1;
+ if (flags & LTM_PRIME_BBS) {
+ maskOR_lsb |= 3;
+ }
+
+ do {
+ /* read the bytes */
+ if (cb(tmp, bsize, dat) != bsize) {
+ err = MP_VAL;
+ goto error;
+ }
+
+ /* work over the MSbyte */
+ tmp[0] &= maskAND;
+ tmp[0] |= 1 << ((size - 1) & 7);
+
+ /* mix in the maskORs */
+ tmp[maskOR_msb_offset] |= maskOR_msb;
+ tmp[bsize-1] |= maskOR_lsb;
+
+ /* read it in */
+ if ((err = mp_read_unsigned_bin(a, tmp, bsize)) != MP_OKAY) { goto error; }
+
+ /* is it prime? */
+ if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { goto error; }
+ if (res == MP_NO) {
+ continue;
+ }
+
+ if (flags & LTM_PRIME_SAFE) {
+ /* see if (a-1)/2 is prime */
+ if ((err = mp_sub_d(a, 1, a)) != MP_OKAY) { goto error; }
+ if ((err = mp_div_2(a, a)) != MP_OKAY) { goto error; }
+
+ /* is it prime? */
+ if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { goto error; }
+ }
+ } while (res == MP_NO);
+
+ if (flags & LTM_PRIME_SAFE) {
+ /* restore a to the original value */
+ if ((err = mp_mul_2(a, a)) != MP_OKAY) { goto error; }
+ if ((err = mp_add_d(a, 1, a)) != MP_OKAY) { goto error; }
+ }
+
+ err = MP_OKAY;
+error:
+ XFREE(tmp);
+ return err;
+}
+
+
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_RADIX_SIZE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* returns size of ASCII reprensentation */
+int mp_radix_size (mp_int * a, int radix, int *size)
+{
+ int res, digs;
+ mp_int t;
+ mp_digit d;
+
+ *size = 0;
+
+ /* special case for binary */
+ if (radix == 2) {
+ *size = mp_count_bits (a) + (a->sign == MP_NEG ? 1 : 0) + 1;
+ return MP_OKAY;
+ }
+
+ /* make sure the radix is in range */
+ if (radix < 2 || radix > 64) {
+ return MP_VAL;
+ }
+
+ if (mp_iszero(a) == MP_YES) {
+ *size = 2;
+ return MP_OKAY;
+ }
+
+ /* digs is the digit count */
+ digs = 0;
+
+ /* if it's negative add one for the sign */
+ if (a->sign == MP_NEG) {
+ ++digs;
+ }
+
+ /* init a copy of the input */
+ if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
+ return res;
+ }
+
+ /* force temp to positive */
+ t.sign = MP_ZPOS;
+
+ /* fetch out all of the digits */
+ while (mp_iszero (&t) == MP_NO) {
+ if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+ ++digs;
+ }
+ mp_clear (&t);
+
+ /* return digs + 1, the 1 is for the NULL byte that would be required. */
+ *size = digs + 1;
+ return MP_OKAY;
+}
+
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_RADIX_SMAP_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* chars used in radix conversions */
+const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_RAND_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* makes a pseudo-random int of a given size */
+int
+mp_rand (mp_int * a, int digits)
+{
+ int res;
+ mp_digit d;
+
+ mp_zero (a);
+ if (digits <= 0) {
+ return MP_OKAY;
+ }
+
+ /* first place a random non-zero digit */
+ do {
+ d = ((mp_digit) abs (rand ())) & MP_MASK;
+ } while (d == 0);
+
+ if ((res = mp_add_d (a, d, a)) != MP_OKAY) {
+ return res;
+ }
+
+ while (--digits > 0) {
+ if ((res = mp_lshd (a, 1)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_add_d (a, ((mp_digit) abs (rand ())), a)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_READ_RADIX_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* read a string [ASCII] in a given radix */
+int mp_read_radix (mp_int * a, const char *str, int radix)
+{
+ int y, res, neg;
+ char ch;
+
+ /* zero the digit bignum */
+ mp_zero(a);
+
+ /* make sure the radix is ok */
+ if (radix < 2 || radix > 64) {
+ return MP_VAL;
+ }
+
+ /* if the leading digit is a
+ * minus set the sign to negative.
+ */
+ if (*str == '-') {
+ ++str;
+ neg = MP_NEG;
+ } else {
+ neg = MP_ZPOS;
+ }
+
+ /* set the integer to the default of zero */
+ mp_zero (a);
+
+ /* process each digit of the string */
+ while (*str) {
+ /* if the radix < 36 the conversion is case insensitive
+ * this allows numbers like 1AB and 1ab to represent the same value
+ * [e.g. in hex]
+ */
+ ch = (char) ((radix < 36) ? toupper ((int)*str) : *str);
+ for (y = 0; y < 64; y++) {
+ if (ch == mp_s_rmap[y]) {
+ break;
+ }
+ }
+
+ /* if the char was found in the map
+ * and is less than the given radix add it
+ * to the number, otherwise exit the loop.
+ */
+ if (y < radix) {
+ if ((res = mp_mul_d (a, (mp_digit) radix, a)) != MP_OKAY) {
+ return res;
+ }
+ if ((res = mp_add_d (a, (mp_digit) y, a)) != MP_OKAY) {
+ return res;
+ }
+ } else {
+ break;
+ }
+ ++str;
+ }
+
+ /* set the sign only if a != 0 */
+ if (mp_iszero(a) != 1) {
+ a->sign = neg;
+ }
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_READ_SIGNED_BIN_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* read signed bin, big endian, first byte is 0==positive or 1==negative */
+int mp_read_signed_bin (mp_int * a, const unsigned char *b, int c)
+{
+ int res;
+
+ /* read magnitude */
+ if ((res = mp_read_unsigned_bin (a, b + 1, c - 1)) != MP_OKAY) {
+ return res;
+ }
+
+ /* first byte is 0 for positive, non-zero for negative */
+ if (b[0] == 0) {
+ a->sign = MP_ZPOS;
+ } else {
+ a->sign = MP_NEG;
+ }
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_READ_UNSIGNED_BIN_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* reads a unsigned char array, assumes the msb is stored first [big endian] */
+int mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c)
+{
+ int res;
+
+ /* make sure there are at least two digits */
+ if (a->alloc < 2) {
+ if ((res = mp_grow(a, 2)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* zero the int */
+ mp_zero (a);
+
+ /* read the bytes in */
+ while (c-- > 0) {
+ if ((res = mp_mul_2d (a, 8, a)) != MP_OKAY) {
+ return res;
+ }
+
+#ifndef MP_8BIT
+ a->dp[0] |= *b++;
+ a->used += 1;
+#else
+ a->dp[0] = (*b & MP_MASK);
+ a->dp[1] |= ((*b++ >> 7U) & 1);
+ a->used += 2;
+#endif
+ }
+ mp_clamp (a);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* reduces x mod m, assumes 0 < x < m**2, mu is
+ * precomputed via mp_reduce_setup.
+ * From HAC pp.604 Algorithm 14.42
+ */
+int mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
+{
+ mp_int q;
+ int res, um = m->used;
+
+ /* q = x */
+ if ((res = mp_init_copy (&q, x)) != MP_OKAY) {
+ return res;
+ }
+
+ /* q1 = x / b**(k-1) */
+ mp_rshd (&q, um - 1);
+
+ /* according to HAC this optimization is ok */
+ if (((unsigned long) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) {
+ if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+ } else {
+#ifdef BN_S_MP_MUL_HIGH_DIGS_C
+ if ((res = s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+#elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
+ if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+#else
+ {
+ res = MP_VAL;
+ goto CLEANUP;
+ }
+#endif
+ }
+
+ /* q3 = q2 / b**(k+1) */
+ mp_rshd (&q, um + 1);
+
+ /* x = x mod b**(k+1), quick (no division) */
+ if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+
+ /* q = q * m mod b**(k+1), quick (no division) */
+ if ((res = s_mp_mul_digs (&q, m, &q, um + 1)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+
+ /* x = x - q */
+ if ((res = mp_sub (x, &q, x)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+
+ /* If x < 0, add b**(k+1) to it */
+ if (mp_cmp_d (x, 0) == MP_LT) {
+ mp_set (&q, 1);
+ if ((res = mp_lshd (&q, um + 1)) != MP_OKAY)
+ goto CLEANUP;
+ if ((res = mp_add (x, &q, x)) != MP_OKAY)
+ goto CLEANUP;
+ }
+
+ /* Back off if it's too big */
+ while (mp_cmp (x, m) != MP_LT) {
+ if ((res = s_mp_sub (x, m, x)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+ }
+
+CLEANUP:
+ mp_clear (&q);
+
+ return res;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_2K_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* reduces a modulo n where n is of the form 2**p - d */
+int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d)
+{
+ mp_int q;
+ int p, res;
+
+ if ((res = mp_init(&q)) != MP_OKAY) {
+ return res;
+ }
+
+ p = mp_count_bits(n);
+top:
+ /* q = a/2**p, a = a mod 2**p */
+ if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if (d != 1) {
+ /* q = q * d */
+ if ((res = mp_mul_d(&q, d, &q)) != MP_OKAY) {
+ goto ERR;
+ }
+ }
+
+ /* a = a + q */
+ if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if (mp_cmp_mag(a, n) != MP_LT) {
+ s_mp_sub(a, n, a);
+ goto top;
+ }
+
+ERR:
+ mp_clear(&q);
+ return res;
+}
+
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_2K_L_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* reduces a modulo n where n is of the form 2**p - d
+ This differs from reduce_2k since "d" can be larger
+ than a single digit.
+*/
+int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d)
+{
+ mp_int q;
+ int p, res;
+
+ if ((res = mp_init(&q)) != MP_OKAY) {
+ return res;
+ }
+
+ p = mp_count_bits(n);
+top:
+ /* q = a/2**p, a = a mod 2**p */
+ if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* q = q * d */
+ if ((res = mp_mul(&q, d, &q)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* a = a + q */
+ if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if (mp_cmp_mag(a, n) != MP_LT) {
+ s_mp_sub(a, n, a);
+ goto top;
+ }
+
+ERR:
+ mp_clear(&q);
+ return res;
+}
+
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_2K_SETUP_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* determines the setup value */
+int mp_reduce_2k_setup(mp_int *a, mp_digit *d)
+{
+ int res, p;
+ mp_int tmp;
+
+ if ((res = mp_init(&tmp)) != MP_OKAY) {
+ return res;
+ }
+
+ p = mp_count_bits(a);
+ if ((res = mp_2expt(&tmp, p)) != MP_OKAY) {
+ mp_clear(&tmp);
+ return res;
+ }
+
+ if ((res = s_mp_sub(&tmp, a, &tmp)) != MP_OKAY) {
+ mp_clear(&tmp);
+ return res;
+ }
+
+ *d = tmp.dp[0];
+ mp_clear(&tmp);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_2K_SETUP_L_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* determines the setup value */
+int mp_reduce_2k_setup_l(mp_int *a, mp_int *d)
+{
+ int res;
+ mp_int tmp;
+
+ if ((res = mp_init(&tmp)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_2expt(&tmp, mp_count_bits(a))) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = s_mp_sub(&tmp, a, d)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ERR:
+ mp_clear(&tmp);
+ return res;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_IS_2K_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* determines if mp_reduce_2k can be used */
+int mp_reduce_is_2k(mp_int *a)
+{
+ int ix, iy, iw;
+ mp_digit iz;
+
+ if (a->used == 0) {
+ return MP_NO;
+ } else if (a->used == 1) {
+ return MP_YES;
+ } else if (a->used > 1) {
+ iy = mp_count_bits(a);
+ iz = 1;
+ iw = 1;
+
+ /* Test every bit from the second digit up, must be 1 */
+ for (ix = DIGIT_BIT; ix < iy; ix++) {
+ if ((a->dp[iw] & iz) == 0) {
+ return MP_NO;
+ }
+ iz <<= 1;
+ if (iz > (mp_digit)MP_MASK) {
+ ++iw;
+ iz = 1;
+ }
+ }
+ }
+ return MP_YES;
+}
+
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_IS_2K_L_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* determines if reduce_2k_l can be used */
+int mp_reduce_is_2k_l(mp_int *a)
+{
+ int ix, iy;
+
+ if (a->used == 0) {
+ return MP_NO;
+ } else if (a->used == 1) {
+ return MP_YES;
+ } else if (a->used > 1) {
+ /* if more than half of the digits are -1 we're sold */
+ for (iy = ix = 0; ix < a->used; ix++) {
+ if (a->dp[ix] == MP_MASK) {
+ ++iy;
+ }
+ }
+ return (iy >= (a->used/2)) ? MP_YES : MP_NO;
+
+ }
+ return MP_NO;
+}
+
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_SETUP_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* pre-calculate the value required for Barrett reduction
+ * For a given modulus "b" it calulates the value required in "a"
+ */
+int mp_reduce_setup (mp_int * a, mp_int * b)
+{
+ int res;
+
+ if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) {
+ return res;
+ }
+ return mp_div (a, b, a, NULL);
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_RSHD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* shift right a certain amount of digits */
+void mp_rshd (mp_int * a, int b)
+{
+ int x;
+
+ /* if b <= 0 then ignore it */
+ if (b <= 0) {
+ return;
+ }
+
+ /* if b > used then simply zero it and return */
+ if (a->used <= b) {
+ mp_zero (a);
+ return;
+ }
+
+ {
+ register mp_digit *bottom, *top;
+
+ /* shift the digits down */
+
+ /* bottom */
+ bottom = a->dp;
+
+ /* top [offset into digits] */
+ top = a->dp + b;
+
+ /* this is implemented as a sliding window where
+ * the window is b-digits long and digits from
+ * the top of the window are copied to the bottom
+ *
+ * e.g.
+
+ b-2 | b-1 | b0 | b1 | b2 | ... | bb | ---->
+ /\ | ---->
+ \-------------------/ ---->
+ */
+ for (x = 0; x < (a->used - b); x++) {
+ *bottom++ = *top++;
+ }
+
+ /* zero the top digits */
+ for (; x < a->used; x++) {
+ *bottom++ = 0;
+ }
+ }
+
+ /* remove excess digits */
+ a->used -= b;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_SET_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* set to a digit */
+void mp_set (mp_int * a, mp_digit b)
+{
+ mp_zero (a);
+ a->dp[0] = b & MP_MASK;
+ a->used = (a->dp[0] != 0) ? 1 : 0;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_SET_INT_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* set a 32-bit const */
+int mp_set_int (mp_int * a, unsigned long b)
+{
+ int x, res;
+
+ mp_zero (a);
+
+ /* set four bits at a time */
+ for (x = 0; x < 8; x++) {
+ /* shift the number up four bits */
+ if ((res = mp_mul_2d (a, 4, a)) != MP_OKAY) {
+ return res;
+ }
+
+ /* OR in the top four bits of the source */
+ a->dp[0] |= (b >> 28) & 15;
+
+ /* shift the source up to the next four bits */
+ b <<= 4;
+
+ /* ensure that digits are not clamped off */
+ a->used += 1;
+ }
+ mp_clamp (a);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_SHRINK_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* shrink a bignum */
+int mp_shrink (mp_int * a)
+{
+ mp_digit *tmp;
+ int used = 1;
+
+ if(a->used > 0)
+ used = a->used;
+
+ if (a->alloc != used) {
+ if ((tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * used)) == NULL) {
+ return MP_MEM;
+ }
+ a->dp = tmp;
+ a->alloc = used;
+ }
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_SIGNED_BIN_SIZE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* get the size for an signed equivalent */
+int mp_signed_bin_size (mp_int * a)
+{
+ return 1 + mp_unsigned_bin_size (a);
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_SQR_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* computes b = a*a */
+int
+mp_sqr (mp_int * a, mp_int * b)
+{
+ int res;
+
+#ifdef BN_MP_TOOM_SQR_C
+ /* use Toom-Cook? */
+ if (a->used >= TOOM_SQR_CUTOFF) {
+ res = mp_toom_sqr(a, b);
+ /* Karatsuba? */
+ } else
+#endif
+#ifdef BN_MP_KARATSUBA_SQR_C
+if (a->used >= KARATSUBA_SQR_CUTOFF) {
+ res = mp_karatsuba_sqr (a, b);
+ } else
+#endif
+ {
+#ifdef BN_FAST_S_MP_SQR_C
+ /* can we use the fast comba multiplier? */
+ if ((a->used * 2 + 1) < MP_WARRAY &&
+ a->used <
+ (1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) {
+ res = fast_s_mp_sqr (a, b);
+ } else
+#endif
+#ifdef BN_S_MP_SQR_C
+ res = s_mp_sqr (a, b);
+#else
+ res = MP_VAL;
+#endif
+ }
+ b->sign = MP_ZPOS;
+ return res;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_SQRMOD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* c = a * a (mod b) */
+int
+mp_sqrmod (mp_int * a, mp_int * b, mp_int * c)
+{
+ int res;
+ mp_int t;
+
+ if ((res = mp_init (&t)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_sqr (a, &t)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+ res = mp_mod (&t, b, c);
+ mp_clear (&t);
+ return res;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_SQRT_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* this function is less generic than mp_n_root, simpler and faster */
+int mp_sqrt(mp_int *arg, mp_int *ret)
+{
+ int res;
+ mp_int t1,t2;
+
+ /* must be positive */
+ if (arg->sign == MP_NEG) {
+ return MP_VAL;
+ }
+
+ /* easy out */
+ if (mp_iszero(arg) == MP_YES) {
+ mp_zero(ret);
+ return MP_OKAY;
+ }
+
+ if ((res = mp_init_copy(&t1, arg)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_init(&t2)) != MP_OKAY) {
+ goto E2;
+ }
+
+ /* First approx. (not very bad for large arg) */
+ mp_rshd (&t1,t1.used/2);
+
+ /* t1 > 0 */
+ if ((res = mp_div(arg,&t1,&t2,NULL)) != MP_OKAY) {
+ goto E1;
+ }
+ if ((res = mp_add(&t1,&t2,&t1)) != MP_OKAY) {
+ goto E1;
+ }
+ if ((res = mp_div_2(&t1,&t1)) != MP_OKAY) {
+ goto E1;
+ }
+ /* And now t1 > sqrt(arg) */
+ do {
+ if ((res = mp_div(arg,&t1,&t2,NULL)) != MP_OKAY) {
+ goto E1;
+ }
+ if ((res = mp_add(&t1,&t2,&t1)) != MP_OKAY) {
+ goto E1;
+ }
+ if ((res = mp_div_2(&t1,&t1)) != MP_OKAY) {
+ goto E1;
+ }
+ /* t1 >= sqrt(arg) >= t2 at this point */
+ } while (mp_cmp_mag(&t1,&t2) == MP_GT);
+
+ mp_exch(&t1,ret);
+
+E1: mp_clear(&t2);
+E2: mp_clear(&t1);
+ return res;
+}
+
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_SUB_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* high level subtraction (handles signs) */
+int
+mp_sub (mp_int * a, mp_int * b, mp_int * c)
+{
+ int sa, sb, res;
+
+ sa = a->sign;
+ sb = b->sign;
+
+ if (sa != sb) {
+ /* subtract a negative from a positive, OR */
+ /* subtract a positive from a negative. */
+ /* In either case, ADD their magnitudes, */
+ /* and use the sign of the first number. */
+ c->sign = sa;
+ res = s_mp_add (a, b, c);
+ } else {
+ /* subtract a positive from a positive, OR */
+ /* subtract a negative from a negative. */
+ /* First, take the difference between their */
+ /* magnitudes, then... */
+ if (mp_cmp_mag (a, b) != MP_LT) {
+ /* Copy the sign from the first */
+ c->sign = sa;
+ /* The first has a larger or equal magnitude */
+ res = s_mp_sub (a, b, c);
+ } else {
+ /* The result has the *opposite* sign from */
+ /* the first number. */
+ c->sign = (sa == MP_ZPOS) ? MP_NEG : MP_ZPOS;
+ /* The second has a larger magnitude */
+ res = s_mp_sub (b, a, c);
+ }
+ }
+ return res;
+}
+
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_SUB_D_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* single digit subtraction */
+int
+mp_sub_d (mp_int * a, mp_digit b, mp_int * c)
+{
+ mp_digit *tmpa, *tmpc, mu;
+ int res, ix, oldused;
+
+ /* grow c as required */
+ if (c->alloc < a->used + 1) {
+ if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* if a is negative just do an unsigned
+ * addition [with fudged signs]
+ */
+ if (a->sign == MP_NEG) {
+ a->sign = MP_ZPOS;
+ res = mp_add_d(a, b, c);
+ a->sign = c->sign = MP_NEG;
+
+ /* clamp */
+ mp_clamp(c);
+
+ return res;
+ }
+
+ /* setup regs */
+ oldused = c->used;
+ tmpa = a->dp;
+ tmpc = c->dp;
+
+ /* if a <= b simply fix the single digit */
+ if ((a->used == 1 && a->dp[0] <= b) || a->used == 0) {
+ if (a->used == 1) {
+ *tmpc++ = b - *tmpa;
+ } else {
+ *tmpc++ = b;
+ }
+ ix = 1;
+
+ /* negative/1digit */
+ c->sign = MP_NEG;
+ c->used = 1;
+ } else {
+ /* positive/size */
+ c->sign = MP_ZPOS;
+ c->used = a->used;
+
+ /* subtract first digit */
+ *tmpc = *tmpa++ - b;
+ mu = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1);
+ *tmpc++ &= MP_MASK;
+
+ /* handle rest of the digits */
+ for (ix = 1; ix < a->used; ix++) {
+ *tmpc = *tmpa++ - mu;
+ mu = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1);
+ *tmpc++ &= MP_MASK;
+ }
+ }
+
+ /* zero excess digits */
+ while (ix++ < oldused) {
+ *tmpc++ = 0;
+ }
+ mp_clamp(c);
+ return MP_OKAY;
+}
+
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_SUBMOD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* d = a - b (mod c) */
+int
+mp_submod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
+{
+ int res;
+ mp_int t;
+
+
+ if ((res = mp_init (&t)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_sub (a, b, &t)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+ res = mp_mod (&t, c, d);
+ mp_clear (&t);
+ return res;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_TO_SIGNED_BIN_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* store in signed [big endian] format */
+int mp_to_signed_bin (mp_int * a, unsigned char *b)
+{
+ int res;
+
+ if ((res = mp_to_unsigned_bin (a, b + 1)) != MP_OKAY) {
+ return res;
+ }
+ b[0] = (unsigned char) ((a->sign == MP_ZPOS) ? 0 : 1);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_TO_SIGNED_BIN_N_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* store in signed [big endian] format */
+int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen)
+{
+ if (*outlen < (unsigned long)mp_signed_bin_size(a)) {
+ return MP_VAL;
+ }
+ *outlen = mp_signed_bin_size(a);
+ return mp_to_signed_bin(a, b);
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_TO_UNSIGNED_BIN_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* store in unsigned [big endian] format */
+int mp_to_unsigned_bin (mp_int * a, unsigned char *b)
+{
+ int x, res;
+ mp_int t;
+
+ if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
+ return res;
+ }
+
+ x = 0;
+ while (mp_iszero (&t) == 0) {
+#ifndef MP_8BIT
+ b[x++] = (unsigned char) (t.dp[0] & 255);
+#else
+ b[x++] = (unsigned char) (t.dp[0] | ((t.dp[1] & 0x01) << 7));
+#endif
+ if ((res = mp_div_2d (&t, 8, &t, NULL)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+ }
+ bn_reverse (b, x);
+ mp_clear (&t);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_TO_UNSIGNED_BIN_N_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* store in unsigned [big endian] format */
+int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen)
+{
+ if (*outlen < (unsigned long)mp_unsigned_bin_size(a)) {
+ return MP_VAL;
+ }
+ *outlen = mp_unsigned_bin_size(a);
+ return mp_to_unsigned_bin(a, b);
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_TOOM_MUL_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* multiplication using the Toom-Cook 3-way algorithm
+ *
+ * Much more complicated than Karatsuba but has a lower
+ * asymptotic running time of O(N**1.464). This algorithm is
+ * only particularly useful on VERY large inputs
+ * (we're talking 1000s of digits here...).
+*/
+int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
+{
+ mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
+ int res, B;
+
+ /* init temps */
+ if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4,
+ &a0, &a1, &a2, &b0, &b1,
+ &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) {
+ return res;
+ }
+
+ /* B */
+ B = MIN(a->used, b->used) / 3;
+
+ /* a = a2 * B**2 + a1 * B + a0 */
+ if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_copy(a, &a1)) != MP_OKAY) {
+ goto ERR;
+ }
+ mp_rshd(&a1, B);
+ mp_mod_2d(&a1, DIGIT_BIT * B, &a1);
+
+ if ((res = mp_copy(a, &a2)) != MP_OKAY) {
+ goto ERR;
+ }
+ mp_rshd(&a2, B*2);
+
+ /* b = b2 * B**2 + b1 * B + b0 */
+ if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_copy(b, &b1)) != MP_OKAY) {
+ goto ERR;
+ }
+ mp_rshd(&b1, B);
+ mp_mod_2d(&b1, DIGIT_BIT * B, &b1);
+
+ if ((res = mp_copy(b, &b2)) != MP_OKAY) {
+ goto ERR;
+ }
+ mp_rshd(&b2, B*2);
+
+ /* w0 = a0*b0 */
+ if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* w4 = a2 * b2 */
+ if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */
+ if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */
+ if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+
+
+ /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */
+ if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&b2, &b1, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* now solve the matrix
+
+ 0 0 0 0 1
+ 1 2 4 8 16
+ 1 1 1 1 1
+ 16 8 4 2 1
+ 1 0 0 0 0
+
+ using 12 subtractions, 4 shifts,
+ 2 small divisions and 1 small multiplication
+ */
+
+ /* r1 - r4 */
+ if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3 - r0 */
+ if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1/2 */
+ if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3/2 */
+ if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r2 - r0 - r4 */
+ if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1 - r2 */
+ if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3 - r2 */
+ if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1 - 8r0 */
+ if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3 - 8r4 */
+ if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* 3r2 - r1 - r3 */
+ if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1 - r2 */
+ if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3 - r2 */
+ if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1/3 */
+ if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3/3 */
+ if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* at this point shift W[n] by B*n */
+ if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ERR:
+ mp_clear_multi(&w0, &w1, &w2, &w3, &w4,
+ &a0, &a1, &a2, &b0, &b1,
+ &b2, &tmp1, &tmp2, NULL);
+ return res;
+}
+
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
--- /dev/null
+#include <tommath.h>
+#ifdef BN_MP_TOOM_SQR_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* squaring using Toom-Cook 3-way algorithm */
+int
+mp_toom_sqr(mp_int *a, mp_int *b)
+{
+ mp_int w0, w1, w2, w3, w4, tmp1, a0, a1, a2;
+ int res, B;
+
+ /* init temps */
+ if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL)) != MP_OKAY) {
+ return res;
+ }
+
+ /* B */
+ B = a->used / 3;
+
+ /* a = a2 * B**2 + a1 * B + a0 */
+ if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_copy(a, &a1)) != MP_OKAY) {
+ goto ERR;
+ }
+ mp_rshd(&a1, B);
+ mp_mod_2d(&a1, DIGIT_BIT * B, &a1);
+
+ if ((res = mp_copy(a, &a2)) != MP_OKAY) {
+ goto ERR;
+ }
+ mp_rshd(&a2, B*2);
+
+ /* w0 = a0*a0 */
+ if ((res = mp_sqr(&a0, &w0)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* w4 = a2 * a2 */
+ if ((res = mp_sqr(&a2, &w4)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* w1 = (a2 + 2(a1 + 2a0))**2 */
+ if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_sqr(&tmp1, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* w3 = (a0 + 2(a1 + 2a2))**2 */
+ if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
+ goto ERR;
+
projects / barrelfish / commitdiff
