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added libtommath-0.32

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Tom St Denis 2004-10-29 22:07:18 +00:00 committed by Steffen Jaeckel
parent 8eaa98807b
commit e549ccfec5
147 changed files with 17871 additions and 5351 deletions
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156
bn.ind
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@ -1,82 +1,82 @@
\begin{theindex}
\item mp\_add, \hyperpage{25}
\item mp\_add\_d, \hyperpage{48}
\item mp\_and, \hyperpage{25}
\item mp\_clear, \hyperpage{7}
\item mp\_clear\_multi, \hyperpage{8}
\item mp\_cmp, \hyperpage{20}
\item mp\_cmp\_d, \hyperpage{21}
\item mp\_cmp\_mag, \hyperpage{19}
\item mp\_div, \hyperpage{26}
\item mp\_div\_2, \hyperpage{22}
\item mp\_div\_2d, \hyperpage{24}
\item mp\_div\_d, \hyperpage{48}
\item mp\_dr\_reduce, \hyperpage{36}
\item mp\_dr\_setup, \hyperpage{36}
\item MP\_EQ, \hyperpage{18}
\item mp\_error\_to\_string, \hyperpage{6}
\item mp\_expt\_d, \hyperpage{39}
\item mp\_exptmod, \hyperpage{39}
\item mp\_exteuclid, \hyperpage{47}
\item mp\_gcd, \hyperpage{47}
\item mp\_get\_int, \hyperpage{16}
\item mp\_grow, \hyperpage{12}
\item MP\_GT, \hyperpage{18}
\item mp\_init, \hyperpage{7}
\item mp\_init\_copy, \hyperpage{9}
\item mp\_init\_multi, \hyperpage{8}
\item mp\_init\_set, \hyperpage{17}
\item mp\_init\_set\_int, \hyperpage{17}
\item mp\_init\_size, \hyperpage{10}
\item mp\_int, \hyperpage{6}
\item mp\_invmod, \hyperpage{48}
\item mp\_jacobi, \hyperpage{48}
\item mp\_lcm, \hyperpage{47}
\item mp\_lshd, \hyperpage{24}
\item MP\_LT, \hyperpage{18}
\item MP\_MEM, \hyperpage{5}
\item mp\_mod, \hyperpage{31}
\item mp\_mod\_d, \hyperpage{48}
\item mp\_montgomery\_calc\_normalization, \hyperpage{34}
\item mp\_montgomery\_reduce, \hyperpage{33}
\item mp\_montgomery\_setup, \hyperpage{33}
\item mp\_mul, \hyperpage{27}
\item mp\_mul\_2, \hyperpage{22}
\item mp\_mul\_2d, \hyperpage{24}
\item mp\_mul\_d, \hyperpage{48}
\item mp\_n\_root, \hyperpage{40}
\item mp\_neg, \hyperpage{25}
\item MP\_NO, \hyperpage{5}
\item MP\_OKAY, \hyperpage{5}
\item mp\_or, \hyperpage{25}
\item mp\_prime\_fermat, \hyperpage{41}
\item mp\_prime\_is\_divisible, \hyperpage{41}
\item mp\_prime\_is\_prime, \hyperpage{42}
\item mp\_prime\_miller\_rabin, \hyperpage{41}
\item mp\_prime\_next\_prime, \hyperpage{42}
\item mp\_prime\_rabin\_miller\_trials, \hyperpage{42}
\item mp\_prime\_random, \hyperpage{43}
\item mp\_prime\_random\_ex, \hyperpage{43}
\item mp\_radix\_size, \hyperpage{45}
\item mp\_read\_radix, \hyperpage{45}
\item mp\_read\_unsigned\_bin, \hyperpage{46}
\item mp\_reduce, \hyperpage{32}
\item mp\_reduce\_2k, \hyperpage{37}
\item mp\_reduce\_2k\_setup, \hyperpage{37}
\item mp\_reduce\_setup, \hyperpage{32}
\item mp\_rshd, \hyperpage{24}
\item mp\_set, \hyperpage{15}
\item mp\_set\_int, \hyperpage{16}
\item mp\_shrink, \hyperpage{11}
\item mp\_sqr, \hyperpage{29}
\item mp\_sub, \hyperpage{25}
\item mp\_sub\_d, \hyperpage{48}
\item mp\_to\_unsigned\_bin, \hyperpage{46}
\item mp\_toradix, \hyperpage{45}
\item mp\_unsigned\_bin\_size, \hyperpage{46}
\item MP\_VAL, \hyperpage{5}
\item mp\_xor, \hyperpage{25}
\item MP\_YES, \hyperpage{5}
\item mp\_add, \hyperpage{29}
\item mp\_add\_d, \hyperpage{52}
\item mp\_and, \hyperpage{29}
\item mp\_clear, \hyperpage{11}
\item mp\_clear\_multi, \hyperpage{12}
\item mp\_cmp, \hyperpage{24}
\item mp\_cmp\_d, \hyperpage{25}
\item mp\_cmp\_mag, \hyperpage{23}
\item mp\_div, \hyperpage{30}
\item mp\_div\_2, \hyperpage{26}
\item mp\_div\_2d, \hyperpage{28}
\item mp\_div\_d, \hyperpage{52}
\item mp\_dr\_reduce, \hyperpage{40}
\item mp\_dr\_setup, \hyperpage{40}
\item MP\_EQ, \hyperpage{22}
\item mp\_error\_to\_string, \hyperpage{10}
\item mp\_expt\_d, \hyperpage{43}
\item mp\_exptmod, \hyperpage{43}
\item mp\_exteuclid, \hyperpage{51}
\item mp\_gcd, \hyperpage{51}
\item mp\_get\_int, \hyperpage{20}
\item mp\_grow, \hyperpage{16}
\item MP\_GT, \hyperpage{22}
\item mp\_init, \hyperpage{11}
\item mp\_init\_copy, \hyperpage{13}
\item mp\_init\_multi, \hyperpage{12}
\item mp\_init\_set, \hyperpage{21}
\item mp\_init\_set\_int, \hyperpage{21}
\item mp\_init\_size, \hyperpage{14}
\item mp\_int, \hyperpage{10}
\item mp\_invmod, \hyperpage{52}
\item mp\_jacobi, \hyperpage{52}
\item mp\_lcm, \hyperpage{51}
\item mp\_lshd, \hyperpage{28}
\item MP\_LT, \hyperpage{22}
\item MP\_MEM, \hyperpage{9}
\item mp\_mod, \hyperpage{35}
\item mp\_mod\_d, \hyperpage{52}
\item mp\_montgomery\_calc\_normalization, \hyperpage{38}
\item mp\_montgomery\_reduce, \hyperpage{37}
\item mp\_montgomery\_setup, \hyperpage{37}
\item mp\_mul, \hyperpage{31}
\item mp\_mul\_2, \hyperpage{26}
\item mp\_mul\_2d, \hyperpage{28}
\item mp\_mul\_d, \hyperpage{52}
\item mp\_n\_root, \hyperpage{44}
\item mp\_neg, \hyperpage{29}
\item MP\_NO, \hyperpage{9}
\item MP\_OKAY, \hyperpage{9}
\item mp\_or, \hyperpage{29}
\item mp\_prime\_fermat, \hyperpage{45}
\item mp\_prime\_is\_divisible, \hyperpage{45}
\item mp\_prime\_is\_prime, \hyperpage{46}
\item mp\_prime\_miller\_rabin, \hyperpage{45}
\item mp\_prime\_next\_prime, \hyperpage{46}
\item mp\_prime\_rabin\_miller\_trials, \hyperpage{46}
\item mp\_prime\_random, \hyperpage{47}
\item mp\_prime\_random\_ex, \hyperpage{47}
\item mp\_radix\_size, \hyperpage{49}
\item mp\_read\_radix, \hyperpage{49}
\item mp\_read\_unsigned\_bin, \hyperpage{50}
\item mp\_reduce, \hyperpage{36}
\item mp\_reduce\_2k, \hyperpage{41}
\item mp\_reduce\_2k\_setup, \hyperpage{41}
\item mp\_reduce\_setup, \hyperpage{36}
\item mp\_rshd, \hyperpage{28}
\item mp\_set, \hyperpage{19}
\item mp\_set\_int, \hyperpage{20}
\item mp\_shrink, \hyperpage{15}
\item mp\_sqr, \hyperpage{33}
\item mp\_sub, \hyperpage{29}
\item mp\_sub\_d, \hyperpage{52}
\item mp\_to\_unsigned\_bin, \hyperpage{50}
\item mp\_toradix, \hyperpage{49}
\item mp\_unsigned\_bin\_size, \hyperpage{50}
\item MP\_VAL, \hyperpage{9}
\item mp\_xor, \hyperpage{29}
\item MP\_YES, \hyperpage{9}
\end{theindex}

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123
bn.tex
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@ -49,7 +49,7 @@
\begin{document}
\frontmatter
\pagestyle{empty}
\title{LibTomMath User Manual \\ v0.31}
\title{LibTomMath User Manual \\ v0.32}
\author{Tom St Denis \\ tomstdenis@iahu.ca}
\maketitle
This text, the library and the accompanying textbook are all hereby placed in the public domain. This book has been
@ -96,27 +96,34 @@ LibTomMath is meant to be very ``GCC friendly'' as it comes with a makefile well
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.
To build the library for GCC simply issue the
\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 simply link against that
and include ``tommath.h'' within your programs.
Alternatively to build with MSVC type
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.
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.
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 imprt library ``libtomcrypt.dll.a''
can be used to link LibTomMath dynamically to any Windows program using Cygwin.
\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
@ -144,6 +151,96 @@ This will output a row of numbers that are increasing. Each column is a differe
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

4
bn_error.c
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@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_ERROR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
static const struct {
int code;
@ -39,3 +40,4 @@ char *mp_error_to_string(int code)
return "Invalid error code";
}
#endif

6
bn_fast_mp_invmod.c
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@ -1,3 +1,5 @@
#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
@ -12,12 +14,11 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* computes the modular inverse via binary extended euclidean algorithm,
* that is c = 1/a mod b
*
* Based on mp_invmod except this is optimized for the case where b is
* 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
@ -141,3 +142,4 @@ top:
__ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
return res;
}
#endif

6
bn_fast_mp_montgomery_reduce.c
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@ -1,3 +1,5 @@
#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
@ -12,11 +14,10 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* computes xR**-1 == x (mod N) via Montgomery Reduction
*
* This is an optimized implementation of mp_montgomery_reduce
* This is an optimized implementation of montgomery_reduce
* which uses the comba method to quickly calculate the columns of the
* reduction.
*
@ -165,3 +166,4 @@ fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
}
return MP_OKAY;
}
#endif

93
bn_fast_s_mp_mul_digs.c
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@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* Fast (comba) multiplier
*
@ -33,8 +34,9 @@
int
fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
{
int olduse, res, pa, ix;
mp_word W[MP_WARRAY];
int olduse, res, pa, ix, iz;
mp_digit W[MP_WARRAY];
register mp_word _W;
/* grow the destination as required */
if (c->alloc < digs) {
@ -43,48 +45,39 @@ fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
}
}
/* clear temp buf (the columns) */
memset (W, 0, sizeof (mp_word) * digs);
/* number of output digits to produce */
pa = MIN(digs, a->used + b->used);
/* calculate the columns */
pa = a->used;
for (ix = 0; ix < pa; ix++) {
/* this multiplier has been modified to allow you to
* control how many digits of output are produced.
* So at most we want to make upto "digs" digits of output.
*
* this adds products to distinct columns (at ix+iy) of W
* note that each step through the loop is not dependent on
* the previous which means the compiler can easily unroll
* the loop without scheduling problems
*/
{
register mp_digit tmpx, *tmpy;
register mp_word *_W;
register int iy, pb;
/* clear the carry */
_W = 0;
for (ix = 0; ix <= pa; ix++) {
int tx, ty;
int iy;
mp_digit *tmpx, *tmpy;
/* alias for the the word on the left e.g. A[ix] * A[iy] */
tmpx = a->dp[ix];
/* get offsets into the two bignums */
ty = MIN(b->used-1, ix);
tx = ix - ty;
/* alias for the right side */
tmpy = b->dp;
/* setup temp aliases */
tmpx = a->dp + tx;
tmpy = b->dp + ty;
/* alias for the columns, each step through the loop adds a new
term to each column
/* this is the number of times the loop will iterrate, essentially its
while (tx++ < a->used && ty-- >= 0) { ... }
*/
_W = W + ix;
iy = MIN(a->used-tx, ty+1);
/* the number of digits is limited by their placement. E.g.
we avoid multiplying digits that will end up above the # of
digits of precision requested
*/
pb = MIN (b->used, digs - ix);
for (iy = 0; iy < pb; iy++) {
*_W++ += ((mp_word)tmpx) * ((mp_word)*tmpy++);
/* 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 */
@ -93,32 +86,11 @@ fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
{
register mp_digit *tmpc;
/* At this point W[] contains the sums of each column. To get the
* correct result we must take the extra bits from each column and
* carry them down
*
* Note that while this adds extra code to the multiplier it
* saves time since the carry propagation is removed from the
* above nested loop.This has the effect of reducing the work
* from N*(N+N*c)==N**2 + c*N**2 to N**2 + N*c where c is the
* cost of the shifting. On very small numbers this is slower
* but on most cryptographic size numbers it is faster.
*
* In this particular implementation we feed the carries from
* behind which means when the loop terminates we still have one
* last digit to copy
*/
tmpc = c->dp;
for (ix = 1; ix < digs; ix++) {
/* forward the carry from the previous temp */
W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT));
for (ix = 0; ix < digs; ix++) {
/* now extract the previous digit [below the carry] */
*tmpc++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
*tmpc++ = W[ix];
}
/* fetch the last digit */
*tmpc++ = (mp_digit) (W[digs - 1] & ((mp_word) MP_MASK));
/* clear unused digits [that existed in the old copy of c] */
for (; ix < olduse; ix++) {
@ -128,3 +100,4 @@ fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
mp_clamp (c);
return MP_OKAY;
}
#endif

103
bn_fast_s_mp_mul_high_digs.c
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@ -1,3 +1,5 @@
#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
@ -12,10 +14,9 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* this is a modified version of fast_s_mp_mul_digs that only produces
* output digits *above* digs. See the comments for fast_s_mp_mul_digs
/* 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
@ -26,73 +27,69 @@
int
fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
{
int oldused, newused, res, pa, pb, ix;
mp_word W[MP_WARRAY];
int olduse, res, pa, ix, iz;
mp_digit W[MP_WARRAY];
mp_word _W;
/* calculate size of product and allocate more space if required */
newused = a->used + b->used + 1;
if (c->alloc < newused) {
if ((res = mp_grow (c, newused)) != MP_OKAY) {
/* grow the destination as required */
pa = a->used + b->used;
if (c->alloc < pa) {
if ((res = mp_grow (c, pa)) != MP_OKAY) {
return res;
}
}
/* like the other comba method we compute the columns first */
pa = a->used;
pb = b->used;
memset (W + digs, 0, (pa + pb + 1 - digs) * sizeof (mp_word));
for (ix = 0; ix < pa; ix++) {
{
register mp_digit tmpx, *tmpy;
register int iy;
register mp_word *_W;
/* 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;
/* work todo, that is we only calculate digits that are at "digs" or above */
iy = digs - ix;
/* get offsets into the two bignums */
ty = MIN(b->used-1, ix);
tx = ix - ty;
/* copy of word on the left of A[ix] * B[iy] */
tmpx = a->dp[ix];
/* setup temp aliases */
tmpx = a->dp + tx;
tmpy = b->dp + ty;
/* alias for right side */
tmpy = b->dp + iy;
/* alias for the columns of output. Offset to be equal to or above the
* smallest digit place requested
/* this is the number of times the loop will iterrate, essentially its
while (tx++ < a->used && ty-- >= 0) { ... }
*/
_W = W + digs;
/* skip cases below zero where ix > digs */
if (iy < 0) {
iy = abs(iy);
tmpy += iy;
_W += iy;
iy = 0;
iy = MIN(a->used-tx, ty+1);
/* execute loop */
for (iz = 0; iz < iy; iz++) {
_W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
}
/* compute column products for digits above the minimum */
for (; iy < pb; iy++) {
*_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 */
oldused = c->used;
c->used = newused;
olduse = c->used;
c->used = pa;
/* now convert the array W downto what we need
*
* See comments in bn_fast_s_mp_mul_digs.c
*/
for (ix = digs + 1; ix < newused; ix++) {
W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT));
c->dp[ix - 1] = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
}
c->dp[newused - 1] = (mp_digit) (W[newused - 1] & ((mp_word) MP_MASK));
{
register mp_digit *tmpc;
for (; ix < oldused; ix++) {
c->dp[ix] = 0;
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

144
bn_fast_s_mp_sqr.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* fast squaring
*
@ -31,109 +32,98 @@
* Based on Algorithm 14.16 on pp.597 of HAC.
*
*/
/* 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.
Remove W2 and don't memset W
*/
int fast_s_mp_sqr (mp_int * a, mp_int * b)
{
int olduse, newused, res, ix, pa;
mp_word W2[MP_WARRAY], W[MP_WARRAY];
int olduse, res, pa, ix, iz;
mp_digit W[MP_WARRAY], *tmpx;
mp_word W1;
/* calculate size of product and allocate as required */
pa = a->used;
newused = pa + pa + 1;
if (b->alloc < newused) {
if ((res = mp_grow (b, newused)) != MP_OKAY) {
/* grow the destination as required */
pa = a->used + a->used;
if (b->alloc < pa) {
if ((res = mp_grow (b, pa)) != MP_OKAY) {
return res;
}
}
/* zero temp buffer (columns)
* Note that there are two buffers. Since squaring requires
* a outer and inner product and the inner product requires
* computing a product and doubling it (a relatively expensive
* op to perform n**2 times if you don't have to) the inner and
* outer products are computed in different buffers. This way
* the inner product can be doubled using n doublings instead of
* n**2
*/
memset (W, 0, newused * sizeof (mp_word));
memset (W2, 0, newused * sizeof (mp_word));
/* number of output digits to produce */
W1 = 0;
for (ix = 0; ix <= pa; ix++) {
int tx, ty, iy;
mp_word _W;
mp_digit *tmpy;
/* This computes the inner product. To simplify the inner N**2 loop
* the multiplication by two is done afterwards in the N loop.
*/
for (ix = 0; ix < pa; ix++) {
/* compute the outer product
*
* Note that every outer product is computed
* for a particular column only once which means that
* there is no need todo a double precision addition
* into the W2[] array.
*/
W2[ix + ix] = ((mp_word)a->dp[ix]) * ((mp_word)a->dp[ix]);
/* clear counter */
_W = 0;
{
register mp_digit tmpx, *tmpy;
register mp_word *_W;
register int iy;
/* get offsets into the two bignums */
ty = MIN(a->used-1, ix);
tx = ix - ty;
/* copy of left side */
tmpx = a->dp[ix];
/* setup temp aliases */
tmpx = a->dp + tx;
tmpy = a->dp + ty;
/* alias for right side */
tmpy = a->dp + (ix + 1);
/* 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);
/* the column to store the result in */
_W = W + (ix + ix + 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);
/* inner products */
for (iy = ix + 1; iy < pa; iy++) {
*_W++ += ((mp_word)tmpx) * ((mp_word)*tmpy++);
/* 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] = _W;
/* make next carry */
W1 = _W >> ((mp_word)DIGIT_BIT);
}
/* setup dest */
olduse = b->used;
b->used = newused;
b->used = a->used+a->used;
/* now compute digits
*
* We have to double the inner product sums, add in the
* outer product sums, propagate carries and convert
* to single precision.
*/
{
register mp_digit *tmpb;
/* double first value, since the inner products are
* half of what they should be
*/
W[0] += W[0] + W2[0];
mp_digit *tmpb;
tmpb = b->dp;
for (ix = 1; ix < newused; ix++) {
/* double/add next digit */
W[ix] += W[ix] + W2[ix];
/* propagate carry forwards [from the previous digit] */
W[ix] = W[ix] + (W[ix - 1] >> ((mp_word) DIGIT_BIT));
/* store the current digit now that the carry isn't
* needed
*/
*tmpb++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
for (ix = 0; ix < pa; ix++) {
*tmpb++ = W[ix] & MP_MASK;
}
/* set the last value. Note even if the carry is zero
* this is required since the next step will not zero
* it if b originally had a value at b->dp[2*a.used]
*/
*tmpb++ = (mp_digit) (W[(newused) - 1] & ((mp_word) MP_MASK));
/* clear high digits of b if there were any originally */
/* clear unused digits [that existed in the old copy of c] */
for (; ix < olduse; ix++) {
*tmpb++ = 0;
}
}
mp_clamp (b);
return MP_OKAY;
}
#endif

4
bn_mp_2expt.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_2EXPT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* computes a = 2**b
*
@ -40,3 +41,4 @@ mp_2expt (mp_int * a, int b)
return MP_OKAY;
}
#endif

4
bn_mp_abs.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_ABS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* b = |a|
*
@ -35,3 +36,4 @@ mp_abs (mp_int * a, mp_int * b)
return MP_OKAY;
}
#endif

4
bn_mp_add.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_ADD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* high level addition (handles signs) */
int mp_add (mp_int * a, mp_int * b, mp_int * c)
@ -45,3 +46,4 @@ int mp_add (mp_int * a, mp_int * b, mp_int * c)
return res;
}
#endif

4
bn_mp_add_d.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* single digit addition */
int
@ -101,3 +102,4 @@ mp_add_d (mp_int * a, mp_digit b, mp_int * c)
return MP_OKAY;
}
#endif

4
bn_mp_addmod.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_ADDMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* d = a + b (mod c) */
int
@ -33,3 +34,4 @@ mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
mp_clear (&t);
return res;
}
#endif

4
bn_mp_and.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_AND_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* AND two ints together */
int
@ -49,3 +50,4 @@ mp_and (mp_int * a, mp_int * b, mp_int * c)
mp_clear (&t);
return MP_OKAY;
}
#endif

4
bn_mp_clamp.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_CLAMP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* trim unused digits
*
@ -36,3 +37,4 @@ mp_clamp (mp_int * a)
a->sign = MP_ZPOS;
}
}
#endif

4
bn_mp_clear.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_CLEAR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* clear one (frees) */
void
@ -36,3 +37,4 @@ mp_clear (mp_int * a)
a->sign = MP_ZPOS;
}
}
#endif

4
bn_mp_clear_multi.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
#include <stdarg.h>
void mp_clear_multi(mp_int *mp, ...)
@ -26,3 +27,4 @@ void mp_clear_multi(mp_int *mp, ...)
}
va_end(args);
}
#endif

4
bn_mp_cmp.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_CMP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* compare two ints (signed)*/
int
@ -35,3 +36,4 @@ mp_cmp (mp_int * a, mp_int * b)
return mp_cmp_mag(a, b);
}
}
#endif

4
bn_mp_cmp_d.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* compare a digit */
int mp_cmp_d(mp_int * a, mp_digit b)
@ -36,3 +37,4 @@ int mp_cmp_d(mp_int * a, mp_digit b)
return MP_EQ;
}
}
#endif

4
bn_mp_cmp_mag.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* compare maginitude of two ints (unsigned) */
int mp_cmp_mag (mp_int * a, mp_int * b)
@ -47,3 +48,4 @@ int mp_cmp_mag (mp_int * a, mp_int * b)
}
return MP_EQ;
}
#endif

4
bn_mp_cnt_lsb.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
static const int lnz[16] = {
4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
@ -45,3 +46,4 @@ int mp_cnt_lsb(mp_int *a)
return x;
}
#endif

4
bn_mp_copy.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_COPY_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* copy, b = a */
int
@ -60,3 +61,4 @@ mp_copy (mp_int * a, mp_int * b)
b->sign = a->sign;
return MP_OKAY;
}
#endif

4
bn_mp_count_bits.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* returns the number of bits in an int */
int
@ -37,3 +38,4 @@ mp_count_bits (mp_int * a)
}
return r;
}
#endif

79
bn_mp_div.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_DIV_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,78 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
#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_copy(a, &ta)) != MP_OKAY) ||
((res = mp_copy(b, &tb)) != MP_OKAY) ||
((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
goto __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 __ERR;
}
}
if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
goto __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 = n2;
}
if (d != NULL) {
mp_exch(d, &ta);
d->sign = n;
}
__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]
@ -209,3 +282,7 @@ __T1:mp_clear (&t1);
__Q:mp_clear (&q);
return res;
}
#endif
#endif

4
bn_mp_div_2.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* b = a/2 */
int mp_div_2(mp_int * a, mp_int * b)
@ -60,3 +61,4 @@ int mp_div_2(mp_int * a, mp_int * b)
mp_clamp (b);
return MP_OKAY;
}
#endif

4
bn_mp_div_2d.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* 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)
@ -89,3 +90,4 @@ int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
mp_clear (&t);
return MP_OKAY;
}
#endif

4
bn_mp_div_3.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* divide by three (based on routine from MPI and the GMP manual) */
int
@ -71,3 +72,4 @@ mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
return res;
}
#endif

8
bn_mp_div_d.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
static int s_is_power_of_two(mp_digit b, int *p)
{
@ -54,7 +55,7 @@ int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
/* power of two ? */
if (s_is_power_of_two(b, &ix) == 1) {
if (d != NULL) {
*d = a->dp[0] & ((1<<ix) - 1);
*d = a->dp[0] & ((((mp_digit)1)<<ix) - 1);
}
if (c != NULL) {
return mp_div_2d(a, ix, c, NULL);
@ -62,10 +63,12 @@ int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
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) {
@ -100,3 +103,4 @@ int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
return res;
}
#endif

4
bn_mp_dr_is_modulus.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* determines if a number is a valid DR modulus */
int mp_dr_is_modulus(mp_int *a)
@ -35,3 +36,4 @@ int mp_dr_is_modulus(mp_int *a)
return 1;
}
#endif

4
bn_mp_dr_reduce.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* reduce "x" in place modulo "n" using the Diminished Radix algorithm.
*
@ -86,3 +87,4 @@ top:
}
return MP_OKAY;
}
#endif

4
bn_mp_dr_setup.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* determines the setup value */
void mp_dr_setup(mp_int *a, mp_digit *d)
@ -24,3 +25,4 @@ void mp_dr_setup(mp_int *a, mp_digit *d)
((mp_word)a->dp[0]));
}
#endif

4
bn_mp_exch.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_EXCH_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* swap the elements of two integers, for cases where you can't simply swap the
* mp_int pointers around
@ -26,3 +27,4 @@ mp_exch (mp_int * a, mp_int * b)
*a = *b;
*b = t;
}
#endif

4
bn_mp_expt_d.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* calculate c = a**b using a square-multiply algorithm */
int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
@ -49,3 +50,4 @@ int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
mp_clear (&g);
return MP_OKAY;
}
#endif

24
bn_mp_exptmod.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_EXPTMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* this is a shell function that calls either the normal or Montgomery
@ -31,6 +32,7 @@ int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
/* 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;
@ -57,22 +59,42 @@ int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
err = mp_exptmod(&tmpG, &tmpX, P, Y);
mp_clear_multi(&tmpG, &tmpX, NULL);
return err;
#else
/* no invmod */
return MP_VAL
#endif
}
#ifdef BN_MP_DR_IS_MODULUS_C
/* is it a DR modulus? */
dr = mp_dr_is_modulus(P);
#else
dr = 0;
#endif
#ifdef BN_MP_REDUCE_IS_2K_C
/* if not, is it a uDR modulus? */
if (dr == 0) {
dr = mp_reduce_is_2k(P) << 1;
}
#endif
/* if the modulus is odd or dr != 0 use the fast 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);
#else
/* no exptmod for evens */
return MP_VAL;
#endif
#ifdef BN_MP_EXPTMOD_FAST_C
}
#endif
}
#endif

39
bn_mp_exptmod_fast.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
*
@ -84,29 +85,52 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
/* 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 __M;
}
#else
err = MP_VAL;
goto __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 {
} else
#endif
{
#ifdef BN_MP_MONTGOMERY_REDUCE_C
/* use slower baseline Montgomery method */
redux = mp_montgomery_reduce;
#else
err = MP_VAL;
goto __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 __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 __M;
}
redux = mp_reduce_2k;
#else
err = MP_VAL;
goto __M;
#endif
}
/* setup result */
@ -116,16 +140,21 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
/* create M table
*
* The M table contains powers of the input base, e.g. M[x] = G^x mod P
*
* 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 __RES;
}
#else
err = MP_VAL;
goto __RES;
#endif
/* now set M[1] to G * R mod m */
if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
@ -269,7 +298,7 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
* to reduce one more time to cancel out the factor
* of R.
*/
if ((err = mp_montgomery_reduce (&res, P, mp)) != MP_OKAY) {
if ((err = redux(&res, P, mp)) != MP_OKAY) {
goto __RES;
}
}
@ -285,3 +314,5 @@ __M:
}
return err;
}
#endif

4
bn_mp_exteuclid.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_EXTEUCLID_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* Extended euclidean algorithm of (a, b) produces
a*u1 + b*u2 = u3
@ -67,3 +68,4 @@ int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3)
_ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL);
return err;
}
#endif

4
bn_mp_fread.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_FREAD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* read a bigint from a file stream in ASCII */
int mp_fread(mp_int *a, int radix, FILE *stream)
@ -59,3 +60,4 @@ int mp_fread(mp_int *a, int radix, FILE *stream)
return MP_OKAY;
}
#endif

4
bn_mp_fwrite.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_FWRITE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
int mp_fwrite(mp_int *a, int radix, FILE *stream)
{
@ -44,3 +45,4 @@ int mp_fwrite(mp_int *a, int radix, FILE *stream)
return MP_OKAY;
}
#endif

4
bn_mp_gcd.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_GCD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* Greatest Common Divisor using the binary method */
int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
@ -105,3 +106,4 @@ __V:mp_clear (&u);
__U:mp_clear (&v);
return res;
}
#endif

4
bn_mp_get_int.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* get the lower 32-bits of an mp_int */
unsigned long mp_get_int(mp_int * a)
@ -37,3 +38,4 @@ unsigned long mp_get_int(mp_int * a)
/* force result to 32-bits always so it is consistent on non 32-bit platforms */
return res & 0xFFFFFFFFUL;
}
#endif

4
bn_mp_grow.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_GROW_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* grow as required */
int mp_grow (mp_int * a, int size)
@ -49,3 +50,4 @@ int mp_grow (mp_int * a, int size)
}
return MP_OKAY;
}
#endif

4
bn_mp_init.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_INIT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* init a new mp_int */
int mp_init (mp_int * a)
@ -38,3 +39,4 @@ int mp_init (mp_int * a)
return MP_OKAY;
}
#endif

4
bn_mp_init_copy.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* creates "a" then copies b into it */
int mp_init_copy (mp_int * a, mp_int * b)
@ -24,3 +25,4 @@ int mp_init_copy (mp_int * a, mp_int * b)
}
return mp_copy (b, a);
}
#endif

4
bn_mp_init_multi.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
#include <stdarg.h>
int mp_init_multi(mp_int *mp, ...)
@ -51,3 +52,4 @@ int mp_init_multi(mp_int *mp, ...)
return res; /* Assumed ok, if error flagged above. */
}
#endif

4
bn_mp_init_set.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* initialize and set a digit */
int mp_init_set (mp_int * a, mp_digit b)
@ -24,3 +25,4 @@ int mp_init_set (mp_int * a, mp_digit b)
mp_set(a, b);
return err;
}
#endif

4
bn_mp_init_set_int.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* initialize and set a digit */
int mp_init_set_int (mp_int * a, unsigned long b)
@ -23,3 +24,4 @@ int mp_init_set_int (mp_int * a, unsigned long b)
}
return mp_set_int(a, b);
}
#endif

15
bn_mp_init_size.c
View File

@ -1,3 +1,5 @@
#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
@ -12,22 +14,31 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* 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) XCALLOC (sizeof (mp_digit), size);
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

153
bn_mp_invmod.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_INVMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,163 +14,26 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* hac 14.61, pp608 */
int mp_invmod (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;
}
#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);
}
/* init temps */
if ((res = mp_init_multi(&x, &y, &u, &v,
&A, &B, &C, &D, NULL)) != MP_OKAY) {
return res;
}
#endif
/* x = a, y = b */
if ((res = mp_copy (a, &x)) != MP_OKAY) {
goto __ERR;
}
if ((res = mp_copy (b, &y)) != MP_OKAY) {
goto __ERR;
}
#ifdef BN_MP_INVMOD_SLOW_C
return mp_invmod_slow(a, b, c);
#endif
/* 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 __ERR;
}
/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
if ((res = mp_copy (&x, &u)) != MP_OKAY) {
goto __ERR;
}
if ((res = mp_copy (&y, &v)) != MP_OKAY) {
goto __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 __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 __ERR;
}
if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
goto __ERR;
}
}
/* A = A/2, B = B/2 */
if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
goto __ERR;
}
if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
goto __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 __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 __ERR;
}
if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
goto __ERR;
}
}
/* C = C/2, D = D/2 */
if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
goto __ERR;
}
if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
goto __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 __ERR;
}
if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
goto __ERR;
}
if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
goto __ERR;
}
} else {
/* v - v - u, C = C - A, D = D - B */
if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
goto __ERR;
}
if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
goto __ERR;
}
if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
goto __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 __ERR;
}
/* if its too low */
while (mp_cmp_d(&C, 0) == MP_LT) {
if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
goto __ERR;
}
}
/* too big */
while (mp_cmp_mag(&C, b) != MP_LT) {
if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
goto __ERR;
}
}
/* C is now the inverse */
mp_exch (&C, c);
res = MP_OKAY;
__ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
return res;
return MP_VAL;
}
#endif

171
bn_mp_invmod_slow.c Normal file
View File

@ -0,0 +1,171 @@
#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@iahu.ca, http://math.libtomcrypt.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_copy (a, &x)) != MP_OKAY) {
goto __ERR;
}
if ((res = mp_copy (b, &y)) != MP_OKAY) {
goto __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 __ERR;
}
/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
if ((res = mp_copy (&x, &u)) != MP_OKAY) {
goto __ERR;
}
if ((res = mp_copy (&y, &v)) != MP_OKAY) {
goto __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 __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 __ERR;
}
if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
goto __ERR;
}
}
/* A = A/2, B = B/2 */
if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
goto __ERR;
}
if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
goto __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 __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 __ERR;
}
if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
goto __ERR;
}
}
/* C = C/2, D = D/2 */
if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
goto __ERR;
}
if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
goto __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 __ERR;
}
if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
goto __ERR;
}
if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
goto __ERR;
}
} else {
/* v - v - u, C = C - A, D = D - B */
if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
goto __ERR;
}
if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
goto __ERR;
}
if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
goto __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 __ERR;
}
/* if its too low */
while (mp_cmp_d(&C, 0) == MP_LT) {
if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
goto __ERR;
}
}
/* too big */
while (mp_cmp_mag(&C, b) != MP_LT) {
if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
goto __ERR;
}
}
/* C is now the inverse */
mp_exch (&C, c);
res = MP_OKAY;
__ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
return res;
}
#endif

6
bn_mp_is_square.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* Check if remainders are possible squares - fast exclude non-squares */
static const char rem_128[128] = {
@ -69,7 +70,7 @@ int mp_is_square(mp_int *arg,int *ret)
return MP_OKAY;
}
/* product of primes less than 2^31 */
if ((res = mp_init_set_int(&t,11L*13L*17L*19L*23L*29L*31L)) != MP_OKAY) {
return res;
}
@ -101,3 +102,4 @@ int mp_is_square(mp_int *arg,int *ret)
ERR:mp_clear(&t);
return res;
}
#endif

4
bn_mp_jacobi.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_JACOBI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* computes the jacobi c = (a | n) (or Legendre if n is prime)
* HAC pp. 73 Algorithm 2.149
@ -97,3 +98,4 @@ __P1:mp_clear (&p1);
__A1:mp_clear (&a1);
return res;
}
#endif

4
bn_mp_karatsuba_mul.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* c = |a| * |b| using Karatsuba Multiplication using
* three half size multiplications
@ -159,3 +160,4 @@ X0:mp_clear (&x0);
ERR:
return err;
}
#endif

6
bn_mp_karatsuba_sqr.c
View File

@ -1,3 +1,5 @@
#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
@ -12,12 +14,11 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* Karatsuba squaring, computes b = a*a using three
* half size squarings
*
* See comments of mp_karatsuba_mul for details. It
* See comments of karatsuba_mul for details. It
* is essentially the same algorithm but merely
* tuned to perform recursive squarings.
*/
@ -113,3 +114,4 @@ X0:mp_clear (&x0);
ERR:
return err;
}
#endif

4
bn_mp_lcm.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_LCM_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* computes least common multiple as |a*b|/(a, b) */
int mp_lcm (mp_int * a, mp_int * b, mp_int * c)
@ -52,3 +53,4 @@ __T:
mp_clear_multi (&t1, &t2, NULL);
return res;
}
#endif

4
bn_mp_lshd.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_LSHD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* shift left a certain amount of digits */
int mp_lshd (mp_int * a, int b)
@ -59,3 +60,4 @@ int mp_lshd (mp_int * a, int b)
}
return MP_OKAY;
}
#endif

4
bn_mp_mod.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_MOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* c = a mod b, 0 <= c < b */
int
@ -40,3 +41,4 @@ mp_mod (mp_int * a, mp_int * b, mp_int * c)
mp_clear (&t);
return res;
}
#endif

4
bn_mp_mod_2d.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* calc a value mod 2**b */
int
@ -47,3 +48,4 @@ mp_mod_2d (mp_int * a, int b, mp_int * c)
mp_clamp (c);
return MP_OKAY;
}
#endif

4
bn_mp_mod_d.c
View File

@ -1,3 +1,5 @@
#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
@ -12,10 +14,10 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
int
mp_mod_d (mp_int * a, mp_digit b, mp_digit * c)
{
return mp_div_d(a, b, NULL, c);
}
#endif

25
bn_mp_montgomery_calc_normalization.c
View File

@ -1,3 +1,5 @@
#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
@ -12,31 +14,31 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* calculates a = B^n mod b for Montgomery reduction
* Where B is the base [e.g. 2^DIGIT_BIT].
* B^n mod b is computed by first computing
* A = B^(n-1) which doesn't require a reduction but a simple OR.
* then C = A * B = B^n is computed by performing upto DIGIT_BIT
/*
* 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 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;
/* compute A = B^(n-1) * 2^(bits-1) */
if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) {
return res;
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) {
@ -51,3 +53,4 @@ mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
return MP_OKAY;
}
#endif

8
bn_mp_montgomery_reduce.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* computes xR**-1 == x (mod N) via Montgomery Reduction */
int
@ -23,7 +24,7 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
/* can the fast reduction [comba] method be used?
*
* Note that unlike in mp_mul you're safely allowed *less*
* 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.
*/
@ -46,7 +47,7 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
/* mu = ai * rho mod b
*
* The value of rho must be precalculated via
* bn_mp_montgomery_setup() such that
* 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
@ -110,3 +111,4 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
return MP_OKAY;
}
#endif

6
bn_mp_montgomery_setup.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* setups the montgomery reduction stuff */
int
@ -47,7 +48,8 @@ mp_montgomery_setup (mp_int * n, mp_digit * rho)
#endif
/* rho = -1/m mod b */
*rho = (((mp_digit) 1 << ((mp_digit) DIGIT_BIT)) - x) & MP_MASK;
*rho = (((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
return MP_OKAY;
}
#endif

26
bn_mp_mul.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* high level multiplication (handles sign) */
int mp_mul (mp_int * a, mp_int * b, mp_int * c)
@ -21,12 +22,18 @@ int mp_mul (mp_int * a, mp_int * b, mp_int * c)
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? */
} else if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
res = mp_karatsuba_mul (a, b, c);
} else {
} else
#endif
{
/* can we use the fast multiplier?
*
* The fast multiplier can be used if the output will
@ -35,14 +42,21 @@ int mp_mul (mp_int * a, mp_int * b, mp_int * c)
*/
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 {
res = s_mp_mul (a, b, c);
}
} 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

4
bn_mp_mul_2.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* b = a*2 */
int mp_mul_2(mp_int * a, mp_int * b)
@ -74,3 +75,4 @@ int mp_mul_2(mp_int * a, mp_int * b)
b->sign = a->sign;
return MP_OKAY;
}
#endif

4
bn_mp_mul_2d.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* shift left by a certain bit count */
int mp_mul_2d (mp_int * a, int b, mp_int * c)
@ -77,3 +78,4 @@ int mp_mul_2d (mp_int * a, int b, mp_int * c)
mp_clamp (c);
return MP_OKAY;
}
#endif

4
bn_mp_mul_d.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* multiply by a digit */
int
@ -70,3 +71,4 @@ mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
return MP_OKAY;
}
#endif

4
bn_mp_mulmod.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_MULMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* d = a * b (mod c) */
int
@ -33,3 +34,4 @@ mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
mp_clear (&t);
return res;
}
#endif

4
bn_mp_n_root.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* find the n'th root of an integer
*
@ -124,3 +125,4 @@ __T2:mp_clear (&t2);
__T1:mp_clear (&t1);
return res;
}
#endif

4
bn_mp_neg.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_NEG_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* b = -a */
int mp_neg (mp_int * a, mp_int * b)
@ -26,3 +27,4 @@ int mp_neg (mp_int * a, mp_int * b)
}
return MP_OKAY;
}
#endif

4
bn_mp_or.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_OR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* OR two ints together */
int mp_or (mp_int * a, mp_int * b, mp_int * c)
@ -42,3 +43,4 @@ int mp_or (mp_int * a, mp_int * b, mp_int * c)
mp_clear (&t);
return MP_OKAY;
}
#endif

4
bn_mp_prime_fermat.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* performs one Fermat test.
*
@ -54,3 +55,4 @@ int mp_prime_fermat (mp_int * a, mp_int * b, int *result)
__T:mp_clear (&t);
return err;
}
#endif

4
bn_mp_prime_is_divisible.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* determines if an integers is divisible by one
* of the first PRIME_SIZE primes or not
@ -42,3 +43,4 @@ int mp_prime_is_divisible (mp_int * a, int *result)
return MP_OKAY;
}
#endif

6
bn_mp_prime_is_prime.c
View File

@ -1,3 +1,5 @@
#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
@ -12,12 +14,11 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* performs a variable number of rounds of Miller-Rabin
*
* Probability of error after t rounds is no more than
* (1/4)^t when 1 <= t <= PRIME_SIZE
*
* Sets result to 1 if probably prime, 0 otherwise
*/
@ -75,3 +76,4 @@ int mp_prime_is_prime (mp_int * a, int t, int *result)
__B:mp_clear (&b);
return err;
}
#endif

4
bn_mp_prime_miller_rabin.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* Miller-Rabin test of "a" to the base of "b" as described in
* HAC pp. 139 Algorithm 4.24
@ -95,3 +96,4 @@ __R:mp_clear (&r);
__N1:mp_clear (&n1);
return err;
}
#endif

4
bn_mp_prime_next_prime.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* finds the next prime after the number "a" using "t" trials
* of Miller-Rabin.
@ -162,3 +163,4 @@ __ERR:
return err;
}
#endif

17
bn_prime_sizes_tab.c → bn_mp_prime_rabin_miller_trials.c
View File

@ -1,3 +1,5 @@
#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
@ -12,9 +14,8 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* this table gives the # of rabin miller trials for a prob of failure lower than 2^-96 */
static const struct {
int k, t;
} sizes[] = {
@ -25,13 +26,8 @@ static const struct {
{ 640, 6 },
{ 768, 5 },
{ 896, 4 },
{ 1024, 4 },
{ 1152, 3 },
{ 1280, 3 },
{ 1408, 3 },
{ 1536, 3 },
{ 1664, 3 },
{ 1792, 2 } };
{ 1024, 4 }
};
/* returns # of RM trials required for a given bit size */
int mp_prime_rabin_miller_trials(int size)
@ -45,7 +41,8 @@ int mp_prime_rabin_miller_trials(int size)
return (x == 0) ? sizes[0].t : sizes[x - 1].t;
}
}
return 1;
return sizes[x-1].t + 1;
}
#endif

7
bn_mp_prime_random_ex.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* makes a truly random prime of a given size (bits),
*
@ -92,6 +93,9 @@ int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback
/* 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 */
@ -116,3 +120,4 @@ error:
}
#endif

4
bn_mp_radix_size.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* returns size of ASCII reprensentation */
int mp_radix_size (mp_int * a, int radix, int *size)
@ -63,3 +64,4 @@ int mp_radix_size (mp_int * a, int radix, int *size)
return MP_OKAY;
}
#endif

4
bn_mp_radix_smap.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,7 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* chars used in radix conversions */
const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
#endif

4
bn_mp_rand.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_RAND_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* makes a pseudo-random int of a given size */
int
@ -47,3 +48,4 @@ mp_rand (mp_int * a, int digits)
return MP_OKAY;
}
#endif

4
bn_mp_read_radix.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* read a string [ASCII] in a given radix */
int mp_read_radix (mp_int * a, char *str, int radix)
@ -74,3 +75,4 @@ int mp_read_radix (mp_int * a, char *str, int radix)
}
return MP_OKAY;
}
#endif

4
bn_mp_read_signed_bin.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* read signed bin, big endian, first byte is 0==positive or 1==negative */
int
@ -34,3 +35,4 @@ mp_read_signed_bin (mp_int * a, unsigned char *b, int c)
return MP_OKAY;
}
#endif

4
bn_mp_read_unsigned_bin.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* reads a unsigned char array, assumes the msb is stored first [big endian] */
int
@ -48,3 +49,4 @@ mp_read_unsigned_bin (mp_int * a, unsigned char *b, int c)
mp_clamp (a);
return MP_OKAY;
}
#endif

15
bn_mp_reduce.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* reduces x mod m, assumes 0 < x < m**2, mu is
* precomputed via mp_reduce_setup.
@ -38,9 +39,20 @@ mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
goto CLEANUP;
}
} else {
#ifdef BN_S_MP_MUL_HIGH_DIGS_C
if ((res = s_mp_mul_high_digs (&q, mu, &q, um - 1)) != 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 - 1)) != MP_OKAY) {
goto CLEANUP;
}
#else
{
res = MP_VAL;
goto CLEANUP;
}
#endif
}
/* q3 = q2 / b**(k+1) */
@ -82,3 +94,4 @@ CLEANUP:
return res;
}
#endif

4
bn_mp_reduce_2k.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* reduces a modulo n where n is of the form 2**p - d */
int
@ -54,3 +55,4 @@ ERR:
return res;
}
#endif

4
bn_mp_reduce_2k_setup.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* determines the setup value */
int
@ -40,3 +41,4 @@ mp_reduce_2k_setup(mp_int *a, mp_digit *d)
mp_clear(&tmp);
return MP_OKAY;
}
#endif

4
bn_mp_reduce_is_2k.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* determines if mp_reduce_2k can be used */
int mp_reduce_is_2k(mp_int *a)
@ -44,3 +45,4 @@ int mp_reduce_is_2k(mp_int *a)
return 1;
}
#endif

7
bn_mp_reduce_setup.c
View File

@ -1,3 +1,5 @@
#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
@ -12,13 +14,11 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* 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 mp_reduce_setup (mp_int * a, mp_int * b)
{
int res;
@ -27,3 +27,4 @@ mp_reduce_setup (mp_int * a, mp_int * b)
}
return mp_div (a, b, a, NULL);
}
#endif

4
bn_mp_rshd.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_RSHD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* shift right a certain amount of digits */
void mp_rshd (mp_int * a, int b)
@ -64,3 +65,4 @@ void mp_rshd (mp_int * a, int b)
/* remove excess digits */
a->used -= b;
}
#endif

4
bn_mp_set.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_SET_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* set to a digit */
void mp_set (mp_int * a, mp_digit b)
@ -21,3 +22,4 @@ void mp_set (mp_int * a, mp_digit b)
a->dp[0] = b & MP_MASK;
a->used = (a->dp[0] != 0) ? 1 : 0;
}
#endif

4
bn_mp_set_int.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* set a 32-bit const */
int mp_set_int (mp_int * a, unsigned long b)
@ -40,3 +41,4 @@ int mp_set_int (mp_int * a, unsigned long b)
mp_clamp (a);
return MP_OKAY;
}
#endif

4
bn_mp_shrink.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_SHRINK_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* shrink a bignum */
int mp_shrink (mp_int * a)
@ -27,3 +28,4 @@ int mp_shrink (mp_int * a)
}
return MP_OKAY;
}
#endif

4
bn_mp_signed_bin_size.c
View File

@ -1,3 +1,5 @@
#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
@ -12,10 +14,10 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* get the size for an signed equivalent */
int mp_signed_bin_size (mp_int * a)
{
return 1 + mp_unsigned_bin_size (a);
}
#endif

23
bn_mp_sqr.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* computes b = a*a */
int
@ -20,22 +21,34 @@ 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 if (a->used >= KARATSUBA_SQR_CUTOFF) {
} else
#endif
#ifdef BN_MP_KARATSUBA_SQR_C
if (a->used >= KARATSUBA_SQR_CUTOFF) {
res = mp_karatsuba_sqr (a, b);
} else {
} 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 {
} 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

4
bn_mp_sqrmod.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_SQRMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* c = a * a (mod b) */
int
@ -33,3 +34,4 @@ mp_sqrmod (mp_int * a, mp_int * b, mp_int * c)
mp_clear (&t);
return res;
}
#endif

4
bn_mp_sqrt.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_SQRT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* this function is less generic than mp_n_root, simpler and faster */
int mp_sqrt(mp_int *arg, mp_int *ret)
@ -73,3 +74,4 @@ E2: mp_clear(&t1);
return res;
}
#endif

4
bn_mp_sub.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_SUB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* high level subtraction (handles signs) */
int
@ -51,3 +52,4 @@ mp_sub (mp_int * a, mp_int * b, mp_int * c)
return res;
}
#endif

4
bn_mp_sub_d.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* single digit subtraction */
int
@ -81,3 +82,4 @@ mp_sub_d (mp_int * a, mp_digit b, mp_int * c)
return MP_OKAY;
}
#endif

4
bn_mp_submod.c
View File

@ -1,3 +1,5 @@
#include <tommath.h>
#ifdef BN_MP_SUBMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* d = a - b (mod c) */
int
@ -34,3 +35,4 @@ mp_submod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
mp_clear (&t);
return res;
}
#endif

4
bn_mp_to_signed_bin.c
View File

@ -1,3 +1,5 @@
#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
@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* store in signed [big endian] format */
int
@ -26,3 +27,4 @@ mp_to_signed_bin (mp_int * a, unsigned char *b)
b[0] = (unsigned char) ((a->sign == MP_ZPOS) ? 0 : 1);
return MP_OKAY;
}
#endif

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