TeaSpeak/tomcrypt
1
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity
0f999a4e9e
tomcrypt/mpi.c
Tom St Denis 0f999a4e9e added libtomcrypt-0.81
2010-06-16 12:37:54 +02:00

5374 lines
128 KiB
C
Raw Blame History

/* File Generated Automatically by gen.pl */
/* Start: bncore.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
int KARATSUBA_MUL_CUTOFF = 80, /* Min. number of digits before Karatsuba multiplication is used. */
KARATSUBA_SQR_CUTOFF = 80, /* Min. number of digits before Karatsuba squaring is used. */
MONTGOMERY_EXPT_CUTOFF = 74; /* max. number of digits that montgomery reductions will help for */
/* End: bncore.c */
/* Start: bn_fast_mp_invmod.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#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
* 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;
if ((res = mp_init (&x)) != MP_OKAY) {
goto __ERR;
}
if ((res = mp_init (&y)) != MP_OKAY) {
goto __X;
}
if ((res = mp_init (&u)) != MP_OKAY) {
goto __Y;
}
if ((res = mp_init (&v)) != MP_OKAY) {
goto __U;
}
if ((res = mp_init (&B)) != MP_OKAY) {
goto __V;
}
if ((res = mp_init (&D)) != MP_OKAY) {
goto __B;
}
/* x == modulus, y == value to invert */
if ((res = mp_copy (b, &x)) != MP_OKAY) {
goto __D;
}
if ((res = mp_copy (a, &y)) != MP_OKAY) {
goto __D;
}
if ((res = mp_abs (&y, &y)) != MP_OKAY) {
goto __D;
}
/* 2. [modified] if x,y are both even then return an error!
*
* That is if gcd(x,y) = 2 * k then obviously there is no inverse.
*/
if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
res = MP_VAL;
goto __D;
}
/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
if ((res = mp_copy (&x, &u)) != MP_OKAY) {
goto __D;
}
if ((res = mp_copy (&y, &v)) != MP_OKAY) {
goto __D;
}
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 __D;
}
/* 4.2 if A or B is odd then */
if (mp_iseven (&B) == 0) {
if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
goto __D;
}
}
/* A = A/2, B = B/2 */
if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
goto __D;
}
}
/* 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 __D;
}
/* 5.2 if C,D are even then */
if (mp_iseven (&D) == 0) {
/* C = (C+y)/2, D = (D-x)/2 */
if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
goto __D;
}
}
/* C = C/2, D = D/2 */
if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
goto __D;
}
}
/* 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 __D;
}
if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
goto __D;
}
} else {
/* v - v - u, C = C - A, D = D - B */
if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
goto __D;
}
if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
goto __D;
}
}
/* 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 __D;
}
/* b is now the inverse */
neg = a->sign;
while (D.sign == MP_NEG) {
if ((res = mp_add (&D, b, &D)) != MP_OKAY) {
goto __D;
}
}
mp_exch (&D, c);
c->sign = neg;
res = MP_OKAY;
__D:mp_clear (&D);
__B:mp_clear (&B);
__V:mp_clear (&v);
__U:mp_clear (&u);
__Y:mp_clear (&y);
__X:mp_clear (&x);
__ERR:
return res;
}
/* End: bn_fast_mp_invmod.c */
/* Start: bn_fast_mp_montgomery_reduce.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* computes xR^-1 == x (mod N) via Montgomery Reduction
*
* This is an optimized implementation of mp_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 * a, mp_int * m, mp_digit mp)
{
int ix, res, olduse;
mp_word W[512];
/* get old used count */
olduse = a->used;
/* grow a as required */
if (a->alloc < m->used + 1) {
if ((res = mp_grow (a, m->used + 1)) != MP_OKAY) {
return res;
}
}
{
register mp_word *_W;
register mp_digit *tmpa;
_W = W;
tmpa = a->dp;
/* copy the digits of a */
for (ix = 0; ix < a->used; ix++) {
*_W++ = *tmpa++;
}
/* zero the high words */
for (; ix < m->used * 2 + 1; ix++) {
*_W++ = 0;
}
}
for (ix = 0; ix < m->used; ix++) {
/* ui = 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 ui;
ui = (((mp_digit) (W[ix] & MP_MASK)) * mp) & MP_MASK;
/* a = a + ui * 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 *tmpx;
register mp_word *_W;
/* alias for the digits of the modulus */
tmpx = m->dp;
/* Alias for the columns set by an offset of ix */
_W = W + ix;
/* inner loop */
for (iy = 0; iy < m->used; iy++) {
*_W++ += ((mp_word) ui) * ((mp_word) * tmpx++);
}
}
/* now fix carry for next digit, W[ix+1] */
W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
}
/* nox fix rest of carries */
for (++ix; ix <= m->used * 2 + 1; ix++) {
W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT));
}
{
register mp_digit *tmpa;
register mp_word *_W;
/* 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
*/
tmpa = a->dp;
_W = W + m->used;
for (ix = 0; ix < m->used + 1; ix++) {
*tmpa++ = *_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++) {
*tmpa++ = 0;
}
}
/* set the max used and clamp */
a->used = m->used + 1;
mp_clamp (a);
/* if A >= m then A = A - m */
if (mp_cmp_mag (a, m) != MP_LT) {
return s_mp_sub (a, m, a);
}
return MP_OKAY;
}
/* End: bn_fast_mp_montgomery_reduce.c */
/* Start: bn_fast_s_mp_mul_digs.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* 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;
mp_word W[512];
/* grow the destination as required */
if (c->alloc < digs) {
if ((res = mp_grow (c, digs)) != MP_OKAY) {
return res;
}
}
/* clear temp buf (the columns) */
memset (W, 0, sizeof (mp_word) * digs);
/* 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;
/* alias for the the word on the left e.g. A[ix] * A[iy] */
tmpx = a->dp[ix];
/* alias for the right side */
tmpy = b->dp;
/* alias for the columns, each step through the loop adds a new
term to each column
*/
_W = W + ix;
/* 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++);
}
}
}
/* setup dest */
olduse = c->used;
c->used = 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.
*/
tmpc = c->dp;
for (ix = 1; ix < digs; ix++) {
W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT));
*tmpc++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
}
*tmpc++ = (mp_digit) (W[digs - 1] & ((mp_word) MP_MASK));
/* clear unused */
for (; ix < olduse; ix++) {
*tmpc++ = 0;
}
}
mp_clamp (c);
return MP_OKAY;
}
/* End: bn_fast_s_mp_mul_digs.c */
/* Start: bn_fast_s_mp_mul_high_digs.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#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
* 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 oldused, newused, res, pa, pb, ix;
mp_word W[512];
/* 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) {
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;
/* work todo, that is we only calculate digits that are at "digs" or above */
iy = digs - ix;
/* copy of word on the left of A[ix] * B[iy] */
tmpx = a->dp[ix];
/* 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
*/
_W = &(W[digs]);
/* compute column products for digits above the minimum */
for (; iy < pb; iy++) {
*_W++ += ((mp_word) tmpx) * ((mp_word) * tmpy++);
}
}
}
/* setup dest */
oldused = c->used;
c->used = newused;
/* now convert the array W downto what we need */
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[(pa + pb + 1) - 1] =
(mp_digit) (W[(pa + pb + 1) - 1] & ((mp_word) MP_MASK));
for (; ix < oldused; ix++) {
c->dp[ix] = 0;
}
mp_clamp (c);
return MP_OKAY;
}
/* End: bn_fast_s_mp_mul_high_digs.c */
/* Start: bn_fast_s_mp_sqr.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* fast squaring
*
* This is the comba method where the columns of the product are computed first
* then the carries are computed. This has the effect of making a very simple
* inner loop that is executed the most
*
* W2 represents the outer products and W the inner.
*
* A further optimizations is made because the inner products are of the form
* "A * B * 2". The *2 part does not need to be computed until the end which is
* good because 64-bit shifts are slow!
*
* Based on Algorithm 14.16 on pp.597 of HAC.
*
*/
int
fast_s_mp_sqr (mp_int * a, mp_int * b)
{
int olduse, newused, res, ix, pa;
mp_word W2[512], W[512];
/* 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) {
return res;
}
}
/* zero temp buffer (columns)
* Note that there are two buffers. Since squaring requires
* a outter 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));
/* note optimization
* values in W2 are only written in even locations which means
* we can collapse the array to 256 words [and fixup the memset above]
* provided we also fix up the summations below. Ideally
* the fixup loop should be unrolled twice to handle the even/odd
* cases, and then a final step to handle odd cases [e.g. newused == odd]
*
* This will not only save ~8*256 = 2KB of stack but lower the number of
* operations required to finally fix up the columns
*/
/* 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
*/
W2[ix + ix] = ((mp_word) a->dp[ix]) * ((mp_word) a->dp[ix]);
{
register mp_digit tmpx, *tmpy;
register mp_word *_W;
register int iy;
/* copy of left side */
tmpx = a->dp[ix];
/* alias for right side */
tmpy = a->dp + (ix + 1);
/* the column to store the result in */
_W = W + (ix + ix + 1);
/* inner products */
for (iy = ix + 1; iy < pa; iy++) {
*_W++ += ((mp_word) tmpx) * ((mp_word) * tmpy++);
}
}
}
/* setup dest */
olduse = b->used;
b->used = newused;
/* double first value, since the inner products are half of what they should be */
W[0] += W[0] + W2[0];
/* now compute digits */
{
register mp_digit *tmpb;
tmpb = b->dp;
for (ix = 1; ix < newused; ix++) {
/* double/add next digit */
W[ix] += W[ix] + W2[ix];
W[ix] = W[ix] + (W[ix - 1] >> ((mp_word) DIGIT_BIT));
*tmpb++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
}
*tmpb++ = (mp_digit) (W[(newused) - 1] & ((mp_word) MP_MASK));
/* clear high */
for (; ix < olduse; ix++) {
*tmpb++ = 0;
}
}
/* fix the sign (since we no longer make a fresh temp) */
b->sign = MP_ZPOS;
mp_clamp (b);
return MP_OKAY;
}
/* End: bn_fast_s_mp_sqr.c */
/* Start: bn_mp_2expt.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* 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;
mp_zero (a);
if ((res = mp_grow (a, b / DIGIT_BIT + 1)) != MP_OKAY) {
return res;
}
a->used = b / DIGIT_BIT + 1;
a->dp[b / DIGIT_BIT] = 1 << (b % DIGIT_BIT);
return MP_OKAY;
}
/* End: bn_mp_2expt.c */
/* Start: bn_mp_abs.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* b = |a|
*
* Simple function copies the input and fixes the sign to positive
*/
int
mp_abs (mp_int * a, mp_int * b)
{
int res;
if ((res = mp_copy (a, b)) != MP_OKAY) {
return res;
}
b->sign = MP_ZPOS;
return MP_OKAY;
}
/* End: bn_mp_abs.c */
/* Start: bn_mp_add.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* 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 four cases */
if (sa == MP_ZPOS && sb == MP_ZPOS) {
/* both positive */
res = s_mp_add (a, b, c);
c->sign = MP_ZPOS;
} else if (sa == MP_ZPOS && sb == MP_NEG) {
/* a + -b == a - b, but if b>a then we do it as -(b-a) */
if (mp_cmp_mag (a, b) == MP_LT) {
res = s_mp_sub (b, a, c);
c->sign = MP_NEG;
} else {
res = s_mp_sub (a, b, c);
c->sign = MP_ZPOS;
}
} else if (sa == MP_NEG && sb == MP_ZPOS) {
/* -a + b == b - a, but if a>b then we do it as -(a-b) */
if (mp_cmp_mag (a, b) == MP_GT) {
res = s_mp_sub (a, b, c);
c->sign = MP_NEG;
} else {
res = s_mp_sub (b, a, c);
c->sign = MP_ZPOS;
}
} else {
/* -a + -b == -(a + b) */
res = s_mp_add (a, b, c);
c->sign = MP_NEG;
}
return res;
}
/* End: bn_mp_add.c */
/* Start: bn_mp_addmod.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* 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;
}
/* End: bn_mp_addmod.c */
/* Start: bn_mp_add_d.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* single digit addition */
int
mp_add_d (mp_int * a, mp_digit b, mp_int * c)
{
mp_int t;
int res;
if ((res = mp_init (&t)) != MP_OKAY) {
return res;
}
mp_set (&t, b);
res = mp_add (a, &t, c);
mp_clear (&t);
return res;
}
/* End: bn_mp_add_d.c */
/* Start: bn_mp_and.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* 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;
}
/* End: bn_mp_and.c */
/* Start: bn_mp_clamp.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* 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)
{
while (a->used > 0 && a->dp[a->used - 1] == 0)
--(a->used);
if (a->used == 0) {
a->sign = MP_ZPOS;
}
}
/* End: bn_mp_clamp.c */
/* Start: bn_mp_clear.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* clear one (frees) */
void
mp_clear (mp_int * a)
{
if (a->dp != NULL) {
/* first zero the digits */
memset (a->dp, 0, sizeof (mp_digit) * a->used);
/* free ram */
free (a->dp);
/* reset members to make debugging easier */
a->dp = NULL;
a->alloc = a->used = 0;
}
}
/* End: bn_mp_clear.c */
/* Start: bn_mp_cmp.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* compare two ints (signed)*/
int
mp_cmp (mp_int * a, mp_int * b)
{
/* compare based on sign */
if (a->sign == MP_NEG && b->sign == MP_ZPOS) {
return MP_LT;
} else if (a->sign == MP_ZPOS && b->sign == MP_NEG) {
return MP_GT;
}
return mp_cmp_mag (a, b);
}
/* End: bn_mp_cmp.c */
/* Start: bn_mp_cmp_d.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* compare a digit */
int
mp_cmp_d (mp_int * a, mp_digit b)
{
if (a->sign == MP_NEG) {
return MP_LT;
}
if (a->used > 1) {
return MP_GT;
}
if (a->dp[0] > b) {
return MP_GT;
} else if (a->dp[0] < b) {
return MP_LT;
} else {
return MP_EQ;
}
}
/* End: bn_mp_cmp_d.c */
/* Start: bn_mp_cmp_mag.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* compare maginitude of two ints (unsigned) */
int
mp_cmp_mag (mp_int * a, mp_int * b)
{
int n;
/* compare based on # of non-zero digits */
if (a->used > b->used) {
return MP_GT;
} else if (a->used < b->used) {
return MP_LT;
}
/* compare based on digits */
for (n = a->used - 1; n >= 0; n--) {
if (a->dp[n] > b->dp[n]) {
return MP_GT;
} else if (a->dp[n] < b->dp[n]) {
return MP_LT;
}
}
return MP_EQ;
}
/* End: bn_mp_cmp_mag.c */
/* Start: bn_mp_copy.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* copy, b = a */
int
mp_copy (mp_int * a, mp_int * b)
{
int res, n;
/* if dst == src do nothing */
if (a == b || a->dp == b->dp) {
return MP_OKAY;
}
/* grow dest */
if ((res = mp_grow (b, a->used)) != MP_OKAY) {
return res;
}
/* zero b and copy the parameters over */
b->used = a->used;
b->sign = a->sign;
{
register mp_digit *tmpa, *tmpb;
tmpa = a->dp;
tmpb = b->dp;
/* copy all the digits */
for (n = 0; n < a->used; n++) {
*tmpb++ = *tmpa++;
}
/* clear high digits */
for (; n < b->alloc; n++) {
*tmpb++ = 0;
}
}
return MP_OKAY;
}
/* End: bn_mp_copy.c */
/* Start: bn_mp_count_bits.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* returns the number of bits in an int */
int
mp_count_bits (mp_int * a)
{
int r;
mp_digit q;
if (a->used == 0) {
return 0;
}
r = (a->used - 1) * DIGIT_BIT;
q = a->dp[a->used - 1];
while (q > ((mp_digit) 0)) {
++r;
q >>= ((mp_digit) 1);
}
return r;
}
/* End: bn_mp_count_bits.c */
/* Start: bn_mp_div.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* 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 __Q;
}
if ((res = mp_init (&t2)) != MP_OKAY) {
goto __T1;
}
if ((res = mp_init_copy (&x, a)) != MP_OKAY) {
goto __T2;
}
if ((res = mp_init_copy (&y, b)) != MP_OKAY) {
goto __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 = 0;
while ((y.dp[y.used - 1] & (((mp_digit) 1) << (DIGIT_BIT - 1))) ==
((mp_digit) 0)) {
++norm;
if ((res = mp_mul_2 (&x, &x)) != MP_OKAY) {
goto __Y;
}
if ((res = mp_mul_2 (&y, &y)) != MP_OKAY) {
goto __Y;
}
}
/* 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;
/* step 2. 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 __Y;
}
while (mp_cmp (&x, &y) != MP_LT) {
++(q.dp[n - t]);
if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) {
goto __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.alloc)
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] = ((1UL << DIGIT_BIT) - 1UL);
} 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));
}
/* step 3.2 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 __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 (&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 __Y;
}
if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
goto __Y;
}
if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) {
goto __Y;
}
/* step 3.4 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 __Y;
}
if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
goto __Y;
}
if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) {
goto __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 = 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_clamp (&x);
mp_exch (&x, d);
}
res = MP_OKAY;
__Y:mp_clear (&y);
__X:mp_clear (&x);
__T2:mp_clear (&t2);
__T1:mp_clear (&t1);
__Q:mp_clear (&q);
return res;
}
/* End: bn_mp_div.c */
/* Start: bn_mp_div_2.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* 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;
tmpa = a->dp + b->used - 1;
tmpb = b->dp + b->used - 1;
r = 0;
for (x = b->used - 1; x >= 0; x--) {
rr = *tmpa & 1;
*tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1));
r = rr;
}
tmpb = b->dp + b->used;
for (x = b->used; x < oldused; x++) {
*tmpb++ = 0;
}
}
mp_clamp (b);
return MP_OKAY;
}
/* End: bn_mp_div_2.c */
/* Start: bn_mp_div_2d.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* shift right by a certain bit count (store quotient in c, 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 */
mp_rshd (c, b / DIGIT_BIT);
/* shift any bit count < DIGIT_BIT */
D = (mp_digit) (b % DIGIT_BIT);
if (D != 0) {
r = 0;
for (x = c->used - 1; x >= 0; x--) {
/* get the lower bits of this word in a temp */
rr = c->dp[x] & ((mp_digit) ((1U << D) - 1U));
/* shift the current word and mix in the carry bits from the previous word */
c->dp[x] = (c->dp[x] >> D) | (r << (DIGIT_BIT - D));
/* set the carry to the carry bits of the current word found above */
r = rr;
}
}
mp_clamp (c);
res = MP_OKAY;
if (d != NULL) {
mp_exch (&t, d);
}
mp_clear (&t);
return MP_OKAY;
}
/* End: bn_mp_div_2d.c */
/* Start: bn_mp_div_d.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* single digit division */
int
mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
{
mp_int t, t2;
int res;
if ((res = mp_init (&t)) != MP_OKAY) {
return res;
}
if ((res = mp_init (&t2)) != MP_OKAY) {
mp_clear (&t);
return res;
}
mp_set (&t, b);
res = mp_div (a, &t, c, &t2);
if (d != NULL) {
*d = t2.dp[0];
}
mp_clear (&t);
mp_clear (&t2);
return res;
}
/* End: bn_mp_div_d.c */
/* Start: bn_mp_exch.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
void
mp_exch (mp_int * a, mp_int * b)
{
mp_int t;
t = *a;
*a = *b;
*b = t;
}
/* End: bn_mp_exch.c */
/* Start: bn_mp_exptmod.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
int
mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
{
mp_int M[256], res, mu;
mp_digit buf;
int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
/* if the modulus is odd use the fast method */
if (mp_isodd (P) == 1 && P->used > 4 && P->used < MONTGOMERY_EXPT_CUTOFF) {
err = mp_exptmod_fast (G, X, P, Y);
return err;
}
/* 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;
}
/* init G array */
for (x = 0; x < (1 << winsize); x++) {
if ((err = mp_init_size (&M[x], 1)) != MP_OKAY) {
for (y = 0; y < x; y++) {
mp_clear (&M[y]);
}
return err;
}
}
/* create mu, used for Barrett reduction */
if ((err = mp_init (&mu)) != MP_OKAY) {
goto __M;
}
if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) {
goto __MU;
}
/* 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 ((err = mp_mod (G, P, &M[1])) != MP_OKAY) {
goto __MU;
}
/* 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 __MU;
}
for (x = 0; x < (winsize - 1); x++) {
if ((err =
mp_sqr (&M[1 << (winsize - 1)],
&M[1 << (winsize - 1)])) != MP_OKAY) {
goto __MU;
}
if ((err = mp_reduce (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) {
goto __MU;
}
}
/* 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 __MU;
}
if ((err = mp_reduce (&M[x], P, &mu)) != MP_OKAY) {
goto __MU;
}
}
/* setup result */
if ((err = mp_init (&res)) != MP_OKAY) {
goto __MU;
}
mp_set (&res, 1);
/* set initial mode and bit cnt */
mode = 0;
bitcnt = 0;
buf = 0;
digidx = X->used - 1;
bitcpy = bitbuf = 0;
bitcnt = 1;
for (;;) {
/* grab next digit as required */
if (--bitcnt == 0) {
if (digidx == -1) {
break;
}
buf = X->dp[digidx--];
bitcnt = (int) DIGIT_BIT;
}
/* grab the next msb from the exponent */
y = (buf >> (DIGIT_BIT - 1)) & 1;
buf <<= 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 __RES;
}
if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) {
goto __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 multiply */
/* square first */
for (x = 0; x < winsize; x++) {
if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
goto __RES;
}
if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) {
goto __RES;
}
}
/* then multiply */
if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
goto __MU;
}
if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) {
goto __MU;
}
/* empty window and reset */
bitcpy = 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 __RES;
}
if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) {
goto __RES;
}
bitbuf <<= 1;
if ((bitbuf & (1 << winsize)) != 0) {
/* then multiply */
if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
goto __RES;
}
if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) {
goto __RES;
}
}
}
}
mp_exch (&res, Y);
err = MP_OKAY;
__RES:mp_clear (&res);
__MU:mp_clear (&mu);
__M:
for (x = 0; x < (1 << winsize); x++) {
mp_clear (&M[x]);
}
return err;
}
/* End: bn_mp_exptmod.c */
/* Start: bn_mp_exptmod_fast.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* 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 reduction
*/
int
mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
{
mp_int M[256], res;
mp_digit buf, mp;
int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
/* 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;
}
/* init G array */
for (x = 0; x < (1 << winsize); x++) {
if ((err = mp_init (&M[x])) != MP_OKAY) {
for (y = 0; y < x; y++) {
mp_clear (&M[y]);
}
return err;
}
}
/* now setup montgomery */
if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) {
goto __M;
}
/* setup result */
if ((err = mp_init (&res)) != MP_OKAY) {
goto __RES;
}
/* now we need R mod m */
if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
goto __RES;
}
/* 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 ((err = mp_mod (G, P, &M[1])) != MP_OKAY) {
goto __RES;
}
/* now set M[1] to G * R mod m */
if ((err = mp_mulmod (&M[1], &res, P, &M[1])) != MP_OKAY) {
goto __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 __RES;
}
for (x = 0; x < (winsize - 1); x++) {
if ((err =
mp_sqr (&M[1 << (winsize - 1)],
&M[1 << (winsize - 1)])) != MP_OKAY) {
goto __RES;
}
if ((err =
mp_montgomery_reduce (&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) {
goto __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 __RES;
}
if ((err = mp_montgomery_reduce (&M[x], P, mp)) != MP_OKAY) {
goto __RES;
}
}
/* set initial mode and bit cnt */
mode = 0;
bitcnt = 0;
buf = 0;
digidx = X->used - 1;
bitcpy = bitbuf = 0;
bitcnt = 1;
for (;;) {
/* grab next digit as required */
if (--bitcnt == 0) {
if (digidx == -1) {
break;
}
buf = X->dp[digidx--];
bitcnt = (int) DIGIT_BIT;
}
/* grab the next msb from the exponent */
y = (buf >> (DIGIT_BIT - 1)) & 1;
buf <<= 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 __RES;
}
if ((err = mp_montgomery_reduce (&res, P, mp)) != MP_OKAY) {
goto __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 multiply */
/* square first */
for (x = 0; x < winsize; x++) {
if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
goto __RES;
}
if ((err = mp_montgomery_reduce (&res, P, mp)) != MP_OKAY) {
goto __RES;
}
}
/* then multiply */
if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
goto __RES;
}
if ((err = mp_montgomery_reduce (&res, P, mp)) != MP_OKAY) {
goto __RES;
}
/* empty window and reset */
bitcpy = 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 __RES;
}
if ((err = mp_montgomery_reduce (&res, P, mp)) != MP_OKAY) {
goto __RES;
}
bitbuf <<= 1;
if ((bitbuf & (1 << winsize)) != 0) {
/* then multiply */
if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
goto __RES;
}
if ((err = mp_montgomery_reduce (&res, P, mp)) != MP_OKAY) {
goto __RES;
}
}
}
}
/* fixup result */
if ((err = mp_montgomery_reduce (&res, P, mp)) != MP_OKAY) {
goto __RES;
}
mp_exch (&res, Y);
err = MP_OKAY;
__RES:mp_clear (&res);
__M:
for (x = 0; x < (1 << winsize); x++) {
mp_clear (&M[x]);
}
return err;
}
/* End: bn_mp_exptmod_fast.c */
/* Start: bn_mp_expt_d.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
int
mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
{
int res, x;
mp_int g;
if ((res = mp_init_copy (&g, a)) != MP_OKAY) {
return res;
}
/* set initial result */
mp_set (c, 1);
for (x = 0; x < (int) DIGIT_BIT; x++) {
if ((res = mp_sqr (c, c)) != MP_OKAY) {
mp_clear (&g);
return res;
}
if ((b & (mp_digit) (1 << (DIGIT_BIT - 1))) != 0) {
if ((res = mp_mul (c, &g, c)) != MP_OKAY) {
mp_clear (&g);
return res;
}
}
b <<= 1;
}
mp_clear (&g);
return MP_OKAY;
}
/* End: bn_mp_expt_d.c */
/* Start: bn_mp_gcd.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* Greatest Common Divisor using the binary method [Algorithm B, page 338, vol2 of TAOCP]
*/
int
mp_gcd (mp_int * a, mp_int * b, mp_int * c)
{
mp_int u, v, t;
int k, res, neg;
/* either zero than gcd is the largest */
if (mp_iszero (a) == 1 && mp_iszero (b) == 0) {
return mp_copy (b, c);
}
if (mp_iszero (a) == 0 && mp_iszero (b) == 1) {
return mp_copy (a, c);
}
if (mp_iszero (a) == 1 && mp_iszero (b) == 1) {
mp_set (c, 1);
return MP_OKAY;
}
/* if both are negative they share (-1) as a common divisor */
neg = (a->sign == b->sign) ? a->sign : MP_ZPOS;
if ((res = mp_init_copy (&u, a)) != MP_OKAY) {
return res;
}
if ((res = mp_init_copy (&v, b)) != MP_OKAY) {
goto __U;
}
/* must be positive for the remainder of the algorithm */
u.sign = v.sign = MP_ZPOS;
if ((res = mp_init (&t)) != MP_OKAY) {
goto __V;
}
/* B1. Find power of two */
k = 0;
while ((u.dp[0] & 1) == 0 && (v.dp[0] & 1) == 0) {
++k;
if ((res = mp_div_2d (&u, 1, &u, NULL)) != MP_OKAY) {
goto __T;
}
if ((res = mp_div_2d (&v, 1, &v, NULL)) != MP_OKAY) {
goto __T;
}
}
/* B2. Initialize */
if ((u.dp[0] & 1) == 1) {
if ((res = mp_copy (&v, &t)) != MP_OKAY) {
goto __T;
}
t.sign = MP_NEG;
} else {
if ((res = mp_copy (&u, &t)) != MP_OKAY) {
goto __T;
}
}
do {
/* B3 (and B4). Halve t, if even */
while (t.used != 0 && (t.dp[0] & 1) == 0) {
if ((res = mp_div_2d (&t, 1, &t, NULL)) != MP_OKAY) {
goto __T;
}
}
/* B5. if t>0 then u=t otherwise v=-t */
if (t.used != 0 && t.sign != MP_NEG) {
if ((res = mp_copy (&t, &u)) != MP_OKAY) {
goto __T;
}
} else {
if ((res = mp_copy (&t, &v)) != MP_OKAY) {
goto __T;
}
v.sign = (v.sign == MP_ZPOS) ? MP_NEG : MP_ZPOS;
}
/* B6. t = u - v, if t != 0 loop otherwise terminate */
if ((res = mp_sub (&u, &v, &t)) != MP_OKAY) {
goto __T;
}
}
while (t.used != 0);
if ((res = mp_mul_2d (&u, k, &u)) != MP_OKAY) {
goto __T;
}
mp_exch (&u, c);
c->sign = neg;
res = MP_OKAY;
__T:mp_clear (&t);
__V:mp_clear (&u);
__U:mp_clear (&v);
return res;
}
/* End: bn_mp_gcd.c */
/* Start: bn_mp_grow.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* grow as required */
int
mp_grow (mp_int * a, int size)
{
int i, n;
/* if the alloc size is smaller alloc more ram */
if (a->alloc < size) {
size += (MP_PREC * 2) - (size & (MP_PREC - 1)); /* ensure there are always at least MP_PREC digits extra on top */
a->dp = realloc (a->dp, sizeof (mp_digit) * size);
if (a->dp == NULL) {
return MP_MEM;
}
n = a->alloc;
a->alloc = size;
for (i = n; i < a->alloc; i++) {
a->dp[i] = 0;
}
}
return MP_OKAY;
}
/* End: bn_mp_grow.c */
/* Start: bn_mp_init.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* init a new bigint */
int
mp_init (mp_int * a)
{
/* allocate ram required and clear it */
a->dp = calloc (sizeof (mp_digit), MP_PREC);
if (a->dp == NULL) {
return MP_MEM;
}
/* set the used to zero, allocated digit to the default precision
* and sign to positive */
a->used = 0;
a->alloc = MP_PREC;
a->sign = MP_ZPOS;
return MP_OKAY;
}
/* End: bn_mp_init.c */
/* Start: bn_mp_init_copy.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* 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;
}
res = mp_copy (b, a);
return res;
}
/* End: bn_mp_init_copy.c */
/* Start: bn_mp_init_size.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* init a mp_init and grow it to a given size */
int
mp_init_size (mp_int * a, int size)
{
/* pad up so there are at least 16 zero digits */
size += (MP_PREC * 2) - (size & (MP_PREC - 1)); /* ensure there are always at least 16 digits extra on top */
a->dp = calloc (sizeof (mp_digit), size);
if (a->dp == NULL) {
return MP_MEM;
}
a->used = 0;
a->alloc = size;
a->sign = MP_ZPOS;
return MP_OKAY;
}
/* End: bn_mp_init_size.c */
/* Start: bn_mp_invmod.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
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) {
return MP_VAL;
}
/* if the modulus is odd we can use a faster routine instead */
if (mp_iseven (b) == 0) {
return fast_mp_invmod (a, b, c);
}
if ((res = mp_init (&x)) != MP_OKAY) {
goto __ERR;
}
if ((res = mp_init (&y)) != MP_OKAY) {
goto __X;
}
if ((res = mp_init (&u)) != MP_OKAY) {
goto __Y;
}
if ((res = mp_init (&v)) != MP_OKAY) {
goto __U;
}
if ((res = mp_init (&A)) != MP_OKAY) {
goto __V;
}
if ((res = mp_init (&B)) != MP_OKAY) {
goto __A;
}
if ((res = mp_init (&C)) != MP_OKAY) {
goto __B;
}
if ((res = mp_init (&D)) != MP_OKAY) {
goto __C;
}
/* x = a, y = b */
if ((res = mp_copy (a, &x)) != MP_OKAY) {
goto __D;
}
if ((res = mp_copy (b, &y)) != MP_OKAY) {
goto __D;
}
if ((res = mp_abs (&x, &x)) != MP_OKAY) {
goto __D;
}
/* 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 __D;
}
/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
if ((res = mp_copy (&x, &u)) != MP_OKAY) {
goto __D;
}
if ((res = mp_copy (&y, &v)) != MP_OKAY) {
goto __D;
}
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 __D;
}
/* 4.2 if A or B is odd then */
if (mp_iseven (&A) == 0 || mp_iseven (&B) == 0) {
/* A = (A+y)/2, B = (B-x)/2 */
if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
goto __D;
}
if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
goto __D;
}
}
/* A = A/2, B = B/2 */
if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
goto __D;
}
if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
goto __D;
}
}
/* 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 __D;
}
/* 5.2 if C,D are even then */
if (mp_iseven (&C) == 0 || mp_iseven (&D) == 0) {
/* C = (C+y)/2, D = (D-x)/2 */
if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
goto __D;
}
if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
goto __D;
}
}
/* C = C/2, D = D/2 */
if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
goto __D;
}
if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
goto __D;
}
}
/* 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 __D;
}
if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
goto __D;
}
if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
goto __D;
}
} else {
/* v - v - u, C = C - A, D = D - B */
if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
goto __D;
}
if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
goto __D;
}
if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
goto __D;
}
}
/* 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 __D;
}
/* a is now the inverse */
mp_exch (&C, c);
res = MP_OKAY;
__D:mp_clear (&D);
__C:mp_clear (&C);
__B:mp_clear (&B);
__A:mp_clear (&A);
__V:mp_clear (&v);
__U:mp_clear (&u);
__Y:mp_clear (&y);
__X:mp_clear (&x);
__ERR:
return res;
}
/* End: bn_mp_invmod.c */
/* Start: bn_mp_jacobi.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* computes the jacobi c = (a | n) (or Legendre if b is prime)
* HAC pp. 73 Algorithm 2.149
*/
int
mp_jacobi (mp_int * a, mp_int * n, int *c)
{
mp_int a1, n1, e;
int s, r, res;
mp_digit residue;
/* 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^e */
if ((res = mp_init_copy (&a1, a)) != MP_OKAY) {
return res;
}
if ((res = mp_init (&n1)) != MP_OKAY) {
goto __A1;
}
if ((res = mp_init (&e)) != MP_OKAY) {
goto __N1;
}
while (mp_iseven (&a1) == 1) {
if ((res = mp_add_d (&e, 1, &e)) != MP_OKAY) {
goto __E;
}
if ((res = mp_div_2 (&a1, &a1)) != MP_OKAY) {
goto __E;
}
}
/* step 4. if e is even set s=1 */
if (mp_iseven (&e) == 1) {
s = 1;
} else {
/* else set s=1 if n = 1/7 (mod 8) or s=-1 if n = 3/5 (mod 8) */
if ((res = mp_mod_d (n, 8, &residue)) != MP_OKAY) {
goto __E;
}
if (residue == 1 || residue == 7) {
s = 1;
} else if (residue == 3 || residue == 5) {
s = -1;
}
}
/* step 5. if n == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */
if ((res = mp_mod_d (n, 4, &residue)) != MP_OKAY) {
goto __E;
}
if (residue == 3) {
if ((res = mp_mod_d (&a1, 4, &residue)) != MP_OKAY) {
goto __E;
}
if (residue == 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 (n, &a1, &n1)) != MP_OKAY) {
goto __E;
}
if ((res = mp_jacobi (&n1, &a1, &r)) != MP_OKAY) {
goto __E;
}
*c = s * r;
}
/* done */
res = MP_OKAY;
__E:mp_clear (&e);
__N1:mp_clear (&n1);
__A1:mp_clear (&a1);
return res;
}
/* End: bn_mp_jacobi.c */
/* Start: bn_mp_karatsuba_mul.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* 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 - b1)(a0 - 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, t2, x0y0, x1y1;
int B, err, x;
err = MP_MEM;
/* min # of digits */
B = MIN (a->used, b->used);
/* now divide in two */
B = B / 2;
/* 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 (&t1) != MP_OKAY)
goto Y1;
if (mp_init (&t2) != MP_OKAY)
goto T1;
if (mp_init (&x0y0) != MP_OKAY)
goto T2;
if (mp_init (&x1y1) != MP_OKAY)
goto X0Y0;
/* now shift the digits */
x0.sign = x1.sign = a->sign;
y0.sign = y1.sign = b->sign;
x0.used = y0.used = B;
x1.used = a->used - B;
y1.used = b->used - B;
/* we copy the digits directly instead of using higher level functions
* since we also need to shift the digits
*/
for (x = 0; x < B; x++) {
x0.dp[x] = a->dp[x];
y0.dp[x] = b->dp[x];
}
for (x = B; x < a->used; x++) {
x1.dp[x - B] = a->dp[x];
}
for (x = B; x < b->used; x++) {
y1.dp[x - B] = b->dp[x];
}
/* 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 */
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 (mp_sub (&x1, &x0, &t1) != MP_OKAY)
goto X1Y1; /* t1 = x1 - x0 */
if (mp_sub (&y1, &y0, &t2) != MP_OKAY)
goto X1Y1; /* t2 = y1 - y0 */
if (mp_mul (&t1, &t2, &t1) != MP_OKAY)
goto X1Y1; /* t1 = (x1 - x0) * (y1 - y0) */
/* add x0y0 */
if (mp_add (&x0y0, &x1y1, &t2) != MP_OKAY)
goto X1Y1; /* t2 = x0y0 + x1y1 */
if (mp_sub (&t2, &t1, &t1) != MP_OKAY)
goto X1Y1; /* t1 = x0y0 + x1y1 - (x1-x0)*(y1-y0) */
/* 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 */
err = MP_OKAY;
X1Y1:mp_clear (&x1y1);
X0Y0:mp_clear (&x0y0);
T2:mp_clear (&t2);
T1:mp_clear (&t1);
Y1:mp_clear (&y1);
Y0:mp_clear (&y0);
X1:mp_clear (&x1);
X0:mp_clear (&x0);
ERR:
return err;
}
/* End: bn_mp_karatsuba_mul.c */
/* Start: bn_mp_karatsuba_sqr.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* Karatsuba squaring, computes b = a*a using three half size squarings
*
* See comments of mp_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, x;
err = MP_MEM;
/* min # of digits */
B = a->used;
/* now divide in two */
B = B / 2;
/* 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 (&t1) != MP_OKAY)
goto X1;
if (mp_init (&t2) != MP_OKAY)
goto T1;
if (mp_init (&x0x0) != MP_OKAY)
goto T2;
if (mp_init (&x1x1) != MP_OKAY)
goto X0X0;
/* now shift the digits */
for (x = 0; x < B; x++) {
x0.dp[x] = a->dp[x];
}
for (x = B; x < a->used; x++) {
x1.dp[x - B] = a->dp[x];
}
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 and y1-y0 */
if (mp_sub (&x1, &x0, &t1) != MP_OKAY)
goto X1X1; /* t1 = x1 - x0 */
if (mp_sqr (&t1, &t1) != MP_OKAY)
goto X1X1; /* t1 = (x1 - x0) * (y1 - y0) */
/* add x0y0 */
if (mp_add (&x0x0, &x1x1, &t2) != MP_OKAY)
goto X1X1; /* t2 = x0y0 + x1y1 */
if (mp_sub (&t2, &t1, &t1) != MP_OKAY)
goto X1X1; /* t1 = x0y0 + x1y1 - (x1-x0)*(y1-y0) */
/* shift by B */
if (mp_lshd (&t1, B) != MP_OKAY)
goto X1X1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */
if (mp_lshd (&x1x1, B * 2) != MP_OKAY)
goto X1X1; /* x1y1 = x1y1 << 2*B */
if (mp_add (&x0x0, &t1, &t1) != MP_OKAY)
goto X1X1; /* t1 = x0y0 + t1 */
if (mp_add (&t1, &x1x1, b) != MP_OKAY)
goto X1X1; /* t1 = x0y0 + t1 + x1y1 */
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;
}
/* End: bn_mp_karatsuba_sqr.c */
/* Start: bn_mp_lcm.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* 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 t;
if ((res = mp_init (&t)) != MP_OKAY) {
return res;
}
if ((res = mp_mul (a, b, &t)) != MP_OKAY) {
mp_clear (&t);
return res;
}
if ((res = mp_gcd (a, b, c)) != MP_OKAY) {
mp_clear (&t);
return res;
}
res = mp_div (&t, c, c, NULL);
mp_clear (&t);
return res;
}
/* End: bn_mp_lcm.c */
/* Start: bn_mp_lshd.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* 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 ((res = mp_grow (a, a->used + b)) != MP_OKAY) {
return res;
}
/* increment the used by the shift amount than copy upwards */
a->used += b;
for (x = a->used - 1; x >= b; x--) {
a->dp[x] = a->dp[x - b];
}
/* zero the lower digits */
for (x = 0; x < b; x++) {
a->dp[x] = 0;
}
mp_clamp (a);
return MP_OKAY;
}
/* End: bn_mp_lshd.c */
/* Start: bn_mp_mod.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* c = a mod b, 0 <= c < b */
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 (t.sign == MP_NEG) {
res = mp_add (b, &t, c);
} else {
res = MP_OKAY;
mp_exch (&t, c);
}
mp_clear (&t);
return res;
}
/* End: bn_mp_mod.c */
/* Start: bn_mp_mod_2d.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* 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;
}
/* End: bn_mp_mod_2d.c */
/* Start: bn_mp_mod_d.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
int
mp_mod_d (mp_int * a, mp_digit b, mp_digit * c)
{
mp_int t, t2;
int res;
if ((res = mp_init (&t)) != MP_OKAY) {
return res;
}
if ((res = mp_init (&t2)) != MP_OKAY) {
mp_clear (&t);
return res;
}
mp_set (&t, b);
mp_div (a, &t, NULL, &t2);
if (t2.sign == MP_NEG) {
if ((res = mp_add_d (&t2, b, &t2)) != MP_OKAY) {
mp_clear (&t);
mp_clear (&t2);
return res;
}
}
*c = t2.dp[0];
mp_clear (&t);
mp_clear (&t2);
return MP_OKAY;
}
/* End: bn_mp_mod_d.c */
/* Start: bn_mp_montgomery_calc_normalization.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#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 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;
}
/* now compute C = A * B mod b */
for (x = bits - 1; x < 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;
}
/* End: bn_mp_montgomery_calc_normalization.c */
/* Start: bn_mp_montgomery_reduce.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* computes xR^-1 == x (mod N) via Montgomery Reduction */
int
mp_montgomery_reduce (mp_int * a, mp_int * m, mp_digit mp)
{
int ix, res, digs;
mp_digit ui;
digs = m->used * 2 + 1;
if ((digs < 512)
&& digs < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
return fast_mp_montgomery_reduce (a, m, mp);
}
if (a->alloc < m->used * 2 + 1) {
if ((res = mp_grow (a, m->used * 2 + 1)) != MP_OKAY) {
return res;
}
}
a->used = m->used * 2 + 1;
for (ix = 0; ix < m->used; ix++) {
/* ui = ai * m' mod b */
ui = (a->dp[ix] * mp) & MP_MASK;
/* a = a + ui * m * b^i */
{
register int iy;
register mp_digit *tmpx, *tmpy, mu;
register mp_word r;
/* aliases */
tmpx = m->dp;
tmpy = a->dp + ix;
mu = 0;
for (iy = 0; iy < m->used; iy++) {
r =
((mp_word) ui) * ((mp_word) * tmpx++) + ((mp_word) mu) +
((mp_word) * tmpy);
mu = (r >> ((mp_word) DIGIT_BIT));
*tmpy++ = (r & ((mp_word) MP_MASK));
}
/* propagate carries */
while (mu) {
*tmpy += mu;
mu = (*tmpy >> DIGIT_BIT) & 1;
*tmpy++ &= MP_MASK;
}
}
}
/* A = A/b^n */
mp_rshd (a, m->used);
/* if A >= m then A = A - m */
if (mp_cmp_mag (a, m) != MP_LT) {
return s_mp_sub (a, m, a);
}
return MP_OKAY;
}
/* End: bn_mp_montgomery_reduce.c */
/* Start: bn_mp_montgomery_setup.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* setups the montgomery reduction stuff */
int
mp_montgomery_setup (mp_int * a, mp_digit * mp)
{
mp_int t, tt;
int res;
if ((res = mp_init (&t)) != MP_OKAY) {
return res;
}
if ((res = mp_init (&tt)) != MP_OKAY) {
goto __T;
}
/* tt = b */
tt.dp[0] = 0;
tt.dp[1] = 1;
tt.used = 2;
/* t = m mod b */
t.dp[0] = a->dp[0];
t.used = 1;
/* t = 1/m mod b */
if ((res = mp_invmod (&t, &tt, &t)) != MP_OKAY) {
goto __TT;
}
/* t = -1/m mod b */
*mp = ((mp_digit) 1 << ((mp_digit) DIGIT_BIT)) - t.dp[0];
res = MP_OKAY;
__TT:mp_clear (&tt);
__T:mp_clear (&t);
return res;
}
/* End: bn_mp_montgomery_setup.c */
/* Start: bn_mp_mul.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* 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;
if (MIN (a->used, b->used) > KARATSUBA_MUL_CUTOFF) {
res = mp_karatsuba_mul (a, b, c);
} else {
res = s_mp_mul (a, b, c);
}
c->sign = neg;
return res;
}
/* End: bn_mp_mul.c */
/* Start: bn_mp_mulmod.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* 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;
}
/* End: bn_mp_mulmod.c */
/* Start: bn_mp_mul_2.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* b = a*2 */
int
mp_mul_2 (mp_int * a, mp_int * b)
{
int x, res, oldused;
/* Optimization: should copy and shift at the same time */
if (b->alloc < a->used) {
if ((res = mp_grow (b, a->used)) != MP_OKAY) {
return res;
}
}
oldused = b->used;
b->used = a->used;
/* shift any bit count < DIGIT_BIT */
{
register mp_digit r, rr, *tmpa, *tmpb;
r = 0;
tmpa = a->dp;
tmpb = b->dp;
for (x = 0; x < b->used; x++) {
rr = *tmpa >> (DIGIT_BIT - 1);
*tmpb++ = ((*tmpa++ << 1) | r) & MP_MASK;
r = rr;
}
/* new leading digit? */
if (r != 0) {
if (b->alloc == b->used) {
if ((res = mp_grow (b, b->used + 1)) != MP_OKAY) {
return res;
}
}
/* add a MSB of 1 */
*tmpb = 1;
++b->used;
}
tmpb = b->dp + b->used;
for (x = b->used; x < oldused; x++) {
*tmpb++ = 0;
}
}
return MP_OKAY;
}
/* End: bn_mp_mul_2.c */
/* Start: bn_mp_mul_2d.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* shift left by a certain bit count */
int
mp_mul_2d (mp_int * a, int b, mp_int * c)
{
mp_digit d, r, rr;
int x, res;
/* copy */
if ((res = mp_copy (a, c)) != MP_OKAY) {
return res;
}
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 ((res = mp_lshd (c, b / DIGIT_BIT)) != MP_OKAY) {
return res;
}
c->used = c->alloc;
/* shift any bit count < DIGIT_BIT */
d = (mp_digit) (b % DIGIT_BIT);
if (d != 0) {
r = 0;
for (x = 0; x < c->used; x++) {
/* get the higher bits of the current word */
rr = (c->dp[x] >> (DIGIT_BIT - d)) & ((mp_digit) ((1U << d) - 1U));
/* shift the current word and OR in the carry */
c->dp[x] = ((c->dp[x] << d) | r) & MP_MASK;
/* set the carry to the carry bits of the current word */
r = rr;
}
}
mp_clamp (c);
return MP_OKAY;
}
/* End: bn_mp_mul_2d.c */
/* Start: bn_mp_mul_d.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* multiply by a digit */
int
mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
{
int res, pa, olduse;
pa = a->used;
if (c->alloc < pa + 1) {
if ((res = mp_grow (c, pa + 1)) != MP_OKAY) {
return res;
}
}
olduse = c->used;
c->used = pa + 1;
{
register mp_digit u, *tmpa, *tmpc;
register mp_word r;
register int ix;
tmpc = c->dp + c->used;
for (ix = c->used; ix < olduse; ix++) {
*tmpc++ = 0;
}
tmpa = a->dp;
tmpc = c->dp;
u = 0;
for (ix = 0; ix < pa; ix++) {
r = ((mp_word) u) + ((mp_word) * tmpa++) * ((mp_word) b);
*tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK));
u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
}
*tmpc = u;
}
mp_clamp (c);
return MP_OKAY;
}
/* End: bn_mp_mul_d.c */
/* Start: bn_mp_neg.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* b = -a */
int
mp_neg (mp_int * a, mp_int * b)
{
int res;
if ((res = mp_copy (a, b)) != MP_OKAY) {
return res;
}
b->sign = (a->sign == MP_ZPOS) ? MP_NEG : MP_ZPOS;
return MP_OKAY;
}
/* End: bn_mp_neg.c */
/* Start: bn_mp_n_root.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* 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 at most].
*/
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 __T1;
}
if ((res = mp_init (&t3)) != MP_OKAY) {
goto __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 __T3;
}
/* t2 = t1 - ((t1^b - a) / (b * t1^(b-1))) */
if ((res = mp_expt_d (&t1, b - 1, &t3)) != MP_OKAY) { /* t3 = t1^(b-1) */
goto __T3;
}
/* numerator */
if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) { /* t2 = t1^b */
goto __T3;
}
if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) { /* t2 = t1^b - a */
goto __T3;
}
if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) { /* t3 = t1^(b-1) * b */
goto __T3;
}
if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) { /* t3 = (t1^b - a)/(b * t1^(b-1)) */
goto __T3;
}
if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) {
goto __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 __T3;
}
if (mp_cmp (&t2, a) == MP_GT) {
if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) {
goto __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;
__T3:mp_clear (&t3);
__T2:mp_clear (&t2);
__T1:mp_clear (&t1);
return res;
}
/* End: bn_mp_n_root.c */
/* Start: bn_mp_or.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* 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;
}
/* End: bn_mp_or.c */
/* Start: bn_mp_rand.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* 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 ()));
} 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;
}
/* End: bn_mp_rand.c */
/* Start: bn_mp_read_signed_bin.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* read signed bin, big endian, first byte is 0==positive or 1==negative */
int
mp_read_signed_bin (mp_int * a, unsigned char *b, int c)
{
int res;
if ((res = mp_read_unsigned_bin (a, b + 1, c - 1)) != MP_OKAY) {
return res;
}
a->sign = ((b[0] == (unsigned char) 0) ? MP_ZPOS : MP_NEG);
return MP_OKAY;
}
/* End: bn_mp_read_signed_bin.c */
/* Start: bn_mp_read_unsigned_bin.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* reads a unsigned char array, assumes the msb is stored first [big endian] */
int
mp_read_unsigned_bin (mp_int * a, unsigned char *b, int c)
{
int res;
mp_zero (a);
while (c-- > 0) {
if ((res = mp_mul_2d (a, 8, a)) != MP_OKAY) {
return res;
}
if (DIGIT_BIT != 7) {
a->dp[0] |= *b++;
a->used += 1;
} else {
a->dp[0] = (*b & MP_MASK);
a->dp[1] |= ((*b++ >> 7U) & 1);
a->used += 2;
}
}
mp_clamp (a);
return MP_OKAY;
}
/* End: bn_mp_read_unsigned_bin.c */
/* Start: bn_mp_reduce.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#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 res;
if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) {
return res;
}
res = mp_div (a, b, a, NULL);
return res;
}
/* 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;
if ((res = mp_init_copy (&q, x)) != MP_OKAY) {
return res;
}
mp_rshd (&q, um - 1); /* q1 = x / b^(k-1) */
/* according to HAC this is optimization is ok */
if (((unsigned long) m->used) > (1UL << (unsigned long) (DIGIT_BIT - 1UL))) {
if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) {
goto CLEANUP;
}
} else {
if ((res = s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) {
goto CLEANUP;
}
}
mp_rshd (&q, um + 1); /* q3 = q2 / b^(k+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)
break;
}
CLEANUP:
mp_clear (&q);
return res;
}
/* End: bn_mp_reduce.c */
/* Start: bn_mp_rshd.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* 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;
}
/* shift the digits down */
for (x = 0; x < (a->used - b); x++) {
a->dp[x] = a->dp[x + b];
}
/* zero the top digits */
for (; x < a->used; x++) {
a->dp[x] = 0;
}
mp_clamp (a);
}
/* End: bn_mp_rshd.c */
/* Start: bn_mp_set.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* 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;
}
/* End: bn_mp_set.c */
/* Start: bn_mp_set_int.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* 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, simplest solution to the what if DIGIT_BIT==7 case */
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 += 32 / DIGIT_BIT + 1;
}
mp_clamp (a);
return MP_OKAY;
}
/* End: bn_mp_set_int.c */
/* Start: bn_mp_shrink.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* shrink a bignum */
int
mp_shrink (mp_int * a)
{
if (a->alloc != a->used) {
if ((a->dp = realloc (a->dp, sizeof (mp_digit) * a->used)) == NULL) {
return MP_MEM;
}
a->alloc = a->used;
}
return MP_OKAY;
}
/* End: bn_mp_shrink.c */
/* Start: bn_mp_signed_bin_size.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#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);
}
/* End: bn_mp_signed_bin_size.c */
/* Start: bn_mp_sqr.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* computes b = a*a */
int
mp_sqr (mp_int * a, mp_int * b)
{
int res;
if (a->used > KARATSUBA_SQR_CUTOFF) {
res = mp_karatsuba_sqr (a, b);
} else {
res = s_mp_sqr (a, b);
}
b->sign = MP_ZPOS;
return res;
}
/* End: bn_mp_sqr.c */
/* Start: bn_mp_sqrmod.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* 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;
}
/* End: bn_mp_sqrmod.c */
/* Start: bn_mp_sub.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* 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;
/* handle four cases */
if (sa == MP_ZPOS && sb == MP_ZPOS) {
/* both positive, a - b, but if b>a then we do -(b - a) */
if (mp_cmp_mag (a, b) == MP_LT) {
/* b>a */
res = s_mp_sub (b, a, c);
c->sign = MP_NEG;
} else {
res = s_mp_sub (a, b, c);
c->sign = MP_ZPOS;
}
} else if (sa == MP_ZPOS && sb == MP_NEG) {
/* a - -b == a + b */
res = s_mp_add (a, b, c);
c->sign = MP_ZPOS;
} else if (sa == MP_NEG && sb == MP_ZPOS) {
/* -a - b == -(a + b) */
res = s_mp_add (a, b, c);
c->sign = MP_NEG;
} else {
/* -a - -b == b - a, but if a>b == -(a - b) */
if (mp_cmp_mag (a, b) == MP_GT) {
res = s_mp_sub (a, b, c);
c->sign = MP_NEG;
} else {
res = s_mp_sub (b, a, c);
c->sign = MP_ZPOS;
}
}
return res;
}
/* End: bn_mp_sub.c */
/* Start: bn_mp_submod.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* 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;
}
/* End: bn_mp_submod.c */
/* Start: bn_mp_sub_d.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* single digit subtraction */
int
mp_sub_d (mp_int * a, mp_digit b, mp_int * c)
{
mp_int t;
int res;
if ((res = mp_init (&t)) != MP_OKAY) {
return res;
}
mp_set (&t, b);
res = mp_sub (a, &t, c);
mp_clear (&t);
return res;
}
/* End: bn_mp_sub_d.c */
/* Start: bn_mp_to_signed_bin.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* 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;
}
/* End: bn_mp_to_signed_bin.c */
/* Start: bn_mp_to_unsigned_bin.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* 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) {
if (DIGIT_BIT != 7) {
b[x++] = (unsigned char) (t.dp[0] & 255);
} else {
b[x++] = (unsigned char) (t.dp[0] | ((t.dp[1] & 0x01) << 7));
}
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;
}
/* End: bn_mp_to_unsigned_bin.c */
/* Start: bn_mp_unsigned_bin_size.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* get the size for an unsigned equivalent */
int
mp_unsigned_bin_size (mp_int * a)
{
int size = mp_count_bits (a);
return (size / 8 + ((size & 7) != 0 ? 1 : 0));
}
/* End: bn_mp_unsigned_bin_size.c */
/* Start: bn_mp_xor.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* XOR two ints together */
int
mp_xor (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;
}
/* End: bn_mp_xor.c */
/* Start: bn_mp_zero.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* set to zero */
void
mp_zero (mp_int * a)
{
a->sign = MP_ZPOS;
a->used = 0;
memset (a->dp, 0, sizeof (mp_digit) * a->alloc);
}
/* End: bn_mp_zero.c */
/* Start: bn_radix.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* chars used in radix conversions */
static const char *s_rmap =
"0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
/* read a string [ASCII] in a given radix */
int
mp_read_radix (mp_int * a, char *str, int radix)
{
int y, res, neg;
char ch;
if (radix < 2 || radix > 64) {
return MP_VAL;
}
if (*str == '-') {
++str;
neg = MP_NEG;
} else {
neg = MP_ZPOS;
}
mp_zero (a);
while (*str) {
ch = (char) ((radix < 36) ? toupper (*str) : *str);
for (y = 0; y < 64; y++) {
if (ch == s_rmap[y]) {
break;
}
}
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;
}
a->sign = neg;
return MP_OKAY;
}
/* stores a bignum as a ASCII string in a given radix (2..64) */
int
mp_toradix (mp_int * a, char *str, int radix)
{
int res, digs;
mp_int t;
mp_digit d;
char *_s = str;
if (radix < 2 || radix > 64) {
return MP_VAL;
}
if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
return res;
}
if (t.sign == MP_NEG) {
++_s;
*str++ = '-';
t.sign = MP_ZPOS;
}
digs = 0;
while (mp_iszero (&t) == 0) {
if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
mp_clear (&t);
return res;
}
*str++ = s_rmap[d];
++digs;
}
bn_reverse ((unsigned char *) _s, digs);
*str++ = '\0';
mp_clear (&t);
return MP_OKAY;
}
/* returns size of ASCII reprensentation */
int
mp_radix_size (mp_int * a, int radix)
{
int res, digs;
mp_int t;
mp_digit d;
/* special case for binary */
if (radix == 2) {
return mp_count_bits (a) + (a->sign == MP_NEG ? 1 : 0) + 1;
}
if (radix < 2 || radix > 64) {
return 0;
}
if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
return 0;
}
digs = 0;
if (t.sign == MP_NEG) {
++digs;
t.sign = MP_ZPOS;
}
while (mp_iszero (&t) == 0) {
if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
mp_clear (&t);
return 0;
}
++digs;
}
mp_clear (&t);
return digs + 1;
}
/* End: bn_radix.c */
/* Start: bn_reverse.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* reverse an array, used for radix code */
void
bn_reverse (unsigned char *s, int len)
{
int ix, iy;
unsigned char t;
ix = 0;
iy = len - 1;
while (ix < iy) {
t = s[ix];
s[ix] = s[iy];
s[iy] = t;
++ix;
--iy;
}
}
/* End: bn_reverse.c */
/* Start: bn_s_mp_add.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* low level addition, based on HAC pp.594, Algorithm 14.7 */
int
s_mp_add (mp_int * a, mp_int * b, mp_int * c)
{
mp_int *x;
int olduse, res, min, max;
/* find sizes, we let |a| <= |b| which means we have to sort
* them. "x" will point to the input with the most digits
*/
if (a->used > b->used) {
min = b->used;
max = a->used;
x = a;
} else if (a->used < b->used) {
min = a->used;
max = b->used;
x = b;
} else {
min = max = a->used;
x = NULL;
}
/* init result */
if (c->alloc < max + 1) {
if ((res = mp_grow (c, max + 1)) != MP_OKAY) {
return res;
}
}
olduse = c->used;
c->used = max + 1;
/* add digits from lower part */
/* set the carry to zero */
{
register mp_digit u, *tmpa, *tmpb, *tmpc;
register int i;
/* alias for digit pointers */
tmpa = a->dp;
tmpb = b->dp;
tmpc = c->dp;
u = 0;
for (i = 0; i < min; i++) {
/* Compute the sum at one digit, T[i] = A[i] + B[i] + U */
*tmpc = *tmpa++ + *tmpb++ + u;
/* U = carry bit of T[i] */
u = *tmpc >> DIGIT_BIT;
/* take away carry bit from T[i] */
*tmpc++ &= MP_MASK;
}
/* now copy higher words if any, that is in A+B if A or B has more digits add those in */
if (min != max) {
for (; i < max; i++) {
/* T[i] = X[i] + U */
*tmpc = x->dp[i] + u;
/* U = carry bit of T[i] */
u = *tmpc >> DIGIT_BIT;
/* take away carry bit from T[i] */
*tmpc++ &= MP_MASK;
}
}
/* add carry */
*tmpc++ = u;
/* clear digits above used (since we may not have grown result above) */
for (i = c->used; i < olduse; i++) {
*tmpc++ = 0;
}
}
mp_clamp (c);
return MP_OKAY;
}
/* End: bn_s_mp_add.c */
/* Start: bn_s_mp_mul_digs.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* multiplies |a| * |b| and only computes upto digs digits of result
* HAC pp. 595, Algorithm 14.12 Modified so you can control how many digits of
* output are created.
*/
int
s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
{
mp_int t;
int res, pa, pb, ix, iy;
mp_digit u;
mp_word r;
mp_digit tmpx, *tmpt, *tmpy;
/* can we use the fast multiplier?
*
* The fast multiplier can be used if the output will have less than
* 512 digits and the number of digits won't affect carry propagation
*/
if ((digs < 512)
&& digs < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
return fast_s_mp_mul_digs (a, b, c, digs);
}
if ((res = mp_init_size (&t, digs)) != MP_OKAY) {
return res;
}
t.used = digs;
/* compute the digits of the product directly */
pa = a->used;
for (ix = 0; ix < pa; ix++) {
/* set the carry to zero */
u = 0;
/* limit ourselves to making digs digits of output */
pb = MIN (b->used, digs - ix);
/* setup some aliases */
tmpx = a->dp[ix];
tmpt = &(t.dp[ix]);
tmpy = b->dp;
/* compute the columns of the output and propagate the carry */
for (iy = 0; iy < pb; iy++) {
/* compute the column as a mp_word */
r =
((mp_word) * tmpt) + ((mp_word) tmpx) * ((mp_word) * tmpy++) +
((mp_word) u);
/* the new column is the lower part of the result */
*tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
/* get the carry word from the result */
u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
}
if (ix + iy < digs)
*tmpt = u;
}
mp_clamp (&t);
mp_exch (&t, c);
mp_clear (&t);
return MP_OKAY;
}
/* End: bn_s_mp_mul_digs.c */
/* Start: bn_s_mp_mul_high_digs.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* multiplies |a| * |b| and does not compute the lower digs digits
* [meant to get the higher part of the product]
*/
int
s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
{
mp_int t;
int res, pa, pb, ix, iy;
mp_digit u;
mp_word r;
mp_digit tmpx, *tmpt, *tmpy;
/* can we use the fast multiplier? */
if (((a->used + b->used + 1) < 512)
&& MAX (a->used,
b->used) <
(1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
return fast_s_mp_mul_high_digs (a, b, c, digs);
}
if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) {
return res;
}
t.used = a->used + b->used + 1;
pa = a->used;
pb = b->used;
for (ix = 0; ix < pa; ix++) {
/* clear the carry */
u = 0;
/* left hand side of A[ix] * B[iy] */
tmpx = a->dp[ix];
/* alias to the address of where the digits will be stored */
tmpt = &(t.dp[digs]);
/* alias for where to read the right hand side from */
tmpy = b->dp + (digs - ix);
for (iy = digs - ix; iy < pb; iy++) {
/* calculate the double precision result */
r =
((mp_word) * tmpt) + ((mp_word) tmpx) * ((mp_word) * tmpy++) +
((mp_word) u);
/* get the lower part */
*tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
/* carry the carry */
u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
}
*tmpt = u;
}
mp_clamp (&t);
mp_exch (&t, c);
mp_clear (&t);
return MP_OKAY;
}
/* End: bn_s_mp_mul_high_digs.c */
/* Start: bn_s_mp_sqr.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
int
s_mp_sqr (mp_int * a, mp_int * b)
{
mp_int t;
int res, ix, iy, pa;
mp_word r, u;
mp_digit tmpx, *tmpt;
/* can we use the fast multiplier? */
if (((a->used * 2 + 1) < 512)
&& a->used <
(1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT) - 1))) {
return fast_s_mp_sqr (a, b);
}
pa = a->used;
if ((res = mp_init_size (&t, pa + pa + 1)) != MP_OKAY) {
return res;
}
t.used = pa + pa + 1;
for (ix = 0; ix < pa; ix++) {
/* first calculate the digit at 2*ix */
/* calculate double precision result */
r =
((mp_word) t.dp[ix + ix]) +
((mp_word) a->dp[ix]) * ((mp_word) a->dp[ix]);
/* store lower part in result */
t.dp[ix + ix] = (mp_digit) (r & ((mp_word) MP_MASK));
/* get the carry */
u = (r >> ((mp_word) DIGIT_BIT));
/* left hand side of A[ix] * A[iy] */
tmpx = a->dp[ix];
/* alias for where to store the results */
tmpt = &(t.dp[ix + ix + 1]);
for (iy = ix + 1; iy < pa; iy++) {
/* first calculate the product */
r = ((mp_word) tmpx) * ((mp_word) a->dp[iy]);
/* now calculate the double precision result, note we use
* addition instead of *2 since its easier to optimize
*/
r = ((mp_word) * tmpt) + r + r + ((mp_word) u);
/* store lower part */
*tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
/* get carry */
u = (r >> ((mp_word) DIGIT_BIT));
}
r = ((mp_word) * tmpt) + u;
*tmpt = (mp_digit) (r & ((mp_word) MP_MASK));
u = (r >> ((mp_word) DIGIT_BIT));
/* propagate upwards */
++tmpt;
while (u != ((mp_word) 0)) {
r = ((mp_word) * tmpt) + ((mp_word) 1);
*tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
u = (r >> ((mp_word) DIGIT_BIT));
}
}
mp_clamp (&t);
mp_exch (&t, b);
mp_clear (&t);
return MP_OKAY;
}
/* End: bn_s_mp_sqr.c */
/* Start: bn_s_mp_sub.c */
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* low level subtraction (assumes a > b), HAC pp.595 Algorithm 14.9 */
int
s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
{
int olduse, res, min, max;
/* find sizes */
min = b->used;
max = a->used;
/* init result */
if (c->alloc < max) {
if ((res = mp_grow (c, max)) != MP_OKAY) {
return res;
}
}
olduse = c->used;
c->used = max;
/* sub digits from lower part */
{
register mp_digit u, *tmpa, *tmpb, *tmpc;
register int i;
/* alias for digit pointers */
tmpa = a->dp;
tmpb = b->dp;
tmpc = c->dp;
/* set carry to zero */
u = 0;
for (i = 0; i < min; i++) {
/* T[i] = A[i] - B[i] - U */
*tmpc = *tmpa++ - *tmpb++ - u;
/* U = carry bit of T[i]
* Note this saves performing an AND operation since
* if a carry does occur it will propagate all the way to the
* MSB. As a result a single shift is required to get the carry
*/
u = *tmpc >> (CHAR_BIT * sizeof (mp_digit) - 1);
/* Clear carry from T[i] */
*tmpc++ &= MP_MASK;
}
/* now copy higher words if any, e.g. if A has more digits than B */
for (; i < max; i++) {
/* T[i] = A[i] - U */
*tmpc = *tmpa++ - u;
/* U = carry bit of T[i] */
u = *tmpc >> (CHAR_BIT * sizeof (mp_digit) - 1);
/* Clear carry from T[i] */
*tmpc++ &= MP_MASK;
}
/* clear digits above used (since we may not have grown result above) */
for (i = c->used; i < olduse; i++) {
*tmpc++ = 0;
}
}
mp_clamp (c);
return MP_OKAY;
}
/* End: bn_s_mp_sub.c */
/* EOF */
Reference in New Issue View Git Blame Copy Permalink