6052 lines
146 KiB
C
6052 lines
146 KiB
C
/* File Generated Automatically by gen.pl */
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/* Start: bncore.c */
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/* LibTomMath, multiple-precision integer library -- Tom St Denis
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|
*
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|
* LibTomMath is library that provides for multiple-precision
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|
* 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.
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|
*
|
|
* The library is free for all purposes without any express
|
|
* guarantee it works.
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|
*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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*/
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#include <tommath.h>
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/* configured for a AMD Duron Morgan core with etc/tune.c */
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int KARATSUBA_MUL_CUTOFF = 73, /* Min. number of digits before Karatsuba multiplication is used. */
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KARATSUBA_SQR_CUTOFF = 121, /* Min. number of digits before Karatsuba squaring is used. */
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MONTGOMERY_EXPT_CUTOFF = 128; /* max. number of digits that montgomery reductions will help for */
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/* End: bncore.c */
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/* Start: bn_fast_mp_invmod.c */
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/* LibTomMath, multiple-precision integer library -- Tom St Denis
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|
*
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|
* 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.
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|
*
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|
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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*/
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#include <tommath.h>
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/* computes the modular inverse via binary extended euclidean algorithm,
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* that is c = 1/a mod b
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*
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* Based on mp_invmod except this is optimized for the case where b is
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* odd as per HAC Note 14.64 on pp. 610
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*/
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int
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fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
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{
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mp_int x, y, u, v, B, D;
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int res, neg;
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/* init all our temps */
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if ((res = mp_init (&x)) != MP_OKAY) {
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goto __ERR;
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}
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if ((res = mp_init (&y)) != MP_OKAY) {
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goto __X;
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}
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if ((res = mp_init (&u)) != MP_OKAY) {
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goto __Y;
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}
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if ((res = mp_init (&v)) != MP_OKAY) {
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goto __U;
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}
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if ((res = mp_init (&B)) != MP_OKAY) {
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goto __V;
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}
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if ((res = mp_init (&D)) != MP_OKAY) {
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goto __B;
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}
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/* x == modulus, y == value to invert */
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if ((res = mp_copy (b, &x)) != MP_OKAY) {
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goto __D;
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}
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if ((res = mp_copy (a, &y)) != MP_OKAY) {
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goto __D;
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}
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/* we need |y| */
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if ((res = mp_abs (&y, &y)) != MP_OKAY) {
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goto __D;
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}
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/* 2. [modified] if x,y are both even then return an error!
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*
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* That is if gcd(x,y) = 2 * k then obviously there is no inverse.
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*/
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if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
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res = MP_VAL;
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goto __D;
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}
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/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
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if ((res = mp_copy (&x, &u)) != MP_OKAY) {
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goto __D;
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}
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if ((res = mp_copy (&y, &v)) != MP_OKAY) {
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goto __D;
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}
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mp_set (&D, 1);
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top:
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/* 4. while u is even do */
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while (mp_iseven (&u) == 1) {
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/* 4.1 u = u/2 */
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if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
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goto __D;
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}
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/* 4.2 if A or B is odd then */
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if (mp_iseven (&B) == 0) {
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if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
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goto __D;
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}
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}
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/* B = B/2 */
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if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
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goto __D;
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}
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}
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/* 5. while v is even do */
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while (mp_iseven (&v) == 1) {
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/* 5.1 v = v/2 */
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if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
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goto __D;
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}
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/* 5.2 if C,D are even then */
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if (mp_iseven (&D) == 0) {
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/* D = (D-x)/2 */
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|
if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
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|
goto __D;
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|
}
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}
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/* D = D/2 */
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if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
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|
goto __D;
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|
}
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|
}
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/* 6. if u >= v then */
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if (mp_cmp (&u, &v) != MP_LT) {
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|
/* u = u - v, B = B - D */
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if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
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|
goto __D;
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}
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if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
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|
goto __D;
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|
}
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|
} else {
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|
/* v - v - u, D = D - B */
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if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
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goto __D;
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}
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if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
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goto __D;
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}
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}
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/* if not zero goto step 4 */
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if (mp_iszero (&u) == 0) {
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goto top;
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|
}
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/* now a = C, b = D, gcd == g*v */
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|
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/* if v != 1 then there is no inverse */
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if (mp_cmp_d (&v, 1) != MP_EQ) {
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|
res = MP_VAL;
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|
goto __D;
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|
}
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|
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/* b is now the inverse */
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neg = a->sign;
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while (D.sign == MP_NEG) {
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if ((res = mp_add (&D, b, &D)) != MP_OKAY) {
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|
goto __D;
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}
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|
}
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|
mp_exch (&D, c);
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|
c->sign = neg;
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res = MP_OKAY;
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__D:mp_clear (&D);
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__B:mp_clear (&B);
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__V:mp_clear (&v);
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__U:mp_clear (&u);
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__Y:mp_clear (&y);
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__X:mp_clear (&x);
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__ERR:
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return res;
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}
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/* End: bn_fast_mp_invmod.c */
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/* Start: bn_fast_mp_montgomery_reduce.c */
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|
/* 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://math.libtomcrypt.org
|
|
*/
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#include <tommath.h>
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/* computes xR^-1 == x (mod N) via Montgomery Reduction
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*
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|
* This is an optimized implementation of mp_montgomery_reduce
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|
* which uses the comba method to quickly calculate the columns of the
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* reduction.
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*
|
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* Based on Algorithm 14.32 on pp.601 of HAC.
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|
*/
|
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int
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fast_mp_montgomery_reduce (mp_int * a, mp_int * m, mp_digit mp)
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|
{
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int ix, res, olduse;
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mp_word W[512];
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/* get old used count */
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olduse = a->used;
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/* grow a as required */
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if (a->alloc < m->used + 1) {
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if ((res = mp_grow (a, m->used + 1)) != MP_OKAY) {
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return res;
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}
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}
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{
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register mp_word *_W;
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register mp_digit *tmpa;
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_W = W;
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tmpa = a->dp;
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/* copy the digits of a into W[0..a->used-1] */
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for (ix = 0; ix < a->used; ix++) {
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*_W++ = *tmpa++;
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}
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/* zero the high words of W[a->used..m->used*2] */
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|
for (; ix < m->used * 2 + 1; ix++) {
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*_W++ = 0;
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}
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|
}
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for (ix = 0; ix < m->used; ix++) {
|
|
/* ui = ai * m' mod b
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|
*
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|
* 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
|
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* the carry cleared (see after the inner loop)
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*/
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register mp_digit ui;
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ui = (((mp_digit) (W[ix] & MP_MASK)) * mp) & MP_MASK;
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|
|
/* a = a + ui * m * b^i
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|
*
|
|
* This is computed in place and on the fly. The multiplication
|
|
* by b^i is handled by offseting which columns the results
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* 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
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*/
|
|
{
|
|
register int iy;
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|
register mp_digit *tmpx;
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|
register mp_word *_W;
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|
|
|
/* alias for the digits of the modulus */
|
|
tmpx = m->dp;
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|
|
|
/* Alias for the columns set by an offset of ix */
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|
_W = W + ix;
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|
|
|
/* inner loop */
|
|
for (iy = 0; iy < m->used; iy++) {
|
|
*_W++ += ((mp_word) ui) * ((mp_word) * tmpx++);
|
|
}
|
|
}
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|
|
|
/* now fix carry for next digit, W[ix+1] */
|
|
W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
|
|
}
|
|
|
|
|
|
{
|
|
register mp_digit *tmpa;
|
|
register mp_word *_W, *_W1;
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|
|
|
/* nox fix rest of carries */
|
|
_W1 = W + ix;
|
|
_W = W + ++ix;
|
|
|
|
for (; ix <= m->used * 2 + 1; ix++) {
|
|
*_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
|
|
}
|
|
|
|
/* copy out, A = A/b^n
|
|
*
|
|
* The result is A/b^n but instead of converting from an array of mp_word
|
|
* to mp_digit than calling mp_rshd we just copy them in the right
|
|
* order
|
|
*/
|
|
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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#include <tommath.h>
|
|
|
|
/* this is a modified version of fast_s_mp_mul_digs that only produces
|
|
* output digits *above* digs. See the comments for fast_s_mp_mul_digs
|
|
* 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://math.libtomcrypt.org
|
|
*/
|
|
#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;
|
|
}
|
|
}
|
|
|
|
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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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_size(&t, 1)) != 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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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 */
|
|
XFREE (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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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;
|
|
|
|
/* point aliases */
|
|
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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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 = mp_count_bits(&y) % DIGIT_BIT;
|
|
if (norm < (DIGIT_BIT-1)) {
|
|
norm = (DIGIT_BIT-1) - norm;
|
|
if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) {
|
|
goto __Y;
|
|
}
|
|
if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) {
|
|
goto __Y;
|
|
}
|
|
} else {
|
|
norm = 0;
|
|
}
|
|
|
|
/* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
|
|
n = x.used - 1;
|
|
t = y.used - 1;
|
|
|
|
/* 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.used)
|
|
continue;
|
|
|
|
/* step 3.1 if xi == yt then set q{i-t-1} to b-1, otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */
|
|
if (x.dp[i] == y.dp[t]) {
|
|
q.dp[i - t - 1] = ((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_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://math.libtomcrypt.org
|
|
*/
|
|
#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;
|
|
|
|
/* source alias */
|
|
tmpa = a->dp + b->used - 1;
|
|
|
|
/* dest alias */
|
|
tmpb = b->dp + b->used - 1;
|
|
|
|
/* carry */
|
|
r = 0;
|
|
for (x = b->used - 1; x >= 0; x--) {
|
|
/* get the carry for the next iteration */
|
|
rr = *tmpa & 1;
|
|
|
|
/* shift the current digit, add in carry and store */
|
|
*tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1));
|
|
|
|
/* forward carry to next iteration */
|
|
r = rr;
|
|
}
|
|
|
|
/* zero excess digits */
|
|
tmpb = b->dp + b->used;
|
|
for (x = b->used; x < oldused; x++) {
|
|
*tmpb++ = 0;
|
|
}
|
|
}
|
|
b->sign = a->sign;
|
|
mp_clamp (b);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* 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://math.libtomcrypt.org
|
|
*/
|
|
#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 */
|
|
if (b >= DIGIT_BIT) {
|
|
mp_rshd (c, b / DIGIT_BIT);
|
|
}
|
|
|
|
/* shift any bit count < DIGIT_BIT */
|
|
D = (mp_digit) (b % DIGIT_BIT);
|
|
if (D != 0) {
|
|
register mp_digit *tmpc, mask;
|
|
|
|
/* mask */
|
|
mask = (1U << D) - 1U;
|
|
|
|
/* alias */
|
|
tmpc = c->dp + (c->used - 1);
|
|
|
|
/* carry */
|
|
r = 0;
|
|
for (x = c->used - 1; x >= 0; x--) {
|
|
/* get the lower bits of this word in a temp */
|
|
rr = *tmpc & mask;
|
|
|
|
/* shift the current word and mix in the carry bits from the previous word */
|
|
*tmpc = (*tmpc >> D) | (r << (DIGIT_BIT - D));
|
|
--tmpc;
|
|
|
|
/* 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://math.libtomcrypt.org
|
|
*/
|
|
#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);
|
|
|
|
/* set remainder if not null */
|
|
if (d != NULL) {
|
|
*d = t2.dp[0];
|
|
}
|
|
|
|
mp_clear (&t);
|
|
mp_clear (&t2);
|
|
return res;
|
|
}
|
|
|
|
/* End: bn_mp_div_d.c */
|
|
|
|
/* Start: bn_mp_dr_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://math.libtomcrypt.org
|
|
*/
|
|
#include <tommath.h>
|
|
|
|
/* reduce "a" in place modulo "b" using the Diminished Radix algorithm.
|
|
*
|
|
* Based on algorithm from the paper
|
|
*
|
|
* "Generating Efficient Primes for Discrete Log Cryptosystems"
|
|
* Chae Hoon Lim, Pil Loong Lee,
|
|
* POSTECH Information Research Laboratories
|
|
*
|
|
* The modulus must be of a special format [see manual]
|
|
*/
|
|
int
|
|
mp_dr_reduce (mp_int * a, mp_int * b, mp_digit mp)
|
|
{
|
|
int err, i, j, k;
|
|
mp_word r;
|
|
mp_digit mu, *tmpj, *tmpi;
|
|
|
|
/* k = digits in modulus */
|
|
k = b->used;
|
|
|
|
/* ensure that "a" has at least 2k digits */
|
|
if (a->alloc < k + k) {
|
|
if ((err = mp_grow (a, k + k)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
}
|
|
|
|
/* alias for a->dp[i] */
|
|
tmpi = a->dp + k + k - 1;
|
|
|
|
/* for (i = 2k - 1; i >= k; i = i - 1)
|
|
*
|
|
* This is the main loop of the reduction. Note that at the end
|
|
* the words above position k are not zeroed as expected. The end
|
|
* result is that the digits from 0 to k-1 are the residue. So
|
|
* we have to clear those afterwards.
|
|
*/
|
|
for (i = k + k - 1; i >= k; i = i - 1) {
|
|
/* x[i - 1 : i - k] += x[i]*mp */
|
|
|
|
/* x[i] * mp */
|
|
r = ((mp_word) *tmpi--) * ((mp_word) mp);
|
|
|
|
/* now add r to x[i-1:i-k]
|
|
*
|
|
* First add it to the first digit x[i-k] then form the carry
|
|
* then enter the main loop
|
|
*/
|
|
j = i - k;
|
|
|
|
/* alias for a->dp[j] */
|
|
tmpj = a->dp + j;
|
|
|
|
/* add digit */
|
|
*tmpj += (mp_digit)(r & MP_MASK);
|
|
|
|
/* this is the carry */
|
|
mu = (r >> ((mp_word) DIGIT_BIT)) + (*tmpj >> DIGIT_BIT);
|
|
|
|
/* clear carry from a->dp[j] */
|
|
*tmpj++ &= MP_MASK;
|
|
|
|
/* now add rest of the digits
|
|
*
|
|
* Note this is basically a simple single digit addition to
|
|
* a larger multiple digit number. This is optimized somewhat
|
|
* because the propagation of carries is not likely to move
|
|
* more than a few digits.
|
|
*
|
|
*/
|
|
for (++j; mu != 0 && j <= (i - 1); ++j) {
|
|
*tmpj += mu;
|
|
mu = *tmpj >> DIGIT_BIT;
|
|
*tmpj++ &= MP_MASK;
|
|
}
|
|
|
|
/* if final carry */
|
|
if (mu != 0) {
|
|
/* add mp to this to correct */
|
|
j = i - k;
|
|
tmpj = a->dp + j;
|
|
|
|
*tmpj += mp;
|
|
mu = *tmpj >> DIGIT_BIT;
|
|
*tmpj++ &= MP_MASK;
|
|
|
|
/* now handle carries */
|
|
for (++j; mu != 0 && j <= (i - 1); j++) {
|
|
*tmpj += mu;
|
|
mu = *tmpj >> DIGIT_BIT;
|
|
*tmpj++ &= MP_MASK;
|
|
}
|
|
}
|
|
}
|
|
|
|
/* zero words above k */
|
|
tmpi = a->dp + k;
|
|
for (i = k; i < a->used; i++) {
|
|
*tmpi++ = 0;
|
|
}
|
|
|
|
/* clamp, sub and return */
|
|
mp_clamp (a);
|
|
|
|
if (mp_cmp_mag (a, b) != MP_LT) {
|
|
return s_mp_sub (a, b, a);
|
|
}
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* determines if a number is a valid DR modulus */
|
|
int mp_dr_is_modulus(mp_int *a)
|
|
{
|
|
int ix;
|
|
|
|
/* must be at least two digits */
|
|
if (a->used < 2) {
|
|
return 0;
|
|
}
|
|
|
|
for (ix = 1; ix < a->used; ix++) {
|
|
if (a->dp[ix] != MP_MASK) {
|
|
return 0;
|
|
}
|
|
}
|
|
return 1;
|
|
}
|
|
|
|
/* determines the setup value */
|
|
void mp_dr_setup(mp_int *a, mp_digit *d)
|
|
{
|
|
*d = (1 << DIGIT_BIT) - a->dp[0];
|
|
}
|
|
|
|
|
|
/* End: bn_mp_dr_reduce.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://math.libtomcrypt.org
|
|
*/
|
|
#include <tommath.h>
|
|
|
|
/* swap the elements of two integers, for cases where you can't simply swap the
|
|
* mp_int pointers around
|
|
*/
|
|
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://math.libtomcrypt.org
|
|
*/
|
|
#include <tommath.h>
|
|
|
|
static int f_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y);
|
|
|
|
/* this is a shell function that calls either the normal or Montgomery
|
|
* exptmod functions. Originally the call to the montgomery code was
|
|
* embedded in the normal function but that wasted alot of stack space
|
|
* for nothing (since 99% of the time the Montgomery code would be called)
|
|
*/
|
|
int
|
|
mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
|
|
{
|
|
int dr;
|
|
|
|
dr = mp_dr_is_modulus(P);
|
|
/* if the modulus is odd use the fast method */
|
|
if (((mp_isodd (P) == 1 && P->used < MONTGOMERY_EXPT_CUTOFF) || dr == 1) && P->used > 4) {
|
|
return mp_exptmod_fast (G, X, P, Y, dr);
|
|
} else {
|
|
return f_mp_exptmod (G, X, P, Y);
|
|
}
|
|
}
|
|
|
|
static int
|
|
f_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;
|
|
|
|
/* 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 */
|
|
/* 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://math.libtomcrypt.org
|
|
*/
|
|
#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 or Diminished Radix reduction [whichever appropriate]
|
|
*/
|
|
int
|
|
mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
|
|
{
|
|
mp_int M[256], res;
|
|
mp_digit buf, mp;
|
|
int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
|
|
int (*redux)(mp_int*,mp_int*,mp_digit);
|
|
|
|
/* find window size */
|
|
x = mp_count_bits (X);
|
|
if (x <= 7) {
|
|
winsize = 2;
|
|
} else if (x <= 36) {
|
|
winsize = 3;
|
|
} else if (x <= 140) {
|
|
winsize = 4;
|
|
} else if (x <= 450) {
|
|
winsize = 5;
|
|
} else if (x <= 1303) {
|
|
winsize = 6;
|
|
} else if (x <= 3529) {
|
|
winsize = 7;
|
|
} else {
|
|
winsize = 8;
|
|
}
|
|
|
|
/* 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;
|
|
}
|
|
}
|
|
|
|
if (redmode == 0) {
|
|
/* now setup montgomery */
|
|
if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) {
|
|
goto __M;
|
|
}
|
|
redux = mp_montgomery_reduce;
|
|
} else {
|
|
/* setup DR reduction */
|
|
mp_dr_setup(P, &mp);
|
|
redux = mp_dr_reduce;
|
|
}
|
|
|
|
/* setup result */
|
|
if ((err = mp_init (&res)) != 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 (redmode == 0) {
|
|
/* now we need R mod m */
|
|
if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
|
|
goto __RES;
|
|
}
|
|
|
|
/* now set M[1] to G * R mod m */
|
|
if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
|
|
goto __RES;
|
|
}
|
|
} else {
|
|
mp_set(&res, 1);
|
|
if ((err = mp_mod(G, 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 = redux (&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 = redux (&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 = redux (&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 */
|
|
/* square first */
|
|
for (x = 0; x < winsize; x++) {
|
|
if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
|
|
goto __RES;
|
|
}
|
|
if ((err = redux (&res, P, mp)) != MP_OKAY) {
|
|
goto __RES;
|
|
}
|
|
}
|
|
|
|
/* then multiply */
|
|
if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
|
|
goto __RES;
|
|
}
|
|
if ((err = redux (&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 = redux (&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 = redux (&res, P, mp)) != MP_OKAY) {
|
|
goto __RES;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
if (redmode == 0) {
|
|
/* 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://math.libtomcrypt.org
|
|
*/
|
|
#include <tommath.h>
|
|
|
|
/* calculate c = a^b using a square-multiply algorithm */
|
|
int
|
|
mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
|
|
{
|
|
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++) {
|
|
/* square */
|
|
if ((res = mp_sqr (c, c)) != MP_OKAY) {
|
|
mp_clear (&g);
|
|
return res;
|
|
}
|
|
|
|
/* if the bit is set multiply */
|
|
if ((b & (mp_digit) (1 << (DIGIT_BIT - 1))) != 0) {
|
|
if ((res = mp_mul (c, &g, c)) != MP_OKAY) {
|
|
mp_clear (&g);
|
|
return res;
|
|
}
|
|
}
|
|
|
|
/* shift to next bit */
|
|
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://math.libtomcrypt.org
|
|
*/
|
|
#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 (mp_iseven(&u) == 1 && mp_iseven(&v) == 1) {
|
|
++k;
|
|
if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
|
|
goto __T;
|
|
}
|
|
if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
|
|
goto __T;
|
|
}
|
|
}
|
|
|
|
/* B2. Initialize */
|
|
if (mp_isodd(&u) == 1) {
|
|
/* t = -v */
|
|
if ((res = mp_copy (&v, &t)) != MP_OKAY) {
|
|
goto __T;
|
|
}
|
|
t.sign = MP_NEG;
|
|
} else {
|
|
/* t = u */
|
|
if ((res = mp_copy (&u, &t)) != MP_OKAY) {
|
|
goto __T;
|
|
}
|
|
}
|
|
|
|
do {
|
|
/* B3 (and B4). Halve t, if even */
|
|
while (t.used != 0 && mp_iseven(&t) == 1) {
|
|
if ((res = mp_div_2 (&t, &t)) != 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://math.libtomcrypt.org
|
|
*/
|
|
#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) {
|
|
/* ensure there are always at least MP_PREC digits extra on top */
|
|
size += (MP_PREC * 2) - (size & (MP_PREC - 1));
|
|
|
|
a->dp = OPT_CAST XREALLOC (a->dp, sizeof (mp_digit) * size);
|
|
if (a->dp == NULL) {
|
|
return MP_MEM;
|
|
}
|
|
|
|
/* zero excess digits */
|
|
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://math.libtomcrypt.org
|
|
*/
|
|
#include <tommath.h>
|
|
|
|
/* init a new bigint */
|
|
int
|
|
mp_init (mp_int * a)
|
|
{
|
|
|
|
/* allocate ram required and clear it */
|
|
a->dp = OPT_CAST XCALLOC (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://math.libtomcrypt.org
|
|
*/
|
|
#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;
|
|
}
|
|
return mp_copy (b, a);
|
|
}
|
|
|
|
/* 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://math.libtomcrypt.org
|
|
*/
|
|
#include <tommath.h>
|
|
|
|
/* init a mp_init and grow it to a given size */
|
|
int
|
|
mp_init_size (mp_int * a, int size)
|
|
{
|
|
|
|
/* pad size so there are always extra digits */
|
|
size += (MP_PREC * 2) - (size & (MP_PREC - 1));
|
|
|
|
/* alloc mem */
|
|
a->dp = OPT_CAST XCALLOC (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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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;
|
|
|
|
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_size (&t1, B * 2) != MP_OKAY)
|
|
goto Y1;
|
|
if (mp_init_size (&t2, B * 2) != MP_OKAY)
|
|
goto T1;
|
|
if (mp_init_size (&x0y0, B * 2) != MP_OKAY)
|
|
goto T2;
|
|
if (mp_init_size (&x1y1, B * 2) != 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;
|
|
|
|
{
|
|
register int x;
|
|
register mp_digit *tmpa, *tmpb, *tmpx, *tmpy;
|
|
|
|
/* we copy the digits directly instead of using higher level functions
|
|
* since we also need to shift the digits
|
|
*/
|
|
tmpa = a->dp;
|
|
tmpb = b->dp;
|
|
|
|
tmpx = x0.dp;
|
|
tmpy = y0.dp;
|
|
for (x = 0; x < B; x++) {
|
|
*tmpx++ = *tmpa++;
|
|
*tmpy++ = *tmpb++;
|
|
}
|
|
|
|
tmpx = x1.dp;
|
|
for (x = B; x < a->used; x++) {
|
|
*tmpx++ = *tmpa++;
|
|
}
|
|
|
|
tmpy = y1.dp;
|
|
for (x = B; x < b->used; x++) {
|
|
*tmpy++ = *tmpb++;
|
|
}
|
|
}
|
|
|
|
/* only need to clamp the lower words since by definition the upper words x1/y1 must
|
|
* have a known number of digits
|
|
*/
|
|
mp_clamp (&x0);
|
|
mp_clamp (&y0);
|
|
|
|
/* now calc the products x0y0 and x1y1 */
|
|
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://math.libtomcrypt.org
|
|
*/
|
|
#include <tommath.h>
|
|
|
|
/* Karatsuba squaring, computes b = a*a using three half size squarings
|
|
*
|
|
* See comments of mp_karatsuba_mul for details. It is essentially the same algorithm
|
|
* but merely tuned to perform recursive squarings.
|
|
*/
|
|
int
|
|
mp_karatsuba_sqr (mp_int * a, mp_int * b)
|
|
{
|
|
mp_int x0, x1, t1, t2, x0x0, x1x1;
|
|
int B, err;
|
|
|
|
err = MP_MEM;
|
|
|
|
/* min # of digits */
|
|
B = a->used;
|
|
|
|
/* now divide in two */
|
|
B = B / 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_size (&t1, a->used * 2) != MP_OKAY)
|
|
goto X1;
|
|
if (mp_init_size (&t2, a->used * 2) != MP_OKAY)
|
|
goto T1;
|
|
if (mp_init_size (&x0x0, B * 2) != MP_OKAY)
|
|
goto T2;
|
|
if (mp_init_size (&x1x1, (a->used - B) * 2) != MP_OKAY)
|
|
goto X0X0;
|
|
|
|
{
|
|
register int x;
|
|
register mp_digit *dst, *src;
|
|
|
|
src = a->dp;
|
|
|
|
/* now shift the digits */
|
|
dst = x0.dp;
|
|
for (x = 0; x < B; x++) {
|
|
*dst++ = *src++;
|
|
}
|
|
|
|
dst = x1.dp;
|
|
for (x = B; x < a->used; x++) {
|
|
*dst++ = *src++;
|
|
}
|
|
}
|
|
|
|
x0.used = B;
|
|
x1.used = a->used - B;
|
|
|
|
mp_clamp (&x0);
|
|
|
|
/* now calc the products x0*x0 and x1*x1 */
|
|
if (mp_sqr (&x0, &x0x0) != MP_OKAY)
|
|
goto X1X1; /* x0x0 = x0*x0 */
|
|
if (mp_sqr (&x1, &x1x1) != MP_OKAY)
|
|
goto X1X1; /* x1x1 = x1*x1 */
|
|
|
|
/* now calc x1-x0 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 (s_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://math.libtomcrypt.org
|
|
*/
|
|
#include <tommath.h>
|
|
|
|
/* computes least common multiple as a*b/(a, b) */
|
|
int
|
|
mp_lcm (mp_int * a, mp_int * b, mp_int * c)
|
|
{
|
|
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://math.libtomcrypt.org
|
|
*/
|
|
#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;
|
|
}
|
|
|
|
{
|
|
register mp_digit *tmpa, *tmpaa;
|
|
|
|
/* increment the used by the shift amount than copy upwards */
|
|
a->used += b;
|
|
|
|
/* top */
|
|
tmpa = a->dp + a->used - 1;
|
|
|
|
/* base */
|
|
tmpaa = a->dp + a->used - 1 - b;
|
|
|
|
/* much like mp_rshd this is implemented using a sliding window
|
|
* except the window goes the otherway around. Copying from
|
|
* the bottom to the top. see bn_mp_rshd.c for more info.
|
|
*/
|
|
for (x = a->used - 1; x >= b; x--) {
|
|
*tmpa-- = *tmpaa--;
|
|
}
|
|
|
|
/* zero the lower digits */
|
|
tmpa = a->dp;
|
|
for (x = 0; x < b; x++) {
|
|
*tmpa++ = 0;
|
|
}
|
|
}
|
|
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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#include <tommath.h>
|
|
|
|
/* calculates a = B^n mod b for Montgomery reduction
|
|
* Where B is the base [e.g. 2^DIGIT_BIT].
|
|
* B^n mod b is computed by first computing
|
|
* A = B^(n-1) which doesn't require a reduction but a simple OR.
|
|
* then C = A * B = B^n is computed by performing upto DIGIT_BIT
|
|
* shifts with subtractions when the result is greater than b.
|
|
*
|
|
* The method is slightly modified to shift B unconditionally upto just under
|
|
* the leading bit of b. This saves alot of multiple precision shifting.
|
|
*/
|
|
int
|
|
mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
|
|
{
|
|
int 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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#include <tommath.h>
|
|
|
|
/* setups the montgomery reduction stuff */
|
|
int
|
|
mp_montgomery_setup (mp_int * a, mp_digit * mp)
|
|
{
|
|
unsigned long x, b;
|
|
|
|
/* fast inversion mod 2^32
|
|
*
|
|
* Based on the fact that
|
|
*
|
|
* XA = 1 (mod 2^n) => (X(2-XA)) A = 1 (mod 2^2n)
|
|
* => 2*X*A - X*X*A*A = 1
|
|
* => 2*(1) - (1) = 1
|
|
*/
|
|
b = a->dp[0];
|
|
|
|
if ((b & 1) == 0) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2^4 */
|
|
x *= 2 - b * x; /* here x*a==1 mod 2^8 */
|
|
x *= 2 - b * x; /* here x*a==1 mod 2^16; each step doubles the nb of bits */
|
|
x *= 2 - b * x; /* here x*a==1 mod 2^32 */
|
|
|
|
/* t = -1/m mod b */
|
|
*mp = ((mp_digit) 1 << ((mp_digit) DIGIT_BIT)) - (x & MP_MASK);
|
|
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* 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://math.libtomcrypt.org
|
|
*/
|
|
#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 {
|
|
|
|
/* 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
|
|
*/
|
|
int digs = a->used + b->used + 1;
|
|
|
|
if ((digs < 512)
|
|
&& digs < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
|
|
res = fast_s_mp_mul_digs (a, b, c, digs);
|
|
} else {
|
|
res = s_mp_mul (a, b, c);
|
|
}
|
|
|
|
}
|
|
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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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;
|
|
|
|
/* alias for source */
|
|
tmpa = a->dp;
|
|
|
|
/* alias for dest */
|
|
tmpb = b->dp;
|
|
|
|
/* carry */
|
|
r = 0;
|
|
for (x = 0; x < b->used; x++) {
|
|
|
|
/* get what will be the *next* carry bit from the MSB of the current digit */
|
|
rr = *tmpa >> (DIGIT_BIT - 1);
|
|
|
|
/* now shift up this digit, add in the carry [from the previous] */
|
|
*tmpb++ = ((*tmpa++ << 1) | r) & MP_MASK;
|
|
|
|
/* copy the carry that would be from the source digit into the next iteration */
|
|
r = rr;
|
|
}
|
|
|
|
/* new leading digit? */
|
|
if (r != 0) {
|
|
/* do we have to grow to accomodate the new digit? */
|
|
if (b->alloc == b->used) {
|
|
if ((res = mp_grow (b, b->used + 1)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
/* after the grow *tmpb is no longer valid so we have to reset it!
|
|
* (this bug took me about 17 minutes to find...!)
|
|
*/
|
|
tmpb = b->dp + b->used;
|
|
}
|
|
/* add a MSB which is always 1 at this point */
|
|
*tmpb = 1;
|
|
++b->used;
|
|
}
|
|
|
|
/* now zero any excess digits on the destination that we didn't write to */
|
|
tmpb = b->dp + b->used;
|
|
for (x = b->used; x < oldused; x++) {
|
|
*tmpb++ = 0;
|
|
}
|
|
}
|
|
b->sign = a->sign;
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* 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://math.libtomcrypt.org
|
|
*/
|
|
#include <tommath.h>
|
|
|
|
/* shift left by a certain bit count */
|
|
int
|
|
mp_mul_2d (mp_int * a, int b, mp_int * c)
|
|
{
|
|
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 (b >= DIGIT_BIT) {
|
|
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) {
|
|
register mp_digit *tmpc, mask;
|
|
|
|
/* bitmask for carries */
|
|
mask = (1U << d) - 1U;
|
|
|
|
/* alias */
|
|
tmpc = c->dp;
|
|
|
|
/* carry */
|
|
r = 0;
|
|
for (x = 0; x < c->used; x++) {
|
|
/* get the higher bits of the current word */
|
|
rr = (*tmpc >> (DIGIT_BIT - d)) & mask;
|
|
|
|
/* shift the current word and OR in the carry */
|
|
*tmpc = ((*tmpc << d) | r) & MP_MASK;
|
|
++tmpc;
|
|
|
|
/* set the carry to the carry bits of the current word */
|
|
r = rr;
|
|
}
|
|
}
|
|
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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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_prime_fermat.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://math.libtomcrypt.org
|
|
*/
|
|
#include <tommath.h>
|
|
|
|
/* performs one Fermat test.
|
|
*
|
|
* If "a" were prime then b^a == b (mod a) since the order of
|
|
* the multiplicative sub-group would be phi(a) = a-1. That means
|
|
* it would be the same as b^(a mod (a-1)) == b^1 == b (mod a).
|
|
*
|
|
* Sets result to 1 if the congruence holds, or zero otherwise.
|
|
*/
|
|
int
|
|
mp_prime_fermat (mp_int * a, mp_int * b, int *result)
|
|
{
|
|
mp_int t;
|
|
int err;
|
|
|
|
/* default to fail */
|
|
*result = 0;
|
|
|
|
/* init t */
|
|
if ((err = mp_init (&t)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* compute t = b^a mod a */
|
|
if ((err = mp_exptmod (b, a, a, &t)) != MP_OKAY) {
|
|
goto __T;
|
|
}
|
|
|
|
/* is it equal to b? */
|
|
if (mp_cmp (&t, b) == MP_EQ) {
|
|
*result = 1;
|
|
}
|
|
|
|
err = MP_OKAY;
|
|
__T:mp_clear (&t);
|
|
return err;
|
|
}
|
|
|
|
/* End: bn_mp_prime_fermat.c */
|
|
|
|
/* Start: bn_mp_prime_is_divisible.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://math.libtomcrypt.org
|
|
*/
|
|
#include <tommath.h>
|
|
|
|
/* determines if an integers is divisible by one of the first 256 primes or not
|
|
*
|
|
* sets result to 0 if not, 1 if yes
|
|
*/
|
|
int
|
|
mp_prime_is_divisible (mp_int * a, int *result)
|
|
{
|
|
int err, ix;
|
|
mp_digit res;
|
|
|
|
/* default to not */
|
|
*result = 0;
|
|
|
|
for (ix = 0; ix < 256; ix++) {
|
|
/* is it equal to the prime? */
|
|
if (mp_cmp_d (a, __prime_tab[ix]) == MP_EQ) {
|
|
*result = 1;
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* what is a mod __prime_tab[ix] */
|
|
if ((err = mp_mod_d (a, __prime_tab[ix], &res)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* is the residue zero? */
|
|
if (res == 0) {
|
|
*result = 1;
|
|
return MP_OKAY;
|
|
}
|
|
}
|
|
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* End: bn_mp_prime_is_divisible.c */
|
|
|
|
/* Start: bn_mp_prime_is_prime.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://math.libtomcrypt.org
|
|
*/
|
|
#include <tommath.h>
|
|
|
|
/* performs a variable number of rounds of Miller-Rabin
|
|
*
|
|
* Probability of error after t rounds is no more than
|
|
* (1/4)^t when 1 <= t <= 256
|
|
*
|
|
* Sets result to 1 if probably prime, 0 otherwise
|
|
*/
|
|
int
|
|
mp_prime_is_prime (mp_int * a, int t, int *result)
|
|
{
|
|
mp_int b;
|
|
int ix, err, res;
|
|
|
|
/* default to no */
|
|
*result = 0;
|
|
|
|
/* valid value of t? */
|
|
if (t < 1 || t > 256) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* first perform trial division */
|
|
if ((err = mp_prime_is_divisible (a, &res)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
if (res == 1) {
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* now perform the miller-rabin rounds */
|
|
if ((err = mp_init (&b)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
for (ix = 0; ix < t; ix++) {
|
|
/* set the prime */
|
|
mp_set (&b, __prime_tab[ix]);
|
|
|
|
if ((err = mp_prime_miller_rabin (a, &b, &res)) != MP_OKAY) {
|
|
goto __B;
|
|
}
|
|
|
|
if (res == 0) {
|
|
goto __B;
|
|
}
|
|
}
|
|
|
|
/* passed the test */
|
|
*result = 1;
|
|
__B:mp_clear (&b);
|
|
return err;
|
|
}
|
|
|
|
/* End: bn_mp_prime_is_prime.c */
|
|
|
|
/* Start: bn_mp_prime_miller_rabin.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://math.libtomcrypt.org
|
|
*/
|
|
#include <tommath.h>
|
|
|
|
/* Miller-Rabin test of "a" to the base of "b" as described in
|
|
* HAC pp. 139 Algorithm 4.24
|
|
*
|
|
* Sets result to 0 if definitely composite or 1 if probably prime.
|
|
* Randomly the chance of error is no more than 1/4 and often
|
|
* very much lower.
|
|
*/
|
|
int
|
|
mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)
|
|
{
|
|
mp_int n1, y, r;
|
|
int s, j, err;
|
|
|
|
/* default */
|
|
*result = 0;
|
|
|
|
/* get n1 = a - 1 */
|
|
if ((err = mp_init_copy (&n1, a)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
if ((err = mp_sub_d (&n1, 1, &n1)) != MP_OKAY) {
|
|
goto __N1;
|
|
}
|
|
|
|
/* set 2^s * r = n1 */
|
|
if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) {
|
|
goto __N1;
|
|
}
|
|
s = 0;
|
|
while (mp_iseven (&r) == 1) {
|
|
++s;
|
|
if ((err = mp_div_2 (&r, &r)) != MP_OKAY) {
|
|
goto __R;
|
|
}
|
|
}
|
|
|
|
/* compute y = b^r mod a */
|
|
if ((err = mp_init (&y)) != MP_OKAY) {
|
|
goto __R;
|
|
}
|
|
if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) {
|
|
goto __Y;
|
|
}
|
|
|
|
/* if y != 1 and y != n1 do */
|
|
if (mp_cmp_d (&y, 1) != MP_EQ && mp_cmp (&y, &n1) != MP_EQ) {
|
|
j = 1;
|
|
/* while j <= s-1 and y != n1 */
|
|
while ((j <= (s - 1)) && mp_cmp (&y, &n1) != MP_EQ) {
|
|
if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) {
|
|
goto __Y;
|
|
}
|
|
|
|
/* if y == 1 then composite */
|
|
if (mp_cmp_d (&y, 1) == MP_EQ) {
|
|
goto __Y;
|
|
}
|
|
|
|
++j;
|
|
}
|
|
|
|
/* if y != n1 then composite */
|
|
if (mp_cmp (&y, &n1) != MP_EQ) {
|
|
goto __Y;
|
|
}
|
|
}
|
|
|
|
/* probably prime now */
|
|
*result = 1;
|
|
__Y:mp_clear (&y);
|
|
__R:mp_clear (&r);
|
|
__N1:mp_clear (&n1);
|
|
return err;
|
|
}
|
|
|
|
/* End: bn_mp_prime_miller_rabin.c */
|
|
|
|
/* Start: bn_mp_prime_next_prime.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://math.libtomcrypt.org
|
|
*/
|
|
#include <tommath.h>
|
|
|
|
/* finds the next prime after the number "a" using "t" trials
|
|
* of Miller-Rabin.
|
|
*/
|
|
int mp_prime_next_prime(mp_int *a, int t)
|
|
{
|
|
int err, res;
|
|
|
|
if (mp_iseven(a) == 1) {
|
|
/* force odd */
|
|
if ((err = mp_add_d(a, 1, a)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
} else {
|
|
/* force to next number */
|
|
if ((err = mp_add_d(a, 2, a)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
}
|
|
|
|
for (;;) {
|
|
/* is this prime? */
|
|
if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
if (res == 1) {
|
|
break;
|
|
}
|
|
|
|
/* add two, next candidate */
|
|
if ((err = mp_add_d(a, 2, a)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
}
|
|
|
|
return MP_OKAY;
|
|
}
|
|
|
|
|
|
/* End: bn_mp_prime_next_prime.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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#include <tommath.h>
|
|
|
|
/* pre-calculate the value required for Barrett reduction
|
|
* For a given modulus "b" it calulates the value required in "a"
|
|
*/
|
|
int
|
|
mp_reduce_setup (mp_int * a, mp_int * b)
|
|
{
|
|
int 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://math.libtomcrypt.org
|
|
*/
|
|
#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;
|
|
}
|
|
|
|
{
|
|
register mp_digit *tmpa, *tmpaa;
|
|
|
|
/* shift the digits down */
|
|
|
|
/* base */
|
|
tmpa = a->dp;
|
|
|
|
/* offset into digits */
|
|
tmpaa = a->dp + b;
|
|
|
|
/* this is implemented as a sliding window where the window is b-digits long
|
|
* and digits from the top of the window are copied to the bottom
|
|
*
|
|
* e.g.
|
|
|
|
b-2 | b-1 | b0 | b1 | b2 | ... | bb | ---->
|
|
/\ | ---->
|
|
\-------------------/ ---->
|
|
*/
|
|
for (x = 0; x < (a->used - b); x++) {
|
|
*tmpa++ = *tmpaa++;
|
|
}
|
|
|
|
/* zero the top digits */
|
|
for (; x < a->used; x++) {
|
|
*tmpa++ = 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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#include <tommath.h>
|
|
|
|
/* shrink a bignum */
|
|
int
|
|
mp_shrink (mp_int * a)
|
|
{
|
|
if (a->alloc != a->used) {
|
|
if ((a->dp = OPT_CAST XREALLOC (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://math.libtomcrypt.org
|
|
*/
|
|
#include <tommath.h>
|
|
|
|
/* get the size for an signed equivalent */
|
|
int
|
|
mp_signed_bin_size (mp_int * a)
|
|
{
|
|
return 1 + mp_unsigned_bin_size (a);
|
|
}
|
|
|
|
/* 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://math.libtomcrypt.org
|
|
*/
|
|
#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 {
|
|
|
|
/* can we use the fast multiplier? */
|
|
if (((a->used * 2 + 1) < 512)
|
|
&& a->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT) - 1))) {
|
|
res = fast_s_mp_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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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_prime_tab.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://math.libtomcrypt.org
|
|
*/
|
|
#include <tommath.h>
|
|
const mp_digit __prime_tab[] = {
|
|
0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
|
|
0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
|
|
0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059,
|
|
0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F, 0x0083,
|
|
0x0089, 0x008B, 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD,
|
|
0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, 0x00C7, 0x00D3, 0x00DF,
|
|
0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107,
|
|
0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137,
|
|
|
|
0x0139, 0x013D, 0x014B, 0x0151, 0x015B, 0x015D, 0x0161, 0x0167,
|
|
0x016F, 0x0175, 0x017B, 0x017F, 0x0185, 0x018D, 0x0191, 0x0199,
|
|
0x01A3, 0x01A5, 0x01AF, 0x01B1, 0x01B7, 0x01BB, 0x01C1, 0x01C9,
|
|
0x01CD, 0x01CF, 0x01D3, 0x01DF, 0x01E7, 0x01EB, 0x01F3, 0x01F7,
|
|
0x01FD, 0x0209, 0x020B, 0x021D, 0x0223, 0x022D, 0x0233, 0x0239,
|
|
0x023B, 0x0241, 0x024B, 0x0251, 0x0257, 0x0259, 0x025F, 0x0265,
|
|
0x0269, 0x026B, 0x0277, 0x0281, 0x0283, 0x0287, 0x028D, 0x0293,
|
|
0x0295, 0x02A1, 0x02A5, 0x02AB, 0x02B3, 0x02BD, 0x02C5, 0x02CF,
|
|
|
|
0x02D7, 0x02DD, 0x02E3, 0x02E7, 0x02EF, 0x02F5, 0x02F9, 0x0301,
|
|
0x0305, 0x0313, 0x031D, 0x0329, 0x032B, 0x0335, 0x0337, 0x033B,
|
|
0x033D, 0x0347, 0x0355, 0x0359, 0x035B, 0x035F, 0x036D, 0x0371,
|
|
0x0373, 0x0377, 0x038B, 0x038F, 0x0397, 0x03A1, 0x03A9, 0x03AD,
|
|
0x03B3, 0x03B9, 0x03C7, 0x03CB, 0x03D1, 0x03D7, 0x03DF, 0x03E5,
|
|
0x03F1, 0x03F5, 0x03FB, 0x03FD, 0x0407, 0x0409, 0x040F, 0x0419,
|
|
0x041B, 0x0425, 0x0427, 0x042D, 0x043F, 0x0443, 0x0445, 0x0449,
|
|
0x044F, 0x0455, 0x045D, 0x0463, 0x0469, 0x047F, 0x0481, 0x048B,
|
|
|
|
0x0493, 0x049D, 0x04A3, 0x04A9, 0x04B1, 0x04BD, 0x04C1, 0x04C7,
|
|
0x04CD, 0x04CF, 0x04D5, 0x04E1, 0x04EB, 0x04FD, 0x04FF, 0x0503,
|
|
0x0509, 0x050B, 0x0511, 0x0515, 0x0517, 0x051B, 0x0527, 0x0529,
|
|
0x052F, 0x0551, 0x0557, 0x055D, 0x0565, 0x0577, 0x0581, 0x058F,
|
|
0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3,
|
|
0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7,
|
|
0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623,
|
|
0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653
|
|
};
|
|
|
|
/* End: bn_prime_tab.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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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 */
|
|
|
|
/* first input */
|
|
tmpa = a->dp;
|
|
|
|
/* second input */
|
|
tmpb = b->dp;
|
|
|
|
/* destination */
|
|
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://math.libtomcrypt.org
|
|
*/
|
|
#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;
|
|
|
|
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://math.libtomcrypt.org
|
|
*/
|
|
#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://math.libtomcrypt.org
|
|
*/
|
|
#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;
|
|
|
|
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://math.libtomcrypt.org
|
|
*/
|
|
#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 */
|