208 lines
4.3 KiB
C
208 lines
4.3 KiB
C
/* TomsFastMath, a fast ISO C bignum library.
|
|
*
|
|
* This project is meant to fill in where LibTomMath
|
|
* falls short. That is speed ;-)
|
|
*
|
|
* This project is public domain and free for all purposes.
|
|
*
|
|
* Tom St Denis, tomstdenis@gmail.com
|
|
*/
|
|
#include "bignum_fast.h"
|
|
|
|
static int fp_invmod_slow (fp_int * a, fp_int * b, fp_int * c)
|
|
{
|
|
fp_int x, y, u, v, A, B, C, D;
|
|
int res;
|
|
|
|
/* b cannot be negative */
|
|
if (b->sign == FP_NEG || fp_iszero(b) == 1) {
|
|
return FP_VAL;
|
|
}
|
|
|
|
/* init temps */
|
|
fp_init(&x); fp_init(&y);
|
|
fp_init(&u); fp_init(&v);
|
|
fp_init(&A); fp_init(&B);
|
|
fp_init(&C); fp_init(&D);
|
|
|
|
/* x = a, y = b */
|
|
if ((res = fp_mod(a, b, &x)) != FP_OKAY) {
|
|
return res;
|
|
}
|
|
fp_copy(b, &y);
|
|
|
|
/* 2. [modified] if x,y are both even then return an error! */
|
|
if (fp_iseven (&x) == 1 && fp_iseven (&y) == 1) {
|
|
return FP_VAL;
|
|
}
|
|
|
|
/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
|
|
fp_copy (&x, &u);
|
|
fp_copy (&y, &v);
|
|
fp_set (&A, 1);
|
|
fp_set (&D, 1);
|
|
|
|
top:
|
|
/* 4. while u is even do */
|
|
while (fp_iseven (&u) == 1) {
|
|
/* 4.1 u = u/2 */
|
|
fp_div_2 (&u, &u);
|
|
|
|
/* 4.2 if A or B is odd then */
|
|
if (fp_isodd (&A) == 1 || fp_isodd (&B) == 1) {
|
|
/* A = (A+y)/2, B = (B-x)/2 */
|
|
fp_add (&A, &y, &A);
|
|
fp_sub (&B, &x, &B);
|
|
}
|
|
/* A = A/2, B = B/2 */
|
|
fp_div_2 (&A, &A);
|
|
fp_div_2 (&B, &B);
|
|
}
|
|
|
|
/* 5. while v is even do */
|
|
while (fp_iseven (&v) == 1) {
|
|
/* 5.1 v = v/2 */
|
|
fp_div_2 (&v, &v);
|
|
|
|
/* 5.2 if C or D is odd then */
|
|
if (fp_isodd (&C) == 1 || fp_isodd (&D) == 1) {
|
|
/* C = (C+y)/2, D = (D-x)/2 */
|
|
fp_add (&C, &y, &C);
|
|
fp_sub (&D, &x, &D);
|
|
}
|
|
/* C = C/2, D = D/2 */
|
|
fp_div_2 (&C, &C);
|
|
fp_div_2 (&D, &D);
|
|
}
|
|
|
|
/* 6. if u >= v then */
|
|
if (fp_cmp (&u, &v) != FP_LT) {
|
|
/* u = u - v, A = A - C, B = B - D */
|
|
fp_sub (&u, &v, &u);
|
|
fp_sub (&A, &C, &A);
|
|
fp_sub (&B, &D, &B);
|
|
} else {
|
|
/* v - v - u, C = C - A, D = D - B */
|
|
fp_sub (&v, &u, &v);
|
|
fp_sub (&C, &A, &C);
|
|
fp_sub (&D, &B, &D);
|
|
}
|
|
|
|
/* if not zero goto step 4 */
|
|
if (fp_iszero (&u) == 0)
|
|
goto top;
|
|
|
|
/* now a = C, b = D, gcd == g*v */
|
|
|
|
/* if v != 1 then there is no inverse */
|
|
if (fp_cmp_d (&v, 1) != FP_EQ) {
|
|
return FP_VAL;
|
|
}
|
|
|
|
/* if its too low */
|
|
while (fp_cmp_d(&C, 0) == FP_LT) {
|
|
fp_add(&C, b, &C);
|
|
}
|
|
|
|
/* too big */
|
|
while (fp_cmp_mag(&C, b) != FP_LT) {
|
|
fp_sub(&C, b, &C);
|
|
}
|
|
|
|
/* C is now the inverse */
|
|
fp_copy(&C, c);
|
|
return FP_OKAY;
|
|
}
|
|
|
|
/* c = 1/a (mod b) for odd b only */
|
|
int fp_invmod(fp_int *a, fp_int *b, fp_int *c)
|
|
{
|
|
fp_int x, y, u, v, B, D;
|
|
int neg;
|
|
|
|
/* 2. [modified] b must be odd */
|
|
if (fp_iseven (b) == FP_YES) {
|
|
return fp_invmod_slow(a,b,c);
|
|
}
|
|
|
|
/* init all our temps */
|
|
fp_init(&x); fp_init(&y);
|
|
fp_init(&u); fp_init(&v);
|
|
fp_init(&B); fp_init(&D);
|
|
|
|
/* x == modulus, y == value to invert */
|
|
fp_copy(b, &x);
|
|
|
|
/* we need y = |a| */
|
|
fp_abs(a, &y);
|
|
|
|
/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
|
|
fp_copy(&x, &u);
|
|
fp_copy(&y, &v);
|
|
fp_set (&D, 1);
|
|
|
|
top:
|
|
/* 4. while u is even do */
|
|
while (fp_iseven (&u) == FP_YES) {
|
|
/* 4.1 u = u/2 */
|
|
fp_div_2 (&u, &u);
|
|
|
|
/* 4.2 if B is odd then */
|
|
if (fp_isodd (&B) == FP_YES) {
|
|
fp_sub (&B, &x, &B);
|
|
}
|
|
/* B = B/2 */
|
|
fp_div_2 (&B, &B);
|
|
}
|
|
|
|
/* 5. while v is even do */
|
|
while (fp_iseven (&v) == FP_YES) {
|
|
/* 5.1 v = v/2 */
|
|
fp_div_2 (&v, &v);
|
|
|
|
/* 5.2 if D is odd then */
|
|
if (fp_isodd (&D) == FP_YES) {
|
|
/* D = (D-x)/2 */
|
|
fp_sub (&D, &x, &D);
|
|
}
|
|
/* D = D/2 */
|
|
fp_div_2 (&D, &D);
|
|
}
|
|
|
|
/* 6. if u >= v then */
|
|
if (fp_cmp (&u, &v) != FP_LT) {
|
|
/* u = u - v, B = B - D */
|
|
fp_sub (&u, &v, &u);
|
|
fp_sub (&B, &D, &B);
|
|
} else {
|
|
/* v - v - u, D = D - B */
|
|
fp_sub (&v, &u, &v);
|
|
fp_sub (&D, &B, &D);
|
|
}
|
|
|
|
/* if not zero goto step 4 */
|
|
if (fp_iszero (&u) == FP_NO) {
|
|
goto top;
|
|
}
|
|
|
|
/* now a = C, b = D, gcd == g*v */
|
|
|
|
/* if v != 1 then there is no inverse */
|
|
if (fp_cmp_d (&v, 1) != FP_EQ) {
|
|
return FP_VAL;
|
|
}
|
|
|
|
/* b is now the inverse */
|
|
neg = a->sign;
|
|
while (D.sign == FP_NEG) {
|
|
fp_add (&D, b, &D);
|
|
}
|
|
fp_copy (&D, c);
|
|
c->sign = neg;
|
|
return FP_OKAY;
|
|
}
|
|
|
|
/* $Source: /cvs/libtom/tomsfastmath/src/numtheory/fp_invmod.c,v $ */
|
|
/* $Revision: 1.1 $ */
|
|
/* $Date: 2007/01/24 21:25:19 $ */
|