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ECC mp_jacobi: iterative implementation

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Slightly faster and less stack used.
This commit is contained in:
Sean Parkinson
2020-09-07 11:03:16 +10:00
parent 5b43977b95
commit 6fb1feadc7
1 changed files with 62 additions and 88 deletions
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150
wolfcrypt/src/ecc.c
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@ -10806,104 +10806,33 @@ int wc_ecc_decrypt(ecc_key* privKey, ecc_key* pubKey, const byte* msg,
!defined(WOLFSSL_CRYPTOCELL)
#ifndef WOLFSSL_SP_MATH
int do_mp_jacobi(mp_int* a, mp_int* n, int* c);
int do_mp_jacobi(mp_int* a, mp_int* n, int* c)
{
int k, s, res;
int r = 0; /* initialize to help static analysis out */
mp_digit residue;
/* if a < 0 return MP_VAL */
if (mp_isneg(a) == MP_YES) {
return MP_VAL;
}
/* if n <= 0 return MP_VAL */
if (mp_cmp_d(n, 0) != MP_GT) {
return MP_VAL;
}
/* step 1. handle case of a == 0 */
if (mp_iszero (a) == MP_YES) {
/* special case of a == 0 and n == 1 */
if (mp_cmp_d (n, 1) == MP_EQ) {
*c = 1;
} else {
*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;
/* divide out larger power of two */
k = mp_cnt_lsb(a);
res = mp_div_2d(a, k, a, NULL);
if (res == MP_OKAY) {
/* step 4. if e is even set s=1 */
if ((k & 1) == 0) {
s = 1;
} else {
/* else set s=1 if p = 1/7 (mod 8) or s=-1 if p = 3/5 (mod 8) */
residue = n->dp[0] & 7;
if (residue == 1 || residue == 7) {
s = 1;
} else if (residue == 3 || residue == 5) {
s = -1;
}
}
/* step 5. if p == 3 (mod 4) *and* a == 3 (mod 4) then s = -s */
if ( ((n->dp[0] & 3) == 3) && ((a->dp[0] & 3) == 3)) {
s = -s;
}
}
if (res == MP_OKAY) {
/* if a == 1 we're done */
if (mp_cmp_d(a, 1) == MP_EQ) {
*c = s;
} else {
/* n1 = n mod a */
res = mp_mod (n, a, n);
if (res == MP_OKAY)
res = do_mp_jacobi(n, a, &r);
if (res == MP_OKAY)
*c = s * r;
}
}
return res;
}
/* computes the jacobi c = (a | n) (or Legendre if n is prime)
* HAC pp. 73 Algorithm 2.149
* HAC is wrong here, as the special case of (0 | 1) is not
* handled correctly.
*/
int mp_jacobi(mp_int* a, mp_int* n, int* c)
{
mp_int a1, n1;
int res;
int s = 1;
int k;
mp_int* t[2];
mp_int* ts;
mp_digit residue;
if (mp_isneg(a) == MP_YES) {
return MP_VAL;
}
if (mp_isneg(n) == MP_YES) {
return MP_VAL;
}
if (mp_iseven(n) == MP_YES) {
return MP_VAL;
}
/* step 3. write a = a1 * 2**k */
if ((res = mp_init_multi(&a1, &n1, NULL, NULL, NULL, NULL)) != MP_OKAY) {
return res;
}
if ((res = mp_copy(a, &a1)) != MP_OKAY) {
if ((res = mp_mod(a, n, &a1)) != MP_OKAY) {
goto done;
}
@ -10911,7 +10840,52 @@ int mp_jacobi(mp_int* a, mp_int* n, int* c)
goto done;
}
res = do_mp_jacobi(&a1, &n1, c);
t[0] = &a1;
t[1] = &n1;
/* Keep reducing until first number is 0. */
while (!mp_iszero(t[0])) {
/* Divide by 2 until odd. */
k = mp_cnt_lsb(t[0]);
if (k > 0) {
mp_rshb(t[0], k);
/* Negate s each time we divide by 2 if t[1] mod 8 == 3 or 5.
* Odd number of divides results in a negate.
*/
residue = t[1]->dp[0] & 7;
if ((k & 1) && ((residue == 3) || (residue == 5))) {
s = -s;
}
}
/* Swap t[0] and t[1]. */
ts = t[0];
t[0] = t[1];
t[1] = ts;
/* Negate s if both numbers == 3 mod 4. */
if (((t[0]->dp[0] & 3) == 3) && ((t[1]->dp[0] & 3) == 3)) {
s = -s;
}
/* Reduce first number modulo second. */
if ((k == 0) && (mp_count_bits(t[0]) == mp_count_bits(t[1]))) {
res = mp_sub(t[0], t[1], t[0]);
}
else {
res = mp_mod(t[0], t[1], t[0]);
}
if (res != MP_OKAY) {
goto done;
}
}
/* When the two numbers have divisors in common. */
if (!mp_isone(t[1])) {
s = 0;
}
*c = s;
done:
/* cleanup */