mirror of
https://github.com/rn10950/RetroZilla.git
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378 lines
11 KiB
C
378 lines
11 KiB
C
/* This Source Code Form is subject to the terms of the Mozilla Public
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* License, v. 2.0. If a copy of the MPL was not distributed with this
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* file, You can obtain one at http://mozilla.org/MPL/2.0/. */
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#include "ecp.h"
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#include "mpi.h"
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#include "mplogic.h"
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#include "mpi-priv.h"
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/* Fast modular reduction for p256 = 2^256 - 2^224 + 2^192+ 2^96 - 1. a can be r.
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* Uses algorithm 2.29 from Hankerson, Menezes, Vanstone. Guide to
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* Elliptic Curve Cryptography. */
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static mp_err
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ec_GFp_nistp256_mod(const mp_int *a, mp_int *r, const GFMethod *meth)
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{
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mp_err res = MP_OKAY;
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mp_size a_used = MP_USED(a);
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int a_bits = mpl_significant_bits(a);
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mp_digit carry;
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#ifdef ECL_THIRTY_TWO_BIT
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mp_digit a8=0, a9=0, a10=0, a11=0, a12=0, a13=0, a14=0, a15=0;
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mp_digit r0, r1, r2, r3, r4, r5, r6, r7;
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int r8; /* must be a signed value ! */
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#else
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mp_digit a4=0, a5=0, a6=0, a7=0;
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mp_digit a4h, a4l, a5h, a5l, a6h, a6l, a7h, a7l;
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mp_digit r0, r1, r2, r3;
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int r4; /* must be a signed value ! */
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#endif
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/* for polynomials larger than twice the field size
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* use regular reduction */
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if (a_bits < 256) {
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if (a == r) return MP_OKAY;
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return mp_copy(a,r);
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}
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if (a_bits > 512) {
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MP_CHECKOK(mp_mod(a, &meth->irr, r));
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} else {
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#ifdef ECL_THIRTY_TWO_BIT
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switch (a_used) {
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case 16:
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a15 = MP_DIGIT(a,15);
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case 15:
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a14 = MP_DIGIT(a,14);
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case 14:
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a13 = MP_DIGIT(a,13);
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case 13:
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a12 = MP_DIGIT(a,12);
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case 12:
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a11 = MP_DIGIT(a,11);
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case 11:
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a10 = MP_DIGIT(a,10);
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case 10:
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a9 = MP_DIGIT(a,9);
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case 9:
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a8 = MP_DIGIT(a,8);
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}
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r0 = MP_DIGIT(a,0);
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r1 = MP_DIGIT(a,1);
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r2 = MP_DIGIT(a,2);
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r3 = MP_DIGIT(a,3);
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r4 = MP_DIGIT(a,4);
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r5 = MP_DIGIT(a,5);
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r6 = MP_DIGIT(a,6);
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r7 = MP_DIGIT(a,7);
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/* sum 1 */
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MP_ADD_CARRY(r3, a11, r3, 0, carry);
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MP_ADD_CARRY(r4, a12, r4, carry, carry);
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MP_ADD_CARRY(r5, a13, r5, carry, carry);
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MP_ADD_CARRY(r6, a14, r6, carry, carry);
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MP_ADD_CARRY(r7, a15, r7, carry, carry);
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r8 = carry;
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MP_ADD_CARRY(r3, a11, r3, 0, carry);
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MP_ADD_CARRY(r4, a12, r4, carry, carry);
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MP_ADD_CARRY(r5, a13, r5, carry, carry);
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MP_ADD_CARRY(r6, a14, r6, carry, carry);
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MP_ADD_CARRY(r7, a15, r7, carry, carry);
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r8 += carry;
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/* sum 2 */
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MP_ADD_CARRY(r3, a12, r3, 0, carry);
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MP_ADD_CARRY(r4, a13, r4, carry, carry);
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MP_ADD_CARRY(r5, a14, r5, carry, carry);
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MP_ADD_CARRY(r6, a15, r6, carry, carry);
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MP_ADD_CARRY(r7, 0, r7, carry, carry);
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r8 += carry;
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/* combine last bottom of sum 3 with second sum 2 */
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MP_ADD_CARRY(r0, a8, r0, 0, carry);
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MP_ADD_CARRY(r1, a9, r1, carry, carry);
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MP_ADD_CARRY(r2, a10, r2, carry, carry);
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MP_ADD_CARRY(r3, a12, r3, carry, carry);
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MP_ADD_CARRY(r4, a13, r4, carry, carry);
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MP_ADD_CARRY(r5, a14, r5, carry, carry);
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MP_ADD_CARRY(r6, a15, r6, carry, carry);
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MP_ADD_CARRY(r7, a15, r7, carry, carry); /* from sum 3 */
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r8 += carry;
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/* sum 3 (rest of it)*/
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MP_ADD_CARRY(r6, a14, r6, 0, carry);
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MP_ADD_CARRY(r7, 0, r7, carry, carry);
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r8 += carry;
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/* sum 4 (rest of it)*/
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MP_ADD_CARRY(r0, a9, r0, 0, carry);
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MP_ADD_CARRY(r1, a10, r1, carry, carry);
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MP_ADD_CARRY(r2, a11, r2, carry, carry);
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MP_ADD_CARRY(r3, a13, r3, carry, carry);
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MP_ADD_CARRY(r4, a14, r4, carry, carry);
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MP_ADD_CARRY(r5, a15, r5, carry, carry);
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MP_ADD_CARRY(r6, a13, r6, carry, carry);
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MP_ADD_CARRY(r7, a8, r7, carry, carry);
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r8 += carry;
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/* diff 5 */
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MP_SUB_BORROW(r0, a11, r0, 0, carry);
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MP_SUB_BORROW(r1, a12, r1, carry, carry);
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MP_SUB_BORROW(r2, a13, r2, carry, carry);
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MP_SUB_BORROW(r3, 0, r3, carry, carry);
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MP_SUB_BORROW(r4, 0, r4, carry, carry);
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MP_SUB_BORROW(r5, 0, r5, carry, carry);
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MP_SUB_BORROW(r6, a8, r6, carry, carry);
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MP_SUB_BORROW(r7, a10, r7, carry, carry);
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r8 -= carry;
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/* diff 6 */
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MP_SUB_BORROW(r0, a12, r0, 0, carry);
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MP_SUB_BORROW(r1, a13, r1, carry, carry);
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MP_SUB_BORROW(r2, a14, r2, carry, carry);
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MP_SUB_BORROW(r3, a15, r3, carry, carry);
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MP_SUB_BORROW(r4, 0, r4, carry, carry);
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MP_SUB_BORROW(r5, 0, r5, carry, carry);
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MP_SUB_BORROW(r6, a9, r6, carry, carry);
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MP_SUB_BORROW(r7, a11, r7, carry, carry);
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r8 -= carry;
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/* diff 7 */
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MP_SUB_BORROW(r0, a13, r0, 0, carry);
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MP_SUB_BORROW(r1, a14, r1, carry, carry);
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MP_SUB_BORROW(r2, a15, r2, carry, carry);
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MP_SUB_BORROW(r3, a8, r3, carry, carry);
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MP_SUB_BORROW(r4, a9, r4, carry, carry);
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MP_SUB_BORROW(r5, a10, r5, carry, carry);
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MP_SUB_BORROW(r6, 0, r6, carry, carry);
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MP_SUB_BORROW(r7, a12, r7, carry, carry);
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r8 -= carry;
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/* diff 8 */
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MP_SUB_BORROW(r0, a14, r0, 0, carry);
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MP_SUB_BORROW(r1, a15, r1, carry, carry);
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MP_SUB_BORROW(r2, 0, r2, carry, carry);
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MP_SUB_BORROW(r3, a9, r3, carry, carry);
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MP_SUB_BORROW(r4, a10, r4, carry, carry);
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MP_SUB_BORROW(r5, a11, r5, carry, carry);
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MP_SUB_BORROW(r6, 0, r6, carry, carry);
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MP_SUB_BORROW(r7, a13, r7, carry, carry);
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r8 -= carry;
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/* reduce the overflows */
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while (r8 > 0) {
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mp_digit r8_d = r8;
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MP_ADD_CARRY(r0, r8_d, r0, 0, carry);
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MP_ADD_CARRY(r1, 0, r1, carry, carry);
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MP_ADD_CARRY(r2, 0, r2, carry, carry);
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MP_ADD_CARRY(r3, 0-r8_d, r3, carry, carry);
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MP_ADD_CARRY(r4, MP_DIGIT_MAX, r4, carry, carry);
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MP_ADD_CARRY(r5, MP_DIGIT_MAX, r5, carry, carry);
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MP_ADD_CARRY(r6, 0-(r8_d+1), r6, carry, carry);
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MP_ADD_CARRY(r7, (r8_d-1), r7, carry, carry);
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r8 = carry;
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}
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/* reduce the underflows */
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while (r8 < 0) {
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mp_digit r8_d = -r8;
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MP_SUB_BORROW(r0, r8_d, r0, 0, carry);
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MP_SUB_BORROW(r1, 0, r1, carry, carry);
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MP_SUB_BORROW(r2, 0, r2, carry, carry);
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MP_SUB_BORROW(r3, 0-r8_d, r3, carry, carry);
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MP_SUB_BORROW(r4, MP_DIGIT_MAX, r4, carry, carry);
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MP_SUB_BORROW(r5, MP_DIGIT_MAX, r5, carry, carry);
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MP_SUB_BORROW(r6, 0-(r8_d+1), r6, carry, carry);
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MP_SUB_BORROW(r7, (r8_d-1), r7, carry, carry);
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r8 = 0-carry;
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}
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if (a != r) {
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MP_CHECKOK(s_mp_pad(r,8));
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}
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MP_SIGN(r) = MP_ZPOS;
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MP_USED(r) = 8;
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MP_DIGIT(r,7) = r7;
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MP_DIGIT(r,6) = r6;
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MP_DIGIT(r,5) = r5;
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MP_DIGIT(r,4) = r4;
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MP_DIGIT(r,3) = r3;
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MP_DIGIT(r,2) = r2;
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MP_DIGIT(r,1) = r1;
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MP_DIGIT(r,0) = r0;
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/* final reduction if necessary */
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if ((r7 == MP_DIGIT_MAX) &&
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((r6 > 1) || ((r6 == 1) &&
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(r5 || r4 || r3 ||
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((r2 == MP_DIGIT_MAX) && (r1 == MP_DIGIT_MAX)
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&& (r0 == MP_DIGIT_MAX)))))) {
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MP_CHECKOK(mp_sub(r, &meth->irr, r));
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}
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s_mp_clamp(r);
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#else
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switch (a_used) {
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case 8:
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a7 = MP_DIGIT(a,7);
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case 7:
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a6 = MP_DIGIT(a,6);
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case 6:
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a5 = MP_DIGIT(a,5);
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case 5:
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a4 = MP_DIGIT(a,4);
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}
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a7l = a7 << 32;
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a7h = a7 >> 32;
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a6l = a6 << 32;
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a6h = a6 >> 32;
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a5l = a5 << 32;
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a5h = a5 >> 32;
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a4l = a4 << 32;
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a4h = a4 >> 32;
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r3 = MP_DIGIT(a,3);
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r2 = MP_DIGIT(a,2);
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r1 = MP_DIGIT(a,1);
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r0 = MP_DIGIT(a,0);
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/* sum 1 */
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MP_ADD_CARRY(r1, a5h << 32, r1, 0, carry);
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MP_ADD_CARRY(r2, a6, r2, carry, carry);
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MP_ADD_CARRY(r3, a7, r3, carry, carry);
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r4 = carry;
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MP_ADD_CARRY(r1, a5h << 32, r1, 0, carry);
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MP_ADD_CARRY(r2, a6, r2, carry, carry);
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MP_ADD_CARRY(r3, a7, r3, carry, carry);
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r4 += carry;
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/* sum 2 */
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MP_ADD_CARRY(r1, a6l, r1, 0, carry);
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MP_ADD_CARRY(r2, a6h | a7l, r2, carry, carry);
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MP_ADD_CARRY(r3, a7h, r3, carry, carry);
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r4 += carry;
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MP_ADD_CARRY(r1, a6l, r1, 0, carry);
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MP_ADD_CARRY(r2, a6h | a7l, r2, carry, carry);
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MP_ADD_CARRY(r3, a7h, r3, carry, carry);
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r4 += carry;
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/* sum 3 */
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MP_ADD_CARRY(r0, a4, r0, 0, carry);
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MP_ADD_CARRY(r1, a5l >> 32, r1, carry, carry);
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MP_ADD_CARRY(r2, 0, r2, carry, carry);
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MP_ADD_CARRY(r3, a7, r3, carry, carry);
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r4 += carry;
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/* sum 4 */
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MP_ADD_CARRY(r0, a4h | a5l, r0, 0, carry);
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MP_ADD_CARRY(r1, a5h|(a6h<<32), r1, carry, carry);
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MP_ADD_CARRY(r2, a7, r2, carry, carry);
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MP_ADD_CARRY(r3, a6h | a4l, r3, carry, carry);
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r4 += carry;
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/* diff 5 */
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MP_SUB_BORROW(r0, a5h | a6l, r0, 0, carry);
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MP_SUB_BORROW(r1, a6h, r1, carry, carry);
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MP_SUB_BORROW(r2, 0, r2, carry, carry);
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MP_SUB_BORROW(r3, (a4l>>32)|a5l,r3, carry, carry);
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r4 -= carry;
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/* diff 6 */
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MP_SUB_BORROW(r0, a6, r0, 0, carry);
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MP_SUB_BORROW(r1, a7, r1, carry, carry);
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MP_SUB_BORROW(r2, 0, r2, carry, carry);
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MP_SUB_BORROW(r3, a4h|(a5h<<32),r3, carry, carry);
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r4 -= carry;
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/* diff 7 */
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MP_SUB_BORROW(r0, a6h|a7l, r0, 0, carry);
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MP_SUB_BORROW(r1, a7h|a4l, r1, carry, carry);
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MP_SUB_BORROW(r2, a4h|a5l, r2, carry, carry);
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MP_SUB_BORROW(r3, a6l, r3, carry, carry);
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r4 -= carry;
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/* diff 8 */
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MP_SUB_BORROW(r0, a7, r0, 0, carry);
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MP_SUB_BORROW(r1, a4h<<32, r1, carry, carry);
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MP_SUB_BORROW(r2, a5, r2, carry, carry);
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MP_SUB_BORROW(r3, a6h<<32, r3, carry, carry);
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r4 -= carry;
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/* reduce the overflows */
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while (r4 > 0) {
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mp_digit r4_long = r4;
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mp_digit r4l = (r4_long << 32);
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MP_ADD_CARRY(r0, r4_long, r0, 0, carry);
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MP_ADD_CARRY(r1, 0-r4l, r1, carry, carry);
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MP_ADD_CARRY(r2, MP_DIGIT_MAX, r2, carry, carry);
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MP_ADD_CARRY(r3, r4l-r4_long-1,r3, carry, carry);
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r4 = carry;
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}
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/* reduce the underflows */
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while (r4 < 0) {
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mp_digit r4_long = -r4;
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mp_digit r4l = (r4_long << 32);
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MP_SUB_BORROW(r0, r4_long, r0, 0, carry);
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MP_SUB_BORROW(r1, 0-r4l, r1, carry, carry);
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MP_SUB_BORROW(r2, MP_DIGIT_MAX, r2, carry, carry);
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MP_SUB_BORROW(r3, r4l-r4_long-1,r3, carry, carry);
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r4 = 0-carry;
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}
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if (a != r) {
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MP_CHECKOK(s_mp_pad(r,4));
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}
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MP_SIGN(r) = MP_ZPOS;
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MP_USED(r) = 4;
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MP_DIGIT(r,3) = r3;
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MP_DIGIT(r,2) = r2;
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MP_DIGIT(r,1) = r1;
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MP_DIGIT(r,0) = r0;
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/* final reduction if necessary */
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if ((r3 > 0xFFFFFFFF00000001ULL) ||
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((r3 == 0xFFFFFFFF00000001ULL) &&
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(r2 || (r1 >> 32)||
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(r1 == 0xFFFFFFFFULL && r0 == MP_DIGIT_MAX)))) {
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/* very rare, just use mp_sub */
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MP_CHECKOK(mp_sub(r, &meth->irr, r));
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}
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s_mp_clamp(r);
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#endif
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}
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CLEANUP:
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return res;
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}
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/* Compute the square of polynomial a, reduce modulo p256. Store the
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* result in r. r could be a. Uses optimized modular reduction for p256.
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*/
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static mp_err
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ec_GFp_nistp256_sqr(const mp_int *a, mp_int *r, const GFMethod *meth)
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{
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mp_err res = MP_OKAY;
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MP_CHECKOK(mp_sqr(a, r));
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MP_CHECKOK(ec_GFp_nistp256_mod(r, r, meth));
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CLEANUP:
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return res;
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}
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/* Compute the product of two polynomials a and b, reduce modulo p256.
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* Store the result in r. r could be a or b; a could be b. Uses
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* optimized modular reduction for p256. */
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static mp_err
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ec_GFp_nistp256_mul(const mp_int *a, const mp_int *b, mp_int *r,
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const GFMethod *meth)
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{
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mp_err res = MP_OKAY;
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MP_CHECKOK(mp_mul(a, b, r));
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MP_CHECKOK(ec_GFp_nistp256_mod(r, r, meth));
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CLEANUP:
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return res;
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}
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/* Wire in fast field arithmetic and precomputation of base point for
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* named curves. */
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mp_err
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ec_group_set_gfp256(ECGroup *group, ECCurveName name)
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{
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if (name == ECCurve_NIST_P256) {
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group->meth->field_mod = &ec_GFp_nistp256_mod;
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group->meth->field_mul = &ec_GFp_nistp256_mul;
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group->meth->field_sqr = &ec_GFp_nistp256_sqr;
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}
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return MP_OKAY;
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}
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