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