| /* 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 p384 = 2^384 - 2^128 - 2^96 + 2^32 - 1. a can be r. |
| * Uses algorithm 2.30 from Hankerson, Menezes, Vanstone. Guide to |
| * Elliptic Curve Cryptography. */ |
| static mp_err |
| ec_GFp_nistp384_mod(const mp_int *a, mp_int *r, const GFMethod *meth) |
| { |
| mp_err res = MP_OKAY; |
| int a_bits = mpl_significant_bits(a); |
| int i; |
| |
| /* m1, m2 are statically-allocated mp_int of exactly the size we need */ |
| mp_int m[10]; |
| |
| #ifdef ECL_THIRTY_TWO_BIT |
| mp_digit s[10][12]; |
| for (i = 0; i < 10; i++) { |
| MP_SIGN(&m[i]) = MP_ZPOS; |
| MP_ALLOC(&m[i]) = 12; |
| MP_USED(&m[i]) = 12; |
| MP_DIGITS(&m[i]) = s[i]; |
| } |
| #else |
| mp_digit s[10][6]; |
| for (i = 0; i < 10; i++) { |
| MP_SIGN(&m[i]) = MP_ZPOS; |
| MP_ALLOC(&m[i]) = 6; |
| MP_USED(&m[i]) = 6; |
| MP_DIGITS(&m[i]) = s[i]; |
| } |
| #endif |
| |
| #ifdef ECL_THIRTY_TWO_BIT |
| /* for polynomials larger than twice the field size or polynomials |
| * not using all words, use regular reduction */ |
| if ((a_bits > 768) || (a_bits <= 736)) { |
| MP_CHECKOK(mp_mod(a, &meth->irr, r)); |
| } else { |
| for (i = 0; i < 12; i++) { |
| s[0][i] = MP_DIGIT(a, i); |
| } |
| s[1][0] = 0; |
| s[1][1] = 0; |
| s[1][2] = 0; |
| s[1][3] = 0; |
| s[1][4] = MP_DIGIT(a, 21); |
| s[1][5] = MP_DIGIT(a, 22); |
| s[1][6] = MP_DIGIT(a, 23); |
| s[1][7] = 0; |
| s[1][8] = 0; |
| s[1][9] = 0; |
| s[1][10] = 0; |
| s[1][11] = 0; |
| for (i = 0; i < 12; i++) { |
| s[2][i] = MP_DIGIT(a, i + 12); |
| } |
| s[3][0] = MP_DIGIT(a, 21); |
| s[3][1] = MP_DIGIT(a, 22); |
| s[3][2] = MP_DIGIT(a, 23); |
| for (i = 3; i < 12; i++) { |
| s[3][i] = MP_DIGIT(a, i + 9); |
| } |
| s[4][0] = 0; |
| s[4][1] = MP_DIGIT(a, 23); |
| s[4][2] = 0; |
| s[4][3] = MP_DIGIT(a, 20); |
| for (i = 4; i < 12; i++) { |
| s[4][i] = MP_DIGIT(a, i + 8); |
| } |
| s[5][0] = 0; |
| s[5][1] = 0; |
| s[5][2] = 0; |
| s[5][3] = 0; |
| s[5][4] = MP_DIGIT(a, 20); |
| s[5][5] = MP_DIGIT(a, 21); |
| s[5][6] = MP_DIGIT(a, 22); |
| s[5][7] = MP_DIGIT(a, 23); |
| s[5][8] = 0; |
| s[5][9] = 0; |
| s[5][10] = 0; |
| s[5][11] = 0; |
| s[6][0] = MP_DIGIT(a, 20); |
| s[6][1] = 0; |
| s[6][2] = 0; |
| s[6][3] = MP_DIGIT(a, 21); |
| s[6][4] = MP_DIGIT(a, 22); |
| s[6][5] = MP_DIGIT(a, 23); |
| s[6][6] = 0; |
| s[6][7] = 0; |
| s[6][8] = 0; |
| s[6][9] = 0; |
| s[6][10] = 0; |
| s[6][11] = 0; |
| s[7][0] = MP_DIGIT(a, 23); |
| for (i = 1; i < 12; i++) { |
| s[7][i] = MP_DIGIT(a, i + 11); |
| } |
| s[8][0] = 0; |
| s[8][1] = MP_DIGIT(a, 20); |
| s[8][2] = MP_DIGIT(a, 21); |
| s[8][3] = MP_DIGIT(a, 22); |
| s[8][4] = MP_DIGIT(a, 23); |
| s[8][5] = 0; |
| s[8][6] = 0; |
| s[8][7] = 0; |
| s[8][8] = 0; |
| s[8][9] = 0; |
| s[8][10] = 0; |
| s[8][11] = 0; |
| s[9][0] = 0; |
| s[9][1] = 0; |
| s[9][2] = 0; |
| s[9][3] = MP_DIGIT(a, 23); |
| s[9][4] = MP_DIGIT(a, 23); |
| s[9][5] = 0; |
| s[9][6] = 0; |
| s[9][7] = 0; |
| s[9][8] = 0; |
| s[9][9] = 0; |
| s[9][10] = 0; |
| s[9][11] = 0; |
| |
| MP_CHECKOK(mp_add(&m[0], &m[1], r)); |
| MP_CHECKOK(mp_add(r, &m[1], r)); |
| MP_CHECKOK(mp_add(r, &m[2], r)); |
| MP_CHECKOK(mp_add(r, &m[3], r)); |
| MP_CHECKOK(mp_add(r, &m[4], r)); |
| MP_CHECKOK(mp_add(r, &m[5], r)); |
| MP_CHECKOK(mp_add(r, &m[6], r)); |
| MP_CHECKOK(mp_sub(r, &m[7], r)); |
| MP_CHECKOK(mp_sub(r, &m[8], r)); |
| MP_CHECKOK(mp_submod(r, &m[9], &meth->irr, r)); |
| s_mp_clamp(r); |
| } |
| #else |
| /* for polynomials larger than twice the field size or polynomials |
| * not using all words, use regular reduction */ |
| if ((a_bits > 768) || (a_bits <= 736)) { |
| MP_CHECKOK(mp_mod(a, &meth->irr, r)); |
| } else { |
| for (i = 0; i < 6; i++) { |
| s[0][i] = MP_DIGIT(a, i); |
| } |
| s[1][0] = 0; |
| s[1][1] = 0; |
| s[1][2] = (MP_DIGIT(a, 10) >> 32) | (MP_DIGIT(a, 11) << 32); |
| s[1][3] = MP_DIGIT(a, 11) >> 32; |
| s[1][4] = 0; |
| s[1][5] = 0; |
| for (i = 0; i < 6; i++) { |
| s[2][i] = MP_DIGIT(a, i + 6); |
| } |
| s[3][0] = (MP_DIGIT(a, 10) >> 32) | (MP_DIGIT(a, 11) << 32); |
| s[3][1] = (MP_DIGIT(a, 11) >> 32) | (MP_DIGIT(a, 6) << 32); |
| for (i = 2; i < 6; i++) { |
| s[3][i] = (MP_DIGIT(a, i + 4) >> 32) | (MP_DIGIT(a, i + 5) << 32); |
| } |
| s[4][0] = (MP_DIGIT(a, 11) >> 32) << 32; |
| s[4][1] = MP_DIGIT(a, 10) << 32; |
| for (i = 2; i < 6; i++) { |
| s[4][i] = MP_DIGIT(a, i + 4); |
| } |
| s[5][0] = 0; |
| s[5][1] = 0; |
| s[5][2] = MP_DIGIT(a, 10); |
| s[5][3] = MP_DIGIT(a, 11); |
| s[5][4] = 0; |
| s[5][5] = 0; |
| s[6][0] = (MP_DIGIT(a, 10) << 32) >> 32; |
| s[6][1] = (MP_DIGIT(a, 10) >> 32) << 32; |
| s[6][2] = MP_DIGIT(a, 11); |
| s[6][3] = 0; |
| s[6][4] = 0; |
| s[6][5] = 0; |
| s[7][0] = (MP_DIGIT(a, 11) >> 32) | (MP_DIGIT(a, 6) << 32); |
| for (i = 1; i < 6; i++) { |
| s[7][i] = (MP_DIGIT(a, i + 5) >> 32) | (MP_DIGIT(a, i + 6) << 32); |
| } |
| s[8][0] = MP_DIGIT(a, 10) << 32; |
| s[8][1] = (MP_DIGIT(a, 10) >> 32) | (MP_DIGIT(a, 11) << 32); |
| s[8][2] = MP_DIGIT(a, 11) >> 32; |
| s[8][3] = 0; |
| s[8][4] = 0; |
| s[8][5] = 0; |
| s[9][0] = 0; |
| s[9][1] = (MP_DIGIT(a, 11) >> 32) << 32; |
| s[9][2] = MP_DIGIT(a, 11) >> 32; |
| s[9][3] = 0; |
| s[9][4] = 0; |
| s[9][5] = 0; |
| |
| MP_CHECKOK(mp_add(&m[0], &m[1], r)); |
| MP_CHECKOK(mp_add(r, &m[1], r)); |
| MP_CHECKOK(mp_add(r, &m[2], r)); |
| MP_CHECKOK(mp_add(r, &m[3], r)); |
| MP_CHECKOK(mp_add(r, &m[4], r)); |
| MP_CHECKOK(mp_add(r, &m[5], r)); |
| MP_CHECKOK(mp_add(r, &m[6], r)); |
| MP_CHECKOK(mp_sub(r, &m[7], r)); |
| MP_CHECKOK(mp_sub(r, &m[8], r)); |
| MP_CHECKOK(mp_submod(r, &m[9], &meth->irr, r)); |
| s_mp_clamp(r); |
| } |
| #endif |
| |
| CLEANUP: |
| return res; |
| } |
| |
| /* Compute the square of polynomial a, reduce modulo p384. Store the |
| * result in r. r could be a. Uses optimized modular reduction for p384. |
| */ |
| static mp_err |
| ec_GFp_nistp384_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_nistp384_mod(r, r, meth)); |
| CLEANUP: |
| return res; |
| } |
| |
| /* Compute the product of two polynomials a and b, reduce modulo p384. |
| * Store the result in r. r could be a or b; a could be b. Uses |
| * optimized modular reduction for p384. */ |
| static mp_err |
| ec_GFp_nistp384_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_nistp384_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_gfp384(ECGroup *group, ECCurveName name) |
| { |
| if (name == ECCurve_NIST_P384) { |
| group->meth->field_mod = &ec_GFp_nistp384_mod; |
| group->meth->field_mul = &ec_GFp_nistp384_mul; |
| group->meth->field_sqr = &ec_GFp_nistp384_sqr; |
| } |
| return MP_OKAY; |
| } |