/* 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; }