| /* 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" |
| |
| #define ECP521_DIGITS ECL_CURVE_DIGITS(521) |
| |
| /* Fast modular reduction for p521 = 2^521 - 1. a can be r. Uses |
| * algorithm 2.31 from Hankerson, Menezes, Vanstone. Guide to |
| * Elliptic Curve Cryptography. */ |
| static mp_err |
| ec_GFp_nistp521_mod(const mp_int *a, mp_int *r, const GFMethod *meth) |
| { |
| mp_err res = MP_OKAY; |
| int a_bits = mpl_significant_bits(a); |
| unsigned int i; |
| |
| /* m1, m2 are statically-allocated mp_int of exactly the size we need */ |
| mp_int m1; |
| |
| mp_digit s1[ECP521_DIGITS] = { 0 }; |
| |
| MP_SIGN(&m1) = MP_ZPOS; |
| MP_ALLOC(&m1) = ECP521_DIGITS; |
| MP_USED(&m1) = ECP521_DIGITS; |
| MP_DIGITS(&m1) = s1; |
| |
| if (a_bits < 521) { |
| if (a == r) |
| return MP_OKAY; |
| return mp_copy(a, r); |
| } |
| /* for polynomials larger than twice the field size or polynomials |
| * not using all words, use regular reduction */ |
| if (a_bits > (521 * 2)) { |
| MP_CHECKOK(mp_mod(a, &meth->irr, r)); |
| } else { |
| #define FIRST_DIGIT (ECP521_DIGITS - 1) |
| for (i = FIRST_DIGIT; i < MP_USED(a) - 1; i++) { |
| s1[i - FIRST_DIGIT] = (MP_DIGIT(a, i) >> 9) | (MP_DIGIT(a, 1 + i) << (MP_DIGIT_BIT - 9)); |
| } |
| s1[i - FIRST_DIGIT] = MP_DIGIT(a, i) >> 9; |
| |
| if (a != r) { |
| MP_CHECKOK(s_mp_pad(r, ECP521_DIGITS)); |
| for (i = 0; i < ECP521_DIGITS; i++) { |
| MP_DIGIT(r, i) = MP_DIGIT(a, i); |
| } |
| } |
| MP_USED(r) = ECP521_DIGITS; |
| MP_DIGIT(r, FIRST_DIGIT) &= 0x1FF; |
| |
| MP_CHECKOK(s_mp_add(r, &m1)); |
| if (MP_DIGIT(r, FIRST_DIGIT) & 0x200) { |
| MP_CHECKOK(s_mp_add_d(r, 1)); |
| MP_DIGIT(r, FIRST_DIGIT) &= 0x1FF; |
| } else if (s_mp_cmp(r, &meth->irr) == 0) { |
| mp_zero(r); |
| } |
| s_mp_clamp(r); |
| } |
| |
| CLEANUP: |
| return res; |
| } |
| |
| /* Compute the square of polynomial a, reduce modulo p521. Store the |
| * result in r. r could be a. Uses optimized modular reduction for p521. |
| */ |
| static mp_err |
| ec_GFp_nistp521_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_nistp521_mod(r, r, meth)); |
| CLEANUP: |
| return res; |
| } |
| |
| /* Compute the product of two polynomials a and b, reduce modulo p521. |
| * Store the result in r. r could be a or b; a could be b. Uses |
| * optimized modular reduction for p521. */ |
| static mp_err |
| ec_GFp_nistp521_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_nistp521_mod(r, r, meth)); |
| CLEANUP: |
| return res; |
| } |
| |
| /* Divides two field elements. If a is NULL, then returns the inverse of |
| * b. */ |
| static mp_err |
| ec_GFp_nistp521_div(const mp_int *a, const mp_int *b, mp_int *r, |
| const GFMethod *meth) |
| { |
| mp_err res = MP_OKAY; |
| mp_int t; |
| |
| /* If a is NULL, then return the inverse of b, otherwise return a/b. */ |
| if (a == NULL) { |
| return mp_invmod(b, &meth->irr, r); |
| } else { |
| /* MPI doesn't support divmod, so we implement it using invmod and |
| * mulmod. */ |
| MP_CHECKOK(mp_init(&t)); |
| MP_CHECKOK(mp_invmod(b, &meth->irr, &t)); |
| MP_CHECKOK(mp_mul(a, &t, r)); |
| MP_CHECKOK(ec_GFp_nistp521_mod(r, r, meth)); |
| CLEANUP: |
| mp_clear(&t); |
| return res; |
| } |
| } |
| |
| /* Wire in fast field arithmetic and precomputation of base point for |
| * named curves. */ |
| mp_err |
| ec_group_set_gfp521(ECGroup *group, ECCurveName name) |
| { |
| if (name == ECCurve_NIST_P521) { |
| group->meth->field_mod = &ec_GFp_nistp521_mod; |
| group->meth->field_mul = &ec_GFp_nistp521_mul; |
| group->meth->field_sqr = &ec_GFp_nistp521_sqr; |
| group->meth->field_div = &ec_GFp_nistp521_div; |
| } |
| return MP_OKAY; |
| } |