diff -r 000000000000 -r 6474c204b198 security/nss/lib/freebl/ecl/ec2_mont.c --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/security/nss/lib/freebl/ecl/ec2_mont.c Wed Dec 31 06:09:35 2014 +0100 @@ -0,0 +1,238 @@ +/* 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 "ec2.h" +#include "mplogic.h" +#include "mp_gf2m.h" +#include + +/* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery + * projective coordinates. Uses algorithm Mdouble in appendix of Lopez, J. + * and Dahab, R. "Fast multiplication on elliptic curves over GF(2^m) + * without precomputation". modified to not require precomputation of + * c=b^{2^{m-1}}. */ +static mp_err +gf2m_Mdouble(mp_int *x, mp_int *z, const ECGroup *group) +{ + mp_err res = MP_OKAY; + mp_int t1; + + MP_DIGITS(&t1) = 0; + MP_CHECKOK(mp_init(&t1)); + + MP_CHECKOK(group->meth->field_sqr(x, x, group->meth)); + MP_CHECKOK(group->meth->field_sqr(z, &t1, group->meth)); + MP_CHECKOK(group->meth->field_mul(x, &t1, z, group->meth)); + MP_CHECKOK(group->meth->field_sqr(x, x, group->meth)); + MP_CHECKOK(group->meth->field_sqr(&t1, &t1, group->meth)); + MP_CHECKOK(group->meth-> + field_mul(&group->curveb, &t1, &t1, group->meth)); + MP_CHECKOK(group->meth->field_add(x, &t1, x, group->meth)); + + CLEANUP: + mp_clear(&t1); + return res; +} + +/* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in + * Montgomery projective coordinates. Uses algorithm Madd in appendix of + * Lopex, J. and Dahab, R. "Fast multiplication on elliptic curves over + * GF(2^m) without precomputation". */ +static mp_err +gf2m_Madd(const mp_int *x, mp_int *x1, mp_int *z1, mp_int *x2, mp_int *z2, + const ECGroup *group) +{ + mp_err res = MP_OKAY; + mp_int t1, t2; + + MP_DIGITS(&t1) = 0; + MP_DIGITS(&t2) = 0; + MP_CHECKOK(mp_init(&t1)); + MP_CHECKOK(mp_init(&t2)); + + MP_CHECKOK(mp_copy(x, &t1)); + MP_CHECKOK(group->meth->field_mul(x1, z2, x1, group->meth)); + MP_CHECKOK(group->meth->field_mul(z1, x2, z1, group->meth)); + MP_CHECKOK(group->meth->field_mul(x1, z1, &t2, group->meth)); + MP_CHECKOK(group->meth->field_add(z1, x1, z1, group->meth)); + MP_CHECKOK(group->meth->field_sqr(z1, z1, group->meth)); + MP_CHECKOK(group->meth->field_mul(z1, &t1, x1, group->meth)); + MP_CHECKOK(group->meth->field_add(x1, &t2, x1, group->meth)); + + CLEANUP: + mp_clear(&t1); + mp_clear(&t2); + return res; +} + +/* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2) + * using Montgomery point multiplication algorithm Mxy() in appendix of + * Lopex, J. and Dahab, R. "Fast multiplication on elliptic curves over + * GF(2^m) without precomputation". Returns: 0 on error 1 if return value + * should be the point at infinity 2 otherwise */ +static int +gf2m_Mxy(const mp_int *x, const mp_int *y, mp_int *x1, mp_int *z1, + mp_int *x2, mp_int *z2, const ECGroup *group) +{ + mp_err res = MP_OKAY; + int ret = 0; + mp_int t3, t4, t5; + + MP_DIGITS(&t3) = 0; + MP_DIGITS(&t4) = 0; + MP_DIGITS(&t5) = 0; + MP_CHECKOK(mp_init(&t3)); + MP_CHECKOK(mp_init(&t4)); + MP_CHECKOK(mp_init(&t5)); + + if (mp_cmp_z(z1) == 0) { + mp_zero(x2); + mp_zero(z2); + ret = 1; + goto CLEANUP; + } + + if (mp_cmp_z(z2) == 0) { + MP_CHECKOK(mp_copy(x, x2)); + MP_CHECKOK(group->meth->field_add(x, y, z2, group->meth)); + ret = 2; + goto CLEANUP; + } + + MP_CHECKOK(mp_set_int(&t5, 1)); + if (group->meth->field_enc) { + MP_CHECKOK(group->meth->field_enc(&t5, &t5, group->meth)); + } + + MP_CHECKOK(group->meth->field_mul(z1, z2, &t3, group->meth)); + + MP_CHECKOK(group->meth->field_mul(z1, x, z1, group->meth)); + MP_CHECKOK(group->meth->field_add(z1, x1, z1, group->meth)); + MP_CHECKOK(group->meth->field_mul(z2, x, z2, group->meth)); + MP_CHECKOK(group->meth->field_mul(z2, x1, x1, group->meth)); + MP_CHECKOK(group->meth->field_add(z2, x2, z2, group->meth)); + + MP_CHECKOK(group->meth->field_mul(z2, z1, z2, group->meth)); + MP_CHECKOK(group->meth->field_sqr(x, &t4, group->meth)); + MP_CHECKOK(group->meth->field_add(&t4, y, &t4, group->meth)); + MP_CHECKOK(group->meth->field_mul(&t4, &t3, &t4, group->meth)); + MP_CHECKOK(group->meth->field_add(&t4, z2, &t4, group->meth)); + + MP_CHECKOK(group->meth->field_mul(&t3, x, &t3, group->meth)); + MP_CHECKOK(group->meth->field_div(&t5, &t3, &t3, group->meth)); + MP_CHECKOK(group->meth->field_mul(&t3, &t4, &t4, group->meth)); + MP_CHECKOK(group->meth->field_mul(x1, &t3, x2, group->meth)); + MP_CHECKOK(group->meth->field_add(x2, x, z2, group->meth)); + + MP_CHECKOK(group->meth->field_mul(z2, &t4, z2, group->meth)); + MP_CHECKOK(group->meth->field_add(z2, y, z2, group->meth)); + + ret = 2; + + CLEANUP: + mp_clear(&t3); + mp_clear(&t4); + mp_clear(&t5); + if (res == MP_OKAY) { + return ret; + } else { + return 0; + } +} + +/* Computes R = nP based on algorithm 2P of Lopex, J. and Dahab, R. "Fast + * multiplication on elliptic curves over GF(2^m) without + * precomputation". Elliptic curve points P and R can be identical. Uses + * Montgomery projective coordinates. */ +mp_err +ec_GF2m_pt_mul_mont(const mp_int *n, const mp_int *px, const mp_int *py, + mp_int *rx, mp_int *ry, const ECGroup *group) +{ + mp_err res = MP_OKAY; + mp_int x1, x2, z1, z2; + int i, j; + mp_digit top_bit, mask; + + MP_DIGITS(&x1) = 0; + MP_DIGITS(&x2) = 0; + MP_DIGITS(&z1) = 0; + MP_DIGITS(&z2) = 0; + MP_CHECKOK(mp_init(&x1)); + MP_CHECKOK(mp_init(&x2)); + MP_CHECKOK(mp_init(&z1)); + MP_CHECKOK(mp_init(&z2)); + + /* if result should be point at infinity */ + if ((mp_cmp_z(n) == 0) || (ec_GF2m_pt_is_inf_aff(px, py) == MP_YES)) { + MP_CHECKOK(ec_GF2m_pt_set_inf_aff(rx, ry)); + goto CLEANUP; + } + + MP_CHECKOK(mp_copy(px, &x1)); /* x1 = px */ + MP_CHECKOK(mp_set_int(&z1, 1)); /* z1 = 1 */ + MP_CHECKOK(group->meth->field_sqr(&x1, &z2, group->meth)); /* z2 = + * x1^2 = + * px^2 */ + MP_CHECKOK(group->meth->field_sqr(&z2, &x2, group->meth)); + MP_CHECKOK(group->meth->field_add(&x2, &group->curveb, &x2, group->meth)); /* x2 + * = + * px^4 + * + + * b + */ + + /* find top-most bit and go one past it */ + i = MP_USED(n) - 1; + j = MP_DIGIT_BIT - 1; + top_bit = 1; + top_bit <<= MP_DIGIT_BIT - 1; + mask = top_bit; + while (!(MP_DIGITS(n)[i] & mask)) { + mask >>= 1; + j--; + } + mask >>= 1; + j--; + + /* if top most bit was at word break, go to next word */ + if (!mask) { + i--; + j = MP_DIGIT_BIT - 1; + mask = top_bit; + } + + for (; i >= 0; i--) { + for (; j >= 0; j--) { + if (MP_DIGITS(n)[i] & mask) { + MP_CHECKOK(gf2m_Madd(px, &x1, &z1, &x2, &z2, group)); + MP_CHECKOK(gf2m_Mdouble(&x2, &z2, group)); + } else { + MP_CHECKOK(gf2m_Madd(px, &x2, &z2, &x1, &z1, group)); + MP_CHECKOK(gf2m_Mdouble(&x1, &z1, group)); + } + mask >>= 1; + } + j = MP_DIGIT_BIT - 1; + mask = top_bit; + } + + /* convert out of "projective" coordinates */ + i = gf2m_Mxy(px, py, &x1, &z1, &x2, &z2, group); + if (i == 0) { + res = MP_BADARG; + goto CLEANUP; + } else if (i == 1) { + MP_CHECKOK(ec_GF2m_pt_set_inf_aff(rx, ry)); + } else { + MP_CHECKOK(mp_copy(&x2, rx)); + MP_CHECKOK(mp_copy(&z2, ry)); + } + + CLEANUP: + mp_clear(&x1); + mp_clear(&x2); + mp_clear(&z1); + mp_clear(&z2); + return res; +}