diff options
Diffstat (limited to 'security/nss/lib/freebl/ecl/ecp_jac.c')
| -rw-r--r-- | security/nss/lib/freebl/ecl/ecp_jac.c | 513 |
1 files changed, 513 insertions, 0 deletions
diff --git a/security/nss/lib/freebl/ecl/ecp_jac.c b/security/nss/lib/freebl/ecl/ecp_jac.c new file mode 100644 index 000000000..535e75903 --- /dev/null +++ b/security/nss/lib/freebl/ecl/ecp_jac.c @@ -0,0 +1,513 @@ +/* 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 "mplogic.h" +#include <stdlib.h> +#ifdef ECL_DEBUG +#include <assert.h> +#endif + +/* Converts a point P(px, py) from affine coordinates to Jacobian + * projective coordinates R(rx, ry, rz). Assumes input is already + * field-encoded using field_enc, and returns output that is still + * field-encoded. */ +mp_err +ec_GFp_pt_aff2jac(const mp_int *px, const mp_int *py, mp_int *rx, + mp_int *ry, mp_int *rz, const ECGroup *group) +{ + mp_err res = MP_OKAY; + + if (ec_GFp_pt_is_inf_aff(px, py) == MP_YES) { + MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz)); + } else { + MP_CHECKOK(mp_copy(px, rx)); + MP_CHECKOK(mp_copy(py, ry)); + MP_CHECKOK(mp_set_int(rz, 1)); + if (group->meth->field_enc) { + MP_CHECKOK(group->meth->field_enc(rz, rz, group->meth)); + } + } +CLEANUP: + return res; +} + +/* Converts a point P(px, py, pz) from Jacobian projective coordinates to + * affine coordinates R(rx, ry). P and R can share x and y coordinates. + * Assumes input is already field-encoded using field_enc, and returns + * output that is still field-encoded. */ +mp_err +ec_GFp_pt_jac2aff(const mp_int *px, const mp_int *py, const mp_int *pz, + mp_int *rx, mp_int *ry, const ECGroup *group) +{ + mp_err res = MP_OKAY; + mp_int z1, z2, z3; + + MP_DIGITS(&z1) = 0; + MP_DIGITS(&z2) = 0; + MP_DIGITS(&z3) = 0; + MP_CHECKOK(mp_init(&z1)); + MP_CHECKOK(mp_init(&z2)); + MP_CHECKOK(mp_init(&z3)); + + /* if point at infinity, then set point at infinity and exit */ + if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) { + MP_CHECKOK(ec_GFp_pt_set_inf_aff(rx, ry)); + goto CLEANUP; + } + + /* transform (px, py, pz) into (px / pz^2, py / pz^3) */ + if (mp_cmp_d(pz, 1) == 0) { + MP_CHECKOK(mp_copy(px, rx)); + MP_CHECKOK(mp_copy(py, ry)); + } else { + MP_CHECKOK(group->meth->field_div(NULL, pz, &z1, group->meth)); + MP_CHECKOK(group->meth->field_sqr(&z1, &z2, group->meth)); + MP_CHECKOK(group->meth->field_mul(&z1, &z2, &z3, group->meth)); + MP_CHECKOK(group->meth->field_mul(px, &z2, rx, group->meth)); + MP_CHECKOK(group->meth->field_mul(py, &z3, ry, group->meth)); + } + +CLEANUP: + mp_clear(&z1); + mp_clear(&z2); + mp_clear(&z3); + return res; +} + +/* Checks if point P(px, py, pz) is at infinity. Uses Jacobian + * coordinates. */ +mp_err +ec_GFp_pt_is_inf_jac(const mp_int *px, const mp_int *py, const mp_int *pz) +{ + return mp_cmp_z(pz); +} + +/* Sets P(px, py, pz) to be the point at infinity. Uses Jacobian + * coordinates. */ +mp_err +ec_GFp_pt_set_inf_jac(mp_int *px, mp_int *py, mp_int *pz) +{ + mp_zero(pz); + return MP_OKAY; +} + +/* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is + * (qx, qy, 1). Elliptic curve points P, Q, and R can all be identical. + * Uses mixed Jacobian-affine coordinates. Assumes input is already + * field-encoded using field_enc, and returns output that is still + * field-encoded. Uses equation (2) from Brown, Hankerson, Lopez, and + * Menezes. Software Implementation of the NIST Elliptic Curves Over Prime + * Fields. */ +mp_err +ec_GFp_pt_add_jac_aff(const mp_int *px, const mp_int *py, const mp_int *pz, + const mp_int *qx, const mp_int *qy, mp_int *rx, + mp_int *ry, mp_int *rz, const ECGroup *group) +{ + mp_err res = MP_OKAY; + mp_int A, B, C, D, C2, C3; + + MP_DIGITS(&A) = 0; + MP_DIGITS(&B) = 0; + MP_DIGITS(&C) = 0; + MP_DIGITS(&D) = 0; + MP_DIGITS(&C2) = 0; + MP_DIGITS(&C3) = 0; + MP_CHECKOK(mp_init(&A)); + MP_CHECKOK(mp_init(&B)); + MP_CHECKOK(mp_init(&C)); + MP_CHECKOK(mp_init(&D)); + MP_CHECKOK(mp_init(&C2)); + MP_CHECKOK(mp_init(&C3)); + + /* If either P or Q is the point at infinity, then return the other + * point */ + if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) { + MP_CHECKOK(ec_GFp_pt_aff2jac(qx, qy, rx, ry, rz, group)); + goto CLEANUP; + } + if (ec_GFp_pt_is_inf_aff(qx, qy) == MP_YES) { + MP_CHECKOK(mp_copy(px, rx)); + MP_CHECKOK(mp_copy(py, ry)); + MP_CHECKOK(mp_copy(pz, rz)); + goto CLEANUP; + } + + /* A = qx * pz^2, B = qy * pz^3 */ + MP_CHECKOK(group->meth->field_sqr(pz, &A, group->meth)); + MP_CHECKOK(group->meth->field_mul(&A, pz, &B, group->meth)); + MP_CHECKOK(group->meth->field_mul(&A, qx, &A, group->meth)); + MP_CHECKOK(group->meth->field_mul(&B, qy, &B, group->meth)); + + /* C = A - px, D = B - py */ + MP_CHECKOK(group->meth->field_sub(&A, px, &C, group->meth)); + MP_CHECKOK(group->meth->field_sub(&B, py, &D, group->meth)); + + if (mp_cmp_z(&C) == 0) { + /* P == Q or P == -Q */ + if (mp_cmp_z(&D) == 0) { + /* P == Q */ + /* It is cheaper to double (qx, qy, 1) than (px, py, pz). */ + MP_DIGIT(&D, 0) = 1; /* Set D to 1. */ + MP_CHECKOK(ec_GFp_pt_dbl_jac(qx, qy, &D, rx, ry, rz, group)); + } else { + /* P == -Q */ + MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz)); + } + goto CLEANUP; + } + + /* C2 = C^2, C3 = C^3 */ + MP_CHECKOK(group->meth->field_sqr(&C, &C2, group->meth)); + MP_CHECKOK(group->meth->field_mul(&C, &C2, &C3, group->meth)); + + /* rz = pz * C */ + MP_CHECKOK(group->meth->field_mul(pz, &C, rz, group->meth)); + + /* C = px * C^2 */ + MP_CHECKOK(group->meth->field_mul(px, &C2, &C, group->meth)); + /* A = D^2 */ + MP_CHECKOK(group->meth->field_sqr(&D, &A, group->meth)); + + /* rx = D^2 - (C^3 + 2 * (px * C^2)) */ + MP_CHECKOK(group->meth->field_add(&C, &C, rx, group->meth)); + MP_CHECKOK(group->meth->field_add(&C3, rx, rx, group->meth)); + MP_CHECKOK(group->meth->field_sub(&A, rx, rx, group->meth)); + + /* C3 = py * C^3 */ + MP_CHECKOK(group->meth->field_mul(py, &C3, &C3, group->meth)); + + /* ry = D * (px * C^2 - rx) - py * C^3 */ + MP_CHECKOK(group->meth->field_sub(&C, rx, ry, group->meth)); + MP_CHECKOK(group->meth->field_mul(&D, ry, ry, group->meth)); + MP_CHECKOK(group->meth->field_sub(ry, &C3, ry, group->meth)); + +CLEANUP: + mp_clear(&A); + mp_clear(&B); + mp_clear(&C); + mp_clear(&D); + mp_clear(&C2); + mp_clear(&C3); + return res; +} + +/* Computes R = 2P. Elliptic curve points P and R can be identical. Uses + * Jacobian coordinates. + * + * Assumes input is already field-encoded using field_enc, and returns + * output that is still field-encoded. + * + * This routine implements Point Doubling in the Jacobian Projective + * space as described in the paper "Efficient elliptic curve exponentiation + * using mixed coordinates", by H. Cohen, A Miyaji, T. Ono. + */ +mp_err +ec_GFp_pt_dbl_jac(const mp_int *px, const mp_int *py, const mp_int *pz, + mp_int *rx, mp_int *ry, mp_int *rz, const ECGroup *group) +{ + mp_err res = MP_OKAY; + mp_int t0, t1, M, S; + + MP_DIGITS(&t0) = 0; + MP_DIGITS(&t1) = 0; + MP_DIGITS(&M) = 0; + MP_DIGITS(&S) = 0; + MP_CHECKOK(mp_init(&t0)); + MP_CHECKOK(mp_init(&t1)); + MP_CHECKOK(mp_init(&M)); + MP_CHECKOK(mp_init(&S)); + + /* P == inf or P == -P */ + if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES || mp_cmp_z(py) == 0) { + MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz)); + goto CLEANUP; + } + + if (mp_cmp_d(pz, 1) == 0) { + /* M = 3 * px^2 + a */ + MP_CHECKOK(group->meth->field_sqr(px, &t0, group->meth)); + MP_CHECKOK(group->meth->field_add(&t0, &t0, &M, group->meth)); + MP_CHECKOK(group->meth->field_add(&t0, &M, &t0, group->meth)); + MP_CHECKOK(group->meth->field_add(&t0, &group->curvea, &M, group->meth)); + } else if (MP_SIGN(&group->curvea) == MP_NEG && + MP_USED(&group->curvea) == 1 && + MP_DIGIT(&group->curvea, 0) == 3) { + /* M = 3 * (px + pz^2) * (px - pz^2) */ + MP_CHECKOK(group->meth->field_sqr(pz, &M, group->meth)); + MP_CHECKOK(group->meth->field_add(px, &M, &t0, group->meth)); + MP_CHECKOK(group->meth->field_sub(px, &M, &t1, group->meth)); + MP_CHECKOK(group->meth->field_mul(&t0, &t1, &M, group->meth)); + MP_CHECKOK(group->meth->field_add(&M, &M, &t0, group->meth)); + MP_CHECKOK(group->meth->field_add(&t0, &M, &M, group->meth)); + } else { + /* M = 3 * (px^2) + a * (pz^4) */ + MP_CHECKOK(group->meth->field_sqr(px, &t0, group->meth)); + MP_CHECKOK(group->meth->field_add(&t0, &t0, &M, group->meth)); + MP_CHECKOK(group->meth->field_add(&t0, &M, &t0, group->meth)); + MP_CHECKOK(group->meth->field_sqr(pz, &M, group->meth)); + MP_CHECKOK(group->meth->field_sqr(&M, &M, group->meth)); + MP_CHECKOK(group->meth->field_mul(&M, &group->curvea, &M, group->meth)); + MP_CHECKOK(group->meth->field_add(&M, &t0, &M, group->meth)); + } + + /* rz = 2 * py * pz */ + /* t0 = 4 * py^2 */ + if (mp_cmp_d(pz, 1) == 0) { + MP_CHECKOK(group->meth->field_add(py, py, rz, group->meth)); + MP_CHECKOK(group->meth->field_sqr(rz, &t0, group->meth)); + } else { + MP_CHECKOK(group->meth->field_add(py, py, &t0, group->meth)); + MP_CHECKOK(group->meth->field_mul(&t0, pz, rz, group->meth)); + MP_CHECKOK(group->meth->field_sqr(&t0, &t0, group->meth)); + } + + /* S = 4 * px * py^2 = px * (2 * py)^2 */ + MP_CHECKOK(group->meth->field_mul(px, &t0, &S, group->meth)); + + /* rx = M^2 - 2 * S */ + MP_CHECKOK(group->meth->field_add(&S, &S, &t1, group->meth)); + MP_CHECKOK(group->meth->field_sqr(&M, rx, group->meth)); + MP_CHECKOK(group->meth->field_sub(rx, &t1, rx, group->meth)); + + /* ry = M * (S - rx) - 8 * py^4 */ + MP_CHECKOK(group->meth->field_sqr(&t0, &t1, group->meth)); + if (mp_isodd(&t1)) { + MP_CHECKOK(mp_add(&t1, &group->meth->irr, &t1)); + } + MP_CHECKOK(mp_div_2(&t1, &t1)); + MP_CHECKOK(group->meth->field_sub(&S, rx, &S, group->meth)); + MP_CHECKOK(group->meth->field_mul(&M, &S, &M, group->meth)); + MP_CHECKOK(group->meth->field_sub(&M, &t1, ry, group->meth)); + +CLEANUP: + mp_clear(&t0); + mp_clear(&t1); + mp_clear(&M); + mp_clear(&S); + return res; +} + +/* by default, this routine is unused and thus doesn't need to be compiled */ +#ifdef ECL_ENABLE_GFP_PT_MUL_JAC +/* Computes R = nP where R is (rx, ry) and P is (px, py). The parameters + * a, b and p are the elliptic curve coefficients and the prime that + * determines the field GFp. Elliptic curve points P and R can be + * identical. Uses mixed Jacobian-affine coordinates. Assumes input is + * already field-encoded using field_enc, and returns output that is still + * field-encoded. Uses 4-bit window method. */ +mp_err +ec_GFp_pt_mul_jac(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 precomp[16][2], rz; + int i, ni, d; + + MP_DIGITS(&rz) = 0; + for (i = 0; i < 16; i++) { + MP_DIGITS(&precomp[i][0]) = 0; + MP_DIGITS(&precomp[i][1]) = 0; + } + + ARGCHK(group != NULL, MP_BADARG); + ARGCHK((n != NULL) && (px != NULL) && (py != NULL), MP_BADARG); + + /* initialize precomputation table */ + for (i = 0; i < 16; i++) { + MP_CHECKOK(mp_init(&precomp[i][0])); + MP_CHECKOK(mp_init(&precomp[i][1])); + } + + /* fill precomputation table */ + mp_zero(&precomp[0][0]); + mp_zero(&precomp[0][1]); + MP_CHECKOK(mp_copy(px, &precomp[1][0])); + MP_CHECKOK(mp_copy(py, &precomp[1][1])); + for (i = 2; i < 16; i++) { + MP_CHECKOK(group->point_add(&precomp[1][0], &precomp[1][1], + &precomp[i - 1][0], &precomp[i - 1][1], + &precomp[i][0], &precomp[i][1], group)); + } + + d = (mpl_significant_bits(n) + 3) / 4; + + /* R = inf */ + MP_CHECKOK(mp_init(&rz)); + MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz)); + + for (i = d - 1; i >= 0; i--) { + /* compute window ni */ + ni = MP_GET_BIT(n, 4 * i + 3); + ni <<= 1; + ni |= MP_GET_BIT(n, 4 * i + 2); + ni <<= 1; + ni |= MP_GET_BIT(n, 4 * i + 1); + ni <<= 1; + ni |= MP_GET_BIT(n, 4 * i); + /* R = 2^4 * R */ + MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group)); + MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group)); + MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group)); + MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group)); + /* R = R + (ni * P) */ + MP_CHECKOK(ec_GFp_pt_add_jac_aff(rx, ry, &rz, &precomp[ni][0], &precomp[ni][1], rx, ry, + &rz, group)); + } + + /* convert result S to affine coordinates */ + MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group)); + +CLEANUP: + mp_clear(&rz); + for (i = 0; i < 16; i++) { + mp_clear(&precomp[i][0]); + mp_clear(&precomp[i][1]); + } + return res; +} +#endif + +/* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G + + * k2 * P(x, y), where G is the generator (base point) of the group of + * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL. + * Uses mixed Jacobian-affine coordinates. Input and output values are + * assumed to be NOT field-encoded. Uses algorithm 15 (simultaneous + * multiple point multiplication) from Brown, Hankerson, Lopez, Menezes. + * Software Implementation of the NIST Elliptic Curves over Prime Fields. */ +mp_err +ec_GFp_pts_mul_jac(const mp_int *k1, const mp_int *k2, const mp_int *px, + const mp_int *py, mp_int *rx, mp_int *ry, + const ECGroup *group) +{ + mp_err res = MP_OKAY; + mp_int precomp[4][4][2]; + mp_int rz; + const mp_int *a, *b; + unsigned int i, j; + int ai, bi, d; + + for (i = 0; i < 4; i++) { + for (j = 0; j < 4; j++) { + MP_DIGITS(&precomp[i][j][0]) = 0; + MP_DIGITS(&precomp[i][j][1]) = 0; + } + } + MP_DIGITS(&rz) = 0; + + ARGCHK(group != NULL, MP_BADARG); + ARGCHK(!((k1 == NULL) && ((k2 == NULL) || (px == NULL) || (py == NULL))), MP_BADARG); + + /* if some arguments are not defined used ECPoint_mul */ + if (k1 == NULL) { + return ECPoint_mul(group, k2, px, py, rx, ry); + } else if ((k2 == NULL) || (px == NULL) || (py == NULL)) { + return ECPoint_mul(group, k1, NULL, NULL, rx, ry); + } + + /* initialize precomputation table */ + for (i = 0; i < 4; i++) { + for (j = 0; j < 4; j++) { + MP_CHECKOK(mp_init(&precomp[i][j][0])); + MP_CHECKOK(mp_init(&precomp[i][j][1])); + } + } + + /* fill precomputation table */ + /* assign {k1, k2} = {a, b} such that len(a) >= len(b) */ + if (mpl_significant_bits(k1) < mpl_significant_bits(k2)) { + a = k2; + b = k1; + if (group->meth->field_enc) { + MP_CHECKOK(group->meth->field_enc(px, &precomp[1][0][0], group->meth)); + MP_CHECKOK(group->meth->field_enc(py, &precomp[1][0][1], group->meth)); + } else { + MP_CHECKOK(mp_copy(px, &precomp[1][0][0])); + MP_CHECKOK(mp_copy(py, &precomp[1][0][1])); + } + MP_CHECKOK(mp_copy(&group->genx, &precomp[0][1][0])); + MP_CHECKOK(mp_copy(&group->geny, &precomp[0][1][1])); + } else { + a = k1; + b = k2; + MP_CHECKOK(mp_copy(&group->genx, &precomp[1][0][0])); + MP_CHECKOK(mp_copy(&group->geny, &precomp[1][0][1])); + if (group->meth->field_enc) { + MP_CHECKOK(group->meth->field_enc(px, &precomp[0][1][0], group->meth)); + MP_CHECKOK(group->meth->field_enc(py, &precomp[0][1][1], group->meth)); + } else { + MP_CHECKOK(mp_copy(px, &precomp[0][1][0])); + MP_CHECKOK(mp_copy(py, &precomp[0][1][1])); + } + } + /* precompute [*][0][*] */ + mp_zero(&precomp[0][0][0]); + mp_zero(&precomp[0][0][1]); + MP_CHECKOK(group->point_dbl(&precomp[1][0][0], &precomp[1][0][1], + &precomp[2][0][0], &precomp[2][0][1], group)); + MP_CHECKOK(group->point_add(&precomp[1][0][0], &precomp[1][0][1], + &precomp[2][0][0], &precomp[2][0][1], + &precomp[3][0][0], &precomp[3][0][1], group)); + /* precompute [*][1][*] */ + for (i = 1; i < 4; i++) { + MP_CHECKOK(group->point_add(&precomp[0][1][0], &precomp[0][1][1], + &precomp[i][0][0], &precomp[i][0][1], + &precomp[i][1][0], &precomp[i][1][1], group)); + } + /* precompute [*][2][*] */ + MP_CHECKOK(group->point_dbl(&precomp[0][1][0], &precomp[0][1][1], + &precomp[0][2][0], &precomp[0][2][1], group)); + for (i = 1; i < 4; i++) { + MP_CHECKOK(group->point_add(&precomp[0][2][0], &precomp[0][2][1], + &precomp[i][0][0], &precomp[i][0][1], + &precomp[i][2][0], &precomp[i][2][1], group)); + } + /* precompute [*][3][*] */ + MP_CHECKOK(group->point_add(&precomp[0][1][0], &precomp[0][1][1], + &precomp[0][2][0], &precomp[0][2][1], + &precomp[0][3][0], &precomp[0][3][1], group)); + for (i = 1; i < 4; i++) { + MP_CHECKOK(group->point_add(&precomp[0][3][0], &precomp[0][3][1], + &precomp[i][0][0], &precomp[i][0][1], + &precomp[i][3][0], &precomp[i][3][1], group)); + } + + d = (mpl_significant_bits(a) + 1) / 2; + + /* R = inf */ + MP_CHECKOK(mp_init(&rz)); + MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz)); + + for (i = d; i-- > 0;) { + ai = MP_GET_BIT(a, 2 * i + 1); + ai <<= 1; + ai |= MP_GET_BIT(a, 2 * i); + bi = MP_GET_BIT(b, 2 * i + 1); + bi <<= 1; + bi |= MP_GET_BIT(b, 2 * i); + /* R = 2^2 * R */ + MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group)); + MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group)); + /* R = R + (ai * A + bi * B) */ + MP_CHECKOK(ec_GFp_pt_add_jac_aff(rx, ry, &rz, &precomp[ai][bi][0], &precomp[ai][bi][1], + rx, ry, &rz, group)); + } + + MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group)); + + if (group->meth->field_dec) { + MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth)); + MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth)); + } + +CLEANUP: + mp_clear(&rz); + for (i = 0; i < 4; i++) { + for (j = 0; j < 4; j++) { + mp_clear(&precomp[i][j][0]); + mp_clear(&precomp[i][j][1]); + } + } + return res; +} |