/* * Copyright (c) 2007, 2011, Oracle and/or its affiliates. All rights reserved. * Use is subject to license terms. * * This library is free software; you can redistribute it and/or * modify it under the terms of the GNU Lesser General Public * License as published by the Free Software Foundation; either * version 2.1 of the License, or (at your option) any later version. * * This library is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU * Lesser General Public License for more details. * * You should have received a copy of the GNU Lesser General Public License * along with this library; if not, write to the Free Software Foundation, * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. * * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA * or visit www.oracle.com if you need additional information or have any * questions. */ /* ********************************************************************* * * The Original Code is the elliptic curve math library. * * The Initial Developer of the Original Code is * Sun Microsystems, Inc. * Portions created by the Initial Developer are Copyright (C) 2003 * the Initial Developer. All Rights Reserved. * * Contributor(s): * Douglas Stebila , Sun Microsystems Laboratories * *********************************************************************** */ #include "mpi.h" #include "mplogic.h" #include "ecl.h" #include "ecl-priv.h" #ifndef _KERNEL #include #endif /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k * P(x, * y). If x, y = NULL, then P is assumed to be the generator (base point) * of the group of points on the elliptic curve. Input and output values * are assumed to be NOT field-encoded. */ mp_err ECPoint_mul(const ECGroup *group, const mp_int *k, const mp_int *px, const mp_int *py, mp_int *rx, mp_int *ry) { mp_err res = MP_OKAY; mp_int kt; ARGCHK((k != NULL) && (group != NULL), MP_BADARG); MP_DIGITS(&kt) = 0; /* want scalar to be less than or equal to group order */ if (mp_cmp(k, &group->order) > 0) { MP_CHECKOK(mp_init(&kt, FLAG(k))); MP_CHECKOK(mp_mod(k, &group->order, &kt)); } else { MP_SIGN(&kt) = MP_ZPOS; MP_USED(&kt) = MP_USED(k); MP_ALLOC(&kt) = MP_ALLOC(k); MP_DIGITS(&kt) = MP_DIGITS(k); } if ((px == NULL) || (py == NULL)) { if (group->base_point_mul) { MP_CHECKOK(group->base_point_mul(&kt, rx, ry, group)); } else { kt.flag = (mp_sign)0; MP_CHECKOK(group-> point_mul(&kt, &group->genx, &group->geny, rx, ry, group)); } } else { if (group->meth->field_enc) { MP_CHECKOK(group->meth->field_enc(px, rx, group->meth)); MP_CHECKOK(group->meth->field_enc(py, ry, group->meth)); MP_CHECKOK(group->point_mul(&kt, rx, ry, rx, ry, group)); } else { kt.flag = (mp_sign)0; MP_CHECKOK(group->point_mul(&kt, px, py, 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: if (MP_DIGITS(&kt) != MP_DIGITS(k)) { mp_clear(&kt); } return res; } /* 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. * Input and output values are assumed to be NOT field-encoded. */ mp_err ec_pts_mul_basic(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 sx, sy; 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); } MP_DIGITS(&sx) = 0; MP_DIGITS(&sy) = 0; MP_CHECKOK(mp_init(&sx, FLAG(k1))); MP_CHECKOK(mp_init(&sy, FLAG(k1))); MP_CHECKOK(ECPoint_mul(group, k1, NULL, NULL, &sx, &sy)); MP_CHECKOK(ECPoint_mul(group, k2, px, py, rx, ry)); if (group->meth->field_enc) { MP_CHECKOK(group->meth->field_enc(&sx, &sx, group->meth)); MP_CHECKOK(group->meth->field_enc(&sy, &sy, group->meth)); MP_CHECKOK(group->meth->field_enc(rx, rx, group->meth)); MP_CHECKOK(group->meth->field_enc(ry, ry, group->meth)); } MP_CHECKOK(group->point_add(&sx, &sy, rx, ry, 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(&sx); mp_clear(&sy); return res; } /* 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. * 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_pts_mul_simul_w2(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]; const mp_int *a, *b; int i, j; int ai, bi, d; 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_DIGITS(&precomp[i][j][0]) = 0; MP_DIGITS(&precomp[i][j][1]) = 0; } } for (i = 0; i < 4; i++) { for (j = 0; j < 4; j++) { MP_CHECKOK( mp_init_size(&precomp[i][j][0], ECL_MAX_FIELD_SIZE_DIGITS, FLAG(k1)) ); MP_CHECKOK( mp_init_size(&precomp[i][j][1], ECL_MAX_FIELD_SIZE_DIGITS, FLAG(k1)) ); } } /* 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_zero(rx); mp_zero(ry); for (i = d - 1; i >= 0; i--) { 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(group->point_dbl(rx, ry, rx, ry, group)); MP_CHECKOK(group->point_dbl(rx, ry, rx, ry, group)); /* R = R + (ai * A + bi * B) */ MP_CHECKOK(group-> point_add(rx, ry, &precomp[ai][bi][0], &precomp[ai][bi][1], 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: 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; } /* 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. * Input and output values are assumed to be NOT field-encoded. */ mp_err ECPoints_mul(const ECGroup *group, const mp_int *k1, const mp_int *k2, const mp_int *px, const mp_int *py, mp_int *rx, mp_int *ry) { mp_err res = MP_OKAY; mp_int k1t, k2t; const mp_int *k1p, *k2p; MP_DIGITS(&k1t) = 0; MP_DIGITS(&k2t) = 0; ARGCHK(group != NULL, MP_BADARG); /* want scalar to be less than or equal to group order */ if (k1 != NULL) { if (mp_cmp(k1, &group->order) >= 0) { MP_CHECKOK(mp_init(&k1t, FLAG(k1))); MP_CHECKOK(mp_mod(k1, &group->order, &k1t)); k1p = &k1t; } else { k1p = k1; } } else { k1p = k1; } if (k2 != NULL) { if (mp_cmp(k2, &group->order) >= 0) { MP_CHECKOK(mp_init(&k2t, FLAG(k2))); MP_CHECKOK(mp_mod(k2, &group->order, &k2t)); k2p = &k2t; } else { k2p = k2; } } else { k2p = k2; } /* if points_mul is defined, then use it */ if (group->points_mul) { res = group->points_mul(k1p, k2p, px, py, rx, ry, group); } else { res = ec_pts_mul_simul_w2(k1p, k2p, px, py, rx, ry, group); } CLEANUP: mp_clear(&k1t); mp_clear(&k2t); return res; }