/* ********************************************************************* * * Sun elects to have this file available under and governed by the * Mozilla Public License Version 1.1 ("MPL") (see * http://www.mozilla.org/MPL/ for full license text). For the avoidance * of doubt and subject to the following, Sun also elects to allow * licensees to use this file under the MPL, the GNU General Public * License version 2 only or the Lesser General Public License version * 2.1 only. Any references to the "GNU General Public License version 2 * or later" or "GPL" in the following shall be construed to mean the * GNU General Public License version 2 only. Any references to the "GNU * Lesser General Public License version 2.1 or later" or "LGPL" in the * following shall be construed to mean the GNU Lesser General Public * License version 2.1 only. However, the following notice accompanied * the original version of this file: * * Version: MPL 1.1/GPL 2.0/LGPL 2.1 * * The contents of this file are subject to the Mozilla Public License Version * 1.1 (the "License"); you may not use this file except in compliance with * the License. You may obtain a copy of the License at * http://www.mozilla.org/MPL/ * * Software distributed under the License is distributed on an "AS IS" basis, * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License * for the specific language governing rights and limitations under the * License. * * The Original Code is the elliptic curve math library for prime field curves. * * 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): * Stephen Fung , Sun Microsystems Laboratories * * Alternatively, the contents of this file may be used under the terms of * either the GNU General Public License Version 2 or later (the "GPL"), or * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"), * in which case the provisions of the GPL or the LGPL are applicable instead * of those above. If you wish to allow use of your version of this file only * under the terms of either the GPL or the LGPL, and not to allow others to * use your version of this file under the terms of the MPL, indicate your * decision by deleting the provisions above and replace them with the notice * and other provisions required by the GPL or the LGPL. If you do not delete * the provisions above, a recipient may use your version of this file under * the terms of any one of the MPL, the GPL or the LGPL. * *********************************************************************** */ /* * Copyright (c) 2007, 2011, Oracle and/or its affiliates. All rights reserved. * Use is subject to license terms. */ #include "ecp.h" #include "ecl-priv.h" #include "mplogic.h" #ifndef _KERNEL #include #endif #define MAX_SCRATCH 6 /* Computes R = 2P. Elliptic curve points P and R can be identical. Uses * Modified Jacobian coordinates. * * Assumes input is already field-encoded using field_enc, and returns * output that is still field-encoded. * */ mp_err ec_GFp_pt_dbl_jm(const mp_int *px, const mp_int *py, const mp_int *pz, const mp_int *paz4, mp_int *rx, mp_int *ry, mp_int *rz, mp_int *raz4, mp_int scratch[], const ECGroup *group) { mp_err res = MP_OKAY; mp_int *t0, *t1, *M, *S; t0 = &scratch[0]; t1 = &scratch[1]; M = &scratch[2]; S = &scratch[3]; #if MAX_SCRATCH < 4 #error "Scratch array defined too small " #endif /* Check for point at infinity */ if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) { /* Set r = pt at infinity by setting rz = 0 */ MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz)); goto CLEANUP; } /* 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_add(t0, paz4, M, group->meth)); /* rz = 2 * py * pz */ MP_CHECKOK(group->meth->field_mul(py, pz, S, group->meth)); MP_CHECKOK(group->meth->field_add(S, S, rz, group->meth)); /* t0 = 2y^2 , t1 = 8y^4 */ MP_CHECKOK(group->meth->field_sqr(py, t0, group->meth)); MP_CHECKOK(group->meth->field_add(t0, t0, t0, group->meth)); MP_CHECKOK(group->meth->field_sqr(t0, t1, group->meth)); MP_CHECKOK(group->meth->field_add(t1, t1, t1, group->meth)); /* S = 4 * px * py^2 = 2 * px * t0 */ MP_CHECKOK(group->meth->field_mul(px, t0, S, group->meth)); MP_CHECKOK(group->meth->field_add(S, S, S, group->meth)); /* rx = M^2 - 2S */ MP_CHECKOK(group->meth->field_sqr(M, rx, group->meth)); MP_CHECKOK(group->meth->field_sub(rx, S, rx, group->meth)); MP_CHECKOK(group->meth->field_sub(rx, S, rx, group->meth)); /* ry = M * (S - rx) - t1 */ MP_CHECKOK(group->meth->field_sub(S, rx, S, group->meth)); MP_CHECKOK(group->meth->field_mul(S, M, ry, group->meth)); MP_CHECKOK(group->meth->field_sub(ry, t1, ry, group->meth)); /* ra*z^4 = 2*t1*(apz4) */ MP_CHECKOK(group->meth->field_mul(paz4, t1, raz4, group->meth)); MP_CHECKOK(group->meth->field_add(raz4, raz4, raz4, group->meth)); CLEANUP: return res; } /* 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 Modified_Jacobian-affine coordinates. Assumes input is * already field-encoded using field_enc, and returns output that is still * field-encoded. */ mp_err ec_GFp_pt_add_jm_aff(const mp_int *px, const mp_int *py, const mp_int *pz, const mp_int *paz4, const mp_int *qx, const mp_int *qy, mp_int *rx, mp_int *ry, mp_int *rz, mp_int *raz4, mp_int scratch[], const ECGroup *group) { mp_err res = MP_OKAY; mp_int *A, *B, *C, *D, *C2, *C3; A = &scratch[0]; B = &scratch[1]; C = &scratch[2]; D = &scratch[3]; C2 = &scratch[4]; C3 = &scratch[5]; #if MAX_SCRATCH < 6 #error "Scratch array defined too small " #endif /* 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)); MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth)); MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth)); MP_CHECKOK(group->meth-> field_mul(raz4, &group->curvea, raz4, group->meth)); 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)); MP_CHECKOK(mp_copy(paz4, raz4)); 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)); /* 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)); /* raz4 = a * rz^4 */ MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth)); MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth)); MP_CHECKOK(group->meth-> field_mul(raz4, &group->curvea, raz4, group->meth)); CLEANUP: return res; } /* Computes R = nP where R is (rx, ry) and P is the base point. Elliptic * curve points P and R can be identical. Uses mixed Modified-Jacobian * co-ordinates for doubling and Chudnovsky Jacobian coordinates for * additions. Assumes input is already field-encoded using field_enc, and * returns output that is still field-encoded. Uses 5-bit window NAF * method (algorithm 11) for scalar-point multiplication from Brown, * Hankerson, Lopez, Menezes. Software Implementation of the NIST Elliptic * Curves Over Prime Fields. */ mp_err ec_GFp_pt_mul_jm_wNAF(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, tpx, tpy; mp_int raz4; mp_int scratch[MAX_SCRATCH]; signed char *naf = NULL; int i, orderBitSize; MP_DIGITS(&rz) = 0; MP_DIGITS(&raz4) = 0; MP_DIGITS(&tpx) = 0; MP_DIGITS(&tpy) = 0; for (i = 0; i < 16; i++) { MP_DIGITS(&precomp[i][0]) = 0; MP_DIGITS(&precomp[i][1]) = 0; } for (i = 0; i < MAX_SCRATCH; i++) { MP_DIGITS(&scratch[i]) = 0; } ARGCHK(group != NULL, MP_BADARG); ARGCHK((n != NULL) && (px != NULL) && (py != NULL), MP_BADARG); /* initialize precomputation table */ MP_CHECKOK(mp_init(&tpx, FLAG(n))); MP_CHECKOK(mp_init(&tpy, FLAG(n)));; MP_CHECKOK(mp_init(&rz, FLAG(n))); MP_CHECKOK(mp_init(&raz4, FLAG(n))); for (i = 0; i < 16; i++) { MP_CHECKOK(mp_init(&precomp[i][0], FLAG(n))); MP_CHECKOK(mp_init(&precomp[i][1], FLAG(n))); } for (i = 0; i < MAX_SCRATCH; i++) { MP_CHECKOK(mp_init(&scratch[i], FLAG(n))); } /* Set out[8] = P */ MP_CHECKOK(mp_copy(px, &precomp[8][0])); MP_CHECKOK(mp_copy(py, &precomp[8][1])); /* Set (tpx, tpy) = 2P */ MP_CHECKOK(group-> point_dbl(&precomp[8][0], &precomp[8][1], &tpx, &tpy, group)); /* Set 3P, 5P, ..., 15P */ for (i = 8; i < 15; i++) { MP_CHECKOK(group-> point_add(&precomp[i][0], &precomp[i][1], &tpx, &tpy, &precomp[i + 1][0], &precomp[i + 1][1], group)); } /* Set -15P, -13P, ..., -P */ for (i = 0; i < 8; i++) { MP_CHECKOK(mp_copy(&precomp[15 - i][0], &precomp[i][0])); MP_CHECKOK(group->meth-> field_neg(&precomp[15 - i][1], &precomp[i][1], group->meth)); } /* R = inf */ MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz)); orderBitSize = mpl_significant_bits(&group->order); /* Allocate memory for NAF */ #ifdef _KERNEL naf = (signed char *) kmem_alloc((orderBitSize + 1), FLAG(n)); #else naf = (signed char *) malloc(sizeof(signed char) * (orderBitSize + 1)); if (naf == NULL) { res = MP_MEM; goto CLEANUP; } #endif /* Compute 5NAF */ ec_compute_wNAF(naf, orderBitSize, n, 5); /* wNAF method */ for (i = orderBitSize; i >= 0; i--) { /* R = 2R */ ec_GFp_pt_dbl_jm(rx, ry, &rz, &raz4, rx, ry, &rz, &raz4, scratch, group); if (naf[i] != 0) { ec_GFp_pt_add_jm_aff(rx, ry, &rz, &raz4, &precomp[(naf[i] + 15) / 2][0], &precomp[(naf[i] + 15) / 2][1], rx, ry, &rz, &raz4, scratch, group); } } /* convert result S to affine coordinates */ MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group)); CLEANUP: for (i = 0; i < MAX_SCRATCH; i++) { mp_clear(&scratch[i]); } for (i = 0; i < 16; i++) { mp_clear(&precomp[i][0]); mp_clear(&precomp[i][1]); } mp_clear(&tpx); mp_clear(&tpy); mp_clear(&rz); mp_clear(&raz4); #ifdef _KERNEL kmem_free(naf, (orderBitSize + 1)); #else free(naf); #endif return res; }