| /* |
| * Copyright (c) 2007, 2017, 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 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 <fungstep@hotmail.com>, Sun Microsystems Laboratories |
| * |
| * Last Modified Date from the Original Code: May 2017 |
| *********************************************************************** */ |
| |
| #include "ecp.h" |
| #include "ecl-priv.h" |
| #include "mplogic.h" |
| #ifndef _KERNEL |
| #include <stdlib.h> |
| #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)); |
| |
| /* |
| * Additional checks for point equality and point at infinity |
| */ |
| if (mp_cmp(px, A) == 0 && mp_cmp(py, B) == 0) { |
| /* POINT_DOUBLE(P) */ |
| MP_CHECKOK(ec_GFp_pt_dbl_jm(px, py, pz, paz4, rx, ry, rz, raz4, |
| scratch, group)); |
| goto CLEANUP; |
| } |
| |
| /* 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, |
| int timing) |
| { |
| mp_err res = MP_OKAY; |
| mp_int precomp[16][2], rz, tpx, tpy, tpz; |
| mp_int raz4, tpaz4; |
| mp_int scratch[MAX_SCRATCH]; |
| signed char *naf = NULL; |
| int i, orderBitSize; |
| int numDoubles, numAdds, extraDoubles, extraAdds; |
| |
| MP_DIGITS(&rz) = 0; |
| MP_DIGITS(&raz4) = 0; |
| MP_DIGITS(&tpx) = 0; |
| MP_DIGITS(&tpy) = 0; |
| MP_DIGITS(&tpz) = 0; |
| MP_DIGITS(&tpaz4) = 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(&tpz, FLAG(n))); |
| MP_CHECKOK(mp_init(&tpaz4, 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); |
| |
| numAdds = 0; |
| numDoubles = orderBitSize; |
| /* wNAF method */ |
| for (i = orderBitSize; i >= 0; i--) { |
| |
| if (ec_GFp_pt_is_inf_jac(rx, ry, &rz) == MP_YES) { |
| numDoubles--; |
| } |
| |
| /* 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); |
| numAdds++; |
| } |
| } |
| |
| /* extra operations to make timing less dependent on secrets */ |
| if (timing) { |
| /* low-order bit of timing argument contains no entropy */ |
| timing >>= 1; |
| |
| MP_CHECKOK(ec_GFp_pt_set_inf_jac(&tpx, &tpy, &tpz)); |
| mp_zero(&tpaz4); |
| |
| /* Set the temp value to a non-infinite point */ |
| ec_GFp_pt_add_jm_aff(&tpx, &tpy, &tpz, &tpaz4, |
| &precomp[8][0], |
| &precomp[8][1], &tpx, &tpy, |
| &tpz, &tpaz4, scratch, group); |
| |
| /* two bits of extra adds */ |
| extraAdds = timing & 0x3; |
| timing >>= 2; |
| /* Window size is 5, so the maximum number of additions is ceil(orderBitSize/5) */ |
| /* This is the same as (orderBitSize + 4) / 5 */ |
| for(i = numAdds; i <= (orderBitSize + 4) / 5 + extraAdds; i++) { |
| ec_GFp_pt_add_jm_aff(&tpx, &tpy, &tpz, &tpaz4, |
| &precomp[9 + (i % 3)][0], |
| &precomp[9 + (i % 3)][1], &tpx, &tpy, |
| &tpz, &tpaz4, scratch, group); |
| } |
| |
| /* two bits of extra doubles */ |
| extraDoubles = timing & 0x3; |
| timing >>= 2; |
| for(i = numDoubles; i <= orderBitSize + extraDoubles; i++) { |
| ec_GFp_pt_dbl_jm(&tpx, &tpy, &tpz, &tpaz4, &tpx, &tpy, &tpz, |
| &tpaz4, 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(&tpz); |
| mp_clear(&tpaz4); |
| mp_clear(&rz); |
| mp_clear(&raz4); |
| #ifdef _KERNEL |
| kmem_free(naf, (orderBitSize + 1)); |
| #else |
| free(naf); |
| #endif |
| return res; |
| } |
