author | vinnie |
Mon, 30 May 2011 16:37:42 +0100 | |
changeset 9774 | 50a2b28ca54c |
parent 9035 | 1255eb81cc2f |
permissions | -rw-r--r-- |
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/* |
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* Copyright (c) 2007, 2011, Oracle and/or its affiliates. All rights reserved. |
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* Use is subject to license terms. |
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* |
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* This library is free software; you can redistribute it and/or |
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* modify it under the terms of the GNU Lesser General Public |
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* License as published by the Free Software Foundation; either |
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* version 2.1 of the License, or (at your option) any later version. |
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* |
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* This library is distributed in the hope that it will be useful, |
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* but WITHOUT ANY WARRANTY; without even the implied warranty of |
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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* Lesser General Public License for more details. |
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* |
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* You should have received a copy of the GNU Lesser General Public License |
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* along with this library; if not, write to the Free Software Foundation, |
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* Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. |
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* |
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* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA |
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* or visit www.oracle.com if you need additional information or have any |
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* questions. |
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*/ |
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/* ********************************************************************* |
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* |
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* The Original Code is the elliptic curve math library. |
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* |
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* The Initial Developer of the Original Code is |
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* Sun Microsystems, Inc. |
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* Portions created by the Initial Developer are Copyright (C) 2003 |
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* the Initial Developer. All Rights Reserved. |
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* |
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* Contributor(s): |
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* Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories |
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* |
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*********************************************************************** */ |
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|
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#include "mpi.h" |
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#include "mplogic.h" |
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#include "ecl.h" |
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#include "ecl-priv.h" |
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#ifndef _KERNEL |
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#include <stdlib.h> |
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#endif |
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/* Elliptic curve scalar-point multiplication. Computes R(x, y) = k * P(x, |
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* y). If x, y = NULL, then P is assumed to be the generator (base point) |
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* of the group of points on the elliptic curve. Input and output values |
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* are assumed to be NOT field-encoded. */ |
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mp_err |
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ECPoint_mul(const ECGroup *group, const mp_int *k, const mp_int *px, |
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const mp_int *py, mp_int *rx, mp_int *ry) |
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{ |
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mp_err res = MP_OKAY; |
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mp_int kt; |
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ARGCHK((k != NULL) && (group != NULL), MP_BADARG); |
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MP_DIGITS(&kt) = 0; |
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/* want scalar to be less than or equal to group order */ |
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if (mp_cmp(k, &group->order) > 0) { |
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MP_CHECKOK(mp_init(&kt, FLAG(k))); |
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MP_CHECKOK(mp_mod(k, &group->order, &kt)); |
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} else { |
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MP_SIGN(&kt) = MP_ZPOS; |
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MP_USED(&kt) = MP_USED(k); |
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MP_ALLOC(&kt) = MP_ALLOC(k); |
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MP_DIGITS(&kt) = MP_DIGITS(k); |
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} |
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if ((px == NULL) || (py == NULL)) { |
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if (group->base_point_mul) { |
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MP_CHECKOK(group->base_point_mul(&kt, rx, ry, group)); |
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} else { |
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MP_CHECKOK(group-> |
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point_mul(&kt, &group->genx, &group->geny, rx, ry, |
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group)); |
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} |
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} else { |
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if (group->meth->field_enc) { |
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MP_CHECKOK(group->meth->field_enc(px, rx, group->meth)); |
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MP_CHECKOK(group->meth->field_enc(py, ry, group->meth)); |
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MP_CHECKOK(group->point_mul(&kt, rx, ry, rx, ry, group)); |
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} else { |
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MP_CHECKOK(group->point_mul(&kt, px, py, rx, ry, group)); |
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} |
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} |
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if (group->meth->field_dec) { |
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MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth)); |
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MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth)); |
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} |
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CLEANUP: |
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if (MP_DIGITS(&kt) != MP_DIGITS(k)) { |
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mp_clear(&kt); |
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} |
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return res; |
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} |
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/* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G + |
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* k2 * P(x, y), where G is the generator (base point) of the group of |
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* points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL. |
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* Input and output values are assumed to be NOT field-encoded. */ |
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mp_err |
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ec_pts_mul_basic(const mp_int *k1, const mp_int *k2, const mp_int *px, |
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const mp_int *py, mp_int *rx, mp_int *ry, |
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const ECGroup *group) |
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{ |
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mp_err res = MP_OKAY; |
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mp_int sx, sy; |
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ARGCHK(group != NULL, MP_BADARG); |
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ARGCHK(!((k1 == NULL) |
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114 |
&& ((k2 == NULL) || (px == NULL) |
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|
115 |
|| (py == NULL))), MP_BADARG); |
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|
116 |
|
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117 |
/* if some arguments are not defined used ECPoint_mul */ |
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118 |
if (k1 == NULL) { |
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119 |
return ECPoint_mul(group, k2, px, py, rx, ry); |
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120 |
} else if ((k2 == NULL) || (px == NULL) || (py == NULL)) { |
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121 |
return ECPoint_mul(group, k1, NULL, NULL, rx, ry); |
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122 |
} |
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|
123 |
|
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124 |
MP_DIGITS(&sx) = 0; |
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125 |
MP_DIGITS(&sy) = 0; |
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126 |
MP_CHECKOK(mp_init(&sx, FLAG(k1))); |
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127 |
MP_CHECKOK(mp_init(&sy, FLAG(k1))); |
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|
128 |
|
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|
129 |
MP_CHECKOK(ECPoint_mul(group, k1, NULL, NULL, &sx, &sy)); |
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130 |
MP_CHECKOK(ECPoint_mul(group, k2, px, py, rx, ry)); |
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131 |
|
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132 |
if (group->meth->field_enc) { |
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133 |
MP_CHECKOK(group->meth->field_enc(&sx, &sx, group->meth)); |
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134 |
MP_CHECKOK(group->meth->field_enc(&sy, &sy, group->meth)); |
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135 |
MP_CHECKOK(group->meth->field_enc(rx, rx, group->meth)); |
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|
136 |
MP_CHECKOK(group->meth->field_enc(ry, ry, group->meth)); |
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|
137 |
} |
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|
138 |
|
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|
139 |
MP_CHECKOK(group->point_add(&sx, &sy, rx, ry, rx, ry, group)); |
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|
140 |
|
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|
141 |
if (group->meth->field_dec) { |
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|
142 |
MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth)); |
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|
143 |
MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth)); |
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|
144 |
} |
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|
145 |
|
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|
146 |
CLEANUP: |
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147 |
mp_clear(&sx); |
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148 |
mp_clear(&sy); |
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|
149 |
return res; |
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|
150 |
} |
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|
151 |
|
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152 |
/* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G + |
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153 |
* k2 * P(x, y), where G is the generator (base point) of the group of |
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154 |
* points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL. |
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155 |
* Input and output values are assumed to be NOT field-encoded. Uses |
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156 |
* algorithm 15 (simultaneous multiple point multiplication) from Brown, |
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157 |
* Hankerson, Lopez, Menezes. Software Implementation of the NIST |
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158 |
* Elliptic Curves over Prime Fields. */ |
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|
159 |
mp_err |
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|
160 |
ec_pts_mul_simul_w2(const mp_int *k1, const mp_int *k2, const mp_int *px, |
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161 |
const mp_int *py, mp_int *rx, mp_int *ry, |
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162 |
const ECGroup *group) |
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|
163 |
{ |
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|
164 |
mp_err res = MP_OKAY; |
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165 |
mp_int precomp[4][4][2]; |
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166 |
const mp_int *a, *b; |
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167 |
int i, j; |
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168 |
int ai, bi, d; |
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|
169 |
|
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|
170 |
ARGCHK(group != NULL, MP_BADARG); |
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|
171 |
ARGCHK(!((k1 == NULL) |
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|
172 |
&& ((k2 == NULL) || (px == NULL) |
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|
173 |
|| (py == NULL))), MP_BADARG); |
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|
174 |
|
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|
175 |
/* if some arguments are not defined used ECPoint_mul */ |
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|
176 |
if (k1 == NULL) { |
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|
177 |
return ECPoint_mul(group, k2, px, py, rx, ry); |
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|
178 |
} else if ((k2 == NULL) || (px == NULL) || (py == NULL)) { |
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|
179 |
return ECPoint_mul(group, k1, NULL, NULL, rx, ry); |
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|
180 |
} |
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|
181 |
|
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|
182 |
/* initialize precomputation table */ |
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|
183 |
for (i = 0; i < 4; i++) { |
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|
184 |
for (j = 0; j < 4; j++) { |
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|
185 |
MP_DIGITS(&precomp[i][j][0]) = 0; |
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|
186 |
MP_DIGITS(&precomp[i][j][1]) = 0; |
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|
187 |
} |
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|
188 |
} |
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|
189 |
for (i = 0; i < 4; i++) { |
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|
190 |
for (j = 0; j < 4; j++) { |
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|
191 |
MP_CHECKOK( mp_init_size(&precomp[i][j][0], |
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|
192 |
ECL_MAX_FIELD_SIZE_DIGITS, FLAG(k1)) ); |
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|
193 |
MP_CHECKOK( mp_init_size(&precomp[i][j][1], |
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|
194 |
ECL_MAX_FIELD_SIZE_DIGITS, FLAG(k1)) ); |
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|
195 |
} |
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|
196 |
} |
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|
197 |
|
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|
198 |
/* fill precomputation table */ |
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|
199 |
/* assign {k1, k2} = {a, b} such that len(a) >= len(b) */ |
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|
200 |
if (mpl_significant_bits(k1) < mpl_significant_bits(k2)) { |
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|
201 |
a = k2; |
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|
202 |
b = k1; |
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|
203 |
if (group->meth->field_enc) { |
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|
204 |
MP_CHECKOK(group->meth-> |
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|
205 |
field_enc(px, &precomp[1][0][0], group->meth)); |
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|
206 |
MP_CHECKOK(group->meth-> |
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|
207 |
field_enc(py, &precomp[1][0][1], group->meth)); |
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|
208 |
} else { |
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|
209 |
MP_CHECKOK(mp_copy(px, &precomp[1][0][0])); |
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|
210 |
MP_CHECKOK(mp_copy(py, &precomp[1][0][1])); |
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|
211 |
} |
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|
212 |
MP_CHECKOK(mp_copy(&group->genx, &precomp[0][1][0])); |
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|
213 |
MP_CHECKOK(mp_copy(&group->geny, &precomp[0][1][1])); |
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|
214 |
} else { |
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|
215 |
a = k1; |
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|
216 |
b = k2; |
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|
217 |
MP_CHECKOK(mp_copy(&group->genx, &precomp[1][0][0])); |
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|
218 |
MP_CHECKOK(mp_copy(&group->geny, &precomp[1][0][1])); |
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|
219 |
if (group->meth->field_enc) { |
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|
220 |
MP_CHECKOK(group->meth-> |
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|
221 |
field_enc(px, &precomp[0][1][0], group->meth)); |
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|
222 |
MP_CHECKOK(group->meth-> |
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|
223 |
field_enc(py, &precomp[0][1][1], group->meth)); |
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224 |
} else { |
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225 |
MP_CHECKOK(mp_copy(px, &precomp[0][1][0])); |
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226 |
MP_CHECKOK(mp_copy(py, &precomp[0][1][1])); |
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227 |
} |
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228 |
} |
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229 |
/* precompute [*][0][*] */ |
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230 |
mp_zero(&precomp[0][0][0]); |
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231 |
mp_zero(&precomp[0][0][1]); |
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232 |
MP_CHECKOK(group-> |
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233 |
point_dbl(&precomp[1][0][0], &precomp[1][0][1], |
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234 |
&precomp[2][0][0], &precomp[2][0][1], group)); |
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235 |
MP_CHECKOK(group-> |
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|
236 |
point_add(&precomp[1][0][0], &precomp[1][0][1], |
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237 |
&precomp[2][0][0], &precomp[2][0][1], |
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238 |
&precomp[3][0][0], &precomp[3][0][1], group)); |
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239 |
/* precompute [*][1][*] */ |
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240 |
for (i = 1; i < 4; i++) { |
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241 |
MP_CHECKOK(group-> |
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242 |
point_add(&precomp[0][1][0], &precomp[0][1][1], |
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243 |
&precomp[i][0][0], &precomp[i][0][1], |
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244 |
&precomp[i][1][0], &precomp[i][1][1], group)); |
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245 |
} |
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246 |
/* precompute [*][2][*] */ |
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247 |
MP_CHECKOK(group-> |
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248 |
point_dbl(&precomp[0][1][0], &precomp[0][1][1], |
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|
249 |
&precomp[0][2][0], &precomp[0][2][1], group)); |
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|
250 |
for (i = 1; i < 4; i++) { |
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251 |
MP_CHECKOK(group-> |
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|
252 |
point_add(&precomp[0][2][0], &precomp[0][2][1], |
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253 |
&precomp[i][0][0], &precomp[i][0][1], |
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|
254 |
&precomp[i][2][0], &precomp[i][2][1], group)); |
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255 |
} |
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256 |
/* precompute [*][3][*] */ |
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|
257 |
MP_CHECKOK(group-> |
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|
258 |
point_add(&precomp[0][1][0], &precomp[0][1][1], |
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|
259 |
&precomp[0][2][0], &precomp[0][2][1], |
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|
260 |
&precomp[0][3][0], &precomp[0][3][1], group)); |
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|
261 |
for (i = 1; i < 4; i++) { |
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|
262 |
MP_CHECKOK(group-> |
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|
263 |
point_add(&precomp[0][3][0], &precomp[0][3][1], |
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|
264 |
&precomp[i][0][0], &precomp[i][0][1], |
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|
265 |
&precomp[i][3][0], &precomp[i][3][1], group)); |
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|
266 |
} |
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|
267 |
|
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|
268 |
d = (mpl_significant_bits(a) + 1) / 2; |
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|
269 |
|
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270 |
/* R = inf */ |
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271 |
mp_zero(rx); |
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272 |
mp_zero(ry); |
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|
273 |
|
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|
274 |
for (i = d - 1; i >= 0; i--) { |
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|
275 |
ai = MP_GET_BIT(a, 2 * i + 1); |
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276 |
ai <<= 1; |
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|
277 |
ai |= MP_GET_BIT(a, 2 * i); |
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|
278 |
bi = MP_GET_BIT(b, 2 * i + 1); |
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279 |
bi <<= 1; |
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|
280 |
bi |= MP_GET_BIT(b, 2 * i); |
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|
281 |
/* R = 2^2 * R */ |
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|
282 |
MP_CHECKOK(group->point_dbl(rx, ry, rx, ry, group)); |
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|
283 |
MP_CHECKOK(group->point_dbl(rx, ry, rx, ry, group)); |
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|
284 |
/* R = R + (ai * A + bi * B) */ |
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|
285 |
MP_CHECKOK(group-> |
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|
286 |
point_add(rx, ry, &precomp[ai][bi][0], |
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|
287 |
&precomp[ai][bi][1], rx, ry, group)); |
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|
288 |
} |
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|
289 |
|
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|
290 |
if (group->meth->field_dec) { |
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|
291 |
MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth)); |
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|
292 |
MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth)); |
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|
293 |
} |
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|
294 |
|
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|
295 |
CLEANUP: |
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|
296 |
for (i = 0; i < 4; i++) { |
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|
297 |
for (j = 0; j < 4; j++) { |
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|
298 |
mp_clear(&precomp[i][j][0]); |
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|
299 |
mp_clear(&precomp[i][j][1]); |
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|
300 |
} |
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|
301 |
} |
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|
302 |
return res; |
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|
303 |
} |
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|
304 |
|
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|
305 |
/* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G + |
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306 |
* k2 * P(x, y), where G is the generator (base point) of the group of |
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|
307 |
* points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL. |
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|
308 |
* Input and output values are assumed to be NOT field-encoded. */ |
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|
309 |
mp_err |
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|
310 |
ECPoints_mul(const ECGroup *group, const mp_int *k1, const mp_int *k2, |
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311 |
const mp_int *px, const mp_int *py, mp_int *rx, mp_int *ry) |
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|
312 |
{ |
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|
313 |
mp_err res = MP_OKAY; |
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|
314 |
mp_int k1t, k2t; |
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|
315 |
const mp_int *k1p, *k2p; |
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|
316 |
|
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|
317 |
MP_DIGITS(&k1t) = 0; |
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|
318 |
MP_DIGITS(&k2t) = 0; |
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|
319 |
|
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|
320 |
ARGCHK(group != NULL, MP_BADARG); |
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changeset
|
321 |
|
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|
322 |
/* want scalar to be less than or equal to group order */ |
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|
323 |
if (k1 != NULL) { |
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|
324 |
if (mp_cmp(k1, &group->order) >= 0) { |
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|
325 |
MP_CHECKOK(mp_init(&k1t, FLAG(k1))); |
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parents:
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|
326 |
MP_CHECKOK(mp_mod(k1, &group->order, &k1t)); |
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|
327 |
k1p = &k1t; |
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|
328 |
} else { |
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|
329 |
k1p = k1; |
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|
330 |
} |
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|
331 |
} else { |
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|
332 |
k1p = k1; |
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} |
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if (k2 != NULL) { |
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if (mp_cmp(k2, &group->order) >= 0) { |
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MP_CHECKOK(mp_init(&k2t, FLAG(k2))); |
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MP_CHECKOK(mp_mod(k2, &group->order, &k2t)); |
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k2p = &k2t; |
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339 |
} else { |
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k2p = k2; |
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341 |
} |
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342 |
} else { |
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k2p = k2; |
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344 |
} |
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345 |
|
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/* if points_mul is defined, then use it */ |
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if (group->points_mul) { |
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res = group->points_mul(k1p, k2p, px, py, rx, ry, group); |
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} else { |
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res = ec_pts_mul_simul_w2(k1p, k2p, px, py, rx, ry, group); |
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351 |
} |
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352 |
|
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CLEANUP: |
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mp_clear(&k1t); |
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355 |
mp_clear(&k2t); |
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356 |
return res; |
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357 |
} |