usr/src/common/crypto/ecc/ec2_mont.c

   1 /*
   2  * ***** BEGIN LICENSE BLOCK *****
   3  * Version: MPL 1.1/GPL 2.0/LGPL 2.1
   4  *
   5  * The contents of this file are subject to the Mozilla Public License Version
   6  * 1.1 (the "License"); you may not use this file except in compliance with
   7  * the License. You may obtain a copy of the License at
   8  * http://www.mozilla.org/MPL/
   9  *
  10  * Software distributed under the License is distributed on an "AS IS" basis,
  11  * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
  12  * for the specific language governing rights and limitations under the
  13  * License.
  14  *
  15  * The Original Code is the elliptic curve math library for binary polynomial field curves.
  16  *
  17  * The Initial Developer of the Original Code is
  18  * Sun Microsystems, Inc.
  19  * Portions created by the Initial Developer are Copyright (C) 2003
  20  * the Initial Developer. All Rights Reserved.
  21  *
  22  * Contributor(s):
  23  *   Sheueling Chang-Shantz <sheueling.chang@sun.com>,
  24  *   Stephen Fung <fungstep@hotmail.com>, and
  25  *   Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories.
  26  *
  27  * Alternatively, the contents of this file may be used under the terms of
  28  * either the GNU General Public License Version 2 or later (the "GPL"), or
  29  * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
  30  * in which case the provisions of the GPL or the LGPL are applicable instead
  31  * of those above. If you wish to allow use of your version of this file only
  32  * under the terms of either the GPL or the LGPL, and not to allow others to
  33  * use your version of this file under the terms of the MPL, indicate your
  34  * decision by deleting the provisions above and replace them with the notice
  35  * and other provisions required by the GPL or the LGPL. If you do not delete
  36  * the provisions above, a recipient may use your version of this file under
  37  * the terms of any one of the MPL, the GPL or the LGPL.
  38  *
  39  * ***** END LICENSE BLOCK ***** */
  40 /*
  41  * Copyright 2007 Sun Microsystems, Inc.  All rights reserved.
  42  * Use is subject to license terms.
  43  *
  44  * Sun elects to use this software under the MPL license.
  45  */
  46
  47 #pragma ident   "%Z%%M% %I%     %E% SMI"
  48
  49 #include "ec2.h"
  50 #include "mplogic.h"
  51 #include "mp_gf2m.h"
  52 #ifndef _KERNEL
  53 #include <stdlib.h>
  54 #endif
  55
  56 /* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery
  57  * projective coordinates. Uses algorithm Mdouble in appendix of Lopez, J.
  58  * and Dahab, R.  "Fast multiplication on elliptic curves over GF(2^m)
  59  * without precomputation". modified to not require precomputation of
  60  * c=b^{2^{m-1}}. */
  61 static mp_err
  62 gf2m_Mdouble(mp_int *x, mp_int *z, const ECGroup *group, int kmflag)
  63 {
  64         mp_err res = MP_OKAY;
  65         mp_int t1;
  66
  67         MP_DIGITS(&t1) = 0;
  68         MP_CHECKOK(mp_init(&t1, kmflag));
  69
  70         MP_CHECKOK(group->meth->field_sqr(x, x, group->meth));
  71         MP_CHECKOK(group->meth->field_sqr(z, &t1, group->meth));
  72         MP_CHECKOK(group->meth->field_mul(x, &t1, z, group->meth));
  73         MP_CHECKOK(group->meth->field_sqr(x, x, group->meth));
  74         MP_CHECKOK(group->meth->field_sqr(&t1, &t1, group->meth));
  75         MP_CHECKOK(group->meth->
  76                            field_mul(&group->curveb, &t1, &t1, group->meth));
  77         MP_CHECKOK(group->meth->field_add(x, &t1, x, group->meth));
  78
  79   CLEANUP:
  80         mp_clear(&t1);
  81         return res;
  82 }
  83
  84 /* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in
  85  * Montgomery projective coordinates. Uses algorithm Madd in appendix of
  86  * Lopex, J. and Dahab, R.  "Fast multiplication on elliptic curves over
  87  * GF(2^m) without precomputation". */
  88 static mp_err
  89 gf2m_Madd(const mp_int *x, mp_int *x1, mp_int *z1, mp_int *x2, mp_int *z2,
  90                   const ECGroup *group, int kmflag)
  91 {
  92         mp_err res = MP_OKAY;
  93         mp_int t1, t2;
  94
  95         MP_DIGITS(&t1) = 0;
  96         MP_DIGITS(&t2) = 0;
  97         MP_CHECKOK(mp_init(&t1, kmflag));
  98         MP_CHECKOK(mp_init(&t2, kmflag));
  99
 100         MP_CHECKOK(mp_copy(x, &t1));
 101         MP_CHECKOK(group->meth->field_mul(x1, z2, x1, group->meth));
 102         MP_CHECKOK(group->meth->field_mul(z1, x2, z1, group->meth));
 103         MP_CHECKOK(group->meth->field_mul(x1, z1, &t2, group->meth));
 104         MP_CHECKOK(group->meth->field_add(z1, x1, z1, group->meth));
 105         MP_CHECKOK(group->meth->field_sqr(z1, z1, group->meth));
 106         MP_CHECKOK(group->meth->field_mul(z1, &t1, x1, group->meth));
 107         MP_CHECKOK(group->meth->field_add(x1, &t2, x1, group->meth));
 108
 109   CLEANUP:
 110         mp_clear(&t1);
 111         mp_clear(&t2);
 112         return res;
 113 }
 114
 115 /* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2)
 116  * using Montgomery point multiplication algorithm Mxy() in appendix of
 117  * Lopex, J. and Dahab, R.  "Fast multiplication on elliptic curves over
 118  * GF(2^m) without precomputation". Returns: 0 on error 1 if return value
 119  * should be the point at infinity 2 otherwise */
 120 static int
 121 gf2m_Mxy(const mp_int *x, const mp_int *y, mp_int *x1, mp_int *z1,
 122                  mp_int *x2, mp_int *z2, const ECGroup *group)
 123 {
 124         mp_err res = MP_OKAY;
 125         int ret = 0;
 126         mp_int t3, t4, t5;
 127
 128         MP_DIGITS(&t3) = 0;
 129         MP_DIGITS(&t4) = 0;
 130         MP_DIGITS(&t5) = 0;
 131         MP_CHECKOK(mp_init(&t3, FLAG(x2)));
 132         MP_CHECKOK(mp_init(&t4, FLAG(x2)));
 133         MP_CHECKOK(mp_init(&t5, FLAG(x2)));
 134
 135         if (mp_cmp_z(z1) == 0) {
 136                 mp_zero(x2);
 137                 mp_zero(z2);
 138                 ret = 1;
 139                 goto CLEANUP;
 140         }
 141
 142         if (mp_cmp_z(z2) == 0) {
 143                 MP_CHECKOK(mp_copy(x, x2));
 144                 MP_CHECKOK(group->meth->field_add(x, y, z2, group->meth));
 145                 ret = 2;
 146                 goto CLEANUP;
 147         }
 148
 149         MP_CHECKOK(mp_set_int(&t5, 1));
 150         if (group->meth->field_enc) {
 151                 MP_CHECKOK(group->meth->field_enc(&t5, &t5, group->meth));
 152         }
 153
 154         MP_CHECKOK(group->meth->field_mul(z1, z2, &t3, group->meth));
 155
 156         MP_CHECKOK(group->meth->field_mul(z1, x, z1, group->meth));
 157         MP_CHECKOK(group->meth->field_add(z1, x1, z1, group->meth));
 158         MP_CHECKOK(group->meth->field_mul(z2, x, z2, group->meth));
 159         MP_CHECKOK(group->meth->field_mul(z2, x1, x1, group->meth));
 160         MP_CHECKOK(group->meth->field_add(z2, x2, z2, group->meth));
 161
 162         MP_CHECKOK(group->meth->field_mul(z2, z1, z2, group->meth));
 163         MP_CHECKOK(group->meth->field_sqr(x, &t4, group->meth));
 164         MP_CHECKOK(group->meth->field_add(&t4, y, &t4, group->meth));
 165         MP_CHECKOK(group->meth->field_mul(&t4, &t3, &t4, group->meth));
 166         MP_CHECKOK(group->meth->field_add(&t4, z2, &t4, group->meth));
 167
 168         MP_CHECKOK(group->meth->field_mul(&t3, x, &t3, group->meth));
 169         MP_CHECKOK(group->meth->field_div(&t5, &t3, &t3, group->meth));
 170         MP_CHECKOK(group->meth->field_mul(&t3, &t4, &t4, group->meth));
 171         MP_CHECKOK(group->meth->field_mul(x1, &t3, x2, group->meth));
 172         MP_CHECKOK(group->meth->field_add(x2, x, z2, group->meth));
 173
 174         MP_CHECKOK(group->meth->field_mul(z2, &t4, z2, group->meth));
 175         MP_CHECKOK(group->meth->field_add(z2, y, z2, group->meth));
 176
 177         ret = 2;
 178
 179   CLEANUP:
 180         mp_clear(&t3);
 181         mp_clear(&t4);
 182         mp_clear(&t5);
 183         if (res == MP_OKAY) {
 184                 return ret;
 185         } else {
 186                 return 0;
 187         }
 188 }
 189
 190 /* Computes R = nP based on algorithm 2P of Lopex, J. and Dahab, R.  "Fast
 191  * multiplication on elliptic curves over GF(2^m) without
 192  * precomputation". Elliptic curve points P and R can be identical. Uses
 193  * Montgomery projective coordinates. */
 194 mp_err
 195 ec_GF2m_pt_mul_mont(const mp_int *n, const mp_int *px, const mp_int *py,
 196                                         mp_int *rx, mp_int *ry, const ECGroup *group)
 197 {
 198         mp_err res = MP_OKAY;
 199         mp_int x1, x2, z1, z2;
 200         int i, j;
 201         mp_digit top_bit, mask;
 202
 203         MP_DIGITS(&x1) = 0;
 204         MP_DIGITS(&x2) = 0;
 205         MP_DIGITS(&z1) = 0;
 206         MP_DIGITS(&z2) = 0;
 207         MP_CHECKOK(mp_init(&x1, FLAG(n)));
 208         MP_CHECKOK(mp_init(&x2, FLAG(n)));
 209         MP_CHECKOK(mp_init(&z1, FLAG(n)));
 210         MP_CHECKOK(mp_init(&z2, FLAG(n)));
 211
 212         /* if result should be point at infinity */
 213         if ((mp_cmp_z(n) == 0) || (ec_GF2m_pt_is_inf_aff(px, py) == MP_YES)) {
 214                 MP_CHECKOK(ec_GF2m_pt_set_inf_aff(rx, ry));
 215                 goto CLEANUP;
 216         }
 217
 218         MP_CHECKOK(mp_copy(px, &x1));   /* x1 = px */
 219         MP_CHECKOK(mp_set_int(&z1, 1)); /* z1 = 1 */
 220         MP_CHECKOK(group->meth->field_sqr(&x1, &z2, group->meth));      /* z2 =
 221                                                                                                                                  * x1^2 =
 222                                                                                                                                  * px^2 */
 223         MP_CHECKOK(group->meth->field_sqr(&z2, &x2, group->meth));
 224         MP_CHECKOK(group->meth->field_add(&x2, &group->curveb, &x2, group->meth));      /* x2
 225                                                                                                                                                                  * =
 226                                                                                                                                                                  * px^4
 227                                                                                                                                                                  * +
 228                                                                                                                                                                  * b
 229                                                                                                                                                                  */
 230
 231         /* find top-most bit and go one past it */
 232         i = MP_USED(n) - 1;
 233         j = MP_DIGIT_BIT - 1;
 234         top_bit = 1;
 235         top_bit <<= MP_DIGIT_BIT - 1;
 236         mask = top_bit;
 237         while (!(MP_DIGITS(n)[i] & mask)) {
 238                 mask >>= 1;
 239                 j--;
 240         }
 241         mask >>= 1;
 242         j--;
 243
 244         /* if top most bit was at word break, go to next word */
 245         if (!mask) {
 246                 i--;
 247                 j = MP_DIGIT_BIT - 1;
 248                 mask = top_bit;
 249         }
 250
 251         for (; i >= 0; i--) {
 252                 for (; j >= 0; j--) {
 253                         if (MP_DIGITS(n)[i] & mask) {
 254                                 MP_CHECKOK(gf2m_Madd(px, &x1, &z1, &x2, &z2, group, FLAG(n)));
 255                                 MP_CHECKOK(gf2m_Mdouble(&x2, &z2, group, FLAG(n)));
 256                         } else {
 257                                 MP_CHECKOK(gf2m_Madd(px, &x2, &z2, &x1, &z1, group, FLAG(n)));
 258                                 MP_CHECKOK(gf2m_Mdouble(&x1, &z1, group, FLAG(n)));
 259                         }
 260                         mask >>= 1;
 261                 }
 262                 j = MP_DIGIT_BIT - 1;
 263                 mask = top_bit;
 264         }
 265
 266         /* convert out of "projective" coordinates */
 267         i = gf2m_Mxy(px, py, &x1, &z1, &x2, &z2, group);
 268         if (i == 0) {
 269                 res = MP_BADARG;
 270                 goto CLEANUP;
 271         } else if (i == 1) {
 272                 MP_CHECKOK(ec_GF2m_pt_set_inf_aff(rx, ry));
 273         } else {
 274                 MP_CHECKOK(mp_copy(&x2, rx));
 275                 MP_CHECKOK(mp_copy(&z2, ry));
 276         }
 277
 278   CLEANUP:
 279         mp_clear(&x1);
 280         mp_clear(&x2);
 281         mp_clear(&z1);
 282         mp_clear(&z2);
 283         return res;
 284 }