usr/src/common/crypto/ecc/ec2_aff.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  *   Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories
  24  *
  25  * Alternatively, the contents of this file may be used under the terms of
  26  * either the GNU General Public License Version 2 or later (the "GPL"), or
  27  * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
  28  * in which case the provisions of the GPL or the LGPL are applicable instead
  29  * of those above. If you wish to allow use of your version of this file only
  30  * under the terms of either the GPL or the LGPL, and not to allow others to
  31  * use your version of this file under the terms of the MPL, indicate your
  32  * decision by deleting the provisions above and replace them with the notice
  33  * and other provisions required by the GPL or the LGPL. If you do not delete
  34  * the provisions above, a recipient may use your version of this file under
  35  * the terms of any one of the MPL, the GPL or the LGPL.
  36  *
  37  * ***** END LICENSE BLOCK ***** */
  38 /*
  39  * Copyright 2007 Sun Microsystems, Inc.  All rights reserved.
  40  * Use is subject to license terms.
  41  *
  42  * Sun elects to use this software under the MPL license.
  43  */
  44
  45 #pragma ident   "%Z%%M% %I%     %E% SMI"
  46
  47 #include "ec2.h"
  48 #include "mplogic.h"
  49 #include "mp_gf2m.h"
  50 #ifndef _KERNEL
  51 #include <stdlib.h>
  52 #endif
  53
  54 /* Checks if point P(px, py) is at infinity.  Uses affine coordinates. */
  55 mp_err
  56 ec_GF2m_pt_is_inf_aff(const mp_int *px, const mp_int *py)
  57 {
  58
  59         if ((mp_cmp_z(px) == 0) && (mp_cmp_z(py) == 0)) {
  60                 return MP_YES;
  61         } else {
  62                 return MP_NO;
  63         }
  64
  65 }
  66
  67 /* Sets P(px, py) to be the point at infinity.  Uses affine coordinates. */
  68 mp_err
  69 ec_GF2m_pt_set_inf_aff(mp_int *px, mp_int *py)
  70 {
  71         mp_zero(px);
  72         mp_zero(py);
  73         return MP_OKAY;
  74 }
  75
  76 /* Computes R = P + Q based on IEEE P1363 A.10.2. Elliptic curve points P,
  77  * Q, and R can all be identical. Uses affine coordinates. */
  78 mp_err
  79 ec_GF2m_pt_add_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
  80                                    const mp_int *qy, mp_int *rx, mp_int *ry,
  81                                    const ECGroup *group)
  82 {
  83         mp_err res = MP_OKAY;
  84         mp_int lambda, tempx, tempy;
  85
  86         MP_DIGITS(&lambda) = 0;
  87         MP_DIGITS(&tempx) = 0;
  88         MP_DIGITS(&tempy) = 0;
  89         MP_CHECKOK(mp_init(&lambda, FLAG(px)));
  90         MP_CHECKOK(mp_init(&tempx, FLAG(px)));
  91         MP_CHECKOK(mp_init(&tempy, FLAG(px)));
  92         /* if P = inf, then R = Q */
  93         if (ec_GF2m_pt_is_inf_aff(px, py) == 0) {
  94                 MP_CHECKOK(mp_copy(qx, rx));
  95                 MP_CHECKOK(mp_copy(qy, ry));
  96                 res = MP_OKAY;
  97                 goto CLEANUP;
  98         }
  99         /* if Q = inf, then R = P */
 100         if (ec_GF2m_pt_is_inf_aff(qx, qy) == 0) {
 101                 MP_CHECKOK(mp_copy(px, rx));
 102                 MP_CHECKOK(mp_copy(py, ry));
 103                 res = MP_OKAY;
 104                 goto CLEANUP;
 105         }
 106         /* if px != qx, then lambda = (py+qy) / (px+qx), tempx = a + lambda^2
 107          * + lambda + px + qx */
 108         if (mp_cmp(px, qx) != 0) {
 109                 MP_CHECKOK(group->meth->field_add(py, qy, &tempy, group->meth));
 110                 MP_CHECKOK(group->meth->field_add(px, qx, &tempx, group->meth));
 111                 MP_CHECKOK(group->meth->
 112                                    field_div(&tempy, &tempx, &lambda, group->meth));
 113                 MP_CHECKOK(group->meth->field_sqr(&lambda, &tempx, group->meth));
 114                 MP_CHECKOK(group->meth->
 115                                    field_add(&tempx, &lambda, &tempx, group->meth));
 116                 MP_CHECKOK(group->meth->
 117                                    field_add(&tempx, &group->curvea, &tempx, group->meth));
 118                 MP_CHECKOK(group->meth->
 119                                    field_add(&tempx, px, &tempx, group->meth));
 120                 MP_CHECKOK(group->meth->
 121                                    field_add(&tempx, qx, &tempx, group->meth));
 122         } else {
 123                 /* if py != qy or qx = 0, then R = inf */
 124                 if (((mp_cmp(py, qy) != 0)) || (mp_cmp_z(qx) == 0)) {
 125                         mp_zero(rx);
 126                         mp_zero(ry);
 127                         res = MP_OKAY;
 128                         goto CLEANUP;
 129                 }
 130                 /* lambda = qx + qy / qx */
 131                 MP_CHECKOK(group->meth->field_div(qy, qx, &lambda, group->meth));
 132                 MP_CHECKOK(group->meth->
 133                                    field_add(&lambda, qx, &lambda, group->meth));
 134                 /* tempx = a + lambda^2 + lambda */
 135                 MP_CHECKOK(group->meth->field_sqr(&lambda, &tempx, group->meth));
 136                 MP_CHECKOK(group->meth->
 137                                    field_add(&tempx, &lambda, &tempx, group->meth));
 138                 MP_CHECKOK(group->meth->
 139                                    field_add(&tempx, &group->curvea, &tempx, group->meth));
 140         }
 141         /* ry = (qx + tempx) * lambda + tempx + qy */
 142         MP_CHECKOK(group->meth->field_add(qx, &tempx, &tempy, group->meth));
 143         MP_CHECKOK(group->meth->
 144                            field_mul(&tempy, &lambda, &tempy, group->meth));
 145         MP_CHECKOK(group->meth->
 146                            field_add(&tempy, &tempx, &tempy, group->meth));
 147         MP_CHECKOK(group->meth->field_add(&tempy, qy, ry, group->meth));
 148         /* rx = tempx */
 149         MP_CHECKOK(mp_copy(&tempx, rx));
 150
 151   CLEANUP:
 152         mp_clear(&lambda);
 153         mp_clear(&tempx);
 154         mp_clear(&tempy);
 155         return res;
 156 }
 157
 158 /* Computes R = P - Q. Elliptic curve points P, Q, and R can all be
 159  * identical. Uses affine coordinates. */
 160 mp_err
 161 ec_GF2m_pt_sub_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
 162                                    const mp_int *qy, mp_int *rx, mp_int *ry,
 163                                    const ECGroup *group)
 164 {
 165         mp_err res = MP_OKAY;
 166         mp_int nqy;
 167
 168         MP_DIGITS(&nqy) = 0;
 169         MP_CHECKOK(mp_init(&nqy, FLAG(px)));
 170         /* nqy = qx+qy */
 171         MP_CHECKOK(group->meth->field_add(qx, qy, &nqy, group->meth));
 172         MP_CHECKOK(group->point_add(px, py, qx, &nqy, rx, ry, group));
 173   CLEANUP:
 174         mp_clear(&nqy);
 175         return res;
 176 }
 177
 178 /* Computes R = 2P. Elliptic curve points P and R can be identical. Uses
 179  * affine coordinates. */
 180 mp_err
 181 ec_GF2m_pt_dbl_aff(const mp_int *px, const mp_int *py, mp_int *rx,
 182                                    mp_int *ry, const ECGroup *group)
 183 {
 184         return group->point_add(px, py, px, py, rx, ry, group);
 185 }
 186
 187 /* by default, this routine is unused and thus doesn't need to be compiled */
 188 #ifdef ECL_ENABLE_GF2M_PT_MUL_AFF
 189 /* Computes R = nP based on IEEE P1363 A.10.3. Elliptic curve points P and
 190  * R can be identical. Uses affine coordinates. */
 191 mp_err
 192 ec_GF2m_pt_mul_aff(const mp_int *n, const mp_int *px, const mp_int *py,
 193                                    mp_int *rx, mp_int *ry, const ECGroup *group)
 194 {
 195         mp_err res = MP_OKAY;
 196         mp_int k, k3, qx, qy, sx, sy;
 197         int b1, b3, i, l;
 198
 199         MP_DIGITS(&k) = 0;
 200         MP_DIGITS(&k3) = 0;
 201         MP_DIGITS(&qx) = 0;
 202         MP_DIGITS(&qy) = 0;
 203         MP_DIGITS(&sx) = 0;
 204         MP_DIGITS(&sy) = 0;
 205         MP_CHECKOK(mp_init(&k));
 206         MP_CHECKOK(mp_init(&k3));
 207         MP_CHECKOK(mp_init(&qx));
 208         MP_CHECKOK(mp_init(&qy));
 209         MP_CHECKOK(mp_init(&sx));
 210         MP_CHECKOK(mp_init(&sy));
 211
 212         /* if n = 0 then r = inf */
 213         if (mp_cmp_z(n) == 0) {
 214                 mp_zero(rx);
 215                 mp_zero(ry);
 216                 res = MP_OKAY;
 217                 goto CLEANUP;
 218         }
 219         /* Q = P, k = n */
 220         MP_CHECKOK(mp_copy(px, &qx));
 221         MP_CHECKOK(mp_copy(py, &qy));
 222         MP_CHECKOK(mp_copy(n, &k));
 223         /* if n < 0 then Q = -Q, k = -k */
 224         if (mp_cmp_z(n) < 0) {
 225                 MP_CHECKOK(group->meth->field_add(&qx, &qy, &qy, group->meth));
 226                 MP_CHECKOK(mp_neg(&k, &k));
 227         }
 228 #ifdef ECL_DEBUG                                /* basic double and add method */
 229         l = mpl_significant_bits(&k) - 1;
 230         MP_CHECKOK(mp_copy(&qx, &sx));
 231         MP_CHECKOK(mp_copy(&qy, &sy));
 232         for (i = l - 1; i >= 0; i--) {
 233                 /* S = 2S */
 234                 MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
 235                 /* if k_i = 1, then S = S + Q */
 236                 if (mpl_get_bit(&k, i) != 0) {
 237                         MP_CHECKOK(group->
 238                                            point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
 239                 }
 240         }
 241 #else                                                   /* double and add/subtract method from
 242                                                                  * standard */
 243         /* k3 = 3 * k */
 244         MP_CHECKOK(mp_set_int(&k3, 3));
 245         MP_CHECKOK(mp_mul(&k, &k3, &k3));
 246         /* S = Q */
 247         MP_CHECKOK(mp_copy(&qx, &sx));
 248         MP_CHECKOK(mp_copy(&qy, &sy));
 249         /* l = index of high order bit in binary representation of 3*k */
 250         l = mpl_significant_bits(&k3) - 1;
 251         /* for i = l-1 downto 1 */
 252         for (i = l - 1; i >= 1; i--) {
 253                 /* S = 2S */
 254                 MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
 255                 b3 = MP_GET_BIT(&k3, i);
 256                 b1 = MP_GET_BIT(&k, i);
 257                 /* if k3_i = 1 and k_i = 0, then S = S + Q */
 258                 if ((b3 == 1) && (b1 == 0)) {
 259                         MP_CHECKOK(group->
 260                                            point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
 261                         /* if k3_i = 0 and k_i = 1, then S = S - Q */
 262                 } else if ((b3 == 0) && (b1 == 1)) {
 263                         MP_CHECKOK(group->
 264                                            point_sub(&sx, &sy, &qx, &qy, &sx, &sy, group));
 265                 }
 266         }
 267 #endif
 268         /* output S */
 269         MP_CHECKOK(mp_copy(&sx, rx));
 270         MP_CHECKOK(mp_copy(&sy, ry));
 271
 272   CLEANUP:
 273         mp_clear(&k);
 274         mp_clear(&k3);
 275         mp_clear(&qx);
 276         mp_clear(&qy);
 277         mp_clear(&sx);
 278         mp_clear(&sy);
 279         return res;
 280 }
 281 #endif
 282
 283 /* Validates a point on a GF2m curve. */
 284 mp_err
 285 ec_GF2m_validate_point(const mp_int *px, const mp_int *py, const ECGroup *group)
 286 {
 287         mp_err res = MP_NO;
 288         mp_int accl, accr, tmp, pxt, pyt;
 289
 290         MP_DIGITS(&accl) = 0;
 291         MP_DIGITS(&accr) = 0;
 292         MP_DIGITS(&tmp) = 0;
 293         MP_DIGITS(&pxt) = 0;
 294         MP_DIGITS(&pyt) = 0;
 295         MP_CHECKOK(mp_init(&accl, FLAG(px)));
 296         MP_CHECKOK(mp_init(&accr, FLAG(px)));
 297         MP_CHECKOK(mp_init(&tmp, FLAG(px)));
 298         MP_CHECKOK(mp_init(&pxt, FLAG(px)));
 299         MP_CHECKOK(mp_init(&pyt, FLAG(px)));
 300
 301     /* 1: Verify that publicValue is not the point at infinity */
 302         if (ec_GF2m_pt_is_inf_aff(px, py) == MP_YES) {
 303                 res = MP_NO;
 304                 goto CLEANUP;
 305         }
 306     /* 2: Verify that the coordinates of publicValue are elements
 307      *    of the field.
 308      */
 309         if ((MP_SIGN(px) == MP_NEG) || (mp_cmp(px, &group->meth->irr) >= 0) ||
 310                 (MP_SIGN(py) == MP_NEG) || (mp_cmp(py, &group->meth->irr) >= 0)) {
 311                 res = MP_NO;
 312                 goto CLEANUP;
 313         }
 314     /* 3: Verify that publicValue is on the curve. */
 315         if (group->meth->field_enc) {
 316                 group->meth->field_enc(px, &pxt, group->meth);
 317                 group->meth->field_enc(py, &pyt, group->meth);
 318         } else {
 319                 mp_copy(px, &pxt);
 320                 mp_copy(py, &pyt);
 321         }
 322         /* left-hand side: y^2 + x*y  */
 323         MP_CHECKOK( group->meth->field_sqr(&pyt, &accl, group->meth) );
 324         MP_CHECKOK( group->meth->field_mul(&pxt, &pyt, &tmp, group->meth) );
 325         MP_CHECKOK( group->meth->field_add(&accl, &tmp, &accl, group->meth) );
 326         /* right-hand side: x^3 + a*x^2 + b */
 327         MP_CHECKOK( group->meth->field_sqr(&pxt, &tmp, group->meth) );
 328         MP_CHECKOK( group->meth->field_mul(&pxt, &tmp, &accr, group->meth) );
 329         MP_CHECKOK( group->meth->field_mul(&group->curvea, &tmp, &tmp, group->meth) );
 330         MP_CHECKOK( group->meth->field_add(&tmp, &accr, &accr, group->meth) );
 331         MP_CHECKOK( group->meth->field_add(&accr, &group->curveb, &accr, group->meth) );
 332         /* check LHS - RHS == 0 */
 333         MP_CHECKOK( group->meth->field_add(&accl, &accr, &accr, group->meth) );
 334         if (mp_cmp_z(&accr) != 0) {
 335                 res = MP_NO;
 336                 goto CLEANUP;
 337         }
 338     /* 4: Verify that the order of the curve times the publicValue
 339      *    is the point at infinity.
 340      */
 341         MP_CHECKOK( ECPoint_mul(group, &group->order, px, py, &pxt, &pyt) );
 342         if (ec_GF2m_pt_is_inf_aff(&pxt, &pyt) != MP_YES) {
 343                 res = MP_NO;
 344                 goto CLEANUP;
 345         }
 346
 347         res = MP_YES;
 348
 349 CLEANUP:
 350         mp_clear(&accl);
 351         mp_clear(&accr);
 352         mp_clear(&tmp);
 353         mp_clear(&pxt);
 354         mp_clear(&pyt);
 355         return res;
 356 }