usr/src/common/crypto/ecc/ecp_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 prime 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  *   Bodo Moeller <moeller@cdc.informatik.tu-darmstadt.de>,
  27  *   Nils Larsch <nla@trustcenter.de>, and
  28  *   Lenka Fibikova <fibikova@exp-math.uni-essen.de>, the OpenSSL Project
  29  *
  30  * Alternatively, the contents of this file may be used under the terms of
  31  * either the GNU General Public License Version 2 or later (the "GPL"), or
  32  * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
  33  * in which case the provisions of the GPL or the LGPL are applicable instead
  34  * of those above. If you wish to allow use of your version of this file only
  35  * under the terms of either the GPL or the LGPL, and not to allow others to
  36  * use your version of this file under the terms of the MPL, indicate your
  37  * decision by deleting the provisions above and replace them with the notice
  38  * and other provisions required by the GPL or the LGPL. If you do not delete
  39  * the provisions above, a recipient may use your version of this file under
  40  * the terms of any one of the MPL, the GPL or the LGPL.
  41  *
  42  * ***** END LICENSE BLOCK ***** */
  43 /*
  44  * Copyright 2007 Sun Microsystems, Inc.  All rights reserved.
  45  * Use is subject to license terms.
  46  *
  47  * Sun elects to use this software under the MPL license.
  48  */
  49
  50 #pragma ident   "%Z%%M% %I%     %E% SMI"
  51
  52 #include "ecp.h"
  53 #include "mplogic.h"
  54 #ifndef _KERNEL
  55 #include <stdlib.h>
  56 #endif
  57
  58 /* Checks if point P(px, py) is at infinity.  Uses affine coordinates. */
  59 mp_err
  60 ec_GFp_pt_is_inf_aff(const mp_int *px, const mp_int *py)
  61 {
  62
  63         if ((mp_cmp_z(px) == 0) && (mp_cmp_z(py) == 0)) {
  64                 return MP_YES;
  65         } else {
  66                 return MP_NO;
  67         }
  68
  69 }
  70
  71 /* Sets P(px, py) to be the point at infinity.  Uses affine coordinates. */
  72 mp_err
  73 ec_GFp_pt_set_inf_aff(mp_int *px, mp_int *py)
  74 {
  75         mp_zero(px);
  76         mp_zero(py);
  77         return MP_OKAY;
  78 }
  79
  80 /* Computes R = P + Q based on IEEE P1363 A.10.1. Elliptic curve points P,
  81  * Q, and R can all be identical. Uses affine coordinates. Assumes input
  82  * is already field-encoded using field_enc, and returns output that is
  83  * still field-encoded. */
  84 mp_err
  85 ec_GFp_pt_add_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
  86                                   const mp_int *qy, mp_int *rx, mp_int *ry,
  87                                   const ECGroup *group)
  88 {
  89         mp_err res = MP_OKAY;
  90         mp_int lambda, temp, tempx, tempy;
  91
  92         MP_DIGITS(&lambda) = 0;
  93         MP_DIGITS(&temp) = 0;
  94         MP_DIGITS(&tempx) = 0;
  95         MP_DIGITS(&tempy) = 0;
  96         MP_CHECKOK(mp_init(&lambda, FLAG(px)));
  97         MP_CHECKOK(mp_init(&temp, FLAG(px)));
  98         MP_CHECKOK(mp_init(&tempx, FLAG(px)));
  99         MP_CHECKOK(mp_init(&tempy, FLAG(px)));
 100         /* if P = inf, then R = Q */
 101         if (ec_GFp_pt_is_inf_aff(px, py) == 0) {
 102                 MP_CHECKOK(mp_copy(qx, rx));
 103                 MP_CHECKOK(mp_copy(qy, ry));
 104                 res = MP_OKAY;
 105                 goto CLEANUP;
 106         }
 107         /* if Q = inf, then R = P */
 108         if (ec_GFp_pt_is_inf_aff(qx, qy) == 0) {
 109                 MP_CHECKOK(mp_copy(px, rx));
 110                 MP_CHECKOK(mp_copy(py, ry));
 111                 res = MP_OKAY;
 112                 goto CLEANUP;
 113         }
 114         /* if px != qx, then lambda = (py-qy) / (px-qx) */
 115         if (mp_cmp(px, qx) != 0) {
 116                 MP_CHECKOK(group->meth->field_sub(py, qy, &tempy, group->meth));
 117                 MP_CHECKOK(group->meth->field_sub(px, qx, &tempx, group->meth));
 118                 MP_CHECKOK(group->meth->
 119                                    field_div(&tempy, &tempx, &lambda, group->meth));
 120         } else {
 121                 /* if py != qy or qy = 0, then R = inf */
 122                 if (((mp_cmp(py, qy) != 0)) || (mp_cmp_z(qy) == 0)) {
 123                         mp_zero(rx);
 124                         mp_zero(ry);
 125                         res = MP_OKAY;
 126                         goto CLEANUP;
 127                 }
 128                 /* lambda = (3qx^2+a) / (2qy) */
 129                 MP_CHECKOK(group->meth->field_sqr(qx, &tempx, group->meth));
 130                 MP_CHECKOK(mp_set_int(&temp, 3));
 131                 if (group->meth->field_enc) {
 132                         MP_CHECKOK(group->meth->field_enc(&temp, &temp, group->meth));
 133                 }
 134                 MP_CHECKOK(group->meth->
 135                                    field_mul(&tempx, &temp, &tempx, group->meth));
 136                 MP_CHECKOK(group->meth->
 137                                    field_add(&tempx, &group->curvea, &tempx, group->meth));
 138                 MP_CHECKOK(mp_set_int(&temp, 2));
 139                 if (group->meth->field_enc) {
 140                         MP_CHECKOK(group->meth->field_enc(&temp, &temp, group->meth));
 141                 }
 142                 MP_CHECKOK(group->meth->field_mul(qy, &temp, &tempy, group->meth));
 143                 MP_CHECKOK(group->meth->
 144                                    field_div(&tempx, &tempy, &lambda, group->meth));
 145         }
 146         /* rx = lambda^2 - px - qx */
 147         MP_CHECKOK(group->meth->field_sqr(&lambda, &tempx, group->meth));
 148         MP_CHECKOK(group->meth->field_sub(&tempx, px, &tempx, group->meth));
 149         MP_CHECKOK(group->meth->field_sub(&tempx, qx, &tempx, group->meth));
 150         /* ry = (x1-x2) * lambda - y1 */
 151         MP_CHECKOK(group->meth->field_sub(qx, &tempx, &tempy, group->meth));
 152         MP_CHECKOK(group->meth->
 153                            field_mul(&tempy, &lambda, &tempy, group->meth));
 154         MP_CHECKOK(group->meth->field_sub(&tempy, qy, &tempy, group->meth));
 155         MP_CHECKOK(mp_copy(&tempx, rx));
 156         MP_CHECKOK(mp_copy(&tempy, ry));
 157
 158   CLEANUP:
 159         mp_clear(&lambda);
 160         mp_clear(&temp);
 161         mp_clear(&tempx);
 162         mp_clear(&tempy);
 163         return res;
 164 }
 165
 166 /* Computes R = P - Q. Elliptic curve points P, Q, and R can all be
 167  * identical. Uses affine coordinates. Assumes input is already
 168  * field-encoded using field_enc, and returns output that is still
 169  * field-encoded. */
 170 mp_err
 171 ec_GFp_pt_sub_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
 172                                   const mp_int *qy, mp_int *rx, mp_int *ry,
 173                                   const ECGroup *group)
 174 {
 175         mp_err res = MP_OKAY;
 176         mp_int nqy;
 177
 178         MP_DIGITS(&nqy) = 0;
 179         MP_CHECKOK(mp_init(&nqy, FLAG(px)));
 180         /* nqy = -qy */
 181         MP_CHECKOK(group->meth->field_neg(qy, &nqy, group->meth));
 182         res = group->point_add(px, py, qx, &nqy, rx, ry, group);
 183   CLEANUP:
 184         mp_clear(&nqy);
 185         return res;
 186 }
 187
 188 /* Computes R = 2P. Elliptic curve points P and R can be identical. Uses
 189  * affine coordinates. Assumes input is already field-encoded using
 190  * field_enc, and returns output that is still field-encoded. */
 191 mp_err
 192 ec_GFp_pt_dbl_aff(const mp_int *px, const mp_int *py, mp_int *rx,
 193                                   mp_int *ry, const ECGroup *group)
 194 {
 195         return ec_GFp_pt_add_aff(px, py, px, py, rx, ry, group);
 196 }
 197
 198 /* by default, this routine is unused and thus doesn't need to be compiled */
 199 #ifdef ECL_ENABLE_GFP_PT_MUL_AFF
 200 /* Computes R = nP based on IEEE P1363 A.10.3. Elliptic curve points P and
 201  * R can be identical. Uses affine coordinates. Assumes input is already
 202  * field-encoded using field_enc, and returns output that is still
 203  * field-encoded. */
 204 mp_err
 205 ec_GFp_pt_mul_aff(const mp_int *n, const mp_int *px, const mp_int *py,
 206                                   mp_int *rx, mp_int *ry, const ECGroup *group)
 207 {
 208         mp_err res = MP_OKAY;
 209         mp_int k, k3, qx, qy, sx, sy;
 210         int b1, b3, i, l;
 211
 212         MP_DIGITS(&k) = 0;
 213         MP_DIGITS(&k3) = 0;
 214         MP_DIGITS(&qx) = 0;
 215         MP_DIGITS(&qy) = 0;
 216         MP_DIGITS(&sx) = 0;
 217         MP_DIGITS(&sy) = 0;
 218         MP_CHECKOK(mp_init(&k));
 219         MP_CHECKOK(mp_init(&k3));
 220         MP_CHECKOK(mp_init(&qx));
 221         MP_CHECKOK(mp_init(&qy));
 222         MP_CHECKOK(mp_init(&sx));
 223         MP_CHECKOK(mp_init(&sy));
 224
 225         /* if n = 0 then r = inf */
 226         if (mp_cmp_z(n) == 0) {
 227                 mp_zero(rx);
 228                 mp_zero(ry);
 229                 res = MP_OKAY;
 230                 goto CLEANUP;
 231         }
 232         /* Q = P, k = n */
 233         MP_CHECKOK(mp_copy(px, &qx));
 234         MP_CHECKOK(mp_copy(py, &qy));
 235         MP_CHECKOK(mp_copy(n, &k));
 236         /* if n < 0 then Q = -Q, k = -k */
 237         if (mp_cmp_z(n) < 0) {
 238                 MP_CHECKOK(group->meth->field_neg(&qy, &qy, group->meth));
 239                 MP_CHECKOK(mp_neg(&k, &k));
 240         }
 241 #ifdef ECL_DEBUG                                /* basic double and add method */
 242         l = mpl_significant_bits(&k) - 1;
 243         MP_CHECKOK(mp_copy(&qx, &sx));
 244         MP_CHECKOK(mp_copy(&qy, &sy));
 245         for (i = l - 1; i >= 0; i--) {
 246                 /* S = 2S */
 247                 MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
 248                 /* if k_i = 1, then S = S + Q */
 249                 if (mpl_get_bit(&k, i) != 0) {
 250                         MP_CHECKOK(group->
 251                                            point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
 252                 }
 253         }
 254 #else                                                   /* double and add/subtract method from
 255                                                                  * standard */
 256         /* k3 = 3 * k */
 257         MP_CHECKOK(mp_set_int(&k3, 3));
 258         MP_CHECKOK(mp_mul(&k, &k3, &k3));
 259         /* S = Q */
 260         MP_CHECKOK(mp_copy(&qx, &sx));
 261         MP_CHECKOK(mp_copy(&qy, &sy));
 262         /* l = index of high order bit in binary representation of 3*k */
 263         l = mpl_significant_bits(&k3) - 1;
 264         /* for i = l-1 downto 1 */
 265         for (i = l - 1; i >= 1; i--) {
 266                 /* S = 2S */
 267                 MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
 268                 b3 = MP_GET_BIT(&k3, i);
 269                 b1 = MP_GET_BIT(&k, i);
 270                 /* if k3_i = 1 and k_i = 0, then S = S + Q */
 271                 if ((b3 == 1) && (b1 == 0)) {
 272                         MP_CHECKOK(group->
 273                                            point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
 274                         /* if k3_i = 0 and k_i = 1, then S = S - Q */
 275                 } else if ((b3 == 0) && (b1 == 1)) {
 276                         MP_CHECKOK(group->
 277                                            point_sub(&sx, &sy, &qx, &qy, &sx, &sy, group));
 278                 }
 279         }
 280 #endif
 281         /* output S */
 282         MP_CHECKOK(mp_copy(&sx, rx));
 283         MP_CHECKOK(mp_copy(&sy, ry));
 284
 285   CLEANUP:
 286         mp_clear(&k);
 287         mp_clear(&k3);
 288         mp_clear(&qx);
 289         mp_clear(&qy);
 290         mp_clear(&sx);
 291         mp_clear(&sy);
 292         return res;
 293 }
 294 #endif
 295
 296 /* Validates a point on a GFp curve. */
 297 mp_err
 298 ec_GFp_validate_point(const mp_int *px, const mp_int *py, const ECGroup *group)
 299 {
 300         mp_err res = MP_NO;
 301         mp_int accl, accr, tmp, pxt, pyt;
 302
 303         MP_DIGITS(&accl) = 0;
 304         MP_DIGITS(&accr) = 0;
 305         MP_DIGITS(&tmp) = 0;
 306         MP_DIGITS(&pxt) = 0;
 307         MP_DIGITS(&pyt) = 0;
 308         MP_CHECKOK(mp_init(&accl, FLAG(px)));
 309         MP_CHECKOK(mp_init(&accr, FLAG(px)));
 310         MP_CHECKOK(mp_init(&tmp, FLAG(px)));
 311         MP_CHECKOK(mp_init(&pxt, FLAG(px)));
 312         MP_CHECKOK(mp_init(&pyt, FLAG(px)));
 313
 314     /* 1: Verify that publicValue is not the point at infinity */
 315         if (ec_GFp_pt_is_inf_aff(px, py) == MP_YES) {
 316                 res = MP_NO;
 317                 goto CLEANUP;
 318         }
 319     /* 2: Verify that the coordinates of publicValue are elements
 320      *    of the field.
 321      */
 322         if ((MP_SIGN(px) == MP_NEG) || (mp_cmp(px, &group->meth->irr) >= 0) ||
 323                 (MP_SIGN(py) == MP_NEG) || (mp_cmp(py, &group->meth->irr) >= 0)) {
 324                 res = MP_NO;
 325                 goto CLEANUP;
 326         }
 327     /* 3: Verify that publicValue is on the curve. */
 328         if (group->meth->field_enc) {
 329                 group->meth->field_enc(px, &pxt, group->meth);
 330                 group->meth->field_enc(py, &pyt, group->meth);
 331         } else {
 332                 mp_copy(px, &pxt);
 333                 mp_copy(py, &pyt);
 334         }
 335         /* left-hand side: y^2  */
 336         MP_CHECKOK( group->meth->field_sqr(&pyt, &accl, group->meth) );
 337         /* right-hand side: x^3 + a*x + b */
 338         MP_CHECKOK( group->meth->field_sqr(&pxt, &tmp, group->meth) );
 339         MP_CHECKOK( group->meth->field_mul(&pxt, &tmp, &accr, group->meth) );
 340         MP_CHECKOK( group->meth->field_mul(&group->curvea, &pxt, &tmp, group->meth) );
 341         MP_CHECKOK( group->meth->field_add(&tmp, &accr, &accr, group->meth) );
 342         MP_CHECKOK( group->meth->field_add(&accr, &group->curveb, &accr, group->meth) );
 343         /* check LHS - RHS == 0 */
 344         MP_CHECKOK( group->meth->field_sub(&accl, &accr, &accr, group->meth) );
 345         if (mp_cmp_z(&accr) != 0) {
 346                 res = MP_NO;
 347                 goto CLEANUP;
 348         }
 349     /* 4: Verify that the order of the curve times the publicValue
 350      *    is the point at infinity.
 351      */
 352         MP_CHECKOK( ECPoint_mul(group, &group->order, px, py, &pxt, &pyt) );
 353         if (ec_GFp_pt_is_inf_aff(&pxt, &pyt) != MP_YES) {
 354                 res = MP_NO;
 355                 goto CLEANUP;
 356         }
 357
 358         res = MP_YES;
 359
 360 CLEANUP:
 361         mp_clear(&accl);
 362         mp_clear(&accr);
 363         mp_clear(&tmp);
 364         mp_clear(&pxt);
 365         mp_clear(&pyt);
 366         return res;
 367 }