security/nss/lib/freebl/ecl/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 #include "ecp.h"
  45 #include "mplogic.h"
  46 #include <stdlib.h>
  47
  48 /* Checks if point P(px, py) is at infinity.  Uses affine coordinates. */
  49 mp_err
  50 ec_GFp_pt_is_inf_aff(const mp_int *px, const mp_int *py)
  51 {
  52
  53         if ((mp_cmp_z(px) == 0) && (mp_cmp_z(py) == 0)) {
  54                 return MP_YES;
  55         } else {
  56                 return MP_NO;
  57         }
  58
  59 }
  60
  61 /* Sets P(px, py) to be the point at infinity.  Uses affine coordinates. */
  62 mp_err
  63 ec_GFp_pt_set_inf_aff(mp_int *px, mp_int *py)
  64 {
  65         mp_zero(px);
  66         mp_zero(py);
  67         return MP_OKAY;
  68 }
  69
  70 /* Computes R = P + Q based on IEEE P1363 A.10.1. Elliptic curve points P,
  71  * Q, and R can all be identical. Uses affine coordinates. Assumes input
  72  * is already field-encoded using field_enc, and returns output that is
  73  * still field-encoded. */
  74 mp_err
  75 ec_GFp_pt_add_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
  76                                   const mp_int *qy, mp_int *rx, mp_int *ry,
  77                                   const ECGroup *group)
  78 {
  79         mp_err res = MP_OKAY;
  80         mp_int lambda, temp, tempx, tempy;
  81
  82         MP_DIGITS(&lambda) = 0;
  83         MP_DIGITS(&temp) = 0;
  84         MP_DIGITS(&tempx) = 0;
  85         MP_DIGITS(&tempy) = 0;
  86         MP_CHECKOK(mp_init(&lambda));
  87         MP_CHECKOK(mp_init(&temp));
  88         MP_CHECKOK(mp_init(&tempx));
  89         MP_CHECKOK(mp_init(&tempy));
  90         /* if P = inf, then R = Q */
  91         if (ec_GFp_pt_is_inf_aff(px, py) == 0) {
  92                 MP_CHECKOK(mp_copy(qx, rx));
  93                 MP_CHECKOK(mp_copy(qy, ry));
  94                 res = MP_OKAY;
  95                 goto CLEANUP;
  96         }
  97         /* if Q = inf, then R = P */
  98         if (ec_GFp_pt_is_inf_aff(qx, qy) == 0) {
  99                 MP_CHECKOK(mp_copy(px, rx));
 100                 MP_CHECKOK(mp_copy(py, ry));
 101                 res = MP_OKAY;
 102                 goto CLEANUP;
 103         }
 104         /* if px != qx, then lambda = (py-qy) / (px-qx) */
 105         if (mp_cmp(px, qx) != 0) {
 106                 MP_CHECKOK(group->meth->field_sub(py, qy, &tempy, group->meth));
 107                 MP_CHECKOK(group->meth->field_sub(px, qx, &tempx, group->meth));
 108                 MP_CHECKOK(group->meth->
 109                                    field_div(&tempy, &tempx, &lambda, group->meth));
 110         } else {
 111                 /* if py != qy or qy = 0, then R = inf */
 112                 if (((mp_cmp(py, qy) != 0)) || (mp_cmp_z(qy) == 0)) {
 113                         mp_zero(rx);
 114                         mp_zero(ry);
 115                         res = MP_OKAY;
 116                         goto CLEANUP;
 117                 }
 118                 /* lambda = (3qx^2+a) / (2qy) */
 119                 MP_CHECKOK(group->meth->field_sqr(qx, &tempx, group->meth));
 120                 MP_CHECKOK(mp_set_int(&temp, 3));
 121                 if (group->meth->field_enc) {
 122                         MP_CHECKOK(group->meth->field_enc(&temp, &temp, group->meth));
 123                 }
 124                 MP_CHECKOK(group->meth->
 125                                    field_mul(&tempx, &temp, &tempx, group->meth));
 126                 MP_CHECKOK(group->meth->
 127                                    field_add(&tempx, &group->curvea, &tempx, group->meth));
 128                 MP_CHECKOK(mp_set_int(&temp, 2));
 129                 if (group->meth->field_enc) {
 130                         MP_CHECKOK(group->meth->field_enc(&temp, &temp, group->meth));
 131                 }
 132                 MP_CHECKOK(group->meth->field_mul(qy, &temp, &tempy, group->meth));
 133                 MP_CHECKOK(group->meth->
 134                                    field_div(&tempx, &tempy, &lambda, group->meth));
 135         }
 136         /* rx = lambda^2 - px - qx */
 137         MP_CHECKOK(group->meth->field_sqr(&lambda, &tempx, group->meth));
 138         MP_CHECKOK(group->meth->field_sub(&tempx, px, &tempx, group->meth));
 139         MP_CHECKOK(group->meth->field_sub(&tempx, qx, &tempx, group->meth));
 140         /* ry = (x1-x2) * lambda - y1 */
 141         MP_CHECKOK(group->meth->field_sub(qx, &tempx, &tempy, group->meth));
 142         MP_CHECKOK(group->meth->
 143                            field_mul(&tempy, &lambda, &tempy, group->meth));
 144         MP_CHECKOK(group->meth->field_sub(&tempy, qy, &tempy, group->meth));
 145         MP_CHECKOK(mp_copy(&tempx, rx));
 146         MP_CHECKOK(mp_copy(&tempy, ry));
 147
 148   CLEANUP:
 149         mp_clear(&lambda);
 150         mp_clear(&temp);
 151         mp_clear(&tempx);
 152         mp_clear(&tempy);
 153         return res;
 154 }
 155
 156 /* Computes R = P - Q. Elliptic curve points P, Q, and R can all be
 157  * identical. Uses affine coordinates. Assumes input is already
 158  * field-encoded using field_enc, and returns output that is still
 159  * field-encoded. */
 160 mp_err
 161 ec_GFp_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));
 170         /* nqy = -qy */
 171         MP_CHECKOK(group->meth->field_neg(qy, &nqy, group->meth));
 172         res = 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. Assumes input is already field-encoded using
 180  * field_enc, and returns output that is still field-encoded. */
 181 mp_err
 182 ec_GFp_pt_dbl_aff(const mp_int *px, const mp_int *py, mp_int *rx,
 183                                   mp_int *ry, const ECGroup *group)
 184 {
 185         return ec_GFp_pt_add_aff(px, py, px, py, rx, ry, group);
 186 }
 187
 188 /* by default, this routine is unused and thus doesn't need to be compiled */
 189 #ifdef ECL_ENABLE_GFP_PT_MUL_AFF
 190 /* Computes R = nP based on IEEE P1363 A.10.3. Elliptic curve points P and
 191  * R can be identical. Uses affine coordinates. Assumes input is already
 192  * field-encoded using field_enc, and returns output that is still
 193  * field-encoded. */
 194 mp_err
 195 ec_GFp_pt_mul_aff(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 k, k3, qx, qy, sx, sy;
 200         int b1, b3, i, l;
 201
 202         MP_DIGITS(&k) = 0;
 203         MP_DIGITS(&k3) = 0;
 204         MP_DIGITS(&qx) = 0;
 205         MP_DIGITS(&qy) = 0;
 206         MP_DIGITS(&sx) = 0;
 207         MP_DIGITS(&sy) = 0;
 208         MP_CHECKOK(mp_init(&k));
 209         MP_CHECKOK(mp_init(&k3));
 210         MP_CHECKOK(mp_init(&qx));
 211         MP_CHECKOK(mp_init(&qy));
 212         MP_CHECKOK(mp_init(&sx));
 213         MP_CHECKOK(mp_init(&sy));
 214
 215         /* if n = 0 then r = inf */
 216         if (mp_cmp_z(n) == 0) {
 217                 mp_zero(rx);
 218                 mp_zero(ry);
 219                 res = MP_OKAY;
 220                 goto CLEANUP;
 221         }
 222         /* Q = P, k = n */
 223         MP_CHECKOK(mp_copy(px, &qx));
 224         MP_CHECKOK(mp_copy(py, &qy));
 225         MP_CHECKOK(mp_copy(n, &k));
 226         /* if n < 0 then Q = -Q, k = -k */
 227         if (mp_cmp_z(n) < 0) {
 228                 MP_CHECKOK(group->meth->field_neg(&qy, &qy, group->meth));
 229                 MP_CHECKOK(mp_neg(&k, &k));
 230         }
 231 #ifdef ECL_DEBUG                                /* basic double and add method */
 232         l = mpl_significant_bits(&k) - 1;
 233         MP_CHECKOK(mp_copy(&qx, &sx));
 234         MP_CHECKOK(mp_copy(&qy, &sy));
 235         for (i = l - 1; i >= 0; i--) {
 236                 /* S = 2S */
 237                 MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
 238                 /* if k_i = 1, then S = S + Q */
 239                 if (mpl_get_bit(&k, i) != 0) {
 240                         MP_CHECKOK(group->
 241                                            point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
 242                 }
 243         }
 244 #else                                                   /* double and add/subtract method from
 245                                                                  * standard */
 246         /* k3 = 3 * k */
 247         MP_CHECKOK(mp_set_int(&k3, 3));
 248         MP_CHECKOK(mp_mul(&k, &k3, &k3));
 249         /* S = Q */
 250         MP_CHECKOK(mp_copy(&qx, &sx));
 251         MP_CHECKOK(mp_copy(&qy, &sy));
 252         /* l = index of high order bit in binary representation of 3*k */
 253         l = mpl_significant_bits(&k3) - 1;
 254         /* for i = l-1 downto 1 */
 255         for (i = l - 1; i >= 1; i--) {
 256                 /* S = 2S */
 257                 MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
 258                 b3 = MP_GET_BIT(&k3, i);
 259                 b1 = MP_GET_BIT(&k, i);
 260                 /* if k3_i = 1 and k_i = 0, then S = S + Q */
 261                 if ((b3 == 1) && (b1 == 0)) {
 262                         MP_CHECKOK(group->
 263                                            point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
 264                         /* if k3_i = 0 and k_i = 1, then S = S - Q */
 265                 } else if ((b3 == 0) && (b1 == 1)) {
 266                         MP_CHECKOK(group->
 267                                            point_sub(&sx, &sy, &qx, &qy, &sx, &sy, group));
 268                 }
 269         }
 270 #endif
 271         /* output S */
 272         MP_CHECKOK(mp_copy(&sx, rx));
 273         MP_CHECKOK(mp_copy(&sy, ry));
 274
 275   CLEANUP:
 276         mp_clear(&k);
 277         mp_clear(&k3);
 278         mp_clear(&qx);
 279         mp_clear(&qy);
 280         mp_clear(&sx);
 281         mp_clear(&sy);
 282         return res;
 283 }
 284 #endif
 285
 286 /* Validates a point on a GFp curve. */
 287 mp_err
 288 ec_GFp_validate_point(const mp_int *px, const mp_int *py, const ECGroup *group)
 289 {
 290         mp_err res = MP_NO;
 291         mp_int accl, accr, tmp, pxt, pyt;
 292
 293         MP_DIGITS(&accl) = 0;
 294         MP_DIGITS(&accr) = 0;
 295         MP_DIGITS(&tmp) = 0;
 296         MP_DIGITS(&pxt) = 0;
 297         MP_DIGITS(&pyt) = 0;
 298         MP_CHECKOK(mp_init(&accl));
 299         MP_CHECKOK(mp_init(&accr));
 300         MP_CHECKOK(mp_init(&tmp));
 301         MP_CHECKOK(mp_init(&pxt));
 302         MP_CHECKOK(mp_init(&pyt));
 303
 304     /* 1: Verify that publicValue is not the point at infinity */
 305         if (ec_GFp_pt_is_inf_aff(px, py) == MP_YES) {
 306                 res = MP_NO;
 307                 goto CLEANUP;
 308         }
 309     /* 2: Verify that the coordinates of publicValue are elements
 310      *    of the field.
 311      */
 312         if ((MP_SIGN(px) == MP_NEG) || (mp_cmp(px, &group->meth->irr) >= 0) ||
 313                 (MP_SIGN(py) == MP_NEG) || (mp_cmp(py, &group->meth->irr) >= 0)) {
 314                 res = MP_NO;
 315                 goto CLEANUP;
 316         }
 317     /* 3: Verify that publicValue is on the curve. */
 318         if (group->meth->field_enc) {
 319                 group->meth->field_enc(px, &pxt, group->meth);
 320                 group->meth->field_enc(py, &pyt, group->meth);
 321         } else {
 322                 mp_copy(px, &pxt);
 323                 mp_copy(py, &pyt);
 324         }
 325         /* left-hand side: y^2  */
 326         MP_CHECKOK( group->meth->field_sqr(&pyt, &accl, group->meth) );
 327         /* right-hand side: x^3 + a*x + b */
 328         MP_CHECKOK( group->meth->field_sqr(&pxt, &tmp, group->meth) );
 329         MP_CHECKOK( group->meth->field_mul(&pxt, &tmp, &accr, group->meth) );
 330         MP_CHECKOK( group->meth->field_mul(&group->curvea, &pxt, &tmp, group->meth) );
 331         MP_CHECKOK( group->meth->field_add(&tmp, &accr, &accr, group->meth) );
 332         MP_CHECKOK( group->meth->field_add(&accr, &group->curveb, &accr, group->meth) );
 333         /* check LHS - RHS == 0 */
 334         MP_CHECKOK( group->meth->field_sub(&accl, &accr, &accr, group->meth) );
 335         if (mp_cmp_z(&accr) != 0) {
 336                 res = MP_NO;
 337                 goto CLEANUP;
 338         }
 339     /* 4: Verify that the order of the curve times the publicValue
 340      *    is the point at infinity.
 341      */
 342         MP_CHECKOK( ECPoint_mul(group, &group->order, px, py, &pxt, &pyt) );
 343         if (ec_GFp_pt_is_inf_aff(&pxt, &pyt) != MP_YES) {
 344                 res = MP_NO;
 345                 goto CLEANUP;
 346         }
 347
 348         res = MP_YES;
 349
 350 CLEANUP:
 351         mp_clear(&accl);
 352         mp_clear(&accr);
 353         mp_clear(&tmp);
 354         mp_clear(&pxt);
 355         mp_clear(&pyt);
 356         return res;
 357 }