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