usr/src/common/crypto/ecc/ecp_224.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  *   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 "ecp.h"
  48 #include "mpi.h"
  49 #include "mplogic.h"
  50 #include "mpi-priv.h"
  51 #ifndef _KERNEL
  52 #include <stdlib.h>
  53 #endif
  54
  55 #define ECP224_DIGITS ECL_CURVE_DIGITS(224)
  56
  57 /* Fast modular reduction for p224 = 2^224 - 2^96 + 1.  a can be r. Uses
  58  * algorithm 7 from Brown, Hankerson, Lopez, Menezes. Software
  59  * Implementation of the NIST Elliptic Curves over Prime Fields. */
  60 mp_err
  61 ec_GFp_nistp224_mod(const mp_int *a, mp_int *r, const GFMethod *meth)
  62 {
  63         mp_err res = MP_OKAY;
  64         mp_size a_used = MP_USED(a);
  65
  66         int    r3b;
  67         mp_digit carry;
  68 #ifdef ECL_THIRTY_TWO_BIT
  69         mp_digit a6a = 0, a6b = 0,
  70                 a5a = 0, a5b = 0, a4a = 0, a4b = 0, a3a = 0, a3b = 0;
  71         mp_digit r0a, r0b, r1a, r1b, r2a, r2b, r3a;
  72 #else
  73         mp_digit a6 = 0, a5 = 0, a4 = 0, a3b = 0, a5a = 0;
  74         mp_digit a6b = 0, a6a_a5b = 0, a5b = 0, a5a_a4b = 0, a4a_a3b = 0;
  75         mp_digit r0, r1, r2, r3;
  76 #endif
  77
  78         /* reduction not needed if a is not larger than field size */
  79         if (a_used < ECP224_DIGITS) {
  80                 if (a == r) return MP_OKAY;
  81                 return mp_copy(a, r);
  82         }
  83         /* for polynomials larger than twice the field size, use regular
  84          * reduction */
  85         if (a_used > ECL_CURVE_DIGITS(224*2)) {
  86                 MP_CHECKOK(mp_mod(a, &meth->irr, r));
  87         } else {
  88 #ifdef ECL_THIRTY_TWO_BIT
  89                 /* copy out upper words of a */
  90                 switch (a_used) {
  91                 case 14:
  92                         a6b = MP_DIGIT(a, 13);
  93                 case 13:
  94                         a6a = MP_DIGIT(a, 12);
  95                 case 12:
  96                         a5b = MP_DIGIT(a, 11);
  97                 case 11:
  98                         a5a = MP_DIGIT(a, 10);
  99                 case 10:
 100                         a4b = MP_DIGIT(a, 9);
 101                 case 9:
 102                         a4a = MP_DIGIT(a, 8);
 103                 case 8:
 104                         a3b = MP_DIGIT(a, 7);
 105                 }
 106                 r3a = MP_DIGIT(a, 6);
 107                 r2b= MP_DIGIT(a, 5);
 108                 r2a= MP_DIGIT(a, 4);
 109                 r1b = MP_DIGIT(a, 3);
 110                 r1a = MP_DIGIT(a, 2);
 111                 r0b = MP_DIGIT(a, 1);
 112                 r0a = MP_DIGIT(a, 0);
 113
 114
 115                 /* implement r = (a3a,a2,a1,a0)
 116                         +(a5a, a4,a3b,  0)
 117                         +(  0, a6,a5b,  0)
 118                         -(  0    0,    0|a6b, a6a|a5b )
 119                         -(  a6b, a6a|a5b, a5a|a4b, a4a|a3b ) */
 120                 MP_ADD_CARRY (r1b, a3b, r1b, 0,     carry);
 121                 MP_ADD_CARRY (r2a, a4a, r2a, carry, carry);
 122                 MP_ADD_CARRY (r2b, a4b, r2b, carry, carry);
 123                 MP_ADD_CARRY (r3a, a5a, r3a, carry, carry);
 124                 r3b = carry;
 125                 MP_ADD_CARRY (r1b, a5b, r1b, 0,     carry);
 126                 MP_ADD_CARRY (r2a, a6a, r2a, carry, carry);
 127                 MP_ADD_CARRY (r2b, a6b, r2b, carry, carry);
 128                 MP_ADD_CARRY (r3a,   0, r3a, carry, carry);
 129                 r3b += carry;
 130                 MP_SUB_BORROW(r0a, a3b, r0a, 0,     carry);
 131                 MP_SUB_BORROW(r0b, a4a, r0b, carry, carry);
 132                 MP_SUB_BORROW(r1a, a4b, r1a, carry, carry);
 133                 MP_SUB_BORROW(r1b, a5a, r1b, carry, carry);
 134                 MP_SUB_BORROW(r2a, a5b, r2a, carry, carry);
 135                 MP_SUB_BORROW(r2b, a6a, r2b, carry, carry);
 136                 MP_SUB_BORROW(r3a, a6b, r3a, carry, carry);
 137                 r3b -= carry;
 138                 MP_SUB_BORROW(r0a, a5b, r0a, 0,     carry);
 139                 MP_SUB_BORROW(r0b, a6a, r0b, carry, carry);
 140                 MP_SUB_BORROW(r1a, a6b, r1a, carry, carry);
 141                 if (carry) {
 142                         MP_SUB_BORROW(r1b, 0, r1b, carry, carry);
 143                         MP_SUB_BORROW(r2a, 0, r2a, carry, carry);
 144                         MP_SUB_BORROW(r2b, 0, r2b, carry, carry);
 145                         MP_SUB_BORROW(r3a, 0, r3a, carry, carry);
 146                         r3b -= carry;
 147                 }
 148
 149                 while (r3b > 0) {
 150                         int tmp;
 151                         MP_ADD_CARRY(r1b, r3b, r1b, 0,     carry);
 152                         if (carry) {
 153                                 MP_ADD_CARRY(r2a,  0, r2a, carry, carry);
 154                                 MP_ADD_CARRY(r2b,  0, r2b, carry, carry);
 155                                 MP_ADD_CARRY(r3a,  0, r3a, carry, carry);
 156                         }
 157                         tmp = carry;
 158                         MP_SUB_BORROW(r0a, r3b, r0a, 0,     carry);
 159                         if (carry) {
 160                                 MP_SUB_BORROW(r0b, 0, r0b, carry, carry);
 161                                 MP_SUB_BORROW(r1a, 0, r1a, carry, carry);
 162                                 MP_SUB_BORROW(r1b, 0, r1b, carry, carry);
 163                                 MP_SUB_BORROW(r2a, 0, r2a, carry, carry);
 164                                 MP_SUB_BORROW(r2b, 0, r2b, carry, carry);
 165                                 MP_SUB_BORROW(r3a, 0, r3a, carry, carry);
 166                                 tmp -= carry;
 167                         }
 168                         r3b = tmp;
 169                 }
 170
 171                 while (r3b < 0) {
 172                         mp_digit maxInt = MP_DIGIT_MAX;
 173                         MP_ADD_CARRY (r0a, 1, r0a, 0,     carry);
 174                         MP_ADD_CARRY (r0b, 0, r0b, carry, carry);
 175                         MP_ADD_CARRY (r1a, 0, r1a, carry, carry);
 176                         MP_ADD_CARRY (r1b, maxInt, r1b, carry, carry);
 177                         MP_ADD_CARRY (r2a, maxInt, r2a, carry, carry);
 178                         MP_ADD_CARRY (r2b, maxInt, r2b, carry, carry);
 179                         MP_ADD_CARRY (r3a, maxInt, r3a, carry, carry);
 180                         r3b += carry;
 181                 }
 182                 /* check for final reduction */
 183                 /* now the only way we are over is if the top 4 words are all ones */
 184                 if ((r3a == MP_DIGIT_MAX) && (r2b == MP_DIGIT_MAX)
 185                         && (r2a == MP_DIGIT_MAX) && (r1b == MP_DIGIT_MAX) &&
 186                          ((r1a != 0) || (r0b != 0) || (r0a != 0)) ) {
 187                         /* one last subraction */
 188                         MP_SUB_BORROW(r0a, 1, r0a, 0,     carry);
 189                         MP_SUB_BORROW(r0b, 0, r0b, carry, carry);
 190                         MP_SUB_BORROW(r1a, 0, r1a, carry, carry);
 191                         r1b = r2a = r2b = r3a = 0;
 192                 }
 193
 194
 195                 if (a != r) {
 196                         MP_CHECKOK(s_mp_pad(r, 7));
 197                 }
 198                 /* set the lower words of r */
 199                 MP_SIGN(r) = MP_ZPOS;
 200                 MP_USED(r) = 7;
 201                 MP_DIGIT(r, 6) = r3a;
 202                 MP_DIGIT(r, 5) = r2b;
 203                 MP_DIGIT(r, 4) = r2a;
 204                 MP_DIGIT(r, 3) = r1b;
 205                 MP_DIGIT(r, 2) = r1a;
 206                 MP_DIGIT(r, 1) = r0b;
 207                 MP_DIGIT(r, 0) = r0a;
 208 #else
 209                 /* copy out upper words of a */
 210                 switch (a_used) {
 211                 case 7:
 212                         a6 = MP_DIGIT(a, 6);
 213                         a6b = a6 >> 32;
 214                         a6a_a5b = a6 << 32;
 215                 case 6:
 216                         a5 = MP_DIGIT(a, 5);
 217                         a5b = a5 >> 32;
 218                         a6a_a5b |= a5b;
 219                         a5b = a5b << 32;
 220                         a5a_a4b = a5 << 32;
 221                         a5a = a5 & 0xffffffff;
 222                 case 5:
 223                         a4 = MP_DIGIT(a, 4);
 224                         a5a_a4b |= a4 >> 32;
 225                         a4a_a3b = a4 << 32;
 226                 case 4:
 227                         a3b = MP_DIGIT(a, 3) >> 32;
 228                         a4a_a3b |= a3b;
 229                         a3b = a3b << 32;
 230                 }
 231
 232                 r3 = MP_DIGIT(a, 3) & 0xffffffff;
 233                 r2 = MP_DIGIT(a, 2);
 234                 r1 = MP_DIGIT(a, 1);
 235                 r0 = MP_DIGIT(a, 0);
 236
 237                 /* implement r = (a3a,a2,a1,a0)
 238                         +(a5a, a4,a3b,  0)
 239                         +(  0, a6,a5b,  0)
 240                         -(  0    0,    0|a6b, a6a|a5b )
 241                         -(  a6b, a6a|a5b, a5a|a4b, a4a|a3b ) */
 242                 MP_ADD_CARRY (r1, a3b, r1, 0,     carry);
 243                 MP_ADD_CARRY (r2, a4 , r2, carry, carry);
 244                 MP_ADD_CARRY (r3, a5a, r3, carry, carry);
 245                 MP_ADD_CARRY (r1, a5b, r1, 0,     carry);
 246                 MP_ADD_CARRY (r2, a6 , r2, carry, carry);
 247                 MP_ADD_CARRY (r3,   0, r3, carry, carry);
 248
 249                 MP_SUB_BORROW(r0, a4a_a3b, r0, 0,     carry);
 250                 MP_SUB_BORROW(r1, a5a_a4b, r1, carry, carry);
 251                 MP_SUB_BORROW(r2, a6a_a5b, r2, carry, carry);
 252                 MP_SUB_BORROW(r3, a6b    , r3, carry, carry);
 253                 MP_SUB_BORROW(r0, a6a_a5b, r0, 0,     carry);
 254                 MP_SUB_BORROW(r1, a6b    , r1, carry, carry);
 255                 if (carry) {
 256                         MP_SUB_BORROW(r2, 0, r2, carry, carry);
 257                         MP_SUB_BORROW(r3, 0, r3, carry, carry);
 258                 }
 259
 260
 261                 /* if the value is negative, r3 has a 2's complement
 262                  * high value */
 263                 r3b = (int)(r3 >>32);
 264                 while (r3b > 0) {
 265                         r3 &= 0xffffffff;
 266                         MP_ADD_CARRY(r1,((mp_digit)r3b) << 32, r1, 0, carry);
 267                         if (carry) {
 268                                 MP_ADD_CARRY(r2,  0, r2, carry, carry);
 269                                 MP_ADD_CARRY(r3,  0, r3, carry, carry);
 270                         }
 271                         MP_SUB_BORROW(r0, r3b, r0, 0, carry);
 272                         if (carry) {
 273                                 MP_SUB_BORROW(r1, 0, r1, carry, carry);
 274                                 MP_SUB_BORROW(r2, 0, r2, carry, carry);
 275                                 MP_SUB_BORROW(r3, 0, r3, carry, carry);
 276                         }
 277                         r3b = (int)(r3 >>32);
 278                 }
 279
 280                 while (r3b < 0) {
 281                         MP_ADD_CARRY (r0, 1, r0, 0,     carry);
 282                         MP_ADD_CARRY (r1, MP_DIGIT_MAX <<32, r1, carry, carry);
 283                         MP_ADD_CARRY (r2, MP_DIGIT_MAX, r2, carry, carry);
 284                         MP_ADD_CARRY (r3, MP_DIGIT_MAX >> 32, r3, carry, carry);
 285                         r3b = (int)(r3 >>32);
 286                 }
 287                 /* check for final reduction */
 288                 /* now the only way we are over is if the top 4 words are all ones */
 289                 if ((r3 == (MP_DIGIT_MAX >> 32)) && (r2 == MP_DIGIT_MAX)
 290                         && ((r1 & MP_DIGIT_MAX << 32)== MP_DIGIT_MAX << 32) &&
 291                          ((r1 != MP_DIGIT_MAX << 32 ) || (r0 != 0)) ) {
 292                         /* one last subraction */
 293                         MP_SUB_BORROW(r0, 1, r0, 0,     carry);
 294                         MP_SUB_BORROW(r1, 0, r1, carry, carry);
 295                         r2 = r3 = 0;
 296                 }
 297
 298
 299                 if (a != r) {
 300                         MP_CHECKOK(s_mp_pad(r, 4));
 301                 }
 302                 /* set the lower words of r */
 303                 MP_SIGN(r) = MP_ZPOS;
 304                 MP_USED(r) = 4;
 305                 MP_DIGIT(r, 3) = r3;
 306                 MP_DIGIT(r, 2) = r2;
 307                 MP_DIGIT(r, 1) = r1;
 308                 MP_DIGIT(r, 0) = r0;
 309 #endif
 310         }
 311
 312   CLEANUP:
 313         return res;
 314 }
 315
 316 /* Compute the square of polynomial a, reduce modulo p224. Store the
 317  * result in r.  r could be a.  Uses optimized modular reduction for p224.
 318  */
 319 mp_err
 320 ec_GFp_nistp224_sqr(const mp_int *a, mp_int *r, const GFMethod *meth)
 321 {
 322         mp_err res = MP_OKAY;
 323
 324         MP_CHECKOK(mp_sqr(a, r));
 325         MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth));
 326   CLEANUP:
 327         return res;
 328 }
 329
 330 /* Compute the product of two polynomials a and b, reduce modulo p224.
 331  * Store the result in r.  r could be a or b; a could be b.  Uses
 332  * optimized modular reduction for p224. */
 333 mp_err
 334 ec_GFp_nistp224_mul(const mp_int *a, const mp_int *b, mp_int *r,
 335                                         const GFMethod *meth)
 336 {
 337         mp_err res = MP_OKAY;
 338
 339         MP_CHECKOK(mp_mul(a, b, r));
 340         MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth));
 341   CLEANUP:
 342         return res;
 343 }
 344
 345 /* Divides two field elements. If a is NULL, then returns the inverse of
 346  * b. */
 347 mp_err
 348 ec_GFp_nistp224_div(const mp_int *a, const mp_int *b, mp_int *r,
 349                    const GFMethod *meth)
 350 {
 351         mp_err res = MP_OKAY;
 352         mp_int t;
 353
 354         /* If a is NULL, then return the inverse of b, otherwise return a/b. */
 355         if (a == NULL) {
 356                 return  mp_invmod(b, &meth->irr, r);
 357         } else {
 358                 /* MPI doesn't support divmod, so we implement it using invmod and
 359                  * mulmod. */
 360                 MP_CHECKOK(mp_init(&t, FLAG(b)));
 361                 MP_CHECKOK(mp_invmod(b, &meth->irr, &t));
 362                 MP_CHECKOK(mp_mul(a, &t, r));
 363                 MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth));
 364           CLEANUP:
 365                 mp_clear(&t);
 366                 return res;
 367         }
 368 }
 369
 370 /* Wire in fast field arithmetic and precomputation of base point for
 371  * named curves. */
 372 mp_err
 373 ec_group_set_gfp224(ECGroup *group, ECCurveName name)
 374 {
 375         if (name == ECCurve_NIST_P224) {
 376                 group->meth->field_mod = &ec_GFp_nistp224_mod;
 377                 group->meth->field_mul = &ec_GFp_nistp224_mul;
 378                 group->meth->field_sqr = &ec_GFp_nistp224_sqr;
 379                 group->meth->field_div = &ec_GFp_nistp224_div;
 380         }
 381         return MP_OKAY;
 382 }