crypto/ec/ec_curve.c

   1 /* crypto/ec/ec_curve.c */
   2 /* ====================================================================
   3  * Copyright (c) 1998-2002 The OpenSSL Project.  All rights reserved.
   4  *
   5  * Redistribution and use in source and binary forms, with or without
   6  * modification, are permitted provided that the following conditions
   7  * are met:
   8  *
   9  * 1. Redistributions of source code must retain the above copyright
  10  *    notice, this list of conditions and the following disclaimer.
  11  *
  12  * 2. Redistributions in binary form must reproduce the above copyright
  13  *    notice, this list of conditions and the following disclaimer in
  14  *    the documentation and/or other materials provided with the
  15  *    distribution.
  16  *
  17  * 3. All advertising materials mentioning features or use of this
  18  *    software must display the following acknowledgment:
  19  *    "This product includes software developed by the OpenSSL Project
  20  *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
  21  *
  22  * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
  23  *    endorse or promote products derived from this software without
  24  *    prior written permission. For written permission, please contact
  25  *    openssl-core@openssl.org.
  26  *
  27  * 5. Products derived from this software may not be called "OpenSSL"
  28  *    nor may "OpenSSL" appear in their names without prior written
  29  *    permission of the OpenSSL Project.
  30  *
  31  * 6. Redistributions of any form whatsoever must retain the following
  32  *    acknowledgment:
  33  *    "This product includes software developed by the OpenSSL Project
  34  *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
  35  *
  36  * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
  37  * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  38  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
  39  * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
  40  * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
  41  * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  42  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  43  * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  44  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
  45  * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
  46  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
  47  * OF THE POSSIBILITY OF SUCH DAMAGE.
  48  * ====================================================================
  49  *
  50  * This product includes cryptographic software written by Eric Young
  51  * (eay@cryptsoft.com).  This product includes software written by Tim
  52  * Hudson (tjh@cryptsoft.com).
  53  *
  54  */
  55
  56 #include "ec_lcl.h"
  57 #include <openssl/err.h>
  58 #include <openssl/obj_mac.h>
  59 #include <openssl/asn1.h>
  60 #include <openssl/asn1t.h>
  61
  62 /* #define _EC_GROUP_EXAMPLE_PRIME_CURVE        \
  63  *              "the prime number p", "a", "b", "the compressed base point", "y-bit", "order", "cofacor"
  64  */
  65 /* the nist prime curves */
  66 #define _EC_GROUP_NIST_PRIME_192        \
  67                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF",\
  68                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC",\
  69                 "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1",\
  70                 "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012",1,\
  71                 "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831",1
  72 #define _EC_GROUP_NIST_PRIME_224        \
  73                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001",\
  74                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE",\
  75                 "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4",\
  76                 "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21",0,\
  77                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D",1
  78 #define _EC_GROUP_NIST_PRIME_384        \
  79                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF",\
  80                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC",\
  81                 "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF",\
  82                 "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B9859F741E082542A385502F25DBF55296C3A545E3872760AB7",1,\
  83                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973",1
  84 #define _EC_GROUP_NIST_PRIME_521        \
  85                 "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"\
  86                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",\
  87                 "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"\
  88                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC",\
  89                 "051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B"\
  90                 "315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573DF883D2C34F1EF451FD46B503F00",\
  91                 "C6858E06B70404E9CD9E3ECB662395B4429C648139053F"\
  92                 "B521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B3C1856A429BF97E7E31C2E5BD66",0,\
  93                 "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"\
  94                 "FFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5C9B8899C47AEBB6FB71E91386409",1
  95 /* the x9.62 prime curves (minus the nist prime curves) */
  96 #define _EC_GROUP_X9_62_PRIME_192V2     \
  97                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF",\
  98                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC",\
  99                 "CC22D6DFB95C6B25E49C0D6364A4E5980C393AA21668D953",\
 100                 "EEA2BAE7E1497842F2DE7769CFE9C989C072AD696F48034A",1,\
 101                 "FFFFFFFFFFFFFFFFFFFFFFFE5FB1A724DC80418648D8DD31",1
 102 #define _EC_GROUP_X9_62_PRIME_192V3     \
 103                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF",\
 104                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC",\
 105                 "22123DC2395A05CAA7423DAECCC94760A7D462256BD56916",\
 106                 "7D29778100C65A1DA1783716588DCE2B8B4AEE8E228F1896",0,\
 107                 "FFFFFFFFFFFFFFFFFFFFFFFF7A62D031C83F4294F640EC13",1
 108 #define _EC_GROUP_X9_62_PRIME_239V1     \
 109                 "7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFF",\
 110                 "7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFC",\
 111                 "6B016C3BDCF18941D0D654921475CA71A9DB2FB27D1D37796185C2942C0A",\
 112                 "0FFA963CDCA8816CCC33B8642BEDF905C3D358573D3F27FBBD3B3CB9AAAF",0,\
 113                 "7FFFFFFFFFFFFFFFFFFFFFFF7FFFFF9E5E9A9F5D9071FBD1522688909D0B",1
 114 #define _EC_GROUP_X9_62_PRIME_239V2     \
 115                 "7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFF",\
 116                 "7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFC",\
 117                 "617FAB6832576CBBFED50D99F0249C3FEE58B94BA0038C7AE84C8C832F2C",\
 118                 "38AF09D98727705120C921BB5E9E26296A3CDCF2F35757A0EAFD87B830E7",0,\
 119                 "7FFFFFFFFFFFFFFFFFFFFFFF800000CFA7E8594377D414C03821BC582063",1
 120 #define _EC_GROUP_X9_62_PRIME_239V3     \
 121                 "7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFF",\
 122                 "7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFC",\
 123                 "255705FA2A306654B1F4CB03D6A750A30C250102D4988717D9BA15AB6D3E",\
 124                 "6768AE8E18BB92CFCF005C949AA2C6D94853D0E660BBF854B1C9505FE95A",1,\
 125                 "7FFFFFFFFFFFFFFFFFFFFFFF7FFFFF975DEB41B3A6057C3C432146526551",1
 126 #define _EC_GROUP_X9_62_PRIME_256V1     \
 127                 "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF",\
 128                 "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC",\
 129                 "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B",\
 130                 "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296",1,\
 131                 "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551",1
 132 /* the secg prime curves (minus the nist and x9.62 prime curves) */
 133 #define _EC_GROUP_SECG_PRIME_112R1      \
 134                 "DB7C2ABF62E35E668076BEAD208B",\
 135                 "DB7C2ABF62E35E668076BEAD2088",\
 136                 "659EF8BA043916EEDE8911702B22",\
 137                 "09487239995A5EE76B55F9C2F098",0,\
 138                 "DB7C2ABF62E35E7628DFAC6561C5",1
 139 #define _EC_GROUP_SECG_PRIME_112R2      \
 140                 "DB7C2ABF62E35E668076BEAD208B",\
 141                 "6127C24C05F38A0AAAF65C0EF02C",\
 142                 "51DEF1815DB5ED74FCC34C85D709",\
 143                 "4BA30AB5E892B4E1649DD0928643",1,\
 144                 "36DF0AAFD8B8D7597CA10520D04B",4
 145 #define _EC_GROUP_SECG_PRIME_128R1      \
 146                 "FFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFF",\
 147                 "FFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFC",\
 148                 "E87579C11079F43DD824993C2CEE5ED3",\
 149                 "161FF7528B899B2D0C28607CA52C5B86",1,\
 150                 "FFFFFFFE0000000075A30D1B9038A115",1
 151 #define _EC_GROUP_SECG_PRIME_128R2      \
 152                 "FFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFF",\
 153                 "D6031998D1B3BBFEBF59CC9BBFF9AEE1",\
 154                 "5EEEFCA380D02919DC2C6558BB6D8A5D",\
 155                 "7B6AA5D85E572983E6FB32A7CDEBC140",0,\
 156                 "3FFFFFFF 7FFFFFFF BE002472 0613B5A3",4
 157 #define _EC_GROUP_SECG_PRIME_160K1      \
 158                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC73",\
 159                 "0",\
 160                 "7",\
 161                 "3B4C382CE37AA192A4019E763036F4F5DD4D7EBB",0,\
 162                 "0100000000000000000001B8FA16DFAB9ACA16B6B3",1
 163 #define _EC_GROUP_SECG_PRIME_160R1      \
 164                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF",\
 165                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC",\
 166                 "1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45",\
 167                 "4A96B5688EF573284664698968C38BB913CBFC82",0,\
 168                 "0100000000000000000001F4C8F927AED3CA752257",1
 169 #define _EC_GROUP_SECG_PRIME_160R2      \
 170                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC73",\
 171                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC70",\
 172                 "B4E134D3FB59EB8BAB57274904664D5AF50388BA",\
 173                 "52DCB034293A117E1F4FF11B30F7199D3144CE6D",0,\
 174                 "0100000000000000000000351EE786A818F3A1A16B",1
 175 #define _EC_GROUP_SECG_PRIME_192K1      \
 176                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFEE37",\
 177                 "0",\
 178                 "3",\
 179                 "DB4FF10EC057E9AE26B07D0280B7F4341DA5D1B1EAE06C7D",1,\
 180                 "FFFFFFFFFFFFFFFFFFFFFFFE26F2FC170F69466A74DEFD8D",1
 181 #define _EC_GROUP_SECG_PRIME_224K1      \
 182                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFE56D",\
 183                 "0",\
 184                 "5",\
 185                 "A1455B334DF099DF30FC28A169A467E9E47075A90F7E650EB6B7A45C",1,\
 186                 "010000000000000000000000000001DCE8D2EC6184CAF0A971769FB1F7",1
 187 #define _EC_GROUP_SECG_PRIME_256K1      \
 188                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F",\
 189                 "0",\
 190                 "7",\
 191                 "79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798",0,\
 192                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141",1
 193
 194 static EC_GROUP *ec_group_new_GFp_from_hex(const char *prime_in,
 195             const char *a_in, const char *b_in,
 196             const char *x_in, const int y_bit, const char *order_in, const BN_ULONG cofac_in)
 197         {
 198         EC_GROUP *group=NULL;
 199         EC_POINT *P=NULL;
 200         BN_CTX   *ctx=NULL;
 201         BIGNUM   *prime=NULL,*a=NULL,*b=NULL,*x=NULL,*order=NULL;
 202         int      ok=0;
 203
 204         if ((ctx = BN_CTX_new()) == NULL) goto bn_err;
 205         if ((prime = BN_new()) == NULL || (a = BN_new()) == NULL || (b = BN_new()) == NULL ||
 206                 (x = BN_new()) == NULL || (order = BN_new()) == NULL) goto bn_err;
 207
 208         if (!BN_hex2bn(&prime, prime_in)) goto bn_err;
 209         if (!BN_hex2bn(&a, a_in)) goto bn_err;
 210         if (!BN_hex2bn(&b, b_in)) goto bn_err;
 211
 212         if ((group = EC_GROUP_new_curve_GFp(prime, a, b, ctx)) == NULL) goto err;
 213         if ((P = EC_POINT_new(group)) == NULL) goto err;
 214
 215         if (!BN_hex2bn(&x, x_in)) goto bn_err;
 216         if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, y_bit, ctx)) goto err;
 217         if (!BN_hex2bn(&order, order_in)) goto bn_err;
 218         if (!BN_set_word(x, cofac_in)) goto bn_err;
 219         if (!EC_GROUP_set_generator(group, P, order, x)) goto err;
 220         ok=1;
 221 bn_err:
 222         if (!ok)
 223                 ECerr(EC_F_EC_GROUP_NEW_GFP_FROM_HEX, ERR_R_BN_LIB);
 224 err:
 225         if (!ok)
 226                 {
 227                 EC_GROUP_free(group);
 228                 group = NULL;
 229                 }
 230         if (P)     EC_POINT_free(P);
 231         if (ctx)   BN_CTX_free(ctx);
 232         if (prime) BN_free(prime);
 233         if (a)     BN_free(a);
 234         if (b)     BN_free(b);
 235         if (order) BN_free(order);
 236         if (x)     BN_free(x);
 237         return(group);
 238         }
 239
 240 EC_GROUP *EC_GROUP_new_by_name(int name)
 241         {
 242         EC_GROUP *ret = NULL;
 243         switch (name)
 244                 {
 245         case EC_GROUP_NO_CURVE:
 246                 return NULL;
 247         /* some nist curves */
 248         case EC_GROUP_NIST_PRIME_224: /* EC_GROUP_NIST_PRIME_224 == EC_GROUP_SECG_PRIME_224R1 */
 249                 ret = ec_group_new_GFp_from_hex(_EC_GROUP_NIST_PRIME_224);
 250                 break;
 251
 252         case EC_GROUP_NIST_PRIME_384: /* EC_GROUP_NIST_PRIME_384 == EC_GROUP_SECG_PRIME_384R1 */
 253                 ret = ec_group_new_GFp_from_hex(_EC_GROUP_NIST_PRIME_384);
 254                 break;
 255
 256         case EC_GROUP_NIST_PRIME_521: /* EC_GROUP_NIST_PRIME_521 == EC_GROUP_SECG_PRIME_521R1 */
 257                 ret = ec_group_new_GFp_from_hex(_EC_GROUP_NIST_PRIME_521);
 258                 break;
 259         /* x9.62 prime curves */
 260         case EC_GROUP_NIST_PRIME_192: /* EC_GROUP_NIST_PRIME_192 == EC_GROUP_SECG_PRIME_192R1 */
 261         case EC_GROUP_X9_62_PRIME_192V1:
 262                 ret = ec_group_new_GFp_from_hex(_EC_GROUP_NIST_PRIME_192);
 263                 break;
 264
 265         case EC_GROUP_X9_62_PRIME_192V2:
 266                 ret = ec_group_new_GFp_from_hex(_EC_GROUP_X9_62_PRIME_192V2);
 267                 break;
 268
 269         case EC_GROUP_X9_62_PRIME_192V3:
 270                 ret = ec_group_new_GFp_from_hex(_EC_GROUP_X9_62_PRIME_192V3);
 271                 break;
 272
 273         case EC_GROUP_X9_62_PRIME_239V1:
 274                 ret = ec_group_new_GFp_from_hex(_EC_GROUP_X9_62_PRIME_239V1);
 275                 break;
 276
 277         case EC_GROUP_X9_62_PRIME_239V2:
 278                 ret = ec_group_new_GFp_from_hex(_EC_GROUP_X9_62_PRIME_239V2);
 279                 break;
 280
 281         case EC_GROUP_X9_62_PRIME_239V3:
 282                 ret = ec_group_new_GFp_from_hex(_EC_GROUP_X9_62_PRIME_239V3);
 283                 break;
 284
 285         case EC_GROUP_NIST_PRIME_256: /* EC_GROUP_NIST_PRIME_256 == EC_GROUP_SECG_PRIME_256R1 */
 286         case EC_GROUP_X9_62_PRIME_256V1:
 287                 ret = ec_group_new_GFp_from_hex(_EC_GROUP_X9_62_PRIME_256V1);
 288                 break;
 289         /* the remaining secg curves */
 290         case EC_GROUP_SECG_PRIME_112R1:
 291                 ret = ec_group_new_GFp_from_hex(_EC_GROUP_SECG_PRIME_112R1);
 292                 break;
 293         case EC_GROUP_SECG_PRIME_112R2:
 294                 ret = ec_group_new_GFp_from_hex(_EC_GROUP_SECG_PRIME_112R2);
 295                 break;
 296         case EC_GROUP_SECG_PRIME_128R1:
 297                 ret = ec_group_new_GFp_from_hex(_EC_GROUP_SECG_PRIME_128R1);
 298                 break;
 299         case EC_GROUP_SECG_PRIME_128R2:
 300                 ret = ec_group_new_GFp_from_hex(_EC_GROUP_SECG_PRIME_128R2);
 301                 break;
 302         case EC_GROUP_SECG_PRIME_160K1:
 303                 ret = ec_group_new_GFp_from_hex(_EC_GROUP_SECG_PRIME_160K1);
 304                 break;
 305         case EC_GROUP_SECG_PRIME_160R1:
 306                 ret = ec_group_new_GFp_from_hex(_EC_GROUP_SECG_PRIME_160R1);
 307                 break;
 308         case EC_GROUP_SECG_PRIME_160R2:
 309                 ret = ec_group_new_GFp_from_hex(_EC_GROUP_SECG_PRIME_160R2);
 310                 break;
 311         case EC_GROUP_SECG_PRIME_192K1:
 312                 ret = ec_group_new_GFp_from_hex(_EC_GROUP_SECG_PRIME_192K1);
 313                 break;
 314         case EC_GROUP_SECG_PRIME_224K1:
 315                 ret = ec_group_new_GFp_from_hex(_EC_GROUP_SECG_PRIME_224K1);
 316                 break;
 317         case EC_GROUP_SECG_PRIME_256K1:
 318                 ret = ec_group_new_GFp_from_hex(_EC_GROUP_SECG_PRIME_256K1);
 319                 break;
 320
 321                 }
 322         if (ret == NULL)
 323                 {
 324                 ECerr(EC_F_EC_GROUP_NEW_BY_NAME, EC_R_UNKNOWN_GROUP);
 325                 return NULL;
 326                 }
 327         EC_GROUP_set_nid(ret, name);
 328         return ret;
 329         }
 330
 331
 332 EC_GROUP *EC_GROUP_new_by_nid(int nid)
 333         {
 334         return EC_GROUP_new_by_name(nid);
 335         }