crypto/ec/ecp_nistp224.c

   1 /* crypto/ec/ecp_nistp224.c */
   2 /*
   3  * Written by Emilia Kasper (Google) for the OpenSSL project.
   4  */
   5 /* ====================================================================
   6  * Copyright (c) 2000-2010 The OpenSSL Project.  All rights reserved.
   7  *
   8  * Redistribution and use in source and binary forms, with or without
   9  * modification, are permitted provided that the following conditions
  10  * are met:
  11  *
  12  * 1. Redistributions of source code must retain the above copyright
  13  *    notice, this list of conditions and the following disclaimer.
  14  *
  15  * 2. Redistributions in binary form must reproduce the above copyright
  16  *    notice, this list of conditions and the following disclaimer in
  17  *    the documentation and/or other materials provided with the
  18  *    distribution.
  19  *
  20  * 3. All advertising materials mentioning features or use of this
  21  *    software must display the following acknowledgment:
  22  *    "This product includes software developed by the OpenSSL Project
  23  *    for use in the OpenSSL Toolkit. (http://www.OpenSSL.org/)"
  24  *
  25  * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
  26  *    endorse or promote products derived from this software without
  27  *    prior written permission. For written permission, please contact
  28  *    licensing@OpenSSL.org.
  29  *
  30  * 5. Products derived from this software may not be called "OpenSSL"
  31  *    nor may "OpenSSL" appear in their names without prior written
  32  *    permission of the OpenSSL Project.
  33  *
  34  * 6. Redistributions of any form whatsoever must retain the following
  35  *    acknowledgment:
  36  *    "This product includes software developed by the OpenSSL Project
  37  *    for use in the OpenSSL Toolkit (http://www.OpenSSL.org/)"
  38  *
  39  * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
  40  * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  41  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
  42  * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
  43  * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
  44  * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  45  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  46  * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  47  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
  48  * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
  49  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
  50  * OF THE POSSIBILITY OF SUCH DAMAGE.
  51  * ====================================================================
  52  *
  53  * This product includes cryptographic software written by Eric Young
  54  * (eay@cryptsoft.com).  This product includes software written by Tim
  55  * Hudson (tjh@cryptsoft.com).
  56  *
  57  */
  58
  59 /*
  60  * A 64-bit implementation of the NIST P-224 elliptic curve point multiplication
  61  *
  62  * Inspired by Daniel J. Bernstein's public domain nistp224 implementation
  63  * and Adam Langley's public domain 64-bit C implementation of curve25519
  64  */
  65 #ifdef EC_NISTP224_64_GCC_128
  66 #include <stdint.h>
  67 #include <string.h>
  68 #include <openssl/err.h>
  69 #include "ec_lcl.h"
  70
  71 typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit platforms */
  72
  73 typedef uint8_t u8;
  74
  75 static const u8 nistp224_curve_params[5*28] = {
  76         0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,    /* p */
  77         0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00,
  78         0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01,
  79         0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,    /* a */
  80         0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF,
  81         0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
  82         0xB4,0x05,0x0A,0x85,0x0C,0x04,0xB3,0xAB,0xF5,0x41,    /* b */
  83         0x32,0x56,0x50,0x44,0xB0,0xB7,0xD7,0xBF,0xD8,0xBA,
  84         0x27,0x0B,0x39,0x43,0x23,0x55,0xFF,0xB4,
  85         0xB7,0x0E,0x0C,0xBD,0x6B,0xB4,0xBF,0x7F,0x32,0x13,    /* x */
  86         0x90,0xB9,0x4A,0x03,0xC1,0xD3,0x56,0xC2,0x11,0x22,
  87         0x34,0x32,0x80,0xD6,0x11,0x5C,0x1D,0x21,
  88         0xbd,0x37,0x63,0x88,0xb5,0xf7,0x23,0xfb,0x4c,0x22,    /* y */
  89         0xdf,0xe6,0xcd,0x43,0x75,0xa0,0x5a,0x07,0x47,0x64,
  90         0x44,0xd5,0x81,0x99,0x85,0x00,0x7e,0x34
  91 };
  92
  93 /******************************************************************************/
  94 /*                  INTERNAL REPRESENTATION OF FIELD ELEMENTS
  95  *
  96  * Field elements are represented as a_0 + 2^56*a_1 + 2^112*a_2 + 2^168*a_3
  97  * where each slice a_i is a 64-bit word, i.e., a field element is an fslice
  98  * array a with 4 elements, where a[i] = a_i.
  99  * Outputs from multiplications are represented as unreduced polynomials
 100  * b_0 + 2^56*b_1 + 2^112*b_2 + 2^168*b_3 + 2^224*b_4 + 2^280*b_5 + 2^336*b_6
 101  * where each b_i is a 128-bit word. We ensure that inputs to each field
 102  * multiplication satisfy a_i < 2^60, so outputs satisfy b_i < 4*2^60*2^60,
 103  * and fit into a 128-bit word without overflow. The coefficients are then
 104  * again partially reduced to a_i < 2^57. We only reduce to the unique minimal
 105  * representation at the end of the computation.
 106  *
 107  */
 108
 109 typedef uint64_t fslice;
 110
 111 /* Field element size (and group order size), in bytes: 28*8 = 224 */
 112 static const unsigned fElemSize = 28;
 113
 114 /* Precomputed multiples of the standard generator
 115  * b_0*G + b_1*2^56*G + b_2*2^112*G + b_3*2^168*G for
 116  * (b_3, b_2, b_1, b_0) in [0,15], i.e., gmul[0] = point_at_infinity,
 117  * gmul[1] = G, gmul[2] = 2^56*G, gmul[3] = 2^56*G + G, etc.
 118  * Points are given in Jacobian projective coordinates: words 0-3 represent the
 119  * X-coordinate (slice a_0 is word 0, etc.), words 4-7 represent the
 120  * Y-coordinate and words 8-11 represent the Z-coordinate. */
 121 static const fslice gmul[16][3][4] = {
 122         {{0x00000000000000, 0x00000000000000, 0x00000000000000, 0x00000000000000},
 123          {0x00000000000000, 0x00000000000000, 0x00000000000000, 0x00000000000000},
 124          {0x00000000000000, 0x00000000000000, 0x00000000000000, 0x00000000000000}},
 125         {{0x3280d6115c1d21, 0xc1d356c2112234, 0x7f321390b94a03, 0xb70e0cbd6bb4bf},
 126          {0xd5819985007e34, 0x75a05a07476444, 0xfb4c22dfe6cd43, 0xbd376388b5f723},
 127          {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}},
 128         {{0xfd9675666ebbe9, 0xbca7664d40ce5e, 0x2242df8d8a2a43, 0x1f49bbb0f99bc5},
 129          {0x29e0b892dc9c43, 0xece8608436e662, 0xdc858f185310d0, 0x9812dd4eb8d321},
 130          {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}},
 131         {{0x6d3e678d5d8eb8, 0x559eed1cb362f1, 0x16e9a3bbce8a3f, 0xeedcccd8c2a748},
 132          {0xf19f90ed50266d, 0xabf2b4bf65f9df, 0x313865468fafec, 0x5cb379ba910a17},
 133          {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}},
 134         {{0x0641966cab26e3, 0x91fb2991fab0a0, 0xefec27a4e13a0b, 0x0499aa8a5f8ebe},
 135          {0x7510407766af5d, 0x84d929610d5450, 0x81d77aae82f706, 0x6916f6d4338c5b},
 136          {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}},
 137         {{0xea95ac3b1f15c6, 0x086000905e82d4, 0xdd323ae4d1c8b1, 0x932b56be7685a3},
 138          {0x9ef93dea25dbbf, 0x41665960f390f0, 0xfdec76dbe2a8a7, 0x523e80f019062a},
 139          {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}},
 140         {{0x822fdd26732c73, 0xa01c83531b5d0f, 0x363f37347c1ba4, 0xc391b45c84725c},
 141          {0xbbd5e1b2d6ad24, 0xddfbcde19dfaec, 0xc393da7e222a7f, 0x1efb7890ede244},
 142          {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}},
 143         {{0x4c9e90ca217da1, 0xd11beca79159bb, 0xff8d33c2c98b7c, 0x2610b39409f849},
 144          {0x44d1352ac64da0, 0xcdbb7b2c46b4fb, 0x966c079b753c89, 0xfe67e4e820b112},
 145          {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}},
 146         {{0xe28cae2df5312d, 0xc71b61d16f5c6e, 0x79b7619a3e7c4c, 0x05c73240899b47},
 147          {0x9f7f6382c73e3a, 0x18615165c56bda, 0x641fab2116fd56, 0x72855882b08394},
 148          {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}},
 149         {{0x0469182f161c09, 0x74a98ca8d00fb5, 0xb89da93489a3e0, 0x41c98768fb0c1d},
 150          {0xe5ea05fb32da81, 0x3dce9ffbca6855, 0x1cfe2d3fbf59e6, 0x0e5e03408738a7},
 151          {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}},
 152         {{0xdab22b2333e87f, 0x4430137a5dd2f6, 0xe03ab9f738beb8, 0xcb0c5d0dc34f24},
 153          {0x764a7df0c8fda5, 0x185ba5c3fa2044, 0x9281d688bcbe50, 0xc40331df893881},
 154          {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}},
 155         {{0xb89530796f0f60, 0xade92bd26909a3, 0x1a0c83fb4884da, 0x1765bf22a5a984},
 156          {0x772a9ee75db09e, 0x23bc6c67cec16f, 0x4c1edba8b14e2f, 0xe2a215d9611369},
 157          {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}},
 158         {{0x571e509fb5efb3, 0xade88696410552, 0xc8ae85fada74fe, 0x6c7e4be83bbde3},
 159          {0xff9f51160f4652, 0xb47ce2495a6539, 0xa2946c53b582f4, 0x286d2db3ee9a60},
 160          {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}},
 161         {{0x40bbd5081a44af, 0x0995183b13926c, 0xbcefba6f47f6d0, 0x215619e9cc0057},
 162          {0x8bc94d3b0df45e, 0xf11c54a3694f6f, 0x8631b93cdfe8b5, 0xe7e3f4b0982db9},
 163          {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}},
 164         {{0xb17048ab3e1c7b, 0xac38f36ff8a1d8, 0x1c29819435d2c6, 0xc813132f4c07e9},
 165          {0x2891425503b11f, 0x08781030579fea, 0xf5426ba5cc9674, 0x1e28ebf18562bc},
 166          {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}},
 167         {{0x9f31997cc864eb, 0x06cd91d28b5e4c, 0xff17036691a973, 0xf1aef351497c58},
 168          {0xdd1f2d600564ff, 0xdead073b1402db, 0x74a684435bd693, 0xeea7471f962558},
 169          {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}
 170 };
 171
 172 /* Precomputation for the group generator. */
 173 typedef struct {
 174         fslice g_pre_comp[16][3][4];
 175         int references;
 176 } NISTP224_PRE_COMP;
 177
 178 const EC_METHOD *EC_GFp_nistp224_method(void)
 179         {
 180         static const EC_METHOD ret = {
 181                 NID_X9_62_prime_field,
 182                 ec_GFp_nistp224_group_init,
 183                 ec_GFp_simple_group_finish,
 184                 ec_GFp_simple_group_clear_finish,
 185                 ec_GFp_nist_group_copy,
 186                 ec_GFp_nistp224_group_set_curve,
 187                 ec_GFp_simple_group_get_curve,
 188                 ec_GFp_simple_group_get_degree,
 189                 ec_GFp_simple_group_check_discriminant,
 190                 ec_GFp_simple_point_init,
 191                 ec_GFp_simple_point_finish,
 192                 ec_GFp_simple_point_clear_finish,
 193                 ec_GFp_simple_point_copy,
 194                 ec_GFp_simple_point_set_to_infinity,
 195                 ec_GFp_simple_set_Jprojective_coordinates_GFp,
 196                 ec_GFp_simple_get_Jprojective_coordinates_GFp,
 197                 ec_GFp_simple_point_set_affine_coordinates,
 198                 ec_GFp_nistp224_point_get_affine_coordinates,
 199                 ec_GFp_simple_set_compressed_coordinates,
 200                 ec_GFp_simple_point2oct,
 201                 ec_GFp_simple_oct2point,
 202                 ec_GFp_simple_add,
 203                 ec_GFp_simple_dbl,
 204                 ec_GFp_simple_invert,
 205                 ec_GFp_simple_is_at_infinity,
 206                 ec_GFp_simple_is_on_curve,
 207                 ec_GFp_simple_cmp,
 208                 ec_GFp_simple_make_affine,
 209                 ec_GFp_simple_points_make_affine,
 210                 ec_GFp_nistp224_points_mul,
 211                 ec_GFp_nistp224_precompute_mult,
 212                 ec_GFp_nistp224_have_precompute_mult,
 213                 ec_GFp_nist_field_mul,
 214                 ec_GFp_nist_field_sqr,
 215                 0 /* field_div */,
 216                 0 /* field_encode */,
 217                 0 /* field_decode */,
 218                 0 /* field_set_to_one */ };
 219
 220         return &ret;
 221         }
 222
 223 /* Helper functions to convert field elements to/from internal representation */
 224 static void bin28_to_felem(fslice out[4], const u8 in[28])
 225         {
 226         out[0] = *((const uint64_t *)(in)) & 0x00ffffffffffffff;
 227         out[1] = (*((const uint64_t *)(in+7))) & 0x00ffffffffffffff;
 228         out[2] = (*((const uint64_t *)(in+14))) & 0x00ffffffffffffff;
 229         out[3] = (*((const uint64_t *)(in+21))) & 0x00ffffffffffffff;
 230         }
 231
 232 static void felem_to_bin28(u8 out[28], const fslice in[4])
 233         {
 234         unsigned i;
 235         for (i = 0; i < 7; ++i)
 236                 {
 237                 out[i]    = in[0]>>(8*i);
 238                 out[i+7]  = in[1]>>(8*i);
 239                 out[i+14] = in[2]>>(8*i);
 240                 out[i+21] = in[3]>>(8*i);
 241                 }
 242         }
 243
 244 /* To preserve endianness when using BN_bn2bin and BN_bin2bn */
 245 static void flip_endian(u8 *out, const u8 *in, unsigned len)
 246         {
 247         unsigned i;
 248         for (i = 0; i < len; ++i)
 249                 out[i] = in[len-1-i];
 250         }
 251
 252 /* From OpenSSL BIGNUM to internal representation */
 253 static int BN_to_felem(fslice out[4], const BIGNUM *bn)
 254         {
 255         u8 b_in[fElemSize];
 256         u8 b_out[fElemSize];
 257         /* BN_bn2bin eats leading zeroes */
 258         memset(b_out, 0, fElemSize);
 259         unsigned num_bytes = BN_num_bytes(bn);
 260         if (num_bytes > fElemSize)
 261                 {
 262                 ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE);
 263                 return 0;
 264                 }
 265         if (BN_is_negative(bn))
 266                 {
 267                 ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE);
 268                 return 0;
 269                 }
 270         num_bytes = BN_bn2bin(bn, b_in);
 271         flip_endian(b_out, b_in, num_bytes);
 272         bin28_to_felem(out, b_out);
 273         return 1;
 274         }
 275
 276 /* From internal representation to OpenSSL BIGNUM */
 277 static BIGNUM *felem_to_BN(BIGNUM *out, const fslice in[4])
 278         {
 279         u8 b_in[fElemSize], b_out[fElemSize];
 280         felem_to_bin28(b_in, in);
 281         flip_endian(b_out, b_in, fElemSize);
 282         return BN_bin2bn(b_out, fElemSize, out);
 283         }
 284
 285 /******************************************************************************/
 286 /*                              FIELD OPERATIONS
 287  *
 288  * Field operations, using the internal representation of field elements.
 289  * NB! These operations are specific to our point multiplication and cannot be
 290  * expected to be correct in general - e.g., multiplication with a large scalar
 291  * will cause an overflow.
 292  *
 293  */
 294
 295 /* Sum two field elements: out += in */
 296 static void felem_sum64(fslice out[4], const fslice in[4])
 297         {
 298         out[0] += in[0];
 299         out[1] += in[1];
 300         out[2] += in[2];
 301         out[3] += in[3];
 302         }
 303
 304 /* Subtract field elements: out -= in */
 305 /* Assumes in[i] < 2^57 */
 306 static void felem_diff64(fslice out[4], const fslice in[4])
 307         {
 308         static const uint64_t two58p2 = (1l << 58) + (1l << 2);
 309         static const uint64_t two58m2 = (1l << 58) - (1l << 2);
 310         static const uint64_t two58m42m2 = (1l << 58) - (1l << 42) - (1l << 2);
 311
 312         /* Add 0 mod 2^224-2^96+1 to ensure out > in */
 313         out[0] += two58p2;
 314         out[1] += two58m42m2;
 315         out[2] += two58m2;
 316         out[3] += two58m2;
 317
 318         out[0] -= in[0];
 319         out[1] -= in[1];
 320         out[2] -= in[2];
 321         out[3] -= in[3];
 322         }
 323
 324 /* Subtract in unreduced 128-bit mode: out128 -= in128 */
 325 /* Assumes in[i] < 2^119 */
 326 static void felem_diff128(uint128_t out[7], const uint128_t in[4])
 327         {
 328         static const uint128_t two120 = ((uint128_t) 1) << 120;
 329         static const uint128_t two120m64 = (((uint128_t) 1) << 120) -
 330                 (((uint128_t) 1) << 64);
 331         static const uint128_t two120m104m64 = (((uint128_t) 1) << 120) -
 332                 (((uint128_t) 1) << 104) - (((uint128_t) 1) << 64);
 333
 334         /* Add 0 mod 2^224-2^96+1 to ensure out > in */
 335         out[0] += two120;
 336         out[1] += two120m64;
 337         out[2] += two120m64;
 338         out[3] += two120;
 339         out[4] += two120m104m64;
 340         out[5] += two120m64;
 341         out[6] += two120m64;
 342
 343         out[0] -= in[0];
 344         out[1] -= in[1];
 345         out[2] -= in[2];
 346         out[3] -= in[3];
 347         out[4] -= in[4];
 348         out[5] -= in[5];
 349         out[6] -= in[6];
 350         }
 351
 352 /* Subtract in mixed mode: out128 -= in64 */
 353 /* in[i] < 2^63 */
 354 static void felem_diff_128_64(uint128_t out[7], const fslice in[4])
 355         {
 356         static const uint128_t two64p8 = (((uint128_t) 1) << 64) +
 357                 (((uint128_t) 1) << 8);
 358         static const uint128_t two64m8 = (((uint128_t) 1) << 64) -
 359                 (((uint128_t) 1) << 8);
 360         static const uint128_t two64m48m8 = (((uint128_t) 1) << 64) -
 361                 (((uint128_t) 1) << 48) - (((uint128_t) 1) << 8);
 362
 363         /* Add 0 mod 2^224-2^96+1 to ensure out > in */
 364         out[0] += two64p8;
 365         out[1] += two64m48m8;
 366         out[2] += two64m8;
 367         out[3] += two64m8;
 368
 369         out[0] -= in[0];
 370         out[1] -= in[1];
 371         out[2] -= in[2];
 372         out[3] -= in[3];
 373         }
 374
 375 /* Multiply a field element by a scalar: out64 = out64 * scalar
 376  * The scalars we actually use are small, so results fit without overflow */
 377 static void felem_scalar64(fslice out[4], const fslice scalar)
 378         {
 379         out[0] *= scalar;
 380         out[1] *= scalar;
 381         out[2] *= scalar;
 382         out[3] *= scalar;
 383         }
 384
 385 /* Multiply an unreduced field element by a scalar: out128 = out128 * scalar
 386  * The scalars we actually use are small, so results fit without overflow */
 387 static void felem_scalar128(uint128_t out[7], const uint128_t scalar)
 388         {
 389         out[0] *= scalar;
 390         out[1] *= scalar;
 391         out[2] *= scalar;
 392         out[3] *= scalar;
 393         out[4] *= scalar;
 394         out[5] *= scalar;
 395         out[6] *= scalar;
 396         }
 397
 398 /* Square a field element: out = in^2 */
 399 static void felem_square(uint128_t out[7], const fslice in[4])
 400         {
 401         out[0] = ((uint128_t) in[0]) * in[0];
 402         out[1] = ((uint128_t) in[0]) * in[1] * 2;
 403         out[2] = ((uint128_t) in[0]) * in[2] * 2 + ((uint128_t) in[1]) * in[1];
 404         out[3] = ((uint128_t) in[0]) * in[3] * 2 +
 405                 ((uint128_t) in[1]) * in[2] * 2;
 406         out[4] = ((uint128_t) in[1]) * in[3] * 2 + ((uint128_t) in[2]) * in[2];
 407         out[5] = ((uint128_t) in[2]) * in[3] * 2;
 408         out[6] = ((uint128_t) in[3]) * in[3];
 409         }
 410
 411 /* Multiply two field elements: out = in1 * in2 */
 412 static void felem_mul(uint128_t out[7], const fslice in1[4], const fslice in2[4])
 413         {
 414         out[0] = ((uint128_t) in1[0]) * in2[0];
 415         out[1] = ((uint128_t) in1[0]) * in2[1] + ((uint128_t) in1[1]) * in2[0];
 416         out[2] = ((uint128_t) in1[0]) * in2[2] + ((uint128_t) in1[1]) * in2[1] +
 417                 ((uint128_t) in1[2]) * in2[0];
 418         out[3] = ((uint128_t) in1[0]) * in2[3] + ((uint128_t) in1[1]) * in2[2] +
 419                 ((uint128_t) in1[2]) * in2[1] + ((uint128_t) in1[3]) * in2[0];
 420         out[4] = ((uint128_t) in1[1]) * in2[3] + ((uint128_t) in1[2]) * in2[2] +
 421                 ((uint128_t) in1[3]) * in2[1];
 422         out[5] = ((uint128_t) in1[2]) * in2[3] + ((uint128_t) in1[3]) * in2[2];
 423         out[6] = ((uint128_t) in1[3]) * in2[3];
 424         }
 425
 426 /* Reduce 128-bit coefficients to 64-bit coefficients. Requires in[i] < 2^126,
 427  * ensures out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] < 2^57 */
 428 static void felem_reduce(fslice out[4], const uint128_t in[7])
 429         {
 430         static const uint128_t two127p15 = (((uint128_t) 1) << 127) +
 431                 (((uint128_t) 1) << 15);
 432         static const uint128_t two127m71 = (((uint128_t) 1) << 127) -
 433                 (((uint128_t) 1) << 71);
 434         static const uint128_t two127m71m55 = (((uint128_t) 1) << 127) -
 435                 (((uint128_t) 1) << 71) - (((uint128_t) 1) << 55);
 436         uint128_t output[5];
 437
 438         /* Add 0 mod 2^224-2^96+1 to ensure all differences are positive */
 439         output[0] = in[0] + two127p15;
 440         output[1] = in[1] + two127m71m55;
 441         output[2] = in[2] + two127m71;
 442         output[3] = in[3];
 443         output[4] = in[4];
 444
 445         /* Eliminate in[4], in[5], in[6] */
 446         output[4] += in[6] >> 16;
 447         output[3] += (in[6]&0xffff) << 40;
 448         output[2] -= in[6];
 449
 450         output[3] += in[5] >> 16;
 451         output[2] += (in[5]&0xffff) << 40;
 452         output[1] -= in[5];
 453
 454         output[2] += output[4] >> 16;
 455         output[1] += (output[4]&0xffff) << 40;
 456         output[0] -= output[4];
 457         output[4] = 0;
 458
 459         /* Carry 2 -> 3 -> 4 */
 460         output[3] += output[2] >> 56;
 461         output[2] &= 0x00ffffffffffffff;
 462
 463         output[4] += output[3] >> 56;
 464         output[3] &= 0x00ffffffffffffff;
 465
 466         /* Now output[2] < 2^56, output[3] < 2^56 */
 467
 468         /* Eliminate output[4] */
 469         output[2] += output[4] >> 16;
 470         output[1] += (output[4]&0xffff) << 40;
 471         output[0] -= output[4];
 472
 473         /* Carry 0 -> 1 -> 2 -> 3 */
 474         output[1] += output[0] >> 56;
 475         out[0] = output[0] & 0x00ffffffffffffff;
 476
 477         output[2] += output[1] >> 56;
 478         out[1] = output[1] & 0x00ffffffffffffff;
 479         output[3] += output[2] >> 56;
 480         out[2] = output[2] & 0x00ffffffffffffff;
 481
 482         /* out[0] < 2^56, out[1] < 2^56, out[2] < 2^56,
 483          * out[3] < 2^57 (due to final carry) */
 484         out[3] = output[3];
 485         }
 486
 487 /* Reduce to unique minimal representation */
 488 static void felem_contract(fslice out[4], const fslice in[4])
 489         {
 490         static const int64_t two56 = (1l << 56);
 491         /* 0 <= in < 2^225 */
 492         /* if in > 2^224 , reduce in = in - 2^224 + 2^96 - 1 */
 493         int64_t tmp[4], a;
 494         tmp[0] = (int64_t) in[0] - (in[3] >> 56);
 495         tmp[1] = (int64_t) in[1] + ((in[3] >> 16) & 0x0000010000000000);
 496         tmp[2] = (int64_t) in[2];
 497         tmp[3] = (int64_t) in[3] & 0x00ffffffffffffff;
 498
 499         /* eliminate negative coefficients */
 500         a = tmp[0] >> 63;
 501         tmp[0] += two56 & a;
 502         tmp[1] -= 1 & a;
 503
 504         a = tmp[1] >> 63;
 505         tmp[1] += two56 & a;
 506         tmp[2] -= 1 & a;
 507
 508         a = tmp[2] >> 63;
 509         tmp[2] += two56 & a;
 510         tmp[3] -= 1 & a;
 511
 512         a = tmp[3] >> 63;
 513         tmp[3] += two56 & a;
 514         tmp[0] += 1 & a;
 515         tmp[1] -= (1 & a) << 40;
 516
 517         /* carry 1 -> 2 -> 3 */
 518         tmp[2] += tmp[1] >> 56;
 519         tmp[1] &= 0x00ffffffffffffff;
 520
 521         tmp[3] += tmp[2] >> 56;
 522         tmp[2] &= 0x00ffffffffffffff;
 523
 524         /* 0 <= in < 2^224 + 2^96 - 1 */
 525         /* if in > 2^224 , reduce in = in - 2^224 + 2^96 - 1 */
 526         tmp[0] -= (tmp[3] >> 56);
 527         tmp[1] += ((tmp[3] >> 16) & 0x0000010000000000);
 528         tmp[3] &= 0x00ffffffffffffff;
 529
 530         /* eliminate negative coefficients */
 531         a = tmp[0] >> 63;
 532         tmp[0] += two56 & a;
 533         tmp[1] -= 1 & a;
 534
 535         a = tmp[1] >> 63;
 536         tmp[1] += two56 & a;
 537         tmp[2] -= 1 & a;
 538
 539         a = tmp[2] >> 63;
 540         tmp[2] += two56 & a;
 541         tmp[3] -= 1 & a;
 542
 543         a = tmp[3] >> 63;
 544         tmp[3] += two56 & a;
 545         tmp[0] += 1 & a;
 546         tmp[1] -= (1 & a) << 40;
 547
 548         /* carry 1 -> 2 -> 3 */
 549         tmp[2] += tmp[1] >> 56;
 550         tmp[1] &= 0x00ffffffffffffff;
 551
 552         tmp[3] += tmp[2] >> 56;
 553         tmp[2] &= 0x00ffffffffffffff;
 554
 555         /* Now 0 <= in < 2^224 */
 556
 557         /* if in > 2^224 - 2^96, reduce */
 558         /* a = 0 iff in > 2^224 - 2^96, i.e.,
 559          * the high 128 bits are all 1 and the lower part is non-zero */
 560         a = (tmp[3] + 1) | (tmp[2] + 1) |
 561                 ((tmp[1] | 0x000000ffffffffff) + 1) |
 562                 ((((tmp[1] & 0xffff) - 1) >> 63) & ((tmp[0] - 1) >> 63));
 563         /* turn a into an all-one mask (if a = 0) or an all-zero mask */
 564         a = ((a & 0x00ffffffffffffff) - 1) >> 63;
 565         /* subtract 2^224 - 2^96 + 1 if a is all-one*/
 566         tmp[3] &= a ^ 0xffffffffffffffff;
 567         tmp[2] &= a ^ 0xffffffffffffffff;
 568         tmp[1] &= (a ^ 0xffffffffffffffff) | 0x000000ffffffffff;
 569         tmp[0] -= 1 & a;
 570         /* eliminate negative coefficients: if tmp[0] is negative, tmp[1] must be
 571          * non-zero, so we only need one step */
 572         a = tmp[0] >> 63;
 573         tmp[0] += two56 & a;
 574         tmp[1] -= 1 & a;
 575
 576         out[0] = tmp[0];
 577         out[1] = tmp[1];
 578         out[2] = tmp[2];
 579         out[3] = tmp[3];
 580         }
 581
 582 /* Zero-check: returns 1 if input is 0, and 0 otherwise.
 583  * We know that field elements are reduced to in < 2^225,
 584  * so we only need to check three cases: 0, 2^224 - 2^96 + 1,
 585  * and 2^225 - 2^97 + 2 */
 586 static fslice felem_is_zero(const fslice in[4])
 587         {
 588         fslice zero = (in[0] | in[1] | in[2] | in[3]);
 589         zero = (((int64_t)(zero) - 1) >> 63) & 1;
 590         fslice two224m96p1 = (in[0] ^ 1) | (in[1] ^ 0x00ffff0000000000)
 591                 | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x00ffffffffffffff);
 592         two224m96p1 = (((int64_t)(two224m96p1) - 1) >> 63) & 1;
 593         fslice two225m97p2 = (in[0] ^ 2) | (in[1] ^ 0x00fffe0000000000)
 594                 | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x01ffffffffffffff);
 595         two225m97p2 = (((int64_t)(two225m97p2) - 1) >> 63) & 1;
 596         return  (zero | two224m96p1 | two225m97p2);
 597         }
 598
 599 /* Invert a field element */
 600 /* Computation chain copied from djb's code */
 601 static void felem_inv(fslice out[4], const fslice in[4])
 602         {
 603         fslice ftmp[4], ftmp2[4], ftmp3[4], ftmp4[4];
 604         uint128_t tmp[7];
 605         unsigned i;
 606         felem_square(tmp, in); felem_reduce(ftmp, tmp);         /* 2 */
 607         felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp);      /* 2^2 - 1 */
 608         felem_square(tmp, ftmp); felem_reduce(ftmp, tmp);       /* 2^3 - 2 */
 609         felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp);      /* 2^3 - 1 */
 610         felem_square(tmp, ftmp); felem_reduce(ftmp2, tmp);      /* 2^4 - 2 */
 611         felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp);     /* 2^5 - 4 */
 612         felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp);     /* 2^6 - 8 */
 613         felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp, tmp);   /* 2^6 - 1 */
 614         felem_square(tmp, ftmp); felem_reduce(ftmp2, tmp);      /* 2^7 - 2 */
 615         for (i = 0; i < 5; ++i)                                 /* 2^12 - 2^6 */
 616                 {
 617                 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp);
 618                 }
 619         felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp2, tmp);  /* 2^12 - 1 */
 620         felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp);     /* 2^13 - 2 */
 621         for (i = 0; i < 11; ++i)                                /* 2^24 - 2^12 */
 622                 {
 623                 felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp);
 624                 }
 625         felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp2, tmp); /* 2^24 - 1 */
 626         felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp);     /* 2^25 - 2 */
 627         for (i = 0; i < 23; ++i)                                /* 2^48 - 2^24 */
 628                 {
 629                 felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp);
 630                 }
 631         felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^48 - 1 */
 632         felem_square(tmp, ftmp3); felem_reduce(ftmp4, tmp);     /* 2^49 - 2 */
 633         for (i = 0; i < 47; ++i)                                /* 2^96 - 2^48 */
 634                 {
 635                 felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp);
 636                 }
 637         felem_mul(tmp, ftmp3, ftmp4); felem_reduce(ftmp3, tmp); /* 2^96 - 1 */
 638         felem_square(tmp, ftmp3); felem_reduce(ftmp4, tmp);     /* 2^97 - 2 */
 639         for (i = 0; i < 23; ++i)                                /* 2^120 - 2^24 */
 640                 {
 641                 felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp);
 642                 }
 643         felem_mul(tmp, ftmp2, ftmp4); felem_reduce(ftmp2, tmp); /* 2^120 - 1 */
 644         for (i = 0; i < 6; ++i)                                 /* 2^126 - 2^6 */
 645                 {
 646                 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp);
 647                 }
 648         felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp, tmp);   /* 2^126 - 1 */
 649         felem_square(tmp, ftmp); felem_reduce(ftmp, tmp);       /* 2^127 - 2 */
 650         felem_mul(tmp, ftmp, in); felem_reduce(ftmp, tmp);      /* 2^127 - 1 */
 651         for (i = 0; i < 97; ++i)                                /* 2^224 - 2^97 */
 652                 {
 653                 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp);
 654                 }
 655         felem_mul(tmp, ftmp, ftmp3); felem_reduce(out, tmp);    /* 2^224 - 2^96 - 1 */
 656         }
 657
 658 /* Copy in constant time:
 659  * if icopy == 1, copy in to out,
 660  * if icopy == 0, copy out to itself. */
 661 static void
 662 copy_conditional(fslice *out, const fslice *in, unsigned len, fslice icopy)
 663         {
 664         unsigned i;
 665         /* icopy is a (64-bit) 0 or 1, so copy is either all-zero or all-one */
 666         const fslice copy = -icopy;
 667         for (i = 0; i < len; ++i)
 668                 {
 669                 const fslice tmp = copy & (in[i] ^ out[i]);
 670                 out[i] ^= tmp;
 671                 }
 672         }
 673
 674 /* Copy in constant time:
 675  * if isel == 1, copy in2 to out,
 676  * if isel == 0, copy in1 to out. */
 677 static void select_conditional(fslice *out, const fslice *in1, const fslice *in2,
 678         unsigned len, fslice isel)
 679         {
 680         unsigned i;
 681         /* isel is a (64-bit) 0 or 1, so sel is either all-zero or all-one */
 682         const fslice sel = -isel;
 683         for (i = 0; i < len; ++i)
 684                 {
 685                 const fslice tmp = sel & (in1[i] ^ in2[i]);
 686                 out[i] = in1[i] ^ tmp;
 687                 }
 688 }
 689
 690 /******************************************************************************/
 691 /*                       ELLIPTIC CURVE POINT OPERATIONS
 692  *
 693  * Points are represented in Jacobian projective coordinates:
 694  * (X, Y, Z) corresponds to the affine point (X/Z^2, Y/Z^3),
 695  * or to the point at infinity if Z == 0.
 696  *
 697  */
 698
 699 /* Double an elliptic curve point:
 700  * (X', Y', Z') = 2 * (X, Y, Z), where
 701  * X' = (3 * (X - Z^2) * (X + Z^2))^2 - 8 * X * Y^2
 702  * Y' = 3 * (X - Z^2) * (X + Z^2) * (4 * X * Y^2 - X') - 8 * Y^2
 703  * Z' = (Y + Z)^2 - Y^2 - Z^2 = 2 * Y * Z
 704  * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed,
 705  * while x_out == y_in is not (maybe this works, but it's not tested). */
 706 static void
 707 point_double(fslice x_out[4], fslice y_out[4], fslice z_out[4],
 708              const fslice x_in[4], const fslice y_in[4], const fslice z_in[4])
 709         {
 710         uint128_t tmp[7], tmp2[7];
 711         fslice delta[4];
 712         fslice gamma[4];
 713         fslice beta[4];
 714         fslice alpha[4];
 715         fslice ftmp[4], ftmp2[4];
 716         memcpy(ftmp, x_in, 4 * sizeof(fslice));
 717         memcpy(ftmp2, x_in, 4 * sizeof(fslice));
 718
 719         /* delta = z^2 */
 720         felem_square(tmp, z_in);
 721         felem_reduce(delta, tmp);
 722
 723         /* gamma = y^2 */
 724         felem_square(tmp, y_in);
 725         felem_reduce(gamma, tmp);
 726
 727         /* beta = x*gamma */
 728         felem_mul(tmp, x_in, gamma);
 729         felem_reduce(beta, tmp);
 730
 731         /* alpha = 3*(x-delta)*(x+delta) */
 732         felem_diff64(ftmp, delta);
 733         /* ftmp[i] < 2^57 + 2^58 + 2 < 2^59 */
 734         felem_sum64(ftmp2, delta);
 735         /* ftmp2[i] < 2^57 + 2^57 = 2^58 */
 736         felem_scalar64(ftmp2, 3);
 737         /* ftmp2[i] < 3 * 2^58 < 2^60 */
 738         felem_mul(tmp, ftmp, ftmp2);
 739         /* tmp[i] < 2^60 * 2^59 * 4 = 2^121 */
 740         felem_reduce(alpha, tmp);
 741
 742         /* x' = alpha^2 - 8*beta */
 743         felem_square(tmp, alpha);
 744         /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
 745         memcpy(ftmp, beta, 4 * sizeof(fslice));
 746         felem_scalar64(ftmp, 8);
 747         /* ftmp[i] < 8 * 2^57 = 2^60 */
 748         felem_diff_128_64(tmp, ftmp);
 749         /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */
 750         felem_reduce(x_out, tmp);
 751
 752         /* z' = (y + z)^2 - gamma - delta */
 753         felem_sum64(delta, gamma);
 754         /* delta[i] < 2^57 + 2^57 = 2^58 */
 755         memcpy(ftmp, y_in, 4 * sizeof(fslice));
 756         felem_sum64(ftmp, z_in);
 757         /* ftmp[i] < 2^57 + 2^57 = 2^58 */
 758         felem_square(tmp, ftmp);
 759         /* tmp[i] < 4 * 2^58 * 2^58 = 2^118 */
 760         felem_diff_128_64(tmp, delta);
 761         /* tmp[i] < 2^118 + 2^64 + 8 < 2^119 */
 762         felem_reduce(z_out, tmp);
 763
 764         /* y' = alpha*(4*beta - x') - 8*gamma^2 */
 765         felem_scalar64(beta, 4);
 766         /* beta[i] < 4 * 2^57 = 2^59 */
 767         felem_diff64(beta, x_out);
 768         /* beta[i] < 2^59 + 2^58 + 2 < 2^60 */
 769         felem_mul(tmp, alpha, beta);
 770         /* tmp[i] < 4 * 2^57 * 2^60 = 2^119 */
 771         felem_square(tmp2, gamma);
 772         /* tmp2[i] < 4 * 2^57 * 2^57 = 2^116 */
 773         felem_scalar128(tmp2, 8);
 774         /* tmp2[i] < 8 * 2^116 = 2^119 */
 775         felem_diff128(tmp, tmp2);
 776         /* tmp[i] < 2^119 + 2^120 < 2^121 */
 777         felem_reduce(y_out, tmp);
 778         }
 779
 780 /* Add two elliptic curve points:
 781  * (X_1, Y_1, Z_1) + (X_2, Y_2, Z_2) = (X_3, Y_3, Z_3), where
 782  * X_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1)^2 - (Z_1^2 * X_2 - Z_2^2 * X_1)^3 -
 783  * 2 * Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^2
 784  * Y_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1) * (Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^2 - X_3) -
 785  *        Z_2^3 * Y_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^3
 786  * Z_3 = (Z_1^2 * X_2 - Z_2^2 * X_1) * (Z_1 * Z_2) */
 787
 788 /* This function is not entirely constant-time:
 789  * it includes a branch for checking whether the two input points are equal,
 790  * (while not equal to the point at infinity).
 791  * This case never happens during single point multiplication,
 792  * so there is no timing leak for ECDH or ECDSA signing. */
 793 static void point_add(fslice x3[4], fslice y3[4], fslice z3[4],
 794         const fslice x1[4], const fslice y1[4], const fslice z1[4],
 795         const fslice x2[4], const fslice y2[4], const fslice z2[4])
 796         {
 797         fslice ftmp[4], ftmp2[4], ftmp3[4], ftmp4[4], ftmp5[4];
 798         uint128_t tmp[7], tmp2[7];
 799         fslice z1_is_zero, z2_is_zero, x_equal, y_equal;
 800
 801         /* ftmp = z1^2 */
 802         felem_square(tmp, z1);
 803         felem_reduce(ftmp, tmp);
 804
 805         /* ftmp2 = z2^2 */
 806         felem_square(tmp, z2);
 807         felem_reduce(ftmp2, tmp);
 808
 809         /* ftmp3 = z1^3 */
 810         felem_mul(tmp, ftmp, z1);
 811         felem_reduce(ftmp3, tmp);
 812
 813         /* ftmp4 = z2^3 */
 814         felem_mul(tmp, ftmp2, z2);
 815         felem_reduce(ftmp4, tmp);
 816
 817         /* ftmp3 = z1^3*y2 */
 818         felem_mul(tmp, ftmp3, y2);
 819         /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
 820
 821         /* ftmp4 = z2^3*y1 */
 822         felem_mul(tmp2, ftmp4, y1);
 823         felem_reduce(ftmp4, tmp2);
 824
 825         /* ftmp3 = z1^3*y2 - z2^3*y1 */
 826         felem_diff_128_64(tmp, ftmp4);
 827         /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */
 828         felem_reduce(ftmp3, tmp);
 829
 830         /* ftmp = z1^2*x2 */
 831         felem_mul(tmp, ftmp, x2);
 832         /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
 833
 834         /* ftmp2 =z2^2*x1 */
 835         felem_mul(tmp2, ftmp2, x1);
 836         felem_reduce(ftmp2, tmp2);
 837
 838         /* ftmp = z1^2*x2 - z2^2*x1 */
 839         felem_diff128(tmp, tmp2);
 840         /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */
 841         felem_reduce(ftmp, tmp);
 842
 843         /* the formulae are incorrect if the points are equal
 844          * so we check for this and do doubling if this happens */
 845         x_equal = felem_is_zero(ftmp);
 846         y_equal = felem_is_zero(ftmp3);
 847         z1_is_zero = felem_is_zero(z1);
 848         z2_is_zero = felem_is_zero(z2);
 849         /* In affine coordinates, (X_1, Y_1) == (X_2, Y_2) */
 850         if (x_equal && y_equal && !z1_is_zero && !z2_is_zero)
 851                 {
 852                 point_double(x3, y3, z3, x1, y1, z1);
 853                 return;
 854                 }
 855
 856         /* ftmp5 = z1*z2 */
 857         felem_mul(tmp, z1, z2);
 858         felem_reduce(ftmp5, tmp);
 859
 860         /* z3 = (z1^2*x2 - z2^2*x1)*(z1*z2) */
 861         felem_mul(tmp, ftmp, ftmp5);
 862         felem_reduce(z3, tmp);
 863
 864         /* ftmp = (z1^2*x2 - z2^2*x1)^2 */
 865         memcpy(ftmp5, ftmp, 4 * sizeof(fslice));
 866         felem_square(tmp, ftmp);
 867         felem_reduce(ftmp, tmp);
 868
 869         /* ftmp5 = (z1^2*x2 - z2^2*x1)^3 */
 870         felem_mul(tmp, ftmp, ftmp5);
 871         felem_reduce(ftmp5, tmp);
 872
 873         /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */
 874         felem_mul(tmp, ftmp2, ftmp);
 875         felem_reduce(ftmp2, tmp);
 876
 877         /* ftmp4 = z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */
 878         felem_mul(tmp, ftmp4, ftmp5);
 879         /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
 880
 881         /* tmp2 = (z1^3*y2 - z2^3*y1)^2 */
 882         felem_square(tmp2, ftmp3);
 883         /* tmp2[i] < 4 * 2^57 * 2^57 < 2^116 */
 884
 885         /* tmp2 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 */
 886         felem_diff_128_64(tmp2, ftmp5);
 887         /* tmp2[i] < 2^116 + 2^64 + 8 < 2^117 */
 888
 889         /* ftmp5 = 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */
 890         memcpy(ftmp5, ftmp2, 4 * sizeof(fslice));
 891         felem_scalar64(ftmp5, 2);
 892         /* ftmp5[i] < 2 * 2^57 = 2^58 */
 893
 894         /* x3 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 -
 895            2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */
 896         felem_diff_128_64(tmp2, ftmp5);
 897         /* tmp2[i] < 2^117 + 2^64 + 8 < 2^118 */
 898         felem_reduce(x3, tmp2);
 899
 900         /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x3 */
 901         felem_diff64(ftmp2, x3);
 902         /* ftmp2[i] < 2^57 + 2^58 + 2 < 2^59 */
 903
 904         /* tmp2 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x3) */
 905         felem_mul(tmp2, ftmp3, ftmp2);
 906         /* tmp2[i] < 4 * 2^57 * 2^59 = 2^118 */
 907
 908         /* y3 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x3) -
 909            z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */
 910         felem_diff128(tmp2, tmp);
 911         /* tmp2[i] < 2^118 + 2^120 < 2^121 */
 912         felem_reduce(y3, tmp2);
 913
 914         /* the result (x3, y3, z3) is incorrect if one of the inputs is the
 915          * point at infinity, so we need to check for this separately */
 916
 917         /* if point 1 is at infinity, copy point 2 to output, and vice versa */
 918         copy_conditional(x3, x2, 4, z1_is_zero);
 919         copy_conditional(x3, x1, 4, z2_is_zero);
 920         copy_conditional(y3, y2, 4, z1_is_zero);
 921         copy_conditional(y3, y1, 4, z2_is_zero);
 922         copy_conditional(z3, z2, 4, z1_is_zero);
 923         copy_conditional(z3, z1, 4, z2_is_zero);
 924         }
 925
 926 /* Select a point from an array of 16 precomputed point multiples,
 927  * in constant time: for bits = {b_0, b_1, b_2, b_3}, return the point
 928  * pre_comp[8*b_3 + 4*b_2 + 2*b_1 + b_0] */
 929 static void select_point(const fslice bits[4], const fslice pre_comp[16][3][4],
 930         fslice out[12])
 931         {
 932         fslice tmp[5][12];
 933         select_conditional(tmp[0], pre_comp[7][0], pre_comp[15][0], 12, bits[3]);
 934         select_conditional(tmp[1], pre_comp[3][0], pre_comp[11][0], 12, bits[3]);
 935         select_conditional(tmp[2], tmp[1], tmp[0], 12, bits[2]);
 936         select_conditional(tmp[0], pre_comp[5][0], pre_comp[13][0], 12, bits[3]);
 937         select_conditional(tmp[1], pre_comp[1][0], pre_comp[9][0], 12, bits[3]);
 938         select_conditional(tmp[3], tmp[1], tmp[0], 12, bits[2]);
 939         select_conditional(tmp[4], tmp[3], tmp[2], 12, bits[1]);
 940         select_conditional(tmp[0], pre_comp[6][0], pre_comp[14][0], 12, bits[3]);
 941         select_conditional(tmp[1], pre_comp[2][0], pre_comp[10][0], 12, bits[3]);
 942         select_conditional(tmp[2], tmp[1], tmp[0], 12, bits[2]);
 943         select_conditional(tmp[0], pre_comp[4][0], pre_comp[12][0], 12, bits[3]);
 944         select_conditional(tmp[1], pre_comp[0][0], pre_comp[8][0], 12, bits[3]);
 945         select_conditional(tmp[3], tmp[1], tmp[0], 12, bits[2]);
 946         select_conditional(tmp[1], tmp[3], tmp[2], 12, bits[1]);
 947         select_conditional(out, tmp[1], tmp[4], 12, bits[0]);
 948         }
 949
 950 /* Interleaved point multiplication using precomputed point multiples:
 951  * The small point multiples 0*P, 1*P, ..., 15*P are in pre_comp[],
 952  * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple
 953  * of the generator, using certain (large) precomputed multiples in g_pre_comp.
 954  * Output point (X, Y, Z) is stored in x_out, y_out, z_out */
 955 static void batch_mul(fslice x_out[4], fslice y_out[4], fslice z_out[4],
 956         const u8 scalars[][fElemSize], const unsigned num_points, const u8 *g_scalar,
 957         const fslice pre_comp[][16][3][4], const fslice g_pre_comp[16][3][4])
 958         {
 959         unsigned i, j, num;
 960         unsigned gen_mul = (g_scalar != NULL);
 961         fslice nq[12], nqt[12], tmp[12];
 962         /* set nq to the point at infinity */
 963         memset(nq, 0, 12 * sizeof(fslice));
 964         fslice bits[4];
 965         u8 byte;
 966
 967         /* Loop over all scalars msb-to-lsb, 4 bits at a time: for each nibble,
 968          * double 4 times, then add the precomputed point multiples.
 969          * If we are also adding multiples of the generator, then interleave
 970          * these additions with the last 56 doublings. */
 971         for (i = (num_points ? 28 : 7); i > 0; --i)
 972                 {
 973                 for (j = 0; j < 8; ++j)
 974                         {
 975                         /* double once */
 976                         point_double(nq, nq+4, nq+8, nq, nq+4, nq+8);
 977                         /* add multiples of the generator */
 978                         if ((gen_mul) && (i <= 7))
 979                                 {
 980                                 bits[3] = (g_scalar[i+20] >> (7-j)) & 1;
 981                                 bits[2] = (g_scalar[i+13] >> (7-j)) & 1;
 982                                 bits[1] = (g_scalar[i+6] >> (7-j)) & 1;
 983                                 bits[0] = (g_scalar[i-1] >> (7-j)) & 1;
 984                                 /* select the point to add, in constant time */
 985                                 select_point(bits, g_pre_comp, tmp);
 986                                 memcpy(nqt, nq, 12 * sizeof(fslice));
 987                                 point_add(nq, nq+4, nq+8, nqt, nqt+4, nqt+8,
 988                                         tmp, tmp+4, tmp+8);
 989                                 }
 990                         /* do an addition after every 4 doublings */
 991                         if (j % 4 == 3)
 992                                 {
 993                                 /* loop over all scalars */
 994                                 for (num = 0; num < num_points; ++num)
 995                                         {
 996                                         byte = scalars[num][i-1];
 997                                         bits[3] = (byte >> (10-j)) & 1;
 998                                         bits[2] = (byte >> (9-j)) & 1;
 999                                         bits[1] = (byte >> (8-j)) & 1;
1000                                         bits[0] = (byte >> (7-j)) & 1;
1001                                         /* select the point to add */
1002                                         select_point(bits,
1003                                                 pre_comp[num], tmp);
1004                                         memcpy(nqt, nq, 12 * sizeof(fslice));
1005                                         point_add(nq, nq+4, nq+8, nqt, nqt+4,
1006                                                 nqt+8, tmp, tmp+4, tmp+8);
1007                                         }
1008                                 }
1009                         }
1010                 }
1011         memcpy(x_out, nq, 4 * sizeof(fslice));
1012         memcpy(y_out, nq+4, 4 * sizeof(fslice));
1013         memcpy(z_out, nq+8, 4 * sizeof(fslice));
1014         }
1015
1016 /******************************************************************************/
1017 /*                     FUNCTIONS TO MANAGE PRECOMPUTATION
1018  */
1019
1020 static NISTP224_PRE_COMP *nistp224_pre_comp_new()
1021         {
1022         NISTP224_PRE_COMP *ret = NULL;
1023         ret = (NISTP224_PRE_COMP *)OPENSSL_malloc(sizeof(NISTP224_PRE_COMP));
1024         if (!ret)
1025                 {
1026                 ECerr(EC_F_NISTP224_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
1027                 return ret;
1028                 }
1029         memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp));
1030         ret->references = 1;
1031         return ret;
1032         }
1033
1034 static void *nistp224_pre_comp_dup(void *src_)
1035         {
1036         NISTP224_PRE_COMP *src = src_;
1037
1038         /* no need to actually copy, these objects never change! */
1039         CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
1040
1041         return src_;
1042         }
1043
1044 static void nistp224_pre_comp_free(void *pre_)
1045         {
1046         int i;
1047         NISTP224_PRE_COMP *pre = pre_;
1048
1049         if (!pre)
1050                 return;
1051
1052         i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1053         if (i > 0)
1054                 return;
1055
1056         OPENSSL_free(pre);
1057         }
1058
1059 static void nistp224_pre_comp_clear_free(void *pre_)
1060         {
1061         int i;
1062         NISTP224_PRE_COMP *pre = pre_;
1063
1064         if (!pre)
1065                 return;
1066
1067         i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1068         if (i > 0)
1069                 return;
1070
1071         OPENSSL_cleanse(pre, sizeof *pre);
1072         OPENSSL_free(pre);
1073         }
1074
1075 /******************************************************************************/
1076 /*                         OPENSSL EC_METHOD FUNCTIONS
1077  */
1078
1079 int ec_GFp_nistp224_group_init(EC_GROUP *group)
1080         {
1081         int ret;
1082         ret = ec_GFp_simple_group_init(group);
1083         group->a_is_minus3 = 1;
1084         return ret;
1085         }
1086
1087 int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p,
1088         const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1089         {
1090
1091         int ret = 0;
1092         BN_CTX *new_ctx = NULL;
1093         BIGNUM *curve_p, *curve_a, *curve_b;
1094         if (ctx == NULL)
1095                 if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0;
1096         BN_CTX_start(ctx);
1097         if (((curve_p = BN_CTX_get(ctx)) == NULL) ||
1098                 ((curve_a = BN_CTX_get(ctx)) == NULL) ||
1099                 ((curve_b = BN_CTX_get(ctx)) == NULL)) goto err;
1100         BN_bin2bn(nistp224_curve_params, fElemSize, curve_p);
1101         BN_bin2bn(nistp224_curve_params + 28, fElemSize, curve_a);
1102         BN_bin2bn(nistp224_curve_params + 56, fElemSize, curve_b);
1103         if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) ||
1104                 (BN_cmp(curve_b, b)))
1105                 {
1106                 ECerr(EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE,
1107                         EC_R_WRONG_CURVE_PARAMETERS);
1108                 goto err;
1109                 }
1110         group->field_mod_func = BN_nist_mod_224;
1111         ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx);
1112 err:
1113         BN_CTX_end(ctx);
1114         if (new_ctx != NULL)
1115                 BN_CTX_free(new_ctx);
1116         return ret;
1117         }
1118
1119 /* Takes the Jacobian coordinates (X, Y, Z) of a point and returns
1120  * (X', Y') = (X/Z^2, Y/Z^3) */
1121 int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group,
1122         const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
1123         {
1124         fslice z1[4], z2[4], x_in[4], y_in[4], x_out[4], y_out[4];
1125         uint128_t tmp[7];
1126         if (EC_POINT_is_at_infinity(group, point))
1127                 {
1128                 ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES,
1129                         EC_R_POINT_AT_INFINITY);
1130                 return 0;
1131                 }
1132         if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) ||
1133                 (!BN_to_felem(z1, &point->Z))) return 0;
1134         felem_inv(z2, z1);
1135         felem_square(tmp, z2); felem_reduce(z1, tmp);
1136         felem_mul(tmp, x_in, z1); felem_reduce(x_in, tmp);
1137         felem_contract(x_out, x_in);
1138         if (x != NULL)
1139                 {
1140                 if (!felem_to_BN(x, x_out)) {
1141                 ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES,
1142                         ERR_R_BN_LIB);
1143                 return 0;
1144                 }
1145                 }
1146         felem_mul(tmp, z1, z2); felem_reduce(z1, tmp);
1147         felem_mul(tmp, y_in, z1); felem_reduce(y_in, tmp);
1148         felem_contract(y_out, y_in);
1149         if (y != NULL)
1150                 {
1151                 if (!felem_to_BN(y, y_out)) {
1152                 ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES,
1153                         ERR_R_BN_LIB);
1154                 return 0;
1155                 }
1156                 }
1157         return 1;
1158         }
1159
1160 /* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values
1161  * Result is stored in r (r can equal one of the inputs). */
1162 int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r,
1163         const BIGNUM *scalar, size_t num, const EC_POINT *points[],
1164         const BIGNUM *scalars[], BN_CTX *ctx)
1165         {
1166         int ret = 0;
1167         int i, j;
1168         BN_CTX *new_ctx = NULL;
1169         BIGNUM *x, *y, *z, *tmp_scalar;
1170         u8 g_secret[fElemSize];
1171         u8 (*secrets)[fElemSize] = NULL;
1172         fslice (*pre_comp)[16][3][4] = NULL;
1173         u8 tmp[fElemSize];
1174         unsigned num_bytes;
1175         int have_pre_comp = 0;
1176         size_t num_points = num;
1177         fslice x_in[4], y_in[4], z_in[4], x_out[4], y_out[4], z_out[4];
1178         NISTP224_PRE_COMP *pre = NULL;
1179         fslice (*g_pre_comp)[3][4] = NULL;
1180         EC_POINT *generator = NULL;
1181         const EC_POINT *p = NULL;
1182         const BIGNUM *p_scalar = NULL;
1183         if (ctx == NULL)
1184                 if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0;
1185         BN_CTX_start(ctx);
1186         if (((x = BN_CTX_get(ctx)) == NULL) ||
1187                 ((y = BN_CTX_get(ctx)) == NULL) ||
1188                 ((z = BN_CTX_get(ctx)) == NULL) ||
1189                 ((tmp_scalar = BN_CTX_get(ctx)) == NULL))
1190                 goto err;
1191
1192         if (scalar != NULL)
1193                 {
1194                 pre = EC_EX_DATA_get_data(group->extra_data,
1195                         nistp224_pre_comp_dup, nistp224_pre_comp_free,
1196                         nistp224_pre_comp_clear_free);
1197                 if (pre)
1198                         /* we have precomputation, try to use it */
1199                         g_pre_comp = pre->g_pre_comp;
1200                 else
1201                         /* try to use the standard precomputation */
1202                         g_pre_comp = (fslice (*)[3][4]) gmul;
1203                 generator = EC_POINT_new(group);
1204                 if (generator == NULL)
1205                         goto err;
1206                 /* get the generator from precomputation */
1207                 if (!felem_to_BN(x, g_pre_comp[1][0]) ||
1208                         !felem_to_BN(y, g_pre_comp[1][1]) ||
1209                         !felem_to_BN(z, g_pre_comp[1][2]))
1210                         {
1211                         ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB);
1212                         goto err;
1213                         }
1214                 if (!EC_POINT_set_Jprojective_coordinates_GFp(group,
1215                                 generator, x, y, z, ctx))
1216                         goto err;
1217                 if (0 == EC_POINT_cmp(group, generator, group->generator, ctx))
1218                         /* precomputation matches generator */
1219                         have_pre_comp = 1;
1220                 else
1221                         /* we don't have valid precomputation:
1222                          * treat the generator as a random point */
1223                         num_points = num_points + 1;
1224                 }
1225         secrets = OPENSSL_malloc(num_points * fElemSize);
1226         pre_comp = OPENSSL_malloc(num_points * 16 * 3 * 4 * sizeof(fslice));
1227
1228         if ((num_points) && ((secrets == NULL) || (pre_comp == NULL)))
1229                 {
1230                 ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1231                 goto err;
1232                 }
1233
1234         /* we treat NULL scalars as 0, and NULL points as points at infinity,
1235          * i.e., they contribute nothing to the linear combination */
1236         memset(secrets, 0, num_points * fElemSize);
1237         memset(pre_comp, 0, num_points * 16 * 3 * 4 * sizeof(fslice));
1238         for (i = 0; i < num_points; ++i)
1239                 {
1240                 if (i == num)
1241                         /* the generator */
1242                         {
1243                         p = EC_GROUP_get0_generator(group);
1244                         p_scalar = scalar;
1245                         }
1246                 else
1247                         /* the i^th point */
1248                         {
1249                         p = points[i];
1250                         p_scalar = scalars[i];
1251                         }
1252                 if ((p_scalar != NULL) && (p != NULL))
1253                         {
1254                         num_bytes = BN_num_bytes(p_scalar);
1255                         /* reduce scalar to 0 <= scalar < 2^224 */
1256                         if ((num_bytes > fElemSize) || (BN_is_negative(p_scalar)))
1257                                 {
1258                                 /* this is an unusual input, and we don't guarantee
1259                                  * constant-timeness */
1260                                 if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx))
1261                                         {
1262                                         ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB);
1263                                         goto err;
1264                                         }
1265                                 num_bytes = BN_bn2bin(tmp_scalar, tmp);
1266                                 }
1267                         else
1268                                 BN_bn2bin(p_scalar, tmp);
1269                         flip_endian(secrets[i], tmp, num_bytes);
1270                         /* precompute multiples */
1271                         if ((!BN_to_felem(x_out, &p->X)) ||
1272                                 (!BN_to_felem(y_out, &p->Y)) ||
1273                                 (!BN_to_felem(z_out, &p->Z))) goto err;
1274                         memcpy(pre_comp[i][1][0], x_out, 4 * sizeof(fslice));
1275                         memcpy(pre_comp[i][1][1], y_out, 4 * sizeof(fslice));
1276                         memcpy(pre_comp[i][1][2], z_out, 4 * sizeof(fslice));
1277                         for (j = 1; j < 8; ++j)
1278                                 {
1279                                 point_double(pre_comp[i][2*j][0],
1280                                         pre_comp[i][2*j][1],
1281                                         pre_comp[i][2*j][2],
1282                                         pre_comp[i][j][0],
1283                                         pre_comp[i][j][1],
1284                                         pre_comp[i][j][2]);
1285                                 point_add(pre_comp[i][2*j+1][0],
1286                                         pre_comp[i][2*j+1][1],
1287                                         pre_comp[i][2*j+1][2],
1288                                         pre_comp[i][1][0],
1289                                         pre_comp[i][1][1],
1290                                         pre_comp[i][1][2],
1291                                         pre_comp[i][2*j][0],
1292                                         pre_comp[i][2*j][1],
1293                                         pre_comp[i][2*j][2]);
1294                                 }
1295                         }
1296                 }
1297
1298         /* the scalar for the generator */
1299         if ((scalar != NULL) && (have_pre_comp))
1300                 {
1301                 memset(g_secret, 0, fElemSize);
1302                 num_bytes = BN_num_bytes(scalar);
1303                 /* reduce scalar to 0 <= scalar < 2^224 */
1304                 if ((num_bytes > fElemSize) || (BN_is_negative(scalar)))
1305                         {
1306                         /* this is an unusual input, and we don't guarantee
1307                          * constant-timeness */
1308                         if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx))
1309                                 {
1310                                 ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB);
1311                                 goto err;
1312                                 }
1313                         num_bytes = BN_bn2bin(tmp_scalar, tmp);
1314                         }
1315                 else
1316                         BN_bn2bin(scalar, tmp);
1317                 flip_endian(g_secret, tmp, num_bytes);
1318                 /* do the multiplication with generator precomputation*/
1319                 batch_mul(x_out, y_out, z_out,
1320                         (const u8 (*)[fElemSize]) secrets, num_points,
1321                         g_secret, (const fslice (*)[16][3][4]) pre_comp,
1322                         (const fslice (*)[3][4]) g_pre_comp);
1323                 }
1324         else
1325                 /* do the multiplication without generator precomputation */
1326                 batch_mul(x_out, y_out, z_out,
1327                         (const u8 (*)[fElemSize]) secrets, num_points,
1328                         NULL, (const fslice (*)[16][3][4]) pre_comp, NULL);
1329         /* reduce the output to its unique minimal representation */
1330         felem_contract(x_in, x_out);
1331         felem_contract(y_in, y_out);
1332         felem_contract(z_in, z_out);
1333         if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) ||
1334                 (!felem_to_BN(z, z_in)))
1335                 {
1336                 ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB);
1337                 goto err;
1338                 }
1339         ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx);
1340
1341 err:
1342         BN_CTX_end(ctx);
1343         if (generator != NULL)
1344                 EC_POINT_free(generator);
1345         if (new_ctx != NULL)
1346                 BN_CTX_free(new_ctx);
1347         if (secrets != NULL)
1348                 OPENSSL_free(secrets);
1349         if (pre_comp != NULL)
1350                 OPENSSL_free(pre_comp);
1351         return ret;
1352         }
1353
1354 int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
1355         {
1356         int ret = 0;
1357         NISTP224_PRE_COMP *pre = NULL;
1358         int i, j;
1359         BN_CTX *new_ctx = NULL;
1360         BIGNUM *x, *y;
1361         EC_POINT *generator = NULL;
1362         /* throw away old precomputation */
1363         EC_EX_DATA_free_data(&group->extra_data, nistp224_pre_comp_dup,
1364                 nistp224_pre_comp_free, nistp224_pre_comp_clear_free);
1365         if (ctx == NULL)
1366                 if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0;
1367         BN_CTX_start(ctx);
1368         if (((x = BN_CTX_get(ctx)) == NULL) ||
1369                 ((y = BN_CTX_get(ctx)) == NULL))
1370                 goto err;
1371         /* get the generator */
1372         if (group->generator == NULL) goto err;
1373         generator = EC_POINT_new(group);
1374         if (generator == NULL)
1375                 goto err;
1376         BN_bin2bn(nistp224_curve_params + 84, fElemSize, x);
1377         BN_bin2bn(nistp224_curve_params + 112, fElemSize, y);
1378         if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx))
1379                 goto err;
1380         if ((pre = nistp224_pre_comp_new()) == NULL)
1381                 goto err;
1382         /* if the generator is the standard one, use built-in precomputation */
1383         if (0 == EC_POINT_cmp(group, generator, group->generator, ctx))
1384                 {
1385                 memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp));
1386                 ret = 1;
1387                 goto err;
1388                 }
1389         if ((!BN_to_felem(pre->g_pre_comp[1][0], &group->generator->X)) ||
1390                 (!BN_to_felem(pre->g_pre_comp[1][1], &group->generator->Y)) ||
1391                 (!BN_to_felem(pre->g_pre_comp[1][2], &group->generator->Z)))
1392                 goto err;
1393         /* compute 2^56*G, 2^112*G, 2^168*G */
1394         for (i = 1; i < 5; ++i)
1395                 {
1396                 point_double(pre->g_pre_comp[2*i][0], pre->g_pre_comp[2*i][1],
1397                         pre->g_pre_comp[2*i][2], pre->g_pre_comp[i][0],
1398                         pre->g_pre_comp[i][1], pre->g_pre_comp[i][2]);
1399                 for (j = 0; j < 55; ++j)
1400                         {
1401                         point_double(pre->g_pre_comp[2*i][0],
1402                                 pre->g_pre_comp[2*i][1],
1403                                 pre->g_pre_comp[2*i][2],
1404                                 pre->g_pre_comp[2*i][0],
1405                                 pre->g_pre_comp[2*i][1],
1406                                 pre->g_pre_comp[2*i][2]);
1407                         }
1408                 }
1409         /* g_pre_comp[0] is the point at infinity */
1410         memset(pre->g_pre_comp[0], 0, sizeof(pre->g_pre_comp[0]));
1411         /* the remaining multiples */
1412         /* 2^56*G + 2^112*G */
1413         point_add(pre->g_pre_comp[6][0], pre->g_pre_comp[6][1],
1414                 pre->g_pre_comp[6][2], pre->g_pre_comp[4][0],
1415                 pre->g_pre_comp[4][1], pre->g_pre_comp[4][2],
1416                 pre->g_pre_comp[2][0], pre->g_pre_comp[2][1],
1417                 pre->g_pre_comp[2][2]);
1418         /* 2^56*G + 2^168*G */
1419         point_add(pre->g_pre_comp[10][0], pre->g_pre_comp[10][1],
1420                 pre->g_pre_comp[10][2], pre->g_pre_comp[8][0],
1421                 pre->g_pre_comp[8][1], pre->g_pre_comp[8][2],
1422                 pre->g_pre_comp[2][0], pre->g_pre_comp[2][1],
1423                 pre->g_pre_comp[2][2]);
1424         /* 2^112*G + 2^168*G */
1425         point_add(pre->g_pre_comp[12][0], pre->g_pre_comp[12][1],
1426                 pre->g_pre_comp[12][2], pre->g_pre_comp[8][0],
1427                 pre->g_pre_comp[8][1], pre->g_pre_comp[8][2],
1428                 pre->g_pre_comp[4][0], pre->g_pre_comp[4][1],
1429                 pre->g_pre_comp[4][2]);
1430         /* 2^56*G + 2^112*G + 2^168*G */
1431         point_add(pre->g_pre_comp[14][0], pre->g_pre_comp[14][1],
1432                 pre->g_pre_comp[14][2], pre->g_pre_comp[12][0],
1433                 pre->g_pre_comp[12][1], pre->g_pre_comp[12][2],
1434                 pre->g_pre_comp[2][0], pre->g_pre_comp[2][1],
1435                 pre->g_pre_comp[2][2]);
1436         for (i = 1; i < 8; ++i)
1437                 {
1438                 /* odd multiples: add G */
1439                 point_add(pre->g_pre_comp[2*i+1][0], pre->g_pre_comp[2*i+1][1],
1440                         pre->g_pre_comp[2*i+1][2], pre->g_pre_comp[2*i][0],
1441                         pre->g_pre_comp[2*i][1], pre->g_pre_comp[2*i][2],
1442                         pre->g_pre_comp[1][0], pre->g_pre_comp[1][1],
1443                         pre->g_pre_comp[1][2]);
1444                 }
1445
1446         if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp224_pre_comp_dup,
1447                         nistp224_pre_comp_free, nistp224_pre_comp_clear_free))
1448                 goto err;
1449         ret = 1;
1450         pre = NULL;
1451  err:
1452         BN_CTX_end(ctx);
1453         if (generator != NULL)
1454                 EC_POINT_free(generator);
1455         if (new_ctx != NULL)
1456                 BN_CTX_free(new_ctx);
1457         if (pre)
1458                 nistp224_pre_comp_free(pre);
1459         return ret;
1460         }
1461
1462 int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group)
1463         {
1464         if (EC_EX_DATA_get_data(group->extra_data, nistp224_pre_comp_dup,
1465                         nistp224_pre_comp_free, nistp224_pre_comp_clear_free)
1466                 != NULL)
1467                 return 1;
1468         else
1469                 return 0;
1470         }
1471 #endif