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         unsigned num_bytes;
 258
 259         /* BN_bn2bin eats leading zeroes */
 260         memset(b_out, 0, fElemSize);
 261         num_bytes = BN_num_bytes(bn);
 262         if (num_bytes > fElemSize)
 263                 {
 264                 ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE);
 265                 return 0;
 266                 }
 267         if (BN_is_negative(bn))
 268                 {
 269                 ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE);
 270                 return 0;
 271                 }
 272         num_bytes = BN_bn2bin(bn, b_in);
 273         flip_endian(b_out, b_in, num_bytes);
 274         bin28_to_felem(out, b_out);
 275         return 1;
 276         }
 277
 278 /* From internal representation to OpenSSL BIGNUM */
 279 static BIGNUM *felem_to_BN(BIGNUM *out, const fslice in[4])
 280         {
 281         u8 b_in[fElemSize], b_out[fElemSize];
 282         felem_to_bin28(b_in, in);
 283         flip_endian(b_out, b_in, fElemSize);
 284         return BN_bin2bn(b_out, fElemSize, out);
 285         }
 286
 287 /******************************************************************************/
 288 /*                              FIELD OPERATIONS
 289  *
 290  * Field operations, using the internal representation of field elements.
 291  * NB! These operations are specific to our point multiplication and cannot be
 292  * expected to be correct in general - e.g., multiplication with a large scalar
 293  * will cause an overflow.
 294  *
 295  */
 296
 297 /* Sum two field elements: out += in */
 298 static void felem_sum64(fslice out[4], const fslice in[4])
 299         {
 300         out[0] += in[0];
 301         out[1] += in[1];
 302         out[2] += in[2];
 303         out[3] += in[3];
 304         }
 305
 306 /* Subtract field elements: out -= in */
 307 /* Assumes in[i] < 2^57 */
 308 static void felem_diff64(fslice out[4], const fslice in[4])
 309         {
 310         static const uint64_t two58p2 = (((uint64_t) 1) << 58) + (((uint64_t) 1) << 2);
 311         static const uint64_t two58m2 = (((uint64_t) 1) << 58) - (((uint64_t) 1) << 2);
 312         static const uint64_t two58m42m2 = (((uint64_t) 1) << 58) -
 313             (((uint64_t) 1) << 42) - (((uint64_t) 1) << 2);
 314
 315         /* Add 0 mod 2^224-2^96+1 to ensure out > in */
 316         out[0] += two58p2;
 317         out[1] += two58m42m2;
 318         out[2] += two58m2;
 319         out[3] += two58m2;
 320
 321         out[0] -= in[0];
 322         out[1] -= in[1];
 323         out[2] -= in[2];
 324         out[3] -= in[3];
 325         }
 326
 327 /* Subtract in unreduced 128-bit mode: out128 -= in128 */
 328 /* Assumes in[i] < 2^119 */
 329 static void felem_diff128(uint128_t out[7], const uint128_t in[4])
 330         {
 331         static const uint128_t two120 = ((uint128_t) 1) << 120;
 332         static const uint128_t two120m64 = (((uint128_t) 1) << 120) -
 333                 (((uint128_t) 1) << 64);
 334         static const uint128_t two120m104m64 = (((uint128_t) 1) << 120) -
 335                 (((uint128_t) 1) << 104) - (((uint128_t) 1) << 64);
 336
 337         /* Add 0 mod 2^224-2^96+1 to ensure out > in */
 338         out[0] += two120;
 339         out[1] += two120m64;
 340         out[2] += two120m64;
 341         out[3] += two120;
 342         out[4] += two120m104m64;
 343         out[5] += two120m64;
 344         out[6] += two120m64;
 345
 346         out[0] -= in[0];
 347         out[1] -= in[1];
 348         out[2] -= in[2];
 349         out[3] -= in[3];
 350         out[4] -= in[4];
 351         out[5] -= in[5];
 352         out[6] -= in[6];
 353         }
 354
 355 /* Subtract in mixed mode: out128 -= in64 */
 356 /* in[i] < 2^63 */
 357 static void felem_diff_128_64(uint128_t out[7], const fslice in[4])
 358         {
 359         static const uint128_t two64p8 = (((uint128_t) 1) << 64) +
 360                 (((uint128_t) 1) << 8);
 361         static const uint128_t two64m8 = (((uint128_t) 1) << 64) -
 362                 (((uint128_t) 1) << 8);
 363         static const uint128_t two64m48m8 = (((uint128_t) 1) << 64) -
 364                 (((uint128_t) 1) << 48) - (((uint128_t) 1) << 8);
 365
 366         /* Add 0 mod 2^224-2^96+1 to ensure out > in */
 367         out[0] += two64p8;
 368         out[1] += two64m48m8;
 369         out[2] += two64m8;
 370         out[3] += two64m8;
 371
 372         out[0] -= in[0];
 373         out[1] -= in[1];
 374         out[2] -= in[2];
 375         out[3] -= in[3];
 376         }
 377
 378 /* Multiply a field element by a scalar: out64 = out64 * scalar
 379  * The scalars we actually use are small, so results fit without overflow */
 380 static void felem_scalar64(fslice out[4], const fslice scalar)
 381         {
 382         out[0] *= scalar;
 383         out[1] *= scalar;
 384         out[2] *= scalar;
 385         out[3] *= scalar;
 386         }
 387
 388 /* Multiply an unreduced field element by a scalar: out128 = out128 * scalar
 389  * The scalars we actually use are small, so results fit without overflow */
 390 static void felem_scalar128(uint128_t out[7], const uint128_t scalar)
 391         {
 392         out[0] *= scalar;
 393         out[1] *= scalar;
 394         out[2] *= scalar;
 395         out[3] *= scalar;
 396         out[4] *= scalar;
 397         out[5] *= scalar;
 398         out[6] *= scalar;
 399         }
 400
 401 /* Square a field element: out = in^2 */
 402 static void felem_square(uint128_t out[7], const fslice in[4])
 403         {
 404         out[0] = ((uint128_t) in[0]) * in[0];
 405         out[1] = ((uint128_t) in[0]) * in[1] * 2;
 406         out[2] = ((uint128_t) in[0]) * in[2] * 2 + ((uint128_t) in[1]) * in[1];
 407         out[3] = ((uint128_t) in[0]) * in[3] * 2 +
 408                 ((uint128_t) in[1]) * in[2] * 2;
 409         out[4] = ((uint128_t) in[1]) * in[3] * 2 + ((uint128_t) in[2]) * in[2];
 410         out[5] = ((uint128_t) in[2]) * in[3] * 2;
 411         out[6] = ((uint128_t) in[3]) * in[3];
 412         }
 413
 414 /* Multiply two field elements: out = in1 * in2 */
 415 static void felem_mul(uint128_t out[7], const fslice in1[4], const fslice in2[4])
 416         {
 417         out[0] = ((uint128_t) in1[0]) * in2[0];
 418         out[1] = ((uint128_t) in1[0]) * in2[1] + ((uint128_t) in1[1]) * in2[0];
 419         out[2] = ((uint128_t) in1[0]) * in2[2] + ((uint128_t) in1[1]) * in2[1] +
 420                 ((uint128_t) in1[2]) * in2[0];
 421         out[3] = ((uint128_t) in1[0]) * in2[3] + ((uint128_t) in1[1]) * in2[2] +
 422                 ((uint128_t) in1[2]) * in2[1] + ((uint128_t) in1[3]) * in2[0];
 423         out[4] = ((uint128_t) in1[1]) * in2[3] + ((uint128_t) in1[2]) * in2[2] +
 424                 ((uint128_t) in1[3]) * in2[1];
 425         out[5] = ((uint128_t) in1[2]) * in2[3] + ((uint128_t) in1[3]) * in2[2];
 426         out[6] = ((uint128_t) in1[3]) * in2[3];
 427         }
 428
 429 /* Reduce 128-bit coefficients to 64-bit coefficients. Requires in[i] < 2^126,
 430  * ensures out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] < 2^57 */
 431 static void felem_reduce(fslice out[4], const uint128_t in[7])
 432         {
 433         static const uint128_t two127p15 = (((uint128_t) 1) << 127) +
 434                 (((uint128_t) 1) << 15);
 435         static const uint128_t two127m71 = (((uint128_t) 1) << 127) -
 436                 (((uint128_t) 1) << 71);
 437         static const uint128_t two127m71m55 = (((uint128_t) 1) << 127) -
 438                 (((uint128_t) 1) << 71) - (((uint128_t) 1) << 55);
 439         uint128_t output[5];
 440
 441         /* Add 0 mod 2^224-2^96+1 to ensure all differences are positive */
 442         output[0] = in[0] + two127p15;
 443         output[1] = in[1] + two127m71m55;
 444         output[2] = in[2] + two127m71;
 445         output[3] = in[3];
 446         output[4] = in[4];
 447
 448         /* Eliminate in[4], in[5], in[6] */
 449         output[4] += in[6] >> 16;
 450         output[3] += (in[6]&0xffff) << 40;
 451         output[2] -= in[6];
 452
 453         output[3] += in[5] >> 16;
 454         output[2] += (in[5]&0xffff) << 40;
 455         output[1] -= in[5];
 456
 457         output[2] += output[4] >> 16;
 458         output[1] += (output[4]&0xffff) << 40;
 459         output[0] -= output[4];
 460         output[4] = 0;
 461
 462         /* Carry 2 -> 3 -> 4 */
 463         output[3] += output[2] >> 56;
 464         output[2] &= 0x00ffffffffffffff;
 465
 466         output[4] += output[3] >> 56;
 467         output[3] &= 0x00ffffffffffffff;
 468
 469         /* Now output[2] < 2^56, output[3] < 2^56 */
 470
 471         /* Eliminate output[4] */
 472         output[2] += output[4] >> 16;
 473         output[1] += (output[4]&0xffff) << 40;
 474         output[0] -= output[4];
 475
 476         /* Carry 0 -> 1 -> 2 -> 3 */
 477         output[1] += output[0] >> 56;
 478         out[0] = output[0] & 0x00ffffffffffffff;
 479
 480         output[2] += output[1] >> 56;
 481         out[1] = output[1] & 0x00ffffffffffffff;
 482         output[3] += output[2] >> 56;
 483         out[2] = output[2] & 0x00ffffffffffffff;
 484
 485         /* out[0] < 2^56, out[1] < 2^56, out[2] < 2^56,
 486          * out[3] < 2^57 (due to final carry) */
 487         out[3] = output[3];
 488         }
 489
 490 /* Reduce to unique minimal representation */
 491 static void felem_contract(fslice out[4], const fslice in[4])
 492         {
 493         static const int64_t two56 = ((uint64_t) 1) << 56;
 494         /* 0 <= in < 2^225 */
 495         /* if in > 2^224 , reduce in = in - 2^224 + 2^96 - 1 */
 496         int64_t tmp[4], a;
 497         tmp[0] = (int64_t) in[0] - (in[3] >> 56);
 498         tmp[1] = (int64_t) in[1] + ((in[3] >> 16) & 0x0000010000000000);
 499         tmp[2] = (int64_t) in[2];
 500         tmp[3] = (int64_t) in[3] & 0x00ffffffffffffff;
 501
 502         /* eliminate negative coefficients */
 503         a = tmp[0] >> 63;
 504         tmp[0] += two56 & a;
 505         tmp[1] -= 1 & a;
 506
 507         a = tmp[1] >> 63;
 508         tmp[1] += two56 & a;
 509         tmp[2] -= 1 & a;
 510
 511         a = tmp[2] >> 63;
 512         tmp[2] += two56 & a;
 513         tmp[3] -= 1 & a;
 514
 515         a = tmp[3] >> 63;
 516         tmp[3] += two56 & a;
 517         tmp[0] += 1 & a;
 518         tmp[1] -= (1 & a) << 40;
 519
 520         /* carry 1 -> 2 -> 3 */
 521         tmp[2] += tmp[1] >> 56;
 522         tmp[1] &= 0x00ffffffffffffff;
 523
 524         tmp[3] += tmp[2] >> 56;
 525         tmp[2] &= 0x00ffffffffffffff;
 526
 527         /* 0 <= in < 2^224 + 2^96 - 1 */
 528         /* if in > 2^224 , reduce in = in - 2^224 + 2^96 - 1 */
 529         tmp[0] -= (tmp[3] >> 56);
 530         tmp[1] += ((tmp[3] >> 16) & 0x0000010000000000);
 531         tmp[3] &= 0x00ffffffffffffff;
 532
 533         /* eliminate negative coefficients */
 534         a = tmp[0] >> 63;
 535         tmp[0] += two56 & a;
 536         tmp[1] -= 1 & a;
 537
 538         a = tmp[1] >> 63;
 539         tmp[1] += two56 & a;
 540         tmp[2] -= 1 & a;
 541
 542         a = tmp[2] >> 63;
 543         tmp[2] += two56 & a;
 544         tmp[3] -= 1 & a;
 545
 546         a = tmp[3] >> 63;
 547         tmp[3] += two56 & a;
 548         tmp[0] += 1 & a;
 549         tmp[1] -= (1 & a) << 40;
 550
 551         /* carry 1 -> 2 -> 3 */
 552         tmp[2] += tmp[1] >> 56;
 553         tmp[1] &= 0x00ffffffffffffff;
 554
 555         tmp[3] += tmp[2] >> 56;
 556         tmp[2] &= 0x00ffffffffffffff;
 557
 558         /* Now 0 <= in < 2^224 */
 559
 560         /* if in > 2^224 - 2^96, reduce */
 561         /* a = 0 iff in > 2^224 - 2^96, i.e.,
 562          * the high 128 bits are all 1 and the lower part is non-zero */
 563         a = (tmp[3] + 1) | (tmp[2] + 1) |
 564                 ((tmp[1] | 0x000000ffffffffff) + 1) |
 565                 ((((tmp[1] & 0xffff) - 1) >> 63) & ((tmp[0] - 1) >> 63));
 566         /* turn a into an all-one mask (if a = 0) or an all-zero mask */
 567         a = ((a & 0x00ffffffffffffff) - 1) >> 63;
 568         /* subtract 2^224 - 2^96 + 1 if a is all-one*/
 569         tmp[3] &= a ^ 0xffffffffffffffff;
 570         tmp[2] &= a ^ 0xffffffffffffffff;
 571         tmp[1] &= (a ^ 0xffffffffffffffff) | 0x000000ffffffffff;
 572         tmp[0] -= 1 & a;
 573         /* eliminate negative coefficients: if tmp[0] is negative, tmp[1] must be
 574          * non-zero, so we only need one step */
 575         a = tmp[0] >> 63;
 576         tmp[0] += two56 & a;
 577         tmp[1] -= 1 & a;
 578
 579         out[0] = tmp[0];
 580         out[1] = tmp[1];
 581         out[2] = tmp[2];
 582         out[3] = tmp[3];
 583         }
 584
 585 /* Zero-check: returns 1 if input is 0, and 0 otherwise.
 586  * We know that field elements are reduced to in < 2^225,
 587  * so we only need to check three cases: 0, 2^224 - 2^96 + 1,
 588  * and 2^225 - 2^97 + 2 */
 589 static fslice felem_is_zero(const fslice in[4])
 590         {
 591         fslice zero, two224m96p1, two225m97p2;
 592
 593         zero = in[0] | in[1] | in[2] | in[3];
 594         zero = (((int64_t)(zero) - 1) >> 63) & 1;
 595         two224m96p1 = (in[0] ^ 1) | (in[1] ^ 0x00ffff0000000000)
 596                 | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x00ffffffffffffff);
 597         two224m96p1 = (((int64_t)(two224m96p1) - 1) >> 63) & 1;
 598         two225m97p2 = (in[0] ^ 2) | (in[1] ^ 0x00fffe0000000000)
 599                 | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x01ffffffffffffff);
 600         two225m97p2 = (((int64_t)(two225m97p2) - 1) >> 63) & 1;
 601         return (zero | two224m96p1 | two225m97p2);
 602         }
 603
 604 /* Invert a field element */
 605 /* Computation chain copied from djb's code */
 606 static void felem_inv(fslice out[4], const fslice in[4])
 607         {
 608         fslice ftmp[4], ftmp2[4], ftmp3[4], ftmp4[4];
 609         uint128_t tmp[7];
 610         unsigned i;
 611
 612         felem_square(tmp, in); felem_reduce(ftmp, tmp);         /* 2 */
 613         felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp);      /* 2^2 - 1 */
 614         felem_square(tmp, ftmp); felem_reduce(ftmp, tmp);       /* 2^3 - 2 */
 615         felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp);      /* 2^3 - 1 */
 616         felem_square(tmp, ftmp); felem_reduce(ftmp2, tmp);      /* 2^4 - 2 */
 617         felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp);     /* 2^5 - 4 */
 618         felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp);     /* 2^6 - 8 */
 619         felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp, tmp);   /* 2^6 - 1 */
 620         felem_square(tmp, ftmp); felem_reduce(ftmp2, tmp);      /* 2^7 - 2 */
 621         for (i = 0; i < 5; ++i)                                 /* 2^12 - 2^6 */
 622                 {
 623                 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp);
 624                 }
 625         felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp2, tmp);  /* 2^12 - 1 */
 626         felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp);     /* 2^13 - 2 */
 627         for (i = 0; i < 11; ++i)                                /* 2^24 - 2^12 */
 628                 {
 629                 felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp);
 630                 }
 631         felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp2, tmp); /* 2^24 - 1 */
 632         felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp);     /* 2^25 - 2 */
 633         for (i = 0; i < 23; ++i)                                /* 2^48 - 2^24 */
 634                 {
 635                 felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp);
 636                 }
 637         felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^48 - 1 */
 638         felem_square(tmp, ftmp3); felem_reduce(ftmp4, tmp);     /* 2^49 - 2 */
 639         for (i = 0; i < 47; ++i)                                /* 2^96 - 2^48 */
 640                 {
 641                 felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp);
 642                 }
 643         felem_mul(tmp, ftmp3, ftmp4); felem_reduce(ftmp3, tmp); /* 2^96 - 1 */
 644         felem_square(tmp, ftmp3); felem_reduce(ftmp4, tmp);     /* 2^97 - 2 */
 645         for (i = 0; i < 23; ++i)                                /* 2^120 - 2^24 */
 646                 {
 647                 felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp);
 648                 }
 649         felem_mul(tmp, ftmp2, ftmp4); felem_reduce(ftmp2, tmp); /* 2^120 - 1 */
 650         for (i = 0; i < 6; ++i)                                 /* 2^126 - 2^6 */
 651                 {
 652                 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp);
 653                 }
 654         felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp, tmp);   /* 2^126 - 1 */
 655         felem_square(tmp, ftmp); felem_reduce(ftmp, tmp);       /* 2^127 - 2 */
 656         felem_mul(tmp, ftmp, in); felem_reduce(ftmp, tmp);      /* 2^127 - 1 */
 657         for (i = 0; i < 97; ++i)                                /* 2^224 - 2^97 */
 658                 {
 659                 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp);
 660                 }
 661         felem_mul(tmp, ftmp, ftmp3); felem_reduce(out, tmp);    /* 2^224 - 2^96 - 1 */
 662         }
 663
 664 /* Copy in constant time:
 665  * if icopy == 1, copy in to out,
 666  * if icopy == 0, copy out to itself. */
 667 static void
 668 copy_conditional(fslice *out, const fslice *in, unsigned len, fslice icopy)
 669         {
 670         unsigned i;
 671         /* icopy is a (64-bit) 0 or 1, so copy is either all-zero or all-one */
 672         const fslice copy = -icopy;
 673         for (i = 0; i < len; ++i)
 674                 {
 675                 const fslice tmp = copy & (in[i] ^ out[i]);
 676                 out[i] ^= tmp;
 677                 }
 678         }
 679
 680 /* Copy in constant time:
 681  * if isel == 1, copy in2 to out,
 682  * if isel == 0, copy in1 to out. */
 683 static void select_conditional(fslice *out, const fslice *in1, const fslice *in2,
 684         unsigned len, fslice isel)
 685         {
 686         unsigned i;
 687         /* isel is a (64-bit) 0 or 1, so sel is either all-zero or all-one */
 688         const fslice sel = -isel;
 689         for (i = 0; i < len; ++i)
 690                 {
 691                 const fslice tmp = sel & (in1[i] ^ in2[i]);
 692                 out[i] = in1[i] ^ tmp;
 693                 }
 694 }
 695
 696 /******************************************************************************/
 697 /*                       ELLIPTIC CURVE POINT OPERATIONS
 698  *
 699  * Points are represented in Jacobian projective coordinates:
 700  * (X, Y, Z) corresponds to the affine point (X/Z^2, Y/Z^3),
 701  * or to the point at infinity if Z == 0.
 702  *
 703  */
 704
 705 /* Double an elliptic curve point:
 706  * (X', Y', Z') = 2 * (X, Y, Z), where
 707  * X' = (3 * (X - Z^2) * (X + Z^2))^2 - 8 * X * Y^2
 708  * Y' = 3 * (X - Z^2) * (X + Z^2) * (4 * X * Y^2 - X') - 8 * Y^2
 709  * Z' = (Y + Z)^2 - Y^2 - Z^2 = 2 * Y * Z
 710  * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed,
 711  * while x_out == y_in is not (maybe this works, but it's not tested). */
 712 static void
 713 point_double(fslice x_out[4], fslice y_out[4], fslice z_out[4],
 714              const fslice x_in[4], const fslice y_in[4], const fslice z_in[4])
 715         {
 716         uint128_t tmp[7], tmp2[7];
 717         fslice delta[4];
 718         fslice gamma[4];
 719         fslice beta[4];
 720         fslice alpha[4];
 721         fslice ftmp[4], ftmp2[4];
 722         memcpy(ftmp, x_in, 4 * sizeof(fslice));
 723         memcpy(ftmp2, x_in, 4 * sizeof(fslice));
 724
 725         /* delta = z^2 */
 726         felem_square(tmp, z_in);
 727         felem_reduce(delta, tmp);
 728
 729         /* gamma = y^2 */
 730         felem_square(tmp, y_in);
 731         felem_reduce(gamma, tmp);
 732
 733         /* beta = x*gamma */
 734         felem_mul(tmp, x_in, gamma);
 735         felem_reduce(beta, tmp);
 736
 737         /* alpha = 3*(x-delta)*(x+delta) */
 738         felem_diff64(ftmp, delta);
 739         /* ftmp[i] < 2^57 + 2^58 + 2 < 2^59 */
 740         felem_sum64(ftmp2, delta);
 741         /* ftmp2[i] < 2^57 + 2^57 = 2^58 */
 742         felem_scalar64(ftmp2, 3);
 743         /* ftmp2[i] < 3 * 2^58 < 2^60 */
 744         felem_mul(tmp, ftmp, ftmp2);
 745         /* tmp[i] < 2^60 * 2^59 * 4 = 2^121 */
 746         felem_reduce(alpha, tmp);
 747
 748         /* x' = alpha^2 - 8*beta */
 749         felem_square(tmp, alpha);
 750         /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
 751         memcpy(ftmp, beta, 4 * sizeof(fslice));
 752         felem_scalar64(ftmp, 8);
 753         /* ftmp[i] < 8 * 2^57 = 2^60 */
 754         felem_diff_128_64(tmp, ftmp);
 755         /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */
 756         felem_reduce(x_out, tmp);
 757
 758         /* z' = (y + z)^2 - gamma - delta */
 759         felem_sum64(delta, gamma);
 760         /* delta[i] < 2^57 + 2^57 = 2^58 */
 761         memcpy(ftmp, y_in, 4 * sizeof(fslice));
 762         felem_sum64(ftmp, z_in);
 763         /* ftmp[i] < 2^57 + 2^57 = 2^58 */
 764         felem_square(tmp, ftmp);
 765         /* tmp[i] < 4 * 2^58 * 2^58 = 2^118 */
 766         felem_diff_128_64(tmp, delta);
 767         /* tmp[i] < 2^118 + 2^64 + 8 < 2^119 */
 768         felem_reduce(z_out, tmp);
 769
 770         /* y' = alpha*(4*beta - x') - 8*gamma^2 */
 771         felem_scalar64(beta, 4);
 772         /* beta[i] < 4 * 2^57 = 2^59 */
 773         felem_diff64(beta, x_out);
 774         /* beta[i] < 2^59 + 2^58 + 2 < 2^60 */
 775         felem_mul(tmp, alpha, beta);
 776         /* tmp[i] < 4 * 2^57 * 2^60 = 2^119 */
 777         felem_square(tmp2, gamma);
 778         /* tmp2[i] < 4 * 2^57 * 2^57 = 2^116 */
 779         felem_scalar128(tmp2, 8);
 780         /* tmp2[i] < 8 * 2^116 = 2^119 */
 781         felem_diff128(tmp, tmp2);
 782         /* tmp[i] < 2^119 + 2^120 < 2^121 */
 783         felem_reduce(y_out, tmp);
 784         }
 785
 786 /* Add two elliptic curve points:
 787  * (X_1, Y_1, Z_1) + (X_2, Y_2, Z_2) = (X_3, Y_3, Z_3), where
 788  * X_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1)^2 - (Z_1^2 * X_2 - Z_2^2 * X_1)^3 -
 789  * 2 * Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^2
 790  * 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) -
 791  *        Z_2^3 * Y_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^3
 792  * Z_3 = (Z_1^2 * X_2 - Z_2^2 * X_1) * (Z_1 * Z_2) */
 793
 794 /* This function is not entirely constant-time:
 795  * it includes a branch for checking whether the two input points are equal,
 796  * (while not equal to the point at infinity).
 797  * This case never happens during single point multiplication,
 798  * so there is no timing leak for ECDH or ECDSA signing. */
 799 static void point_add(fslice x3[4], fslice y3[4], fslice z3[4],
 800         const fslice x1[4], const fslice y1[4], const fslice z1[4],
 801         const fslice x2[4], const fslice y2[4], const fslice z2[4])
 802         {
 803         fslice ftmp[4], ftmp2[4], ftmp3[4], ftmp4[4], ftmp5[4];
 804         uint128_t tmp[7], tmp2[7];
 805         fslice z1_is_zero, z2_is_zero, x_equal, y_equal;
 806
 807         /* ftmp = z1^2 */
 808         felem_square(tmp, z1);
 809         felem_reduce(ftmp, tmp);
 810
 811         /* ftmp2 = z2^2 */
 812         felem_square(tmp, z2);
 813         felem_reduce(ftmp2, tmp);
 814
 815         /* ftmp3 = z1^3 */
 816         felem_mul(tmp, ftmp, z1);
 817         felem_reduce(ftmp3, tmp);
 818
 819         /* ftmp4 = z2^3 */
 820         felem_mul(tmp, ftmp2, z2);
 821         felem_reduce(ftmp4, tmp);
 822
 823         /* ftmp3 = z1^3*y2 */
 824         felem_mul(tmp, ftmp3, y2);
 825         /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
 826
 827         /* ftmp4 = z2^3*y1 */
 828         felem_mul(tmp2, ftmp4, y1);
 829         felem_reduce(ftmp4, tmp2);
 830
 831         /* ftmp3 = z1^3*y2 - z2^3*y1 */
 832         felem_diff_128_64(tmp, ftmp4);
 833         /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */
 834         felem_reduce(ftmp3, tmp);
 835
 836         /* ftmp = z1^2*x2 */
 837         felem_mul(tmp, ftmp, x2);
 838         /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
 839
 840         /* ftmp2 =z2^2*x1 */
 841         felem_mul(tmp2, ftmp2, x1);
 842         felem_reduce(ftmp2, tmp2);
 843
 844         /* ftmp = z1^2*x2 - z2^2*x1 */
 845         felem_diff128(tmp, tmp2);
 846         /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */
 847         felem_reduce(ftmp, tmp);
 848
 849         /* the formulae are incorrect if the points are equal
 850          * so we check for this and do doubling if this happens */
 851         x_equal = felem_is_zero(ftmp);
 852         y_equal = felem_is_zero(ftmp3);
 853         z1_is_zero = felem_is_zero(z1);
 854         z2_is_zero = felem_is_zero(z2);
 855         /* In affine coordinates, (X_1, Y_1) == (X_2, Y_2) */
 856         if (x_equal && y_equal && !z1_is_zero && !z2_is_zero)
 857                 {
 858                 point_double(x3, y3, z3, x1, y1, z1);
 859                 return;
 860                 }
 861
 862         /* ftmp5 = z1*z2 */
 863         felem_mul(tmp, z1, z2);
 864         felem_reduce(ftmp5, tmp);
 865
 866         /* z3 = (z1^2*x2 - z2^2*x1)*(z1*z2) */
 867         felem_mul(tmp, ftmp, ftmp5);
 868         felem_reduce(z3, tmp);
 869
 870         /* ftmp = (z1^2*x2 - z2^2*x1)^2 */
 871         memcpy(ftmp5, ftmp, 4 * sizeof(fslice));
 872         felem_square(tmp, ftmp);
 873         felem_reduce(ftmp, tmp);
 874
 875         /* ftmp5 = (z1^2*x2 - z2^2*x1)^3 */
 876         felem_mul(tmp, ftmp, ftmp5);
 877         felem_reduce(ftmp5, tmp);
 878
 879         /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */
 880         felem_mul(tmp, ftmp2, ftmp);
 881         felem_reduce(ftmp2, tmp);
 882
 883         /* ftmp4 = z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */
 884         felem_mul(tmp, ftmp4, ftmp5);
 885         /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
 886
 887         /* tmp2 = (z1^3*y2 - z2^3*y1)^2 */
 888         felem_square(tmp2, ftmp3);
 889         /* tmp2[i] < 4 * 2^57 * 2^57 < 2^116 */
 890
 891         /* tmp2 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 */
 892         felem_diff_128_64(tmp2, ftmp5);
 893         /* tmp2[i] < 2^116 + 2^64 + 8 < 2^117 */
 894
 895         /* ftmp5 = 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */
 896         memcpy(ftmp5, ftmp2, 4 * sizeof(fslice));
 897         felem_scalar64(ftmp5, 2);
 898         /* ftmp5[i] < 2 * 2^57 = 2^58 */
 899
 900         /* x3 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 -
 901            2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */
 902         felem_diff_128_64(tmp2, ftmp5);
 903         /* tmp2[i] < 2^117 + 2^64 + 8 < 2^118 */
 904         felem_reduce(x3, tmp2);
 905
 906         /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x3 */
 907         felem_diff64(ftmp2, x3);
 908         /* ftmp2[i] < 2^57 + 2^58 + 2 < 2^59 */
 909
 910         /* tmp2 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x3) */
 911         felem_mul(tmp2, ftmp3, ftmp2);
 912         /* tmp2[i] < 4 * 2^57 * 2^59 = 2^118 */
 913
 914         /* y3 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x3) -
 915            z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */
 916         felem_diff128(tmp2, tmp);
 917         /* tmp2[i] < 2^118 + 2^120 < 2^121 */
 918         felem_reduce(y3, tmp2);
 919
 920         /* the result (x3, y3, z3) is incorrect if one of the inputs is the
 921          * point at infinity, so we need to check for this separately */
 922
 923         /* if point 1 is at infinity, copy point 2 to output, and vice versa */
 924         copy_conditional(x3, x2, 4, z1_is_zero);
 925         copy_conditional(x3, x1, 4, z2_is_zero);
 926         copy_conditional(y3, y2, 4, z1_is_zero);
 927         copy_conditional(y3, y1, 4, z2_is_zero);
 928         copy_conditional(z3, z2, 4, z1_is_zero);
 929         copy_conditional(z3, z1, 4, z2_is_zero);
 930         }
 931
 932 /* Select a point from an array of 16 precomputed point multiples,
 933  * in constant time: for bits = {b_0, b_1, b_2, b_3}, return the point
 934  * pre_comp[8*b_3 + 4*b_2 + 2*b_1 + b_0] */
 935 static void select_point(const fslice bits[4], const fslice pre_comp[16][3][4],
 936         fslice out[12])
 937         {
 938         fslice tmp[5][12];
 939         select_conditional(tmp[0], pre_comp[7][0], pre_comp[15][0], 12, bits[3]);
 940         select_conditional(tmp[1], pre_comp[3][0], pre_comp[11][0], 12, bits[3]);
 941         select_conditional(tmp[2], tmp[1], tmp[0], 12, bits[2]);
 942         select_conditional(tmp[0], pre_comp[5][0], pre_comp[13][0], 12, bits[3]);
 943         select_conditional(tmp[1], pre_comp[1][0], pre_comp[9][0], 12, bits[3]);
 944         select_conditional(tmp[3], tmp[1], tmp[0], 12, bits[2]);
 945         select_conditional(tmp[4], tmp[3], tmp[2], 12, bits[1]);
 946         select_conditional(tmp[0], pre_comp[6][0], pre_comp[14][0], 12, bits[3]);
 947         select_conditional(tmp[1], pre_comp[2][0], pre_comp[10][0], 12, bits[3]);
 948         select_conditional(tmp[2], tmp[1], tmp[0], 12, bits[2]);
 949         select_conditional(tmp[0], pre_comp[4][0], pre_comp[12][0], 12, bits[3]);
 950         select_conditional(tmp[1], pre_comp[0][0], pre_comp[8][0], 12, bits[3]);
 951         select_conditional(tmp[3], tmp[1], tmp[0], 12, bits[2]);
 952         select_conditional(tmp[1], tmp[3], tmp[2], 12, bits[1]);
 953         select_conditional(out, tmp[1], tmp[4], 12, bits[0]);
 954         }
 955
 956 /* Interleaved point multiplication using precomputed point multiples:
 957  * The small point multiples 0*P, 1*P, ..., 15*P are in pre_comp[],
 958  * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple
 959  * of the generator, using certain (large) precomputed multiples in g_pre_comp.
 960  * Output point (X, Y, Z) is stored in x_out, y_out, z_out */
 961 static void batch_mul(fslice x_out[4], fslice y_out[4], fslice z_out[4],
 962         const u8 scalars[][fElemSize], const unsigned num_points, const u8 *g_scalar,
 963         const fslice pre_comp[][16][3][4], const fslice g_pre_comp[16][3][4])
 964         {
 965         unsigned i, j, num;
 966         unsigned gen_mul = (g_scalar != NULL);
 967         fslice nq[12], nqt[12], tmp[12];
 968         fslice bits[4];
 969         u8 byte;
 970
 971         /* set nq to the point at infinity */
 972         memset(nq, 0, 12 * sizeof(fslice));
 973
 974         /* Loop over all scalars msb-to-lsb, 4 bits at a time: for each nibble,
 975          * double 4 times, then add the precomputed point multiples.
 976          * If we are also adding multiples of the generator, then interleave
 977          * these additions with the last 56 doublings. */
 978         for (i = (num_points ? 28 : 7); i > 0; --i)
 979                 {
 980                 for (j = 0; j < 8; ++j)
 981                         {
 982                         /* double once */
 983                         point_double(nq, nq+4, nq+8, nq, nq+4, nq+8);
 984                         /* add multiples of the generator */
 985                         if ((gen_mul) && (i <= 7))
 986                                 {
 987                                 bits[3] = (g_scalar[i+20] >> (7-j)) & 1;
 988                                 bits[2] = (g_scalar[i+13] >> (7-j)) & 1;
 989                                 bits[1] = (g_scalar[i+6] >> (7-j)) & 1;
 990                                 bits[0] = (g_scalar[i-1] >> (7-j)) & 1;
 991                                 /* select the point to add, in constant time */
 992                                 select_point(bits, g_pre_comp, tmp);
 993                                 memcpy(nqt, nq, 12 * sizeof(fslice));
 994                                 point_add(nq, nq+4, nq+8, nqt, nqt+4, nqt+8,
 995                                         tmp, tmp+4, tmp+8);
 996                                 }
 997                         /* do an addition after every 4 doublings */
 998                         if (j % 4 == 3)
 999                                 {
1000                                 /* loop over all scalars */
1001                                 for (num = 0; num < num_points; ++num)
1002                                         {
1003                                         byte = scalars[num][i-1];
1004                                         bits[3] = (byte >> (10-j)) & 1;
1005                                         bits[2] = (byte >> (9-j)) & 1;
1006                                         bits[1] = (byte >> (8-j)) & 1;
1007                                         bits[0] = (byte >> (7-j)) & 1;
1008                                         /* select the point to add */
1009                                         select_point(bits,
1010                                                 pre_comp[num], tmp);
1011                                         memcpy(nqt, nq, 12 * sizeof(fslice));
1012                                         point_add(nq, nq+4, nq+8, nqt, nqt+4,
1013                                                 nqt+8, tmp, tmp+4, tmp+8);
1014                                         }
1015                                 }
1016                         }
1017                 }
1018         memcpy(x_out, nq, 4 * sizeof(fslice));
1019         memcpy(y_out, nq+4, 4 * sizeof(fslice));
1020         memcpy(z_out, nq+8, 4 * sizeof(fslice));
1021         }
1022
1023 /******************************************************************************/
1024 /*                     FUNCTIONS TO MANAGE PRECOMPUTATION
1025  */
1026
1027 static NISTP224_PRE_COMP *nistp224_pre_comp_new()
1028         {
1029         NISTP224_PRE_COMP *ret = NULL;
1030         ret = (NISTP224_PRE_COMP *)OPENSSL_malloc(sizeof(NISTP224_PRE_COMP));
1031         if (!ret)
1032                 {
1033                 ECerr(EC_F_NISTP224_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
1034                 return ret;
1035                 }
1036         memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp));
1037         ret->references = 1;
1038         return ret;
1039         }
1040
1041 static void *nistp224_pre_comp_dup(void *src_)
1042         {
1043         NISTP224_PRE_COMP *src = src_;
1044
1045         /* no need to actually copy, these objects never change! */
1046         CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
1047
1048         return src_;
1049         }
1050
1051 static void nistp224_pre_comp_free(void *pre_)
1052         {
1053         int i;
1054         NISTP224_PRE_COMP *pre = pre_;
1055
1056         if (!pre)
1057                 return;
1058
1059         i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1060         if (i > 0)
1061                 return;
1062
1063         OPENSSL_free(pre);
1064         }
1065
1066 static void nistp224_pre_comp_clear_free(void *pre_)
1067         {
1068         int i;
1069         NISTP224_PRE_COMP *pre = pre_;
1070
1071         if (!pre)
1072                 return;
1073
1074         i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1075         if (i > 0)
1076                 return;
1077
1078         OPENSSL_cleanse(pre, sizeof *pre);
1079         OPENSSL_free(pre);
1080         }
1081
1082 /******************************************************************************/
1083 /*                         OPENSSL EC_METHOD FUNCTIONS
1084  */
1085
1086 int ec_GFp_nistp224_group_init(EC_GROUP *group)
1087         {
1088         int ret;
1089         ret = ec_GFp_simple_group_init(group);
1090         group->a_is_minus3 = 1;
1091         return ret;
1092         }
1093
1094 int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p,
1095         const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1096         {
1097         int ret = 0;
1098         BN_CTX *new_ctx = NULL;
1099         BIGNUM *curve_p, *curve_a, *curve_b;
1100
1101         if (ctx == NULL)
1102                 if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0;
1103         BN_CTX_start(ctx);
1104         if (((curve_p = BN_CTX_get(ctx)) == NULL) ||
1105                 ((curve_a = BN_CTX_get(ctx)) == NULL) ||
1106                 ((curve_b = BN_CTX_get(ctx)) == NULL)) goto err;
1107         BN_bin2bn(nistp224_curve_params, fElemSize, curve_p);
1108         BN_bin2bn(nistp224_curve_params + 28, fElemSize, curve_a);
1109         BN_bin2bn(nistp224_curve_params + 56, fElemSize, curve_b);
1110         if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) ||
1111                 (BN_cmp(curve_b, b)))
1112                 {
1113                 ECerr(EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE,
1114                         EC_R_WRONG_CURVE_PARAMETERS);
1115                 goto err;
1116                 }
1117         group->field_mod_func = BN_nist_mod_224;
1118         ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx);
1119 err:
1120         BN_CTX_end(ctx);
1121         if (new_ctx != NULL)
1122                 BN_CTX_free(new_ctx);
1123         return ret;
1124         }
1125
1126 /* Takes the Jacobian coordinates (X, Y, Z) of a point and returns
1127  * (X', Y') = (X/Z^2, Y/Z^3) */
1128 int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group,
1129         const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
1130         {
1131         fslice z1[4], z2[4], x_in[4], y_in[4], x_out[4], y_out[4];
1132         uint128_t tmp[7];
1133
1134         if (EC_POINT_is_at_infinity(group, point))
1135                 {
1136                 ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES,
1137                         EC_R_POINT_AT_INFINITY);
1138                 return 0;
1139                 }
1140         if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) ||
1141                 (!BN_to_felem(z1, &point->Z))) return 0;
1142         felem_inv(z2, z1);
1143         felem_square(tmp, z2); felem_reduce(z1, tmp);
1144         felem_mul(tmp, x_in, z1); felem_reduce(x_in, tmp);
1145         felem_contract(x_out, x_in);
1146         if (x != NULL)
1147                 {
1148                 if (!felem_to_BN(x, x_out)) {
1149                 ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES,
1150                         ERR_R_BN_LIB);
1151                 return 0;
1152                 }
1153                 }
1154         felem_mul(tmp, z1, z2); felem_reduce(z1, tmp);
1155         felem_mul(tmp, y_in, z1); felem_reduce(y_in, tmp);
1156         felem_contract(y_out, y_in);
1157         if (y != NULL)
1158                 {
1159                 if (!felem_to_BN(y, y_out)) {
1160                 ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES,
1161                         ERR_R_BN_LIB);
1162                 return 0;
1163                 }
1164                 }
1165         return 1;
1166         }
1167
1168 /* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values
1169  * Result is stored in r (r can equal one of the inputs). */
1170 int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r,
1171         const BIGNUM *scalar, size_t num, const EC_POINT *points[],
1172         const BIGNUM *scalars[], BN_CTX *ctx)
1173         {
1174         int ret = 0;
1175         int i, j;
1176         BN_CTX *new_ctx = NULL;
1177         BIGNUM *x, *y, *z, *tmp_scalar;
1178         u8 g_secret[fElemSize];
1179         u8 (*secrets)[fElemSize] = NULL;
1180         fslice (*pre_comp)[16][3][4] = NULL;
1181         u8 tmp[fElemSize];
1182         unsigned num_bytes;
1183         int have_pre_comp = 0;
1184         size_t num_points = num;
1185         fslice x_in[4], y_in[4], z_in[4], x_out[4], y_out[4], z_out[4];
1186         NISTP224_PRE_COMP *pre = NULL;
1187         fslice (*g_pre_comp)[3][4] = NULL;
1188         EC_POINT *generator = NULL;
1189         const EC_POINT *p = NULL;
1190         const BIGNUM *p_scalar = NULL;
1191
1192         if (ctx == NULL)
1193                 if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0;
1194         BN_CTX_start(ctx);
1195         if (((x = BN_CTX_get(ctx)) == NULL) ||
1196                 ((y = BN_CTX_get(ctx)) == NULL) ||
1197                 ((z = BN_CTX_get(ctx)) == NULL) ||
1198                 ((tmp_scalar = BN_CTX_get(ctx)) == NULL))
1199                 goto err;
1200
1201         if (scalar != NULL)
1202                 {
1203                 pre = EC_EX_DATA_get_data(group->extra_data,
1204                         nistp224_pre_comp_dup, nistp224_pre_comp_free,
1205                         nistp224_pre_comp_clear_free);
1206                 if (pre)
1207                         /* we have precomputation, try to use it */
1208                         g_pre_comp = pre->g_pre_comp;
1209                 else
1210                         /* try to use the standard precomputation */
1211                         g_pre_comp = (fslice (*)[3][4]) gmul;
1212                 generator = EC_POINT_new(group);
1213                 if (generator == NULL)
1214                         goto err;
1215                 /* get the generator from precomputation */
1216                 if (!felem_to_BN(x, g_pre_comp[1][0]) ||
1217                         !felem_to_BN(y, g_pre_comp[1][1]) ||
1218                         !felem_to_BN(z, g_pre_comp[1][2]))
1219                         {
1220                         ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB);
1221                         goto err;
1222                         }
1223                 if (!EC_POINT_set_Jprojective_coordinates_GFp(group,
1224                                 generator, x, y, z, ctx))
1225                         goto err;
1226                 if (0 == EC_POINT_cmp(group, generator, group->generator, ctx))
1227                         /* precomputation matches generator */
1228                         have_pre_comp = 1;
1229                 else
1230                         /* we don't have valid precomputation:
1231                          * treat the generator as a random point */
1232                         num_points = num_points + 1;
1233                 }
1234         secrets = OPENSSL_malloc(num_points * fElemSize);
1235         pre_comp = OPENSSL_malloc(num_points * 16 * 3 * 4 * sizeof(fslice));
1236
1237         if ((num_points) && ((secrets == NULL) || (pre_comp == NULL)))
1238                 {
1239                 ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1240                 goto err;
1241                 }
1242
1243         /* we treat NULL scalars as 0, and NULL points as points at infinity,
1244          * i.e., they contribute nothing to the linear combination */
1245         memset(secrets, 0, num_points * fElemSize);
1246         memset(pre_comp, 0, num_points * 16 * 3 * 4 * sizeof(fslice));
1247         for (i = 0; i < num_points; ++i)
1248                 {
1249                 if (i == num)
1250                         /* the generator */
1251                         {
1252                         p = EC_GROUP_get0_generator(group);
1253                         p_scalar = scalar;
1254                         }
1255                 else
1256                         /* the i^th point */
1257                         {
1258                         p = points[i];
1259                         p_scalar = scalars[i];
1260                         }
1261                 if ((p_scalar != NULL) && (p != NULL))
1262                         {
1263                         num_bytes = BN_num_bytes(p_scalar);
1264                         /* reduce scalar to 0 <= scalar < 2^224 */
1265                         if ((num_bytes > fElemSize) || (BN_is_negative(p_scalar)))
1266                                 {
1267                                 /* this is an unusual input, and we don't guarantee
1268                                  * constant-timeness */
1269                                 if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx))
1270                                         {
1271                                         ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB);
1272                                         goto err;
1273                                         }
1274                                 num_bytes = BN_bn2bin(tmp_scalar, tmp);
1275                                 }
1276                         else
1277                                 BN_bn2bin(p_scalar, tmp);
1278                         flip_endian(secrets[i], tmp, num_bytes);
1279                         /* precompute multiples */
1280                         if ((!BN_to_felem(x_out, &p->X)) ||
1281                                 (!BN_to_felem(y_out, &p->Y)) ||
1282                                 (!BN_to_felem(z_out, &p->Z))) goto err;
1283                         memcpy(pre_comp[i][1][0], x_out, 4 * sizeof(fslice));
1284                         memcpy(pre_comp[i][1][1], y_out, 4 * sizeof(fslice));
1285                         memcpy(pre_comp[i][1][2], z_out, 4 * sizeof(fslice));
1286                         for (j = 1; j < 8; ++j)
1287                                 {
1288                                 point_double(pre_comp[i][2*j][0],
1289                                         pre_comp[i][2*j][1],
1290                                         pre_comp[i][2*j][2],
1291                                         pre_comp[i][j][0],
1292                                         pre_comp[i][j][1],
1293                                         pre_comp[i][j][2]);
1294                                 point_add(pre_comp[i][2*j+1][0],
1295                                         pre_comp[i][2*j+1][1],
1296                                         pre_comp[i][2*j+1][2],
1297                                         pre_comp[i][1][0],
1298                                         pre_comp[i][1][1],
1299                                         pre_comp[i][1][2],
1300                                         pre_comp[i][2*j][0],
1301                                         pre_comp[i][2*j][1],
1302                                         pre_comp[i][2*j][2]);
1303                                 }
1304                         }
1305                 }
1306
1307         /* the scalar for the generator */
1308         if ((scalar != NULL) && (have_pre_comp))
1309                 {
1310                 memset(g_secret, 0, fElemSize);
1311                 num_bytes = BN_num_bytes(scalar);
1312                 /* reduce scalar to 0 <= scalar < 2^224 */
1313                 if ((num_bytes > fElemSize) || (BN_is_negative(scalar)))
1314                         {
1315                         /* this is an unusual input, and we don't guarantee
1316                          * constant-timeness */
1317                         if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx))
1318                                 {
1319                                 ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB);
1320                                 goto err;
1321                                 }
1322                         num_bytes = BN_bn2bin(tmp_scalar, tmp);
1323                         }
1324                 else
1325                         BN_bn2bin(scalar, tmp);
1326                 flip_endian(g_secret, tmp, num_bytes);
1327                 /* do the multiplication with generator precomputation*/
1328                 batch_mul(x_out, y_out, z_out,
1329                         (const u8 (*)[fElemSize]) secrets, num_points,
1330                         g_secret, (const fslice (*)[16][3][4]) pre_comp,
1331                         (const fslice (*)[3][4]) g_pre_comp);
1332                 }
1333         else
1334                 /* do the multiplication without generator precomputation */
1335                 batch_mul(x_out, y_out, z_out,
1336                         (const u8 (*)[fElemSize]) secrets, num_points,
1337                         NULL, (const fslice (*)[16][3][4]) pre_comp, NULL);
1338         /* reduce the output to its unique minimal representation */
1339         felem_contract(x_in, x_out);
1340         felem_contract(y_in, y_out);
1341         felem_contract(z_in, z_out);
1342         if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) ||
1343                 (!felem_to_BN(z, z_in)))
1344                 {
1345                 ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB);
1346                 goto err;
1347                 }
1348         ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx);
1349
1350 err:
1351         BN_CTX_end(ctx);
1352         if (generator != NULL)
1353                 EC_POINT_free(generator);
1354         if (new_ctx != NULL)
1355                 BN_CTX_free(new_ctx);
1356         if (secrets != NULL)
1357                 OPENSSL_free(secrets);
1358         if (pre_comp != NULL)
1359                 OPENSSL_free(pre_comp);
1360         return ret;
1361         }
1362
1363 int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
1364         {
1365         int ret = 0;
1366         NISTP224_PRE_COMP *pre = NULL;
1367         int i, j;
1368         BN_CTX *new_ctx = NULL;
1369         BIGNUM *x, *y;
1370         EC_POINT *generator = NULL;
1371
1372         /* throw away old precomputation */
1373         EC_EX_DATA_free_data(&group->extra_data, nistp224_pre_comp_dup,
1374                 nistp224_pre_comp_free, nistp224_pre_comp_clear_free);
1375         if (ctx == NULL)
1376                 if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0;
1377         BN_CTX_start(ctx);
1378         if (((x = BN_CTX_get(ctx)) == NULL) ||
1379                 ((y = BN_CTX_get(ctx)) == NULL))
1380                 goto err;
1381         /* get the generator */
1382         if (group->generator == NULL) goto err;
1383         generator = EC_POINT_new(group);
1384         if (generator == NULL)
1385                 goto err;
1386         BN_bin2bn(nistp224_curve_params + 84, fElemSize, x);
1387         BN_bin2bn(nistp224_curve_params + 112, fElemSize, y);
1388         if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx))
1389                 goto err;
1390         if ((pre = nistp224_pre_comp_new()) == NULL)
1391                 goto err;
1392         /* if the generator is the standard one, use built-in precomputation */
1393         if (0 == EC_POINT_cmp(group, generator, group->generator, ctx))
1394                 {
1395                 memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp));
1396                 ret = 1;
1397                 goto err;
1398                 }
1399         if ((!BN_to_felem(pre->g_pre_comp[1][0], &group->generator->X)) ||
1400                 (!BN_to_felem(pre->g_pre_comp[1][1], &group->generator->Y)) ||
1401                 (!BN_to_felem(pre->g_pre_comp[1][2], &group->generator->Z)))
1402                 goto err;
1403         /* compute 2^56*G, 2^112*G, 2^168*G */
1404         for (i = 1; i < 5; ++i)
1405                 {
1406                 point_double(pre->g_pre_comp[2*i][0], pre->g_pre_comp[2*i][1],
1407                         pre->g_pre_comp[2*i][2], pre->g_pre_comp[i][0],
1408                         pre->g_pre_comp[i][1], pre->g_pre_comp[i][2]);
1409                 for (j = 0; j < 55; ++j)
1410                         {
1411                         point_double(pre->g_pre_comp[2*i][0],
1412                                 pre->g_pre_comp[2*i][1],
1413                                 pre->g_pre_comp[2*i][2],
1414                                 pre->g_pre_comp[2*i][0],
1415                                 pre->g_pre_comp[2*i][1],
1416                                 pre->g_pre_comp[2*i][2]);
1417                         }
1418                 }
1419         /* g_pre_comp[0] is the point at infinity */
1420         memset(pre->g_pre_comp[0], 0, sizeof(pre->g_pre_comp[0]));
1421         /* the remaining multiples */
1422         /* 2^56*G + 2^112*G */
1423         point_add(pre->g_pre_comp[6][0], pre->g_pre_comp[6][1],
1424                 pre->g_pre_comp[6][2], pre->g_pre_comp[4][0],
1425                 pre->g_pre_comp[4][1], pre->g_pre_comp[4][2],
1426                 pre->g_pre_comp[2][0], pre->g_pre_comp[2][1],
1427                 pre->g_pre_comp[2][2]);
1428         /* 2^56*G + 2^168*G */
1429         point_add(pre->g_pre_comp[10][0], pre->g_pre_comp[10][1],
1430                 pre->g_pre_comp[10][2], pre->g_pre_comp[8][0],
1431                 pre->g_pre_comp[8][1], pre->g_pre_comp[8][2],
1432                 pre->g_pre_comp[2][0], pre->g_pre_comp[2][1],
1433                 pre->g_pre_comp[2][2]);
1434         /* 2^112*G + 2^168*G */
1435         point_add(pre->g_pre_comp[12][0], pre->g_pre_comp[12][1],
1436                 pre->g_pre_comp[12][2], pre->g_pre_comp[8][0],
1437                 pre->g_pre_comp[8][1], pre->g_pre_comp[8][2],
1438                 pre->g_pre_comp[4][0], pre->g_pre_comp[4][1],
1439                 pre->g_pre_comp[4][2]);
1440         /* 2^56*G + 2^112*G + 2^168*G */
1441         point_add(pre->g_pre_comp[14][0], pre->g_pre_comp[14][1],
1442                 pre->g_pre_comp[14][2], pre->g_pre_comp[12][0],
1443                 pre->g_pre_comp[12][1], pre->g_pre_comp[12][2],
1444                 pre->g_pre_comp[2][0], pre->g_pre_comp[2][1],
1445                 pre->g_pre_comp[2][2]);
1446         for (i = 1; i < 8; ++i)
1447                 {
1448                 /* odd multiples: add G */
1449                 point_add(pre->g_pre_comp[2*i+1][0], pre->g_pre_comp[2*i+1][1],
1450                         pre->g_pre_comp[2*i+1][2], pre->g_pre_comp[2*i][0],
1451                         pre->g_pre_comp[2*i][1], pre->g_pre_comp[2*i][2],
1452                         pre->g_pre_comp[1][0], pre->g_pre_comp[1][1],
1453                         pre->g_pre_comp[1][2]);
1454                 }
1455
1456         if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp224_pre_comp_dup,
1457                         nistp224_pre_comp_free, nistp224_pre_comp_clear_free))
1458                 goto err;
1459         ret = 1;
1460         pre = NULL;
1461  err:
1462         BN_CTX_end(ctx);
1463         if (generator != NULL)
1464                 EC_POINT_free(generator);
1465         if (new_ctx != NULL)
1466                 BN_CTX_free(new_ctx);
1467         if (pre)
1468                 nistp224_pre_comp_free(pre);
1469         return ret;
1470         }
1471
1472 int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group)
1473         {
1474         if (EC_EX_DATA_get_data(group->extra_data, nistp224_pre_comp_dup,
1475                         nistp224_pre_comp_free, nistp224_pre_comp_clear_free)
1476                 != NULL)
1477                 return 1;
1478         else
1479                 return 0;
1480         }
1481 #endif