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 #if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 1))
  72   /* even with gcc, the typedef won't work for 32-bit platforms */
  73   typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit platforms */
  74 #else
  75   #error "Need GCC 3.1 or later to define type uint128_t"
  76 #endif
  77
  78 typedef uint8_t u8;
  79
  80
  81 /******************************************************************************/
  82 /*                  INTERNAL REPRESENTATION OF FIELD ELEMENTS
  83  *
  84  * Field elements are represented as a_0 + 2^56*a_1 + 2^112*a_2 + 2^168*a_3
  85  * where each slice a_i is a 64-bit word, i.e., a field element is an fslice
  86  * array a with 4 elements, where a[i] = a_i.
  87  * Outputs from multiplications are represented as unreduced polynomials
  88  * 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
  89  * where each b_i is a 128-bit word. We ensure that inputs to each field
  90  * multiplication satisfy a_i < 2^60, so outputs satisfy b_i < 4*2^60*2^60,
  91  * and fit into a 128-bit word without overflow. The coefficients are then
  92  * again partially reduced to a_i < 2^57. We only reduce to the unique minimal
  93  * representation at the end of the computation.
  94  *
  95  */
  96
  97 typedef uint64_t fslice;
  98
  99 /* Field element represented as a byte arrary.
 100  * 28*8 = 224 bits is also the group order size for the elliptic curve.  */
 101 typedef u8 felem_bytearray[28];
 102
 103 static const felem_bytearray nistp224_curve_params[5] = {
 104         {0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,    /* p */
 105          0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00,
 106          0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01},
 107         {0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,    /* a */
 108          0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF,
 109          0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE},
 110         {0xB4,0x05,0x0A,0x85,0x0C,0x04,0xB3,0xAB,0xF5,0x41,    /* b */
 111          0x32,0x56,0x50,0x44,0xB0,0xB7,0xD7,0xBF,0xD8,0xBA,
 112          0x27,0x0B,0x39,0x43,0x23,0x55,0xFF,0xB4},
 113         {0xB7,0x0E,0x0C,0xBD,0x6B,0xB4,0xBF,0x7F,0x32,0x13,    /* x */
 114          0x90,0xB9,0x4A,0x03,0xC1,0xD3,0x56,0xC2,0x11,0x22,
 115          0x34,0x32,0x80,0xD6,0x11,0x5C,0x1D,0x21},
 116         {0xbd,0x37,0x63,0x88,0xb5,0xf7,0x23,0xfb,0x4c,0x22,    /* y */
 117          0xdf,0xe6,0xcd,0x43,0x75,0xa0,0x5a,0x07,0x47,0x64,
 118          0x44,0xd5,0x81,0x99,0x85,0x00,0x7e,0x34}
 119 };
 120
 121 /* Precomputed multiples of the standard generator
 122  * b_0*G + b_1*2^56*G + b_2*2^112*G + b_3*2^168*G for
 123  * (b_3, b_2, b_1, b_0) in [0,15], i.e., gmul[0] = point_at_infinity,
 124  * gmul[1] = G, gmul[2] = 2^56*G, gmul[3] = 2^56*G + G, etc.
 125  * Points are given in Jacobian projective coordinates: words 0-3 represent the
 126  * X-coordinate (slice a_0 is word 0, etc.), words 4-7 represent the
 127  * Y-coordinate and words 8-11 represent the Z-coordinate. */
 128 static const fslice gmul[16][3][4] = {
 129         {{0x00000000000000, 0x00000000000000, 0x00000000000000, 0x00000000000000},
 130          {0x00000000000000, 0x00000000000000, 0x00000000000000, 0x00000000000000},
 131          {0x00000000000000, 0x00000000000000, 0x00000000000000, 0x00000000000000}},
 132         {{0x3280d6115c1d21, 0xc1d356c2112234, 0x7f321390b94a03, 0xb70e0cbd6bb4bf},
 133          {0xd5819985007e34, 0x75a05a07476444, 0xfb4c22dfe6cd43, 0xbd376388b5f723},
 134          {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}},
 135         {{0xfd9675666ebbe9, 0xbca7664d40ce5e, 0x2242df8d8a2a43, 0x1f49bbb0f99bc5},
 136          {0x29e0b892dc9c43, 0xece8608436e662, 0xdc858f185310d0, 0x9812dd4eb8d321},
 137          {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}},
 138         {{0x6d3e678d5d8eb8, 0x559eed1cb362f1, 0x16e9a3bbce8a3f, 0xeedcccd8c2a748},
 139          {0xf19f90ed50266d, 0xabf2b4bf65f9df, 0x313865468fafec, 0x5cb379ba910a17},
 140          {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}},
 141         {{0x0641966cab26e3, 0x91fb2991fab0a0, 0xefec27a4e13a0b, 0x0499aa8a5f8ebe},
 142          {0x7510407766af5d, 0x84d929610d5450, 0x81d77aae82f706, 0x6916f6d4338c5b},
 143          {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}},
 144         {{0xea95ac3b1f15c6, 0x086000905e82d4, 0xdd323ae4d1c8b1, 0x932b56be7685a3},
 145          {0x9ef93dea25dbbf, 0x41665960f390f0, 0xfdec76dbe2a8a7, 0x523e80f019062a},
 146          {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}},
 147         {{0x822fdd26732c73, 0xa01c83531b5d0f, 0x363f37347c1ba4, 0xc391b45c84725c},
 148          {0xbbd5e1b2d6ad24, 0xddfbcde19dfaec, 0xc393da7e222a7f, 0x1efb7890ede244},
 149          {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}},
 150         {{0x4c9e90ca217da1, 0xd11beca79159bb, 0xff8d33c2c98b7c, 0x2610b39409f849},
 151          {0x44d1352ac64da0, 0xcdbb7b2c46b4fb, 0x966c079b753c89, 0xfe67e4e820b112},
 152          {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}},
 153         {{0xe28cae2df5312d, 0xc71b61d16f5c6e, 0x79b7619a3e7c4c, 0x05c73240899b47},
 154          {0x9f7f6382c73e3a, 0x18615165c56bda, 0x641fab2116fd56, 0x72855882b08394},
 155          {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}},
 156         {{0x0469182f161c09, 0x74a98ca8d00fb5, 0xb89da93489a3e0, 0x41c98768fb0c1d},
 157          {0xe5ea05fb32da81, 0x3dce9ffbca6855, 0x1cfe2d3fbf59e6, 0x0e5e03408738a7},
 158          {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}},
 159         {{0xdab22b2333e87f, 0x4430137a5dd2f6, 0xe03ab9f738beb8, 0xcb0c5d0dc34f24},
 160          {0x764a7df0c8fda5, 0x185ba5c3fa2044, 0x9281d688bcbe50, 0xc40331df893881},
 161          {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}},
 162         {{0xb89530796f0f60, 0xade92bd26909a3, 0x1a0c83fb4884da, 0x1765bf22a5a984},
 163          {0x772a9ee75db09e, 0x23bc6c67cec16f, 0x4c1edba8b14e2f, 0xe2a215d9611369},
 164          {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}},
 165         {{0x571e509fb5efb3, 0xade88696410552, 0xc8ae85fada74fe, 0x6c7e4be83bbde3},
 166          {0xff9f51160f4652, 0xb47ce2495a6539, 0xa2946c53b582f4, 0x286d2db3ee9a60},
 167          {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}},
 168         {{0x40bbd5081a44af, 0x0995183b13926c, 0xbcefba6f47f6d0, 0x215619e9cc0057},
 169          {0x8bc94d3b0df45e, 0xf11c54a3694f6f, 0x8631b93cdfe8b5, 0xe7e3f4b0982db9},
 170          {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}},
 171         {{0xb17048ab3e1c7b, 0xac38f36ff8a1d8, 0x1c29819435d2c6, 0xc813132f4c07e9},
 172          {0x2891425503b11f, 0x08781030579fea, 0xf5426ba5cc9674, 0x1e28ebf18562bc},
 173          {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}},
 174         {{0x9f31997cc864eb, 0x06cd91d28b5e4c, 0xff17036691a973, 0xf1aef351497c58},
 175          {0xdd1f2d600564ff, 0xdead073b1402db, 0x74a684435bd693, 0xeea7471f962558},
 176          {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}
 177 };
 178
 179 /* Precomputation for the group generator. */
 180 typedef struct {
 181         fslice g_pre_comp[16][3][4];
 182         int references;
 183 } NISTP224_PRE_COMP;
 184
 185 const EC_METHOD *EC_GFp_nistp224_method(void)
 186         {
 187         static const EC_METHOD ret = {
 188                 NID_X9_62_prime_field,
 189                 ec_GFp_nistp224_group_init,
 190                 ec_GFp_simple_group_finish,
 191                 ec_GFp_simple_group_clear_finish,
 192                 ec_GFp_nist_group_copy,
 193                 ec_GFp_nistp224_group_set_curve,
 194                 ec_GFp_simple_group_get_curve,
 195                 ec_GFp_simple_group_get_degree,
 196                 ec_GFp_simple_group_check_discriminant,
 197                 ec_GFp_simple_point_init,
 198                 ec_GFp_simple_point_finish,
 199                 ec_GFp_simple_point_clear_finish,
 200                 ec_GFp_simple_point_copy,
 201                 ec_GFp_simple_point_set_to_infinity,
 202                 ec_GFp_simple_set_Jprojective_coordinates_GFp,
 203                 ec_GFp_simple_get_Jprojective_coordinates_GFp,
 204                 ec_GFp_simple_point_set_affine_coordinates,
 205                 ec_GFp_nistp224_point_get_affine_coordinates,
 206                 ec_GFp_simple_set_compressed_coordinates,
 207                 ec_GFp_simple_point2oct,
 208                 ec_GFp_simple_oct2point,
 209                 ec_GFp_simple_add,
 210                 ec_GFp_simple_dbl,
 211                 ec_GFp_simple_invert,
 212                 ec_GFp_simple_is_at_infinity,
 213                 ec_GFp_simple_is_on_curve,
 214                 ec_GFp_simple_cmp,
 215                 ec_GFp_simple_make_affine,
 216                 ec_GFp_simple_points_make_affine,
 217                 ec_GFp_nistp224_points_mul,
 218                 ec_GFp_nistp224_precompute_mult,
 219                 ec_GFp_nistp224_have_precompute_mult,
 220                 ec_GFp_nist_field_mul,
 221                 ec_GFp_nist_field_sqr,
 222                 0 /* field_div */,
 223                 0 /* field_encode */,
 224                 0 /* field_decode */,
 225                 0 /* field_set_to_one */ };
 226
 227         return &ret;
 228         }
 229
 230 /* Helper functions to convert field elements to/from internal representation */
 231 static void bin28_to_felem(fslice out[4], const u8 in[28])
 232         {
 233         out[0] = *((const uint64_t *)(in)) & 0x00ffffffffffffff;
 234         out[1] = (*((const uint64_t *)(in+7))) & 0x00ffffffffffffff;
 235         out[2] = (*((const uint64_t *)(in+14))) & 0x00ffffffffffffff;
 236         out[3] = (*((const uint64_t *)(in+21))) & 0x00ffffffffffffff;
 237         }
 238
 239 static void felem_to_bin28(u8 out[28], const fslice in[4])
 240         {
 241         unsigned i;
 242         for (i = 0; i < 7; ++i)
 243                 {
 244                 out[i]    = in[0]>>(8*i);
 245                 out[i+7]  = in[1]>>(8*i);
 246                 out[i+14] = in[2]>>(8*i);
 247                 out[i+21] = in[3]>>(8*i);
 248                 }
 249         }
 250
 251 /* To preserve endianness when using BN_bn2bin and BN_bin2bn */
 252 static void flip_endian(u8 *out, const u8 *in, unsigned len)
 253         {
 254         unsigned i;
 255         for (i = 0; i < len; ++i)
 256                 out[i] = in[len-1-i];
 257         }
 258
 259 /* From OpenSSL BIGNUM to internal representation */
 260 static int BN_to_felem(fslice out[4], const BIGNUM *bn)
 261         {
 262         felem_bytearray b_in;
 263         felem_bytearray b_out;
 264         unsigned num_bytes;
 265
 266         /* BN_bn2bin eats leading zeroes */
 267         memset(b_out, 0, sizeof b_out);
 268         num_bytes = BN_num_bytes(bn);
 269         if (num_bytes > sizeof b_out)
 270                 {
 271                 ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE);
 272                 return 0;
 273                 }
 274         if (BN_is_negative(bn))
 275                 {
 276                 ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE);
 277                 return 0;
 278                 }
 279         num_bytes = BN_bn2bin(bn, b_in);
 280         flip_endian(b_out, b_in, num_bytes);
 281         bin28_to_felem(out, b_out);
 282         return 1;
 283         }
 284
 285 /* From internal representation to OpenSSL BIGNUM */
 286 static BIGNUM *felem_to_BN(BIGNUM *out, const fslice in[4])
 287         {
 288         felem_bytearray b_in, b_out;
 289         felem_to_bin28(b_in, in);
 290         flip_endian(b_out, b_in, sizeof b_out);
 291         return BN_bin2bn(b_out, sizeof b_out, out);
 292         }
 293
 294 /******************************************************************************/
 295 /*                              FIELD OPERATIONS
 296  *
 297  * Field operations, using the internal representation of field elements.
 298  * NB! These operations are specific to our point multiplication and cannot be
 299  * expected to be correct in general - e.g., multiplication with a large scalar
 300  * will cause an overflow.
 301  *
 302  */
 303
 304 /* Sum two field elements: out += in */
 305 static void felem_sum64(fslice out[4], const fslice in[4])
 306         {
 307         out[0] += in[0];
 308         out[1] += in[1];
 309         out[2] += in[2];
 310         out[3] += in[3];
 311         }
 312
 313 /* Subtract field elements: out -= in */
 314 /* Assumes in[i] < 2^57 */
 315 static void felem_diff64(fslice out[4], const fslice in[4])
 316         {
 317         static const uint64_t two58p2 = (((uint64_t) 1) << 58) + (((uint64_t) 1) << 2);
 318         static const uint64_t two58m2 = (((uint64_t) 1) << 58) - (((uint64_t) 1) << 2);
 319         static const uint64_t two58m42m2 = (((uint64_t) 1) << 58) -
 320             (((uint64_t) 1) << 42) - (((uint64_t) 1) << 2);
 321
 322         /* Add 0 mod 2^224-2^96+1 to ensure out > in */
 323         out[0] += two58p2;
 324         out[1] += two58m42m2;
 325         out[2] += two58m2;
 326         out[3] += two58m2;
 327
 328         out[0] -= in[0];
 329         out[1] -= in[1];
 330         out[2] -= in[2];
 331         out[3] -= in[3];
 332         }
 333
 334 /* Subtract in unreduced 128-bit mode: out128 -= in128 */
 335 /* Assumes in[i] < 2^119 */
 336 static void felem_diff128(uint128_t out[7], const uint128_t in[4])
 337         {
 338         static const uint128_t two120 = ((uint128_t) 1) << 120;
 339         static const uint128_t two120m64 = (((uint128_t) 1) << 120) -
 340                 (((uint128_t) 1) << 64);
 341         static const uint128_t two120m104m64 = (((uint128_t) 1) << 120) -
 342                 (((uint128_t) 1) << 104) - (((uint128_t) 1) << 64);
 343
 344         /* Add 0 mod 2^224-2^96+1 to ensure out > in */
 345         out[0] += two120;
 346         out[1] += two120m64;
 347         out[2] += two120m64;
 348         out[3] += two120;
 349         out[4] += two120m104m64;
 350         out[5] += two120m64;
 351         out[6] += two120m64;
 352
 353         out[0] -= in[0];
 354         out[1] -= in[1];
 355         out[2] -= in[2];
 356         out[3] -= in[3];
 357         out[4] -= in[4];
 358         out[5] -= in[5];
 359         out[6] -= in[6];
 360         }
 361
 362 /* Subtract in mixed mode: out128 -= in64 */
 363 /* in[i] < 2^63 */
 364 static void felem_diff_128_64(uint128_t out[7], const fslice in[4])
 365         {
 366         static const uint128_t two64p8 = (((uint128_t) 1) << 64) +
 367                 (((uint128_t) 1) << 8);
 368         static const uint128_t two64m8 = (((uint128_t) 1) << 64) -
 369                 (((uint128_t) 1) << 8);
 370         static const uint128_t two64m48m8 = (((uint128_t) 1) << 64) -
 371                 (((uint128_t) 1) << 48) - (((uint128_t) 1) << 8);
 372
 373         /* Add 0 mod 2^224-2^96+1 to ensure out > in */
 374         out[0] += two64p8;
 375         out[1] += two64m48m8;
 376         out[2] += two64m8;
 377         out[3] += two64m8;
 378
 379         out[0] -= in[0];
 380         out[1] -= in[1];
 381         out[2] -= in[2];
 382         out[3] -= in[3];
 383         }
 384
 385 /* Multiply a field element by a scalar: out64 = out64 * scalar
 386  * The scalars we actually use are small, so results fit without overflow */
 387 static void felem_scalar64(fslice out[4], const fslice scalar)
 388         {
 389         out[0] *= scalar;
 390         out[1] *= scalar;
 391         out[2] *= scalar;
 392         out[3] *= scalar;
 393         }
 394
 395 /* Multiply an unreduced field element by a scalar: out128 = out128 * scalar
 396  * The scalars we actually use are small, so results fit without overflow */
 397 static void felem_scalar128(uint128_t out[7], const uint128_t scalar)
 398         {
 399         out[0] *= scalar;
 400         out[1] *= scalar;
 401         out[2] *= scalar;
 402         out[3] *= scalar;
 403         out[4] *= scalar;
 404         out[5] *= scalar;
 405         out[6] *= scalar;
 406         }
 407
 408 /* Square a field element: out = in^2 */
 409 static void felem_square(uint128_t out[7], const fslice in[4])
 410         {
 411         out[0] = ((uint128_t) in[0]) * in[0];
 412         out[1] = ((uint128_t) in[0]) * in[1] * 2;
 413         out[2] = ((uint128_t) in[0]) * in[2] * 2 + ((uint128_t) in[1]) * in[1];
 414         out[3] = ((uint128_t) in[0]) * in[3] * 2 +
 415                 ((uint128_t) in[1]) * in[2] * 2;
 416         out[4] = ((uint128_t) in[1]) * in[3] * 2 + ((uint128_t) in[2]) * in[2];
 417         out[5] = ((uint128_t) in[2]) * in[3] * 2;
 418         out[6] = ((uint128_t) in[3]) * in[3];
 419         }
 420
 421 /* Multiply two field elements: out = in1 * in2 */
 422 static void felem_mul(uint128_t out[7], const fslice in1[4], const fslice in2[4])
 423         {
 424         out[0] = ((uint128_t) in1[0]) * in2[0];
 425         out[1] = ((uint128_t) in1[0]) * in2[1] + ((uint128_t) in1[1]) * in2[0];
 426         out[2] = ((uint128_t) in1[0]) * in2[2] + ((uint128_t) in1[1]) * in2[1] +
 427                 ((uint128_t) in1[2]) * in2[0];
 428         out[3] = ((uint128_t) in1[0]) * in2[3] + ((uint128_t) in1[1]) * in2[2] +
 429                 ((uint128_t) in1[2]) * in2[1] + ((uint128_t) in1[3]) * in2[0];
 430         out[4] = ((uint128_t) in1[1]) * in2[3] + ((uint128_t) in1[2]) * in2[2] +
 431                 ((uint128_t) in1[3]) * in2[1];
 432         out[5] = ((uint128_t) in1[2]) * in2[3] + ((uint128_t) in1[3]) * in2[2];
 433         out[6] = ((uint128_t) in1[3]) * in2[3];
 434         }
 435
 436 /* Reduce 128-bit coefficients to 64-bit coefficients. Requires in[i] < 2^126,
 437  * ensures out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] < 2^57 */
 438 static void felem_reduce(fslice out[4], const uint128_t in[7])
 439         {
 440         static const uint128_t two127p15 = (((uint128_t) 1) << 127) +
 441                 (((uint128_t) 1) << 15);
 442         static const uint128_t two127m71 = (((uint128_t) 1) << 127) -
 443                 (((uint128_t) 1) << 71);
 444         static const uint128_t two127m71m55 = (((uint128_t) 1) << 127) -
 445                 (((uint128_t) 1) << 71) - (((uint128_t) 1) << 55);
 446         uint128_t output[5];
 447
 448         /* Add 0 mod 2^224-2^96+1 to ensure all differences are positive */
 449         output[0] = in[0] + two127p15;
 450         output[1] = in[1] + two127m71m55;
 451         output[2] = in[2] + two127m71;
 452         output[3] = in[3];
 453         output[4] = in[4];
 454
 455         /* Eliminate in[4], in[5], in[6] */
 456         output[4] += in[6] >> 16;
 457         output[3] += (in[6]&0xffff) << 40;
 458         output[2] -= in[6];
 459
 460         output[3] += in[5] >> 16;
 461         output[2] += (in[5]&0xffff) << 40;
 462         output[1] -= in[5];
 463
 464         output[2] += output[4] >> 16;
 465         output[1] += (output[4]&0xffff) << 40;
 466         output[0] -= output[4];
 467         output[4] = 0;
 468
 469         /* Carry 2 -> 3 -> 4 */
 470         output[3] += output[2] >> 56;
 471         output[2] &= 0x00ffffffffffffff;
 472
 473         output[4] += output[3] >> 56;
 474         output[3] &= 0x00ffffffffffffff;
 475
 476         /* Now output[2] < 2^56, output[3] < 2^56 */
 477
 478         /* Eliminate output[4] */
 479         output[2] += output[4] >> 16;
 480         output[1] += (output[4]&0xffff) << 40;
 481         output[0] -= output[4];
 482
 483         /* Carry 0 -> 1 -> 2 -> 3 */
 484         output[1] += output[0] >> 56;
 485         out[0] = output[0] & 0x00ffffffffffffff;
 486
 487         output[2] += output[1] >> 56;
 488         out[1] = output[1] & 0x00ffffffffffffff;
 489         output[3] += output[2] >> 56;
 490         out[2] = output[2] & 0x00ffffffffffffff;
 491
 492         /* out[0] < 2^56, out[1] < 2^56, out[2] < 2^56,
 493          * out[3] < 2^57 (due to final carry) */
 494         out[3] = output[3];
 495         }
 496
 497 /* Reduce to unique minimal representation */
 498 static void felem_contract(fslice out[4], const fslice in[4])
 499         {
 500         static const int64_t two56 = ((uint64_t) 1) << 56;
 501         /* 0 <= in < 2^225 */
 502         /* if in > 2^224 , reduce in = in - 2^224 + 2^96 - 1 */
 503         int64_t tmp[4], a;
 504         tmp[0] = (int64_t) in[0] - (in[3] >> 56);
 505         tmp[1] = (int64_t) in[1] + ((in[3] >> 16) & 0x0000010000000000);
 506         tmp[2] = (int64_t) in[2];
 507         tmp[3] = (int64_t) in[3] & 0x00ffffffffffffff;
 508
 509         /* eliminate negative coefficients */
 510         a = tmp[0] >> 63;
 511         tmp[0] += two56 & a;
 512         tmp[1] -= 1 & a;
 513
 514         a = tmp[1] >> 63;
 515         tmp[1] += two56 & a;
 516         tmp[2] -= 1 & a;
 517
 518         a = tmp[2] >> 63;
 519         tmp[2] += two56 & a;
 520         tmp[3] -= 1 & a;
 521
 522         a = tmp[3] >> 63;
 523         tmp[3] += two56 & a;
 524         tmp[0] += 1 & a;
 525         tmp[1] -= (1 & a) << 40;
 526
 527         /* carry 1 -> 2 -> 3 */
 528         tmp[2] += tmp[1] >> 56;
 529         tmp[1] &= 0x00ffffffffffffff;
 530
 531         tmp[3] += tmp[2] >> 56;
 532         tmp[2] &= 0x00ffffffffffffff;
 533
 534         /* 0 <= in < 2^224 + 2^96 - 1 */
 535         /* if in > 2^224 , reduce in = in - 2^224 + 2^96 - 1 */
 536         tmp[0] -= (tmp[3] >> 56);
 537         tmp[1] += ((tmp[3] >> 16) & 0x0000010000000000);
 538         tmp[3] &= 0x00ffffffffffffff;
 539
 540         /* eliminate negative coefficients */
 541         a = tmp[0] >> 63;
 542         tmp[0] += two56 & a;
 543         tmp[1] -= 1 & a;
 544
 545         a = tmp[1] >> 63;
 546         tmp[1] += two56 & a;
 547         tmp[2] -= 1 & a;
 548
 549         a = tmp[2] >> 63;
 550         tmp[2] += two56 & a;
 551         tmp[3] -= 1 & a;
 552
 553         a = tmp[3] >> 63;
 554         tmp[3] += two56 & a;
 555         tmp[0] += 1 & a;
 556         tmp[1] -= (1 & a) << 40;
 557
 558         /* carry 1 -> 2 -> 3 */
 559         tmp[2] += tmp[1] >> 56;
 560         tmp[1] &= 0x00ffffffffffffff;
 561
 562         tmp[3] += tmp[2] >> 56;
 563         tmp[2] &= 0x00ffffffffffffff;
 564
 565         /* Now 0 <= in < 2^224 */
 566
 567         /* if in > 2^224 - 2^96, reduce */
 568         /* a = 0 iff in > 2^224 - 2^96, i.e.,
 569          * the high 128 bits are all 1 and the lower part is non-zero */
 570         a = (tmp[3] + 1) | (tmp[2] + 1) |
 571                 ((tmp[1] | 0x000000ffffffffff) + 1) |
 572                 ((((tmp[1] & 0xffff) - 1) >> 63) & ((tmp[0] - 1) >> 63));
 573         /* turn a into an all-one mask (if a = 0) or an all-zero mask */
 574         a = ((a & 0x00ffffffffffffff) - 1) >> 63;
 575         /* subtract 2^224 - 2^96 + 1 if a is all-one*/
 576         tmp[3] &= a ^ 0xffffffffffffffff;
 577         tmp[2] &= a ^ 0xffffffffffffffff;
 578         tmp[1] &= (a ^ 0xffffffffffffffff) | 0x000000ffffffffff;
 579         tmp[0] -= 1 & a;
 580         /* eliminate negative coefficients: if tmp[0] is negative, tmp[1] must be
 581          * non-zero, so we only need one step */
 582         a = tmp[0] >> 63;
 583         tmp[0] += two56 & a;
 584         tmp[1] -= 1 & a;
 585
 586         out[0] = tmp[0];
 587         out[1] = tmp[1];
 588         out[2] = tmp[2];
 589         out[3] = tmp[3];
 590         }
 591
 592 /* Zero-check: returns 1 if input is 0, and 0 otherwise.
 593  * We know that field elements are reduced to in < 2^225,
 594  * so we only need to check three cases: 0, 2^224 - 2^96 + 1,
 595  * and 2^225 - 2^97 + 2 */
 596 static fslice felem_is_zero(const fslice in[4])
 597         {
 598         fslice zero, two224m96p1, two225m97p2;
 599
 600         zero = in[0] | in[1] | in[2] | in[3];
 601         zero = (((int64_t)(zero) - 1) >> 63) & 1;
 602         two224m96p1 = (in[0] ^ 1) | (in[1] ^ 0x00ffff0000000000)
 603                 | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x00ffffffffffffff);
 604         two224m96p1 = (((int64_t)(two224m96p1) - 1) >> 63) & 1;
 605         two225m97p2 = (in[0] ^ 2) | (in[1] ^ 0x00fffe0000000000)
 606                 | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x01ffffffffffffff);
 607         two225m97p2 = (((int64_t)(two225m97p2) - 1) >> 63) & 1;
 608         return (zero | two224m96p1 | two225m97p2);
 609         }
 610
 611 /* Invert a field element */
 612 /* Computation chain copied from djb's code */
 613 static void felem_inv(fslice out[4], const fslice in[4])
 614         {
 615         fslice ftmp[4], ftmp2[4], ftmp3[4], ftmp4[4];
 616         uint128_t tmp[7];
 617         unsigned i;
 618
 619         felem_square(tmp, in); felem_reduce(ftmp, tmp);         /* 2 */
 620         felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp);      /* 2^2 - 1 */
 621         felem_square(tmp, ftmp); felem_reduce(ftmp, tmp);       /* 2^3 - 2 */
 622         felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp);      /* 2^3 - 1 */
 623         felem_square(tmp, ftmp); felem_reduce(ftmp2, tmp);      /* 2^4 - 2 */
 624         felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp);     /* 2^5 - 4 */
 625         felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp);     /* 2^6 - 8 */
 626         felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp, tmp);   /* 2^6 - 1 */
 627         felem_square(tmp, ftmp); felem_reduce(ftmp2, tmp);      /* 2^7 - 2 */
 628         for (i = 0; i < 5; ++i)                                 /* 2^12 - 2^6 */
 629                 {
 630                 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp);
 631                 }
 632         felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp2, tmp);  /* 2^12 - 1 */
 633         felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp);     /* 2^13 - 2 */
 634         for (i = 0; i < 11; ++i)                                /* 2^24 - 2^12 */
 635                 {
 636                 felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp);
 637                 }
 638         felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp2, tmp); /* 2^24 - 1 */
 639         felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp);     /* 2^25 - 2 */
 640         for (i = 0; i < 23; ++i)                                /* 2^48 - 2^24 */
 641                 {
 642                 felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp);
 643                 }
 644         felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^48 - 1 */
 645         felem_square(tmp, ftmp3); felem_reduce(ftmp4, tmp);     /* 2^49 - 2 */
 646         for (i = 0; i < 47; ++i)                                /* 2^96 - 2^48 */
 647                 {
 648                 felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp);
 649                 }
 650         felem_mul(tmp, ftmp3, ftmp4); felem_reduce(ftmp3, tmp); /* 2^96 - 1 */
 651         felem_square(tmp, ftmp3); felem_reduce(ftmp4, tmp);     /* 2^97 - 2 */
 652         for (i = 0; i < 23; ++i)                                /* 2^120 - 2^24 */
 653                 {
 654                 felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp);
 655                 }
 656         felem_mul(tmp, ftmp2, ftmp4); felem_reduce(ftmp2, tmp); /* 2^120 - 1 */
 657         for (i = 0; i < 6; ++i)                                 /* 2^126 - 2^6 */
 658                 {
 659                 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp);
 660                 }
 661         felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp, tmp);   /* 2^126 - 1 */
 662         felem_square(tmp, ftmp); felem_reduce(ftmp, tmp);       /* 2^127 - 2 */
 663         felem_mul(tmp, ftmp, in); felem_reduce(ftmp, tmp);      /* 2^127 - 1 */
 664         for (i = 0; i < 97; ++i)                                /* 2^224 - 2^97 */
 665                 {
 666                 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp);
 667                 }
 668         felem_mul(tmp, ftmp, ftmp3); felem_reduce(out, tmp);    /* 2^224 - 2^96 - 1 */
 669         }
 670
 671 /* Copy in constant time:
 672  * if icopy == 1, copy in to out,
 673  * if icopy == 0, copy out to itself. */
 674 static void
 675 copy_conditional(fslice *out, const fslice *in, unsigned len, fslice icopy)
 676         {
 677         unsigned i;
 678         /* icopy is a (64-bit) 0 or 1, so copy is either all-zero or all-one */
 679         const fslice copy = -icopy;
 680         for (i = 0; i < len; ++i)
 681                 {
 682                 const fslice tmp = copy & (in[i] ^ out[i]);
 683                 out[i] ^= tmp;
 684                 }
 685         }
 686
 687 /* Copy in constant time:
 688  * if isel == 1, copy in2 to out,
 689  * if isel == 0, copy in1 to out. */
 690 static void select_conditional(fslice *out, const fslice *in1, const fslice *in2,
 691         unsigned len, fslice isel)
 692         {
 693         unsigned i;
 694         /* isel is a (64-bit) 0 or 1, so sel is either all-zero or all-one */
 695         const fslice sel = -isel;
 696         for (i = 0; i < len; ++i)
 697                 {
 698                 const fslice tmp = sel & (in1[i] ^ in2[i]);
 699                 out[i] = in1[i] ^ tmp;
 700                 }
 701 }
 702
 703 /******************************************************************************/
 704 /*                       ELLIPTIC CURVE POINT OPERATIONS
 705  *
 706  * Points are represented in Jacobian projective coordinates:
 707  * (X, Y, Z) corresponds to the affine point (X/Z^2, Y/Z^3),
 708  * or to the point at infinity if Z == 0.
 709  *
 710  */
 711
 712 /* Double an elliptic curve point:
 713  * (X', Y', Z') = 2 * (X, Y, Z), where
 714  * X' = (3 * (X - Z^2) * (X + Z^2))^2 - 8 * X * Y^2
 715  * Y' = 3 * (X - Z^2) * (X + Z^2) * (4 * X * Y^2 - X') - 8 * Y^2
 716  * Z' = (Y + Z)^2 - Y^2 - Z^2 = 2 * Y * Z
 717  * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed,
 718  * while x_out == y_in is not (maybe this works, but it's not tested). */
 719 static void
 720 point_double(fslice x_out[4], fslice y_out[4], fslice z_out[4],
 721              const fslice x_in[4], const fslice y_in[4], const fslice z_in[4])
 722         {
 723         uint128_t tmp[7], tmp2[7];
 724         fslice delta[4];
 725         fslice gamma[4];
 726         fslice beta[4];
 727         fslice alpha[4];
 728         fslice ftmp[4], ftmp2[4];
 729         memcpy(ftmp, x_in, 4 * sizeof(fslice));
 730         memcpy(ftmp2, x_in, 4 * sizeof(fslice));
 731
 732         /* delta = z^2 */
 733         felem_square(tmp, z_in);
 734         felem_reduce(delta, tmp);
 735
 736         /* gamma = y^2 */
 737         felem_square(tmp, y_in);
 738         felem_reduce(gamma, tmp);
 739
 740         /* beta = x*gamma */
 741         felem_mul(tmp, x_in, gamma);
 742         felem_reduce(beta, tmp);
 743
 744         /* alpha = 3*(x-delta)*(x+delta) */
 745         felem_diff64(ftmp, delta);
 746         /* ftmp[i] < 2^57 + 2^58 + 2 < 2^59 */
 747         felem_sum64(ftmp2, delta);
 748         /* ftmp2[i] < 2^57 + 2^57 = 2^58 */
 749         felem_scalar64(ftmp2, 3);
 750         /* ftmp2[i] < 3 * 2^58 < 2^60 */
 751         felem_mul(tmp, ftmp, ftmp2);
 752         /* tmp[i] < 2^60 * 2^59 * 4 = 2^121 */
 753         felem_reduce(alpha, tmp);
 754
 755         /* x' = alpha^2 - 8*beta */
 756         felem_square(tmp, alpha);
 757         /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
 758         memcpy(ftmp, beta, 4 * sizeof(fslice));
 759         felem_scalar64(ftmp, 8);
 760         /* ftmp[i] < 8 * 2^57 = 2^60 */
 761         felem_diff_128_64(tmp, ftmp);
 762         /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */
 763         felem_reduce(x_out, tmp);
 764
 765         /* z' = (y + z)^2 - gamma - delta */
 766         felem_sum64(delta, gamma);
 767         /* delta[i] < 2^57 + 2^57 = 2^58 */
 768         memcpy(ftmp, y_in, 4 * sizeof(fslice));
 769         felem_sum64(ftmp, z_in);
 770         /* ftmp[i] < 2^57 + 2^57 = 2^58 */
 771         felem_square(tmp, ftmp);
 772         /* tmp[i] < 4 * 2^58 * 2^58 = 2^118 */
 773         felem_diff_128_64(tmp, delta);
 774         /* tmp[i] < 2^118 + 2^64 + 8 < 2^119 */
 775         felem_reduce(z_out, tmp);
 776
 777         /* y' = alpha*(4*beta - x') - 8*gamma^2 */
 778         felem_scalar64(beta, 4);
 779         /* beta[i] < 4 * 2^57 = 2^59 */
 780         felem_diff64(beta, x_out);
 781         /* beta[i] < 2^59 + 2^58 + 2 < 2^60 */
 782         felem_mul(tmp, alpha, beta);
 783         /* tmp[i] < 4 * 2^57 * 2^60 = 2^119 */
 784         felem_square(tmp2, gamma);
 785         /* tmp2[i] < 4 * 2^57 * 2^57 = 2^116 */
 786         felem_scalar128(tmp2, 8);
 787         /* tmp2[i] < 8 * 2^116 = 2^119 */
 788         felem_diff128(tmp, tmp2);
 789         /* tmp[i] < 2^119 + 2^120 < 2^121 */
 790         felem_reduce(y_out, tmp);
 791         }
 792
 793 /* Add two elliptic curve points:
 794  * (X_1, Y_1, Z_1) + (X_2, Y_2, Z_2) = (X_3, Y_3, Z_3), where
 795  * X_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1)^2 - (Z_1^2 * X_2 - Z_2^2 * X_1)^3 -
 796  * 2 * Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^2
 797  * 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) -
 798  *        Z_2^3 * Y_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^3
 799  * Z_3 = (Z_1^2 * X_2 - Z_2^2 * X_1) * (Z_1 * Z_2) */
 800
 801 /* This function is not entirely constant-time:
 802  * it includes a branch for checking whether the two input points are equal,
 803  * (while not equal to the point at infinity).
 804  * This case never happens during single point multiplication,
 805  * so there is no timing leak for ECDH or ECDSA signing. */
 806 static void point_add(fslice x3[4], fslice y3[4], fslice z3[4],
 807         const fslice x1[4], const fslice y1[4], const fslice z1[4],
 808         const fslice x2[4], const fslice y2[4], const fslice z2[4])
 809         {
 810         fslice ftmp[4], ftmp2[4], ftmp3[4], ftmp4[4], ftmp5[4];
 811         uint128_t tmp[7], tmp2[7];
 812         fslice z1_is_zero, z2_is_zero, x_equal, y_equal;
 813
 814         /* ftmp = z1^2 */
 815         felem_square(tmp, z1);
 816         felem_reduce(ftmp, tmp);
 817
 818         /* ftmp2 = z2^2 */
 819         felem_square(tmp, z2);
 820         felem_reduce(ftmp2, tmp);
 821
 822         /* ftmp3 = z1^3 */
 823         felem_mul(tmp, ftmp, z1);
 824         felem_reduce(ftmp3, tmp);
 825
 826         /* ftmp4 = z2^3 */
 827         felem_mul(tmp, ftmp2, z2);
 828         felem_reduce(ftmp4, tmp);
 829
 830         /* ftmp3 = z1^3*y2 */
 831         felem_mul(tmp, ftmp3, y2);
 832         /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
 833
 834         /* ftmp4 = z2^3*y1 */
 835         felem_mul(tmp2, ftmp4, y1);
 836         felem_reduce(ftmp4, tmp2);
 837
 838         /* ftmp3 = z1^3*y2 - z2^3*y1 */
 839         felem_diff_128_64(tmp, ftmp4);
 840         /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */
 841         felem_reduce(ftmp3, tmp);
 842
 843         /* ftmp = z1^2*x2 */
 844         felem_mul(tmp, ftmp, x2);
 845         /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
 846
 847         /* ftmp2 =z2^2*x1 */
 848         felem_mul(tmp2, ftmp2, x1);
 849         felem_reduce(ftmp2, tmp2);
 850
 851         /* ftmp = z1^2*x2 - z2^2*x1 */
 852         felem_diff128(tmp, tmp2);
 853         /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */
 854         felem_reduce(ftmp, tmp);
 855
 856         /* the formulae are incorrect if the points are equal
 857          * so we check for this and do doubling if this happens */
 858         x_equal = felem_is_zero(ftmp);
 859         y_equal = felem_is_zero(ftmp3);
 860         z1_is_zero = felem_is_zero(z1);
 861         z2_is_zero = felem_is_zero(z2);
 862         /* In affine coordinates, (X_1, Y_1) == (X_2, Y_2) */
 863         if (x_equal && y_equal && !z1_is_zero && !z2_is_zero)
 864                 {
 865                 point_double(x3, y3, z3, x1, y1, z1);
 866                 return;
 867                 }
 868
 869         /* ftmp5 = z1*z2 */
 870         felem_mul(tmp, z1, z2);
 871         felem_reduce(ftmp5, tmp);
 872
 873         /* z3 = (z1^2*x2 - z2^2*x1)*(z1*z2) */
 874         felem_mul(tmp, ftmp, ftmp5);
 875         felem_reduce(z3, tmp);
 876
 877         /* ftmp = (z1^2*x2 - z2^2*x1)^2 */
 878         memcpy(ftmp5, ftmp, 4 * sizeof(fslice));
 879         felem_square(tmp, ftmp);
 880         felem_reduce(ftmp, tmp);
 881
 882         /* ftmp5 = (z1^2*x2 - z2^2*x1)^3 */
 883         felem_mul(tmp, ftmp, ftmp5);
 884         felem_reduce(ftmp5, tmp);
 885
 886         /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */
 887         felem_mul(tmp, ftmp2, ftmp);
 888         felem_reduce(ftmp2, tmp);
 889
 890         /* ftmp4 = z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */
 891         felem_mul(tmp, ftmp4, ftmp5);
 892         /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
 893
 894         /* tmp2 = (z1^3*y2 - z2^3*y1)^2 */
 895         felem_square(tmp2, ftmp3);
 896         /* tmp2[i] < 4 * 2^57 * 2^57 < 2^116 */
 897
 898         /* tmp2 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 */
 899         felem_diff_128_64(tmp2, ftmp5);
 900         /* tmp2[i] < 2^116 + 2^64 + 8 < 2^117 */
 901
 902         /* ftmp5 = 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */
 903         memcpy(ftmp5, ftmp2, 4 * sizeof(fslice));
 904         felem_scalar64(ftmp5, 2);
 905         /* ftmp5[i] < 2 * 2^57 = 2^58 */
 906
 907         /* x3 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 -
 908            2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */
 909         felem_diff_128_64(tmp2, ftmp5);
 910         /* tmp2[i] < 2^117 + 2^64 + 8 < 2^118 */
 911         felem_reduce(x3, tmp2);
 912
 913         /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x3 */
 914         felem_diff64(ftmp2, x3);
 915         /* ftmp2[i] < 2^57 + 2^58 + 2 < 2^59 */
 916
 917         /* tmp2 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x3) */
 918         felem_mul(tmp2, ftmp3, ftmp2);
 919         /* tmp2[i] < 4 * 2^57 * 2^59 = 2^118 */
 920
 921         /* y3 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x3) -
 922            z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */
 923         felem_diff128(tmp2, tmp);
 924         /* tmp2[i] < 2^118 + 2^120 < 2^121 */
 925         felem_reduce(y3, tmp2);
 926
 927         /* the result (x3, y3, z3) is incorrect if one of the inputs is the
 928          * point at infinity, so we need to check for this separately */
 929
 930         /* if point 1 is at infinity, copy point 2 to output, and vice versa */
 931         copy_conditional(x3, x2, 4, z1_is_zero);
 932         copy_conditional(x3, x1, 4, z2_is_zero);
 933         copy_conditional(y3, y2, 4, z1_is_zero);
 934         copy_conditional(y3, y1, 4, z2_is_zero);
 935         copy_conditional(z3, z2, 4, z1_is_zero);
 936         copy_conditional(z3, z1, 4, z2_is_zero);
 937         }
 938
 939 /* Select a point from an array of 16 precomputed point multiples,
 940  * in constant time: for bits = {b_0, b_1, b_2, b_3}, return the point
 941  * pre_comp[8*b_3 + 4*b_2 + 2*b_1 + b_0] */
 942 static void select_point(const fslice bits[4], const fslice pre_comp[16][3][4],
 943         fslice out[12])
 944         {
 945         fslice tmp[5][12];
 946         select_conditional(tmp[0], pre_comp[7][0], pre_comp[15][0], 12, bits[3]);
 947         select_conditional(tmp[1], pre_comp[3][0], pre_comp[11][0], 12, bits[3]);
 948         select_conditional(tmp[2], tmp[1], tmp[0], 12, bits[2]);
 949         select_conditional(tmp[0], pre_comp[5][0], pre_comp[13][0], 12, bits[3]);
 950         select_conditional(tmp[1], pre_comp[1][0], pre_comp[9][0], 12, bits[3]);
 951         select_conditional(tmp[3], tmp[1], tmp[0], 12, bits[2]);
 952         select_conditional(tmp[4], tmp[3], tmp[2], 12, bits[1]);
 953         select_conditional(tmp[0], pre_comp[6][0], pre_comp[14][0], 12, bits[3]);
 954         select_conditional(tmp[1], pre_comp[2][0], pre_comp[10][0], 12, bits[3]);
 955         select_conditional(tmp[2], tmp[1], tmp[0], 12, bits[2]);
 956         select_conditional(tmp[0], pre_comp[4][0], pre_comp[12][0], 12, bits[3]);
 957         select_conditional(tmp[1], pre_comp[0][0], pre_comp[8][0], 12, bits[3]);
 958         select_conditional(tmp[3], tmp[1], tmp[0], 12, bits[2]);
 959         select_conditional(tmp[1], tmp[3], tmp[2], 12, bits[1]);
 960         select_conditional(out, tmp[1], tmp[4], 12, bits[0]);
 961         }
 962
 963 /* Interleaved point multiplication using precomputed point multiples:
 964  * The small point multiples 0*P, 1*P, ..., 15*P are in pre_comp[],
 965  * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple
 966  * of the generator, using certain (large) precomputed multiples in g_pre_comp.
 967  * Output point (X, Y, Z) is stored in x_out, y_out, z_out */
 968 static void batch_mul(fslice x_out[4], fslice y_out[4], fslice z_out[4],
 969         const felem_bytearray scalars[], const unsigned num_points, const u8 *g_scalar,
 970         const fslice pre_comp[][16][3][4], const fslice g_pre_comp[16][3][4])
 971         {
 972         unsigned i, j, num;
 973         unsigned gen_mul = (g_scalar != NULL);
 974         fslice nq[12], nqt[12], tmp[12];
 975         fslice bits[4];
 976         u8 byte;
 977
 978         /* set nq to the point at infinity */
 979         memset(nq, 0, 12 * sizeof(fslice));
 980
 981         /* Loop over all scalars msb-to-lsb, 4 bits at a time: for each nibble,
 982          * double 4 times, then add the precomputed point multiples.
 983          * If we are also adding multiples of the generator, then interleave
 984          * these additions with the last 56 doublings. */
 985         for (i = (num_points ? 28 : 7); i > 0; --i)
 986                 {
 987                 for (j = 0; j < 8; ++j)
 988                         {
 989                         /* double once */
 990                         point_double(nq, nq+4, nq+8, nq, nq+4, nq+8);
 991                         /* add multiples of the generator */
 992                         if ((gen_mul) && (i <= 7))
 993                                 {
 994                                 bits[3] = (g_scalar[i+20] >> (7-j)) & 1;
 995                                 bits[2] = (g_scalar[i+13] >> (7-j)) & 1;
 996                                 bits[1] = (g_scalar[i+6] >> (7-j)) & 1;
 997                                 bits[0] = (g_scalar[i-1] >> (7-j)) & 1;
 998                                 /* select the point to add, in constant time */
 999                                 select_point(bits, g_pre_comp, tmp);
1000                                 memcpy(nqt, nq, 12 * sizeof(fslice));
1001                                 point_add(nq, nq+4, nq+8, nqt, nqt+4, nqt+8,
1002                                         tmp, tmp+4, tmp+8);
1003                                 }
1004                         /* do an addition after every 4 doublings */
1005                         if (j % 4 == 3)
1006                                 {
1007                                 /* loop over all scalars */
1008                                 for (num = 0; num < num_points; ++num)
1009                                         {
1010                                         byte = scalars[num][i-1];
1011                                         bits[3] = (byte >> (10-j)) & 1;
1012                                         bits[2] = (byte >> (9-j)) & 1;
1013                                         bits[1] = (byte >> (8-j)) & 1;
1014                                         bits[0] = (byte >> (7-j)) & 1;
1015                                         /* select the point to add */
1016                                         select_point(bits,
1017                                                 pre_comp[num], tmp);
1018                                         memcpy(nqt, nq, 12 * sizeof(fslice));
1019                                         point_add(nq, nq+4, nq+8, nqt, nqt+4,
1020                                                 nqt+8, tmp, tmp+4, tmp+8);
1021                                         }
1022                                 }
1023                         }
1024                 }
1025         memcpy(x_out, nq, 4 * sizeof(fslice));
1026         memcpy(y_out, nq+4, 4 * sizeof(fslice));
1027         memcpy(z_out, nq+8, 4 * sizeof(fslice));
1028         }
1029
1030 /******************************************************************************/
1031 /*                     FUNCTIONS TO MANAGE PRECOMPUTATION
1032  */
1033
1034 static NISTP224_PRE_COMP *nistp224_pre_comp_new()
1035         {
1036         NISTP224_PRE_COMP *ret = NULL;
1037         ret = (NISTP224_PRE_COMP *)OPENSSL_malloc(sizeof(NISTP224_PRE_COMP));
1038         if (!ret)
1039                 {
1040                 ECerr(EC_F_NISTP224_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
1041                 return ret;
1042                 }
1043         memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp));
1044         ret->references = 1;
1045         return ret;
1046         }
1047
1048 static void *nistp224_pre_comp_dup(void *src_)
1049         {
1050         NISTP224_PRE_COMP *src = src_;
1051
1052         /* no need to actually copy, these objects never change! */
1053         CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
1054
1055         return src_;
1056         }
1057
1058 static void nistp224_pre_comp_free(void *pre_)
1059         {
1060         int i;
1061         NISTP224_PRE_COMP *pre = pre_;
1062
1063         if (!pre)
1064                 return;
1065
1066         i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1067         if (i > 0)
1068                 return;
1069
1070         OPENSSL_free(pre);
1071         }
1072
1073 static void nistp224_pre_comp_clear_free(void *pre_)
1074         {
1075         int i;
1076         NISTP224_PRE_COMP *pre = pre_;
1077
1078         if (!pre)
1079                 return;
1080
1081         i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1082         if (i > 0)
1083                 return;
1084
1085         OPENSSL_cleanse(pre, sizeof *pre);
1086         OPENSSL_free(pre);
1087         }
1088
1089 /******************************************************************************/
1090 /*                         OPENSSL EC_METHOD FUNCTIONS
1091  */
1092
1093 int ec_GFp_nistp224_group_init(EC_GROUP *group)
1094         {
1095         int ret;
1096         ret = ec_GFp_simple_group_init(group);
1097         group->a_is_minus3 = 1;
1098         return ret;
1099         }
1100
1101 int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p,
1102         const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1103         {
1104         int ret = 0;
1105         BN_CTX *new_ctx = NULL;
1106         BIGNUM *curve_p, *curve_a, *curve_b;
1107
1108         if (ctx == NULL)
1109                 if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0;
1110         BN_CTX_start(ctx);
1111         if (((curve_p = BN_CTX_get(ctx)) == NULL) ||
1112                 ((curve_a = BN_CTX_get(ctx)) == NULL) ||
1113                 ((curve_b = BN_CTX_get(ctx)) == NULL)) goto err;
1114         BN_bin2bn(nistp224_curve_params[0], sizeof(felem_bytearray), curve_p);
1115         BN_bin2bn(nistp224_curve_params[1], sizeof(felem_bytearray), curve_a);
1116         BN_bin2bn(nistp224_curve_params[2], sizeof(felem_bytearray), curve_b);
1117         if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) ||
1118                 (BN_cmp(curve_b, b)))
1119                 {
1120                 ECerr(EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE,
1121                         EC_R_WRONG_CURVE_PARAMETERS);
1122                 goto err;
1123                 }
1124         group->field_mod_func = BN_nist_mod_224;
1125         ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx);
1126 err:
1127         BN_CTX_end(ctx);
1128         if (new_ctx != NULL)
1129                 BN_CTX_free(new_ctx);
1130         return ret;
1131         }
1132
1133 /* Takes the Jacobian coordinates (X, Y, Z) of a point and returns
1134  * (X', Y') = (X/Z^2, Y/Z^3) */
1135 int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group,
1136         const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
1137         {
1138         fslice z1[4], z2[4], x_in[4], y_in[4], x_out[4], y_out[4];
1139         uint128_t tmp[7];
1140
1141         if (EC_POINT_is_at_infinity(group, point))
1142                 {
1143                 ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES,
1144                         EC_R_POINT_AT_INFINITY);
1145                 return 0;
1146                 }
1147         if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) ||
1148                 (!BN_to_felem(z1, &point->Z))) return 0;
1149         felem_inv(z2, z1);
1150         felem_square(tmp, z2); felem_reduce(z1, tmp);
1151         felem_mul(tmp, x_in, z1); felem_reduce(x_in, tmp);
1152         felem_contract(x_out, x_in);
1153         if (x != NULL)
1154                 {
1155                 if (!felem_to_BN(x, x_out)) {
1156                 ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES,
1157                         ERR_R_BN_LIB);
1158                 return 0;
1159                 }
1160                 }
1161         felem_mul(tmp, z1, z2); felem_reduce(z1, tmp);
1162         felem_mul(tmp, y_in, z1); felem_reduce(y_in, tmp);
1163         felem_contract(y_out, y_in);
1164         if (y != NULL)
1165                 {
1166                 if (!felem_to_BN(y, y_out)) {
1167                 ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES,
1168                         ERR_R_BN_LIB);
1169                 return 0;
1170                 }
1171                 }
1172         return 1;
1173         }
1174
1175 /* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values
1176  * Result is stored in r (r can equal one of the inputs). */
1177 int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r,
1178         const BIGNUM *scalar, size_t num, const EC_POINT *points[],
1179         const BIGNUM *scalars[], BN_CTX *ctx)
1180         {
1181         int ret = 0;
1182         int i, j;
1183         BN_CTX *new_ctx = NULL;
1184         BIGNUM *x, *y, *z, *tmp_scalar;
1185         felem_bytearray g_secret;
1186         felem_bytearray *secrets = NULL;
1187         fslice (*pre_comp)[16][3][4] = NULL;
1188         felem_bytearray tmp;
1189         unsigned num_bytes;
1190         int have_pre_comp = 0;
1191         size_t num_points = num;
1192         fslice x_in[4], y_in[4], z_in[4], x_out[4], y_out[4], z_out[4];
1193         NISTP224_PRE_COMP *pre = NULL;
1194         fslice (*g_pre_comp)[3][4] = NULL;
1195         EC_POINT *generator = NULL;
1196         const EC_POINT *p = NULL;
1197         const BIGNUM *p_scalar = NULL;
1198
1199         if (ctx == NULL)
1200                 if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0;
1201         BN_CTX_start(ctx);
1202         if (((x = BN_CTX_get(ctx)) == NULL) ||
1203                 ((y = BN_CTX_get(ctx)) == NULL) ||
1204                 ((z = BN_CTX_get(ctx)) == NULL) ||
1205                 ((tmp_scalar = BN_CTX_get(ctx)) == NULL))
1206                 goto err;
1207
1208         if (scalar != NULL)
1209                 {
1210                 pre = EC_EX_DATA_get_data(group->extra_data,
1211                         nistp224_pre_comp_dup, nistp224_pre_comp_free,
1212                         nistp224_pre_comp_clear_free);
1213                 if (pre)
1214                         /* we have precomputation, try to use it */
1215                         g_pre_comp = pre->g_pre_comp;
1216                 else
1217                         /* try to use the standard precomputation */
1218                         g_pre_comp = (fslice (*)[3][4]) gmul;
1219                 generator = EC_POINT_new(group);
1220                 if (generator == NULL)
1221                         goto err;
1222                 /* get the generator from precomputation */
1223                 if (!felem_to_BN(x, g_pre_comp[1][0]) ||
1224                         !felem_to_BN(y, g_pre_comp[1][1]) ||
1225                         !felem_to_BN(z, g_pre_comp[1][2]))
1226                         {
1227                         ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB);
1228                         goto err;
1229                         }
1230                 if (!EC_POINT_set_Jprojective_coordinates_GFp(group,
1231                                 generator, x, y, z, ctx))
1232                         goto err;
1233                 if (0 == EC_POINT_cmp(group, generator, group->generator, ctx))
1234                         /* precomputation matches generator */
1235                         have_pre_comp = 1;
1236                 else
1237                         /* we don't have valid precomputation:
1238                          * treat the generator as a random point */
1239                         num_points = num_points + 1;
1240                 }
1241         secrets = OPENSSL_malloc(num_points * sizeof(felem_bytearray));
1242         pre_comp = OPENSSL_malloc(num_points * 16 * 3 * 4 * sizeof(fslice));
1243
1244         if ((num_points) && ((secrets == NULL) || (pre_comp == NULL)))
1245                 {
1246                 ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1247                 goto err;
1248                 }
1249
1250         /* we treat NULL scalars as 0, and NULL points as points at infinity,
1251          * i.e., they contribute nothing to the linear combination */
1252         memset(secrets, 0, num_points * sizeof(felem_bytearray));
1253         memset(pre_comp, 0, num_points * 16 * 3 * 4 * sizeof(fslice));
1254         for (i = 0; i < num_points; ++i)
1255                 {
1256                 if (i == num)
1257                         /* the generator */
1258                         {
1259                         p = EC_GROUP_get0_generator(group);
1260                         p_scalar = scalar;
1261                         }
1262                 else
1263                         /* the i^th point */
1264                         {
1265                         p = points[i];
1266                         p_scalar = scalars[i];
1267                         }
1268                 if ((p_scalar != NULL) && (p != NULL))
1269                         {
1270                         num_bytes = BN_num_bytes(p_scalar);
1271                         /* reduce scalar to 0 <= scalar < 2^224 */
1272                         if ((num_bytes > sizeof(felem_bytearray)) || (BN_is_negative(p_scalar)))
1273                                 {
1274                                 /* this is an unusual input, and we don't guarantee
1275                                  * constant-timeness */
1276                                 if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx))
1277                                         {
1278                                         ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB);
1279                                         goto err;
1280                                         }
1281                                 num_bytes = BN_bn2bin(tmp_scalar, tmp);
1282                                 }
1283                         else
1284                                 BN_bn2bin(p_scalar, tmp);
1285                         flip_endian(secrets[i], tmp, num_bytes);
1286                         /* precompute multiples */
1287                         if ((!BN_to_felem(x_out, &p->X)) ||
1288                                 (!BN_to_felem(y_out, &p->Y)) ||
1289                                 (!BN_to_felem(z_out, &p->Z))) goto err;
1290                         memcpy(pre_comp[i][1][0], x_out, 4 * sizeof(fslice));
1291                         memcpy(pre_comp[i][1][1], y_out, 4 * sizeof(fslice));
1292                         memcpy(pre_comp[i][1][2], z_out, 4 * sizeof(fslice));
1293                         for (j = 1; j < 8; ++j)
1294                                 {
1295                                 point_double(pre_comp[i][2*j][0],
1296                                         pre_comp[i][2*j][1],
1297                                         pre_comp[i][2*j][2],
1298                                         pre_comp[i][j][0],
1299                                         pre_comp[i][j][1],
1300                                         pre_comp[i][j][2]);
1301                                 point_add(pre_comp[i][2*j+1][0],
1302                                         pre_comp[i][2*j+1][1],
1303                                         pre_comp[i][2*j+1][2],
1304                                         pre_comp[i][1][0],
1305                                         pre_comp[i][1][1],
1306                                         pre_comp[i][1][2],
1307                                         pre_comp[i][2*j][0],
1308                                         pre_comp[i][2*j][1],
1309                                         pre_comp[i][2*j][2]);
1310                                 }
1311                         }
1312                 }
1313
1314         /* the scalar for the generator */
1315         if ((scalar != NULL) && (have_pre_comp))
1316                 {
1317                 memset(g_secret, 0, sizeof g_secret);
1318                 num_bytes = BN_num_bytes(scalar);
1319                 /* reduce scalar to 0 <= scalar < 2^224 */
1320                 if ((num_bytes > sizeof(felem_bytearray)) || (BN_is_negative(scalar)))
1321                         {
1322                         /* this is an unusual input, and we don't guarantee
1323                          * constant-timeness */
1324                         if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx))
1325                                 {
1326                                 ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB);
1327                                 goto err;
1328                                 }
1329                         num_bytes = BN_bn2bin(tmp_scalar, tmp);
1330                         }
1331                 else
1332                         BN_bn2bin(scalar, tmp);
1333                 flip_endian(g_secret, tmp, num_bytes);
1334                 /* do the multiplication with generator precomputation*/
1335                 batch_mul(x_out, y_out, z_out,
1336                         (const felem_bytearray (*)) secrets, num_points,
1337                         g_secret, (const fslice (*)[16][3][4]) pre_comp,
1338                         (const fslice (*)[3][4]) g_pre_comp);
1339                 }
1340         else
1341                 /* do the multiplication without generator precomputation */
1342                 batch_mul(x_out, y_out, z_out,
1343                         (const felem_bytearray (*)) secrets, num_points,
1344                         NULL, (const fslice (*)[16][3][4]) pre_comp, NULL);
1345         /* reduce the output to its unique minimal representation */
1346         felem_contract(x_in, x_out);
1347         felem_contract(y_in, y_out);
1348         felem_contract(z_in, z_out);
1349         if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) ||
1350                 (!felem_to_BN(z, z_in)))
1351                 {
1352                 ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB);
1353                 goto err;
1354                 }
1355         ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx);
1356
1357 err:
1358         BN_CTX_end(ctx);
1359         if (generator != NULL)
1360                 EC_POINT_free(generator);
1361         if (new_ctx != NULL)
1362                 BN_CTX_free(new_ctx);
1363         if (secrets != NULL)
1364                 OPENSSL_free(secrets);
1365         if (pre_comp != NULL)
1366                 OPENSSL_free(pre_comp);
1367         return ret;
1368         }
1369
1370 int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
1371         {
1372         int ret = 0;
1373         NISTP224_PRE_COMP *pre = NULL;
1374         int i, j;
1375         BN_CTX *new_ctx = NULL;
1376         BIGNUM *x, *y;
1377         EC_POINT *generator = NULL;
1378
1379         /* throw away old precomputation */
1380         EC_EX_DATA_free_data(&group->extra_data, nistp224_pre_comp_dup,
1381                 nistp224_pre_comp_free, nistp224_pre_comp_clear_free);
1382         if (ctx == NULL)
1383                 if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0;
1384         BN_CTX_start(ctx);
1385         if (((x = BN_CTX_get(ctx)) == NULL) ||
1386                 ((y = BN_CTX_get(ctx)) == NULL))
1387                 goto err;
1388         /* get the generator */
1389         if (group->generator == NULL) goto err;
1390         generator = EC_POINT_new(group);
1391         if (generator == NULL)
1392                 goto err;
1393         BN_bin2bn(nistp224_curve_params[3], sizeof (felem_bytearray), x);
1394         BN_bin2bn(nistp224_curve_params[4], sizeof (felem_bytearray), y);
1395         if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx))
1396                 goto err;
1397         if ((pre = nistp224_pre_comp_new()) == NULL)
1398                 goto err;
1399         /* if the generator is the standard one, use built-in precomputation */
1400         if (0 == EC_POINT_cmp(group, generator, group->generator, ctx))
1401                 {
1402                 memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp));
1403                 ret = 1;
1404                 goto err;
1405                 }
1406         if ((!BN_to_felem(pre->g_pre_comp[1][0], &group->generator->X)) ||
1407                 (!BN_to_felem(pre->g_pre_comp[1][1], &group->generator->Y)) ||
1408                 (!BN_to_felem(pre->g_pre_comp[1][2], &group->generator->Z)))
1409                 goto err;
1410         /* compute 2^56*G, 2^112*G, 2^168*G */
1411         for (i = 1; i < 5; ++i)
1412                 {
1413                 point_double(pre->g_pre_comp[2*i][0], pre->g_pre_comp[2*i][1],
1414                         pre->g_pre_comp[2*i][2], pre->g_pre_comp[i][0],
1415                         pre->g_pre_comp[i][1], pre->g_pre_comp[i][2]);
1416                 for (j = 0; j < 55; ++j)
1417                         {
1418                         point_double(pre->g_pre_comp[2*i][0],
1419                                 pre->g_pre_comp[2*i][1],
1420                                 pre->g_pre_comp[2*i][2],
1421                                 pre->g_pre_comp[2*i][0],
1422                                 pre->g_pre_comp[2*i][1],
1423                                 pre->g_pre_comp[2*i][2]);
1424                         }
1425                 }
1426         /* g_pre_comp[0] is the point at infinity */
1427         memset(pre->g_pre_comp[0], 0, sizeof(pre->g_pre_comp[0]));
1428         /* the remaining multiples */
1429         /* 2^56*G + 2^112*G */
1430         point_add(pre->g_pre_comp[6][0], pre->g_pre_comp[6][1],
1431                 pre->g_pre_comp[6][2], pre->g_pre_comp[4][0],
1432                 pre->g_pre_comp[4][1], pre->g_pre_comp[4][2],
1433                 pre->g_pre_comp[2][0], pre->g_pre_comp[2][1],
1434                 pre->g_pre_comp[2][2]);
1435         /* 2^56*G + 2^168*G */
1436         point_add(pre->g_pre_comp[10][0], pre->g_pre_comp[10][1],
1437                 pre->g_pre_comp[10][2], pre->g_pre_comp[8][0],
1438                 pre->g_pre_comp[8][1], pre->g_pre_comp[8][2],
1439                 pre->g_pre_comp[2][0], pre->g_pre_comp[2][1],
1440                 pre->g_pre_comp[2][2]);
1441         /* 2^112*G + 2^168*G */
1442         point_add(pre->g_pre_comp[12][0], pre->g_pre_comp[12][1],
1443                 pre->g_pre_comp[12][2], pre->g_pre_comp[8][0],
1444                 pre->g_pre_comp[8][1], pre->g_pre_comp[8][2],
1445                 pre->g_pre_comp[4][0], pre->g_pre_comp[4][1],
1446                 pre->g_pre_comp[4][2]);
1447         /* 2^56*G + 2^112*G + 2^168*G */
1448         point_add(pre->g_pre_comp[14][0], pre->g_pre_comp[14][1],
1449                 pre->g_pre_comp[14][2], pre->g_pre_comp[12][0],
1450                 pre->g_pre_comp[12][1], pre->g_pre_comp[12][2],
1451                 pre->g_pre_comp[2][0], pre->g_pre_comp[2][1],
1452                 pre->g_pre_comp[2][2]);
1453         for (i = 1; i < 8; ++i)
1454                 {
1455                 /* odd multiples: add G */
1456                 point_add(pre->g_pre_comp[2*i+1][0], pre->g_pre_comp[2*i+1][1],
1457                         pre->g_pre_comp[2*i+1][2], pre->g_pre_comp[2*i][0],
1458                         pre->g_pre_comp[2*i][1], pre->g_pre_comp[2*i][2],
1459                         pre->g_pre_comp[1][0], pre->g_pre_comp[1][1],
1460                         pre->g_pre_comp[1][2]);
1461                 }
1462
1463         if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp224_pre_comp_dup,
1464                         nistp224_pre_comp_free, nistp224_pre_comp_clear_free))
1465                 goto err;
1466         ret = 1;
1467         pre = NULL;
1468  err:
1469         BN_CTX_end(ctx);
1470         if (generator != NULL)
1471                 EC_POINT_free(generator);
1472         if (new_ctx != NULL)
1473                 BN_CTX_free(new_ctx);
1474         if (pre)
1475                 nistp224_pre_comp_free(pre);
1476         return ret;
1477         }
1478
1479 int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group)
1480         {
1481         if (EC_EX_DATA_get_data(group->extra_data, nistp224_pre_comp_dup,
1482                         nistp224_pre_comp_free, nistp224_pre_comp_clear_free)
1483                 != NULL)
1484                 return 1;
1485         else
1486                 return 0;
1487         }
1488
1489 #else
1490 static void *dummy=&dummy;
1491 #endif