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ecp_nistp224.c
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1 /* crypto/ec/ecp_nistp224.c */
2 /*
3  * Written by Emilia Kasper (Google) for the OpenSSL project.
4  */
5 /* Copyright 2011 Google Inc.
6  *
7  * Licensed under the Apache License, Version 2.0 (the "License");
8  *
9  * you may not use this file except in compliance with the License.
10  * You may obtain a copy of the License at
11  *
12  * http://www.apache.org/licenses/LICENSE-2.0
13  *
14  * Unless required by applicable law or agreed to in writing, software
15  * distributed under the License is distributed on an "AS IS" BASIS,
16  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
17  * See the License for the specific language governing permissions and
18  * limitations under the License.
19  */
20 
21 /*
22  * A 64-bit implementation of the NIST P-224 elliptic curve point multiplication
23  *
24  * Inspired by Daniel J. Bernstein's public domain nistp224 implementation
25  * and Adam Langley's public domain 64-bit C implementation of curve25519
26  */
27 
28 #include <openssl/opensslconf.h>
29 #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
30 
31 #ifndef OPENSSL_SYS_VMS
32 #include <stdint.h>
33 #else
34 #include <inttypes.h>
35 #endif
36 
37 #include <string.h>
38 #include <openssl/err.h>
39 #include "ec_lcl.h"
40 
41 #if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 1))
42  /* even with gcc, the typedef won't work for 32-bit platforms */
43  typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit platforms */
44 #else
45  #error "Need GCC 3.1 or later to define type uint128_t"
46 #endif
47 
48 typedef uint8_t u8;
49 typedef uint64_t u64;
50 typedef int64_t s64;
51 
52 
53 /******************************************************************************/
54 /* INTERNAL REPRESENTATION OF FIELD ELEMENTS
55  *
56  * Field elements are represented as a_0 + 2^56*a_1 + 2^112*a_2 + 2^168*a_3
57  * using 64-bit coefficients called 'limbs',
58  * and sometimes (for multiplication results) as
59  * 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
60  * using 128-bit coefficients called 'widelimbs'.
61  * A 4-limb representation is an 'felem';
62  * a 7-widelimb representation is a 'widefelem'.
63  * Even within felems, bits of adjacent limbs overlap, and we don't always
64  * reduce the representations: we ensure that inputs to each felem
65  * multiplication satisfy a_i < 2^60, so outputs satisfy b_i < 4*2^60*2^60,
66  * and fit into a 128-bit word without overflow. The coefficients are then
67  * again partially reduced to obtain an felem satisfying a_i < 2^57.
68  * We only reduce to the unique minimal representation at the end of the
69  * computation.
70  */
71 
72 typedef uint64_t limb;
73 typedef uint128_t widelimb;
74 
75 typedef limb felem[4];
76 typedef widelimb widefelem[7];
77 
78 /* Field element represented as a byte arrary.
79  * 28*8 = 224 bits is also the group order size for the elliptic curve,
80  * and we also use this type for scalars for point multiplication.
81  */
82 typedef u8 felem_bytearray[28];
83 
84 static const felem_bytearray nistp224_curve_params[5] = {
85  {0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */
86  0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00,
87  0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01},
88  {0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */
89  0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF,
90  0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE},
91  {0xB4,0x05,0x0A,0x85,0x0C,0x04,0xB3,0xAB,0xF5,0x41, /* b */
92  0x32,0x56,0x50,0x44,0xB0,0xB7,0xD7,0xBF,0xD8,0xBA,
93  0x27,0x0B,0x39,0x43,0x23,0x55,0xFF,0xB4},
94  {0xB7,0x0E,0x0C,0xBD,0x6B,0xB4,0xBF,0x7F,0x32,0x13, /* x */
95  0x90,0xB9,0x4A,0x03,0xC1,0xD3,0x56,0xC2,0x11,0x22,
96  0x34,0x32,0x80,0xD6,0x11,0x5C,0x1D,0x21},
97  {0xbd,0x37,0x63,0x88,0xb5,0xf7,0x23,0xfb,0x4c,0x22, /* y */
98  0xdf,0xe6,0xcd,0x43,0x75,0xa0,0x5a,0x07,0x47,0x64,
99  0x44,0xd5,0x81,0x99,0x85,0x00,0x7e,0x34}
100 };
101 
102 /* Precomputed multiples of the standard generator
103  * Points are given in coordinates (X, Y, Z) where Z normally is 1
104  * (0 for the point at infinity).
105  * For each field element, slice a_0 is word 0, etc.
106  *
107  * The table has 2 * 16 elements, starting with the following:
108  * index | bits | point
109  * ------+---------+------------------------------
110  * 0 | 0 0 0 0 | 0G
111  * 1 | 0 0 0 1 | 1G
112  * 2 | 0 0 1 0 | 2^56G
113  * 3 | 0 0 1 1 | (2^56 + 1)G
114  * 4 | 0 1 0 0 | 2^112G
115  * 5 | 0 1 0 1 | (2^112 + 1)G
116  * 6 | 0 1 1 0 | (2^112 + 2^56)G
117  * 7 | 0 1 1 1 | (2^112 + 2^56 + 1)G
118  * 8 | 1 0 0 0 | 2^168G
119  * 9 | 1 0 0 1 | (2^168 + 1)G
120  * 10 | 1 0 1 0 | (2^168 + 2^56)G
121  * 11 | 1 0 1 1 | (2^168 + 2^56 + 1)G
122  * 12 | 1 1 0 0 | (2^168 + 2^112)G
123  * 13 | 1 1 0 1 | (2^168 + 2^112 + 1)G
124  * 14 | 1 1 1 0 | (2^168 + 2^112 + 2^56)G
125  * 15 | 1 1 1 1 | (2^168 + 2^112 + 2^56 + 1)G
126  * followed by a copy of this with each element multiplied by 2^28.
127  *
128  * The reason for this is so that we can clock bits into four different
129  * locations when doing simple scalar multiplies against the base point,
130  * and then another four locations using the second 16 elements.
131  */
132 static const felem gmul[2][16][3] =
133 {{{{0, 0, 0, 0},
134  {0, 0, 0, 0},
135  {0, 0, 0, 0}},
136  {{0x3280d6115c1d21, 0xc1d356c2112234, 0x7f321390b94a03, 0xb70e0cbd6bb4bf},
137  {0xd5819985007e34, 0x75a05a07476444, 0xfb4c22dfe6cd43, 0xbd376388b5f723},
138  {1, 0, 0, 0}},
139  {{0xfd9675666ebbe9, 0xbca7664d40ce5e, 0x2242df8d8a2a43, 0x1f49bbb0f99bc5},
140  {0x29e0b892dc9c43, 0xece8608436e662, 0xdc858f185310d0, 0x9812dd4eb8d321},
141  {1, 0, 0, 0}},
142  {{0x6d3e678d5d8eb8, 0x559eed1cb362f1, 0x16e9a3bbce8a3f, 0xeedcccd8c2a748},
143  {0xf19f90ed50266d, 0xabf2b4bf65f9df, 0x313865468fafec, 0x5cb379ba910a17},
144  {1, 0, 0, 0}},
145  {{0x0641966cab26e3, 0x91fb2991fab0a0, 0xefec27a4e13a0b, 0x0499aa8a5f8ebe},
146  {0x7510407766af5d, 0x84d929610d5450, 0x81d77aae82f706, 0x6916f6d4338c5b},
147  {1, 0, 0, 0}},
148  {{0xea95ac3b1f15c6, 0x086000905e82d4, 0xdd323ae4d1c8b1, 0x932b56be7685a3},
149  {0x9ef93dea25dbbf, 0x41665960f390f0, 0xfdec76dbe2a8a7, 0x523e80f019062a},
150  {1, 0, 0, 0}},
151  {{0x822fdd26732c73, 0xa01c83531b5d0f, 0x363f37347c1ba4, 0xc391b45c84725c},
152  {0xbbd5e1b2d6ad24, 0xddfbcde19dfaec, 0xc393da7e222a7f, 0x1efb7890ede244},
153  {1, 0, 0, 0}},
154  {{0x4c9e90ca217da1, 0xd11beca79159bb, 0xff8d33c2c98b7c, 0x2610b39409f849},
155  {0x44d1352ac64da0, 0xcdbb7b2c46b4fb, 0x966c079b753c89, 0xfe67e4e820b112},
156  {1, 0, 0, 0}},
157  {{0xe28cae2df5312d, 0xc71b61d16f5c6e, 0x79b7619a3e7c4c, 0x05c73240899b47},
158  {0x9f7f6382c73e3a, 0x18615165c56bda, 0x641fab2116fd56, 0x72855882b08394},
159  {1, 0, 0, 0}},
160  {{0x0469182f161c09, 0x74a98ca8d00fb5, 0xb89da93489a3e0, 0x41c98768fb0c1d},
161  {0xe5ea05fb32da81, 0x3dce9ffbca6855, 0x1cfe2d3fbf59e6, 0x0e5e03408738a7},
162  {1, 0, 0, 0}},
163  {{0xdab22b2333e87f, 0x4430137a5dd2f6, 0xe03ab9f738beb8, 0xcb0c5d0dc34f24},
164  {0x764a7df0c8fda5, 0x185ba5c3fa2044, 0x9281d688bcbe50, 0xc40331df893881},
165  {1, 0, 0, 0}},
166  {{0xb89530796f0f60, 0xade92bd26909a3, 0x1a0c83fb4884da, 0x1765bf22a5a984},
167  {0x772a9ee75db09e, 0x23bc6c67cec16f, 0x4c1edba8b14e2f, 0xe2a215d9611369},
168  {1, 0, 0, 0}},
169  {{0x571e509fb5efb3, 0xade88696410552, 0xc8ae85fada74fe, 0x6c7e4be83bbde3},
170  {0xff9f51160f4652, 0xb47ce2495a6539, 0xa2946c53b582f4, 0x286d2db3ee9a60},
171  {1, 0, 0, 0}},
172  {{0x40bbd5081a44af, 0x0995183b13926c, 0xbcefba6f47f6d0, 0x215619e9cc0057},
173  {0x8bc94d3b0df45e, 0xf11c54a3694f6f, 0x8631b93cdfe8b5, 0xe7e3f4b0982db9},
174  {1, 0, 0, 0}},
175  {{0xb17048ab3e1c7b, 0xac38f36ff8a1d8, 0x1c29819435d2c6, 0xc813132f4c07e9},
176  {0x2891425503b11f, 0x08781030579fea, 0xf5426ba5cc9674, 0x1e28ebf18562bc},
177  {1, 0, 0, 0}},
178  {{0x9f31997cc864eb, 0x06cd91d28b5e4c, 0xff17036691a973, 0xf1aef351497c58},
179  {0xdd1f2d600564ff, 0xdead073b1402db, 0x74a684435bd693, 0xeea7471f962558},
180  {1, 0, 0, 0}}},
181  {{{0, 0, 0, 0},
182  {0, 0, 0, 0},
183  {0, 0, 0, 0}},
184  {{0x9665266dddf554, 0x9613d78b60ef2d, 0xce27a34cdba417, 0xd35ab74d6afc31},
185  {0x85ccdd22deb15e, 0x2137e5783a6aab, 0xa141cffd8c93c6, 0x355a1830e90f2d},
186  {1, 0, 0, 0}},
187  {{0x1a494eadaade65, 0xd6da4da77fe53c, 0xe7992996abec86, 0x65c3553c6090e3},
188  {0xfa610b1fb09346, 0xf1c6540b8a4aaf, 0xc51a13ccd3cbab, 0x02995b1b18c28a},
189  {1, 0, 0, 0}},
190  {{0x7874568e7295ef, 0x86b419fbe38d04, 0xdc0690a7550d9a, 0xd3966a44beac33},
191  {0x2b7280ec29132f, 0xbeaa3b6a032df3, 0xdc7dd88ae41200, 0xd25e2513e3a100},
192  {1, 0, 0, 0}},
193  {{0x924857eb2efafd, 0xac2bce41223190, 0x8edaa1445553fc, 0x825800fd3562d5},
194  {0x8d79148ea96621, 0x23a01c3dd9ed8d, 0xaf8b219f9416b5, 0xd8db0cc277daea},
195  {1, 0, 0, 0}},
196  {{0x76a9c3b1a700f0, 0xe9acd29bc7e691, 0x69212d1a6b0327, 0x6322e97fe154be},
197  {0x469fc5465d62aa, 0x8d41ed18883b05, 0x1f8eae66c52b88, 0xe4fcbe9325be51},
198  {1, 0, 0, 0}},
199  {{0x825fdf583cac16, 0x020b857c7b023a, 0x683c17744b0165, 0x14ffd0a2daf2f1},
200  {0x323b36184218f9, 0x4944ec4e3b47d4, 0xc15b3080841acf, 0x0bced4b01a28bb},
201  {1, 0, 0, 0}},
202  {{0x92ac22230df5c4, 0x52f33b4063eda8, 0xcb3f19870c0c93, 0x40064f2ba65233},
203  {0xfe16f0924f8992, 0x012da25af5b517, 0x1a57bb24f723a6, 0x06f8bc76760def},
204  {1, 0, 0, 0}},
205  {{0x4a7084f7817cb9, 0xbcab0738ee9a78, 0x3ec11e11d9c326, 0xdc0fe90e0f1aae},
206  {0xcf639ea5f98390, 0x5c350aa22ffb74, 0x9afae98a4047b7, 0x956ec2d617fc45},
207  {1, 0, 0, 0}},
208  {{0x4306d648c1be6a, 0x9247cd8bc9a462, 0xf5595e377d2f2e, 0xbd1c3caff1a52e},
209  {0x045e14472409d0, 0x29f3e17078f773, 0x745a602b2d4f7d, 0x191837685cdfbb},
210  {1, 0, 0, 0}},
211  {{0x5b6ee254a8cb79, 0x4953433f5e7026, 0xe21faeb1d1def4, 0xc4c225785c09de},
212  {0x307ce7bba1e518, 0x31b125b1036db8, 0x47e91868839e8f, 0xc765866e33b9f3},
213  {1, 0, 0, 0}},
214  {{0x3bfece24f96906, 0x4794da641e5093, 0xde5df64f95db26, 0x297ecd89714b05},
215  {0x701bd3ebb2c3aa, 0x7073b4f53cb1d5, 0x13c5665658af16, 0x9895089d66fe58},
216  {1, 0, 0, 0}},
217  {{0x0fef05f78c4790, 0x2d773633b05d2e, 0x94229c3a951c94, 0xbbbd70df4911bb},
218  {0xb2c6963d2c1168, 0x105f47a72b0d73, 0x9fdf6111614080, 0x7b7e94b39e67b0},
219  {1, 0, 0, 0}},
220  {{0xad1a7d6efbe2b3, 0xf012482c0da69d, 0x6b3bdf12438345, 0x40d7558d7aa4d9},
221  {0x8a09fffb5c6d3d, 0x9a356e5d9ffd38, 0x5973f15f4f9b1c, 0xdcd5f59f63c3ea},
222  {1, 0, 0, 0}},
223  {{0xacf39f4c5ca7ab, 0x4c8071cc5fd737, 0xc64e3602cd1184, 0x0acd4644c9abba},
224  {0x6c011a36d8bf6e, 0xfecd87ba24e32a, 0x19f6f56574fad8, 0x050b204ced9405},
225  {1, 0, 0, 0}},
226  {{0xed4f1cae7d9a96, 0x5ceef7ad94c40a, 0x778e4a3bf3ef9b, 0x7405783dc3b55e},
227  {0x32477c61b6e8c6, 0xb46a97570f018b, 0x91176d0a7e95d1, 0x3df90fbc4c7d0e},
228  {1, 0, 0, 0}}}};
229 
230 /* Precomputation for the group generator. */
231 typedef struct {
232  felem g_pre_comp[2][16][3];
233  int references;
234 } NISTP224_PRE_COMP;
235 
236 const EC_METHOD *EC_GFp_nistp224_method(void)
237  {
238  static const EC_METHOD ret = {
239  EC_FLAGS_DEFAULT_OCT,
240  NID_X9_62_prime_field,
241  ec_GFp_nistp224_group_init,
242  ec_GFp_simple_group_finish,
243  ec_GFp_simple_group_clear_finish,
244  ec_GFp_nist_group_copy,
245  ec_GFp_nistp224_group_set_curve,
246  ec_GFp_simple_group_get_curve,
247  ec_GFp_simple_group_get_degree,
248  ec_GFp_simple_group_check_discriminant,
249  ec_GFp_simple_point_init,
250  ec_GFp_simple_point_finish,
251  ec_GFp_simple_point_clear_finish,
252  ec_GFp_simple_point_copy,
253  ec_GFp_simple_point_set_to_infinity,
254  ec_GFp_simple_set_Jprojective_coordinates_GFp,
255  ec_GFp_simple_get_Jprojective_coordinates_GFp,
256  ec_GFp_simple_point_set_affine_coordinates,
257  ec_GFp_nistp224_point_get_affine_coordinates,
258  0 /* point_set_compressed_coordinates */,
259  0 /* point2oct */,
260  0 /* oct2point */,
261  ec_GFp_simple_add,
262  ec_GFp_simple_dbl,
263  ec_GFp_simple_invert,
264  ec_GFp_simple_is_at_infinity,
265  ec_GFp_simple_is_on_curve,
266  ec_GFp_simple_cmp,
267  ec_GFp_simple_make_affine,
268  ec_GFp_simple_points_make_affine,
269  ec_GFp_nistp224_points_mul,
270  ec_GFp_nistp224_precompute_mult,
271  ec_GFp_nistp224_have_precompute_mult,
272  ec_GFp_nist_field_mul,
273  ec_GFp_nist_field_sqr,
274  0 /* field_div */,
275  0 /* field_encode */,
276  0 /* field_decode */,
277  0 /* field_set_to_one */ };
278 
279  return &ret;
280  }
281 
282 /* Helper functions to convert field elements to/from internal representation */
283 static void bin28_to_felem(felem out, const u8 in[28])
284  {
285  out[0] = *((const uint64_t *)(in)) & 0x00ffffffffffffff;
286  out[1] = (*((const uint64_t *)(in+7))) & 0x00ffffffffffffff;
287  out[2] = (*((const uint64_t *)(in+14))) & 0x00ffffffffffffff;
288  out[3] = (*((const uint64_t *)(in+21))) & 0x00ffffffffffffff;
289  }
290 
291 static void felem_to_bin28(u8 out[28], const felem in)
292  {
293  unsigned i;
294  for (i = 0; i < 7; ++i)
295  {
296  out[i] = in[0]>>(8*i);
297  out[i+7] = in[1]>>(8*i);
298  out[i+14] = in[2]>>(8*i);
299  out[i+21] = in[3]>>(8*i);
300  }
301  }
302 
303 /* To preserve endianness when using BN_bn2bin and BN_bin2bn */
304 static void flip_endian(u8 *out, const u8 *in, unsigned len)
305  {
306  unsigned i;
307  for (i = 0; i < len; ++i)
308  out[i] = in[len-1-i];
309  }
310 
311 /* From OpenSSL BIGNUM to internal representation */
312 static int BN_to_felem(felem out, const BIGNUM *bn)
313  {
314  felem_bytearray b_in;
315  felem_bytearray b_out;
316  unsigned num_bytes;
317 
318  /* BN_bn2bin eats leading zeroes */
319  memset(b_out, 0, sizeof b_out);
320  num_bytes = BN_num_bytes(bn);
321  if (num_bytes > sizeof b_out)
322  {
323  ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE);
324  return 0;
325  }
326  if (BN_is_negative(bn))
327  {
328  ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE);
329  return 0;
330  }
331  num_bytes = BN_bn2bin(bn, b_in);
332  flip_endian(b_out, b_in, num_bytes);
333  bin28_to_felem(out, b_out);
334  return 1;
335  }
336 
337 /* From internal representation to OpenSSL BIGNUM */
338 static BIGNUM *felem_to_BN(BIGNUM *out, const felem in)
339  {
340  felem_bytearray b_in, b_out;
341  felem_to_bin28(b_in, in);
342  flip_endian(b_out, b_in, sizeof b_out);
343  return BN_bin2bn(b_out, sizeof b_out, out);
344  }
345 
346 /******************************************************************************/
347 /* FIELD OPERATIONS
348  *
349  * Field operations, using the internal representation of field elements.
350  * NB! These operations are specific to our point multiplication and cannot be
351  * expected to be correct in general - e.g., multiplication with a large scalar
352  * will cause an overflow.
353  *
354  */
355 
356 static void felem_one(felem out)
357  {
358  out[0] = 1;
359  out[1] = 0;
360  out[2] = 0;
361  out[3] = 0;
362  }
363 
364 static void felem_assign(felem out, const felem in)
365  {
366  out[0] = in[0];
367  out[1] = in[1];
368  out[2] = in[2];
369  out[3] = in[3];
370  }
371 
372 /* Sum two field elements: out += in */
373 static void felem_sum(felem out, const felem in)
374  {
375  out[0] += in[0];
376  out[1] += in[1];
377  out[2] += in[2];
378  out[3] += in[3];
379  }
380 
381 /* Get negative value: out = -in */
382 /* Assumes in[i] < 2^57 */
383 static void felem_neg(felem out, const felem in)
384  {
385  static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2);
386  static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2);
387  static const limb two58m42m2 = (((limb) 1) << 58) -
388  (((limb) 1) << 42) - (((limb) 1) << 2);
389 
390  /* Set to 0 mod 2^224-2^96+1 to ensure out > in */
391  out[0] = two58p2 - in[0];
392  out[1] = two58m42m2 - in[1];
393  out[2] = two58m2 - in[2];
394  out[3] = two58m2 - in[3];
395  }
396 
397 /* Subtract field elements: out -= in */
398 /* Assumes in[i] < 2^57 */
399 static void felem_diff(felem out, const felem in)
400  {
401  static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2);
402  static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2);
403  static const limb two58m42m2 = (((limb) 1) << 58) -
404  (((limb) 1) << 42) - (((limb) 1) << 2);
405 
406  /* Add 0 mod 2^224-2^96+1 to ensure out > in */
407  out[0] += two58p2;
408  out[1] += two58m42m2;
409  out[2] += two58m2;
410  out[3] += two58m2;
411 
412  out[0] -= in[0];
413  out[1] -= in[1];
414  out[2] -= in[2];
415  out[3] -= in[3];
416  }
417 
418 /* Subtract in unreduced 128-bit mode: out -= in */
419 /* Assumes in[i] < 2^119 */
420 static void widefelem_diff(widefelem out, const widefelem in)
421  {
422  static const widelimb two120 = ((widelimb) 1) << 120;
423  static const widelimb two120m64 = (((widelimb) 1) << 120) -
424  (((widelimb) 1) << 64);
425  static const widelimb two120m104m64 = (((widelimb) 1) << 120) -
426  (((widelimb) 1) << 104) - (((widelimb) 1) << 64);
427 
428  /* Add 0 mod 2^224-2^96+1 to ensure out > in */
429  out[0] += two120;
430  out[1] += two120m64;
431  out[2] += two120m64;
432  out[3] += two120;
433  out[4] += two120m104m64;
434  out[5] += two120m64;
435  out[6] += two120m64;
436 
437  out[0] -= in[0];
438  out[1] -= in[1];
439  out[2] -= in[2];
440  out[3] -= in[3];
441  out[4] -= in[4];
442  out[5] -= in[5];
443  out[6] -= in[6];
444  }
445 
446 /* Subtract in mixed mode: out128 -= in64 */
447 /* in[i] < 2^63 */
448 static void felem_diff_128_64(widefelem out, const felem in)
449  {
450  static const widelimb two64p8 = (((widelimb) 1) << 64) +
451  (((widelimb) 1) << 8);
452  static const widelimb two64m8 = (((widelimb) 1) << 64) -
453  (((widelimb) 1) << 8);
454  static const widelimb two64m48m8 = (((widelimb) 1) << 64) -
455  (((widelimb) 1) << 48) - (((widelimb) 1) << 8);
456 
457  /* Add 0 mod 2^224-2^96+1 to ensure out > in */
458  out[0] += two64p8;
459  out[1] += two64m48m8;
460  out[2] += two64m8;
461  out[3] += two64m8;
462 
463  out[0] -= in[0];
464  out[1] -= in[1];
465  out[2] -= in[2];
466  out[3] -= in[3];
467  }
468 
469 /* Multiply a field element by a scalar: out = out * scalar
470  * The scalars we actually use are small, so results fit without overflow */
471 static void felem_scalar(felem out, const limb scalar)
472  {
473  out[0] *= scalar;
474  out[1] *= scalar;
475  out[2] *= scalar;
476  out[3] *= scalar;
477  }
478 
479 /* Multiply an unreduced field element by a scalar: out = out * scalar
480  * The scalars we actually use are small, so results fit without overflow */
481 static void widefelem_scalar(widefelem out, const widelimb scalar)
482  {
483  out[0] *= scalar;
484  out[1] *= scalar;
485  out[2] *= scalar;
486  out[3] *= scalar;
487  out[4] *= scalar;
488  out[5] *= scalar;
489  out[6] *= scalar;
490  }
491 
492 /* Square a field element: out = in^2 */
493 static void felem_square(widefelem out, const felem in)
494  {
495  limb tmp0, tmp1, tmp2;
496  tmp0 = 2 * in[0]; tmp1 = 2 * in[1]; tmp2 = 2 * in[2];
497  out[0] = ((widelimb) in[0]) * in[0];
498  out[1] = ((widelimb) in[0]) * tmp1;
499  out[2] = ((widelimb) in[0]) * tmp2 + ((widelimb) in[1]) * in[1];
500  out[3] = ((widelimb) in[3]) * tmp0 +
501  ((widelimb) in[1]) * tmp2;
502  out[4] = ((widelimb) in[3]) * tmp1 + ((widelimb) in[2]) * in[2];
503  out[5] = ((widelimb) in[3]) * tmp2;
504  out[6] = ((widelimb) in[3]) * in[3];
505  }
506 
507 /* Multiply two field elements: out = in1 * in2 */
508 static void felem_mul(widefelem out, const felem in1, const felem in2)
509  {
510  out[0] = ((widelimb) in1[0]) * in2[0];
511  out[1] = ((widelimb) in1[0]) * in2[1] + ((widelimb) in1[1]) * in2[0];
512  out[2] = ((widelimb) in1[0]) * in2[2] + ((widelimb) in1[1]) * in2[1] +
513  ((widelimb) in1[2]) * in2[0];
514  out[3] = ((widelimb) in1[0]) * in2[3] + ((widelimb) in1[1]) * in2[2] +
515  ((widelimb) in1[2]) * in2[1] + ((widelimb) in1[3]) * in2[0];
516  out[4] = ((widelimb) in1[1]) * in2[3] + ((widelimb) in1[2]) * in2[2] +
517  ((widelimb) in1[3]) * in2[1];
518  out[5] = ((widelimb) in1[2]) * in2[3] + ((widelimb) in1[3]) * in2[2];
519  out[6] = ((widelimb) in1[3]) * in2[3];
520  }
521 
522 /* Reduce seven 128-bit coefficients to four 64-bit coefficients.
523  * Requires in[i] < 2^126,
524  * ensures out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] <= 2^56 + 2^16 */
525 static void felem_reduce(felem out, const widefelem in)
526  {
527  static const widelimb two127p15 = (((widelimb) 1) << 127) +
528  (((widelimb) 1) << 15);
529  static const widelimb two127m71 = (((widelimb) 1) << 127) -
530  (((widelimb) 1) << 71);
531  static const widelimb two127m71m55 = (((widelimb) 1) << 127) -
532  (((widelimb) 1) << 71) - (((widelimb) 1) << 55);
533  widelimb output[5];
534 
535  /* Add 0 mod 2^224-2^96+1 to ensure all differences are positive */
536  output[0] = in[0] + two127p15;
537  output[1] = in[1] + two127m71m55;
538  output[2] = in[2] + two127m71;
539  output[3] = in[3];
540  output[4] = in[4];
541 
542  /* Eliminate in[4], in[5], in[6] */
543  output[4] += in[6] >> 16;
544  output[3] += (in[6] & 0xffff) << 40;
545  output[2] -= in[6];
546 
547  output[3] += in[5] >> 16;
548  output[2] += (in[5] & 0xffff) << 40;
549  output[1] -= in[5];
550 
551  output[2] += output[4] >> 16;
552  output[1] += (output[4] & 0xffff) << 40;
553  output[0] -= output[4];
554 
555  /* Carry 2 -> 3 -> 4 */
556  output[3] += output[2] >> 56;
557  output[2] &= 0x00ffffffffffffff;
558 
559  output[4] = output[3] >> 56;
560  output[3] &= 0x00ffffffffffffff;
561 
562  /* Now output[2] < 2^56, output[3] < 2^56, output[4] < 2^72 */
563 
564  /* Eliminate output[4] */
565  output[2] += output[4] >> 16;
566  /* output[2] < 2^56 + 2^56 = 2^57 */
567  output[1] += (output[4] & 0xffff) << 40;
568  output[0] -= output[4];
569 
570  /* Carry 0 -> 1 -> 2 -> 3 */
571  output[1] += output[0] >> 56;
572  out[0] = output[0] & 0x00ffffffffffffff;
573 
574  output[2] += output[1] >> 56;
575  /* output[2] < 2^57 + 2^72 */
576  out[1] = output[1] & 0x00ffffffffffffff;
577  output[3] += output[2] >> 56;
578  /* output[3] <= 2^56 + 2^16 */
579  out[2] = output[2] & 0x00ffffffffffffff;
580 
581  /* out[0] < 2^56, out[1] < 2^56, out[2] < 2^56,
582  * out[3] <= 2^56 + 2^16 (due to final carry),
583  * so out < 2*p */
584  out[3] = output[3];
585  }
586 
587 static void felem_square_reduce(felem out, const felem in)
588  {
589  widefelem tmp;
590  felem_square(tmp, in);
591  felem_reduce(out, tmp);
592  }
593 
594 static void felem_mul_reduce(felem out, const felem in1, const felem in2)
595  {
596  widefelem tmp;
597  felem_mul(tmp, in1, in2);
598  felem_reduce(out, tmp);
599  }
600 
601 /* Reduce to unique minimal representation.
602  * Requires 0 <= in < 2*p (always call felem_reduce first) */
603 static void felem_contract(felem out, const felem in)
604  {
605  static const int64_t two56 = ((limb) 1) << 56;
606  /* 0 <= in < 2*p, p = 2^224 - 2^96 + 1 */
607  /* if in > p , reduce in = in - 2^224 + 2^96 - 1 */
608  int64_t tmp[4], a;
609  tmp[0] = in[0];
610  tmp[1] = in[1];
611  tmp[2] = in[2];
612  tmp[3] = in[3];
613  /* Case 1: a = 1 iff in >= 2^224 */
614  a = (in[3] >> 56);
615  tmp[0] -= a;
616  tmp[1] += a << 40;
617  tmp[3] &= 0x00ffffffffffffff;
618  /* Case 2: a = 0 iff p <= in < 2^224, i.e.,
619  * the high 128 bits are all 1 and the lower part is non-zero */
620  a = ((in[3] & in[2] & (in[1] | 0x000000ffffffffff)) + 1) |
621  (((int64_t)(in[0] + (in[1] & 0x000000ffffffffff)) - 1) >> 63);
622  a &= 0x00ffffffffffffff;
623  /* turn a into an all-one mask (if a = 0) or an all-zero mask */
624  a = (a - 1) >> 63;
625  /* subtract 2^224 - 2^96 + 1 if a is all-one*/
626  tmp[3] &= a ^ 0xffffffffffffffff;
627  tmp[2] &= a ^ 0xffffffffffffffff;
628  tmp[1] &= (a ^ 0xffffffffffffffff) | 0x000000ffffffffff;
629  tmp[0] -= 1 & a;
630 
631  /* eliminate negative coefficients: if tmp[0] is negative, tmp[1] must
632  * be non-zero, so we only need one step */
633  a = tmp[0] >> 63;
634  tmp[0] += two56 & a;
635  tmp[1] -= 1 & a;
636 
637  /* carry 1 -> 2 -> 3 */
638  tmp[2] += tmp[1] >> 56;
639  tmp[1] &= 0x00ffffffffffffff;
640 
641  tmp[3] += tmp[2] >> 56;
642  tmp[2] &= 0x00ffffffffffffff;
643 
644  /* Now 0 <= out < p */
645  out[0] = tmp[0];
646  out[1] = tmp[1];
647  out[2] = tmp[2];
648  out[3] = tmp[3];
649  }
650 
651 /* Zero-check: returns 1 if input is 0, and 0 otherwise.
652  * We know that field elements are reduced to in < 2^225,
653  * so we only need to check three cases: 0, 2^224 - 2^96 + 1,
654  * and 2^225 - 2^97 + 2 */
655 static limb felem_is_zero(const felem in)
656  {
657  limb zero, two224m96p1, two225m97p2;
658 
659  zero = in[0] | in[1] | in[2] | in[3];
660  zero = (((int64_t)(zero) - 1) >> 63) & 1;
661  two224m96p1 = (in[0] ^ 1) | (in[1] ^ 0x00ffff0000000000)
662  | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x00ffffffffffffff);
663  two224m96p1 = (((int64_t)(two224m96p1) - 1) >> 63) & 1;
664  two225m97p2 = (in[0] ^ 2) | (in[1] ^ 0x00fffe0000000000)
665  | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x01ffffffffffffff);
666  two225m97p2 = (((int64_t)(two225m97p2) - 1) >> 63) & 1;
667  return (zero | two224m96p1 | two225m97p2);
668  }
669 
670 static limb felem_is_zero_int(const felem in)
671  {
672  return (int) (felem_is_zero(in) & ((limb)1));
673  }
674 
675 /* Invert a field element */
676 /* Computation chain copied from djb's code */
677 static void felem_inv(felem out, const felem in)
678  {
679  felem ftmp, ftmp2, ftmp3, ftmp4;
680  widefelem tmp;
681  unsigned i;
682 
683  felem_square(tmp, in); felem_reduce(ftmp, tmp); /* 2 */
684  felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^2 - 1 */
685  felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2 */
686  felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 1 */
687  felem_square(tmp, ftmp); felem_reduce(ftmp2, tmp); /* 2^4 - 2 */
688  felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^5 - 4 */
689  felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^6 - 8 */
690  felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp, tmp); /* 2^6 - 1 */
691  felem_square(tmp, ftmp); felem_reduce(ftmp2, tmp); /* 2^7 - 2 */
692  for (i = 0; i < 5; ++i) /* 2^12 - 2^6 */
693  {
694  felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp);
695  }
696  felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp2, tmp); /* 2^12 - 1 */
697  felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp); /* 2^13 - 2 */
698  for (i = 0; i < 11; ++i) /* 2^24 - 2^12 */
699  {
700  felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp);
701  }
702  felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp2, tmp); /* 2^24 - 1 */
703  felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp); /* 2^25 - 2 */
704  for (i = 0; i < 23; ++i) /* 2^48 - 2^24 */
705  {
706  felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp);
707  }
708  felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^48 - 1 */
709  felem_square(tmp, ftmp3); felem_reduce(ftmp4, tmp); /* 2^49 - 2 */
710  for (i = 0; i < 47; ++i) /* 2^96 - 2^48 */
711  {
712  felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp);
713  }
714  felem_mul(tmp, ftmp3, ftmp4); felem_reduce(ftmp3, tmp); /* 2^96 - 1 */
715  felem_square(tmp, ftmp3); felem_reduce(ftmp4, tmp); /* 2^97 - 2 */
716  for (i = 0; i < 23; ++i) /* 2^120 - 2^24 */
717  {
718  felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp);
719  }
720  felem_mul(tmp, ftmp2, ftmp4); felem_reduce(ftmp2, tmp); /* 2^120 - 1 */
721  for (i = 0; i < 6; ++i) /* 2^126 - 2^6 */
722  {
723  felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp);
724  }
725  felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp, tmp); /* 2^126 - 1 */
726  felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^127 - 2 */
727  felem_mul(tmp, ftmp, in); felem_reduce(ftmp, tmp); /* 2^127 - 1 */
728  for (i = 0; i < 97; ++i) /* 2^224 - 2^97 */
729  {
730  felem_square(tmp, ftmp); felem_reduce(ftmp, tmp);
731  }
732  felem_mul(tmp, ftmp, ftmp3); felem_reduce(out, tmp); /* 2^224 - 2^96 - 1 */
733  }
734 
735 /* Copy in constant time:
736  * if icopy == 1, copy in to out,
737  * if icopy == 0, copy out to itself. */
738 static void
739 copy_conditional(felem out, const felem in, limb icopy)
740  {
741  unsigned i;
742  /* icopy is a (64-bit) 0 or 1, so copy is either all-zero or all-one */
743  const limb copy = -icopy;
744  for (i = 0; i < 4; ++i)
745  {
746  const limb tmp = copy & (in[i] ^ out[i]);
747  out[i] ^= tmp;
748  }
749  }
750 
751 /******************************************************************************/
752 /* ELLIPTIC CURVE POINT OPERATIONS
753  *
754  * Points are represented in Jacobian projective coordinates:
755  * (X, Y, Z) corresponds to the affine point (X/Z^2, Y/Z^3),
756  * or to the point at infinity if Z == 0.
757  *
758  */
759 
760 /* Double an elliptic curve point:
761  * (X', Y', Z') = 2 * (X, Y, Z), where
762  * X' = (3 * (X - Z^2) * (X + Z^2))^2 - 8 * X * Y^2
763  * Y' = 3 * (X - Z^2) * (X + Z^2) * (4 * X * Y^2 - X') - 8 * Y^2
764  * Z' = (Y + Z)^2 - Y^2 - Z^2 = 2 * Y * Z
765  * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed,
766  * while x_out == y_in is not (maybe this works, but it's not tested). */
767 static void
768 point_double(felem x_out, felem y_out, felem z_out,
769  const felem x_in, const felem y_in, const felem z_in)
770  {
771  widefelem tmp, tmp2;
772  felem delta, gamma, beta, alpha, ftmp, ftmp2;
773 
774  felem_assign(ftmp, x_in);
775  felem_assign(ftmp2, x_in);
776 
777  /* delta = z^2 */
778  felem_square(tmp, z_in);
779  felem_reduce(delta, tmp);
780 
781  /* gamma = y^2 */
782  felem_square(tmp, y_in);
783  felem_reduce(gamma, tmp);
784 
785  /* beta = x*gamma */
786  felem_mul(tmp, x_in, gamma);
787  felem_reduce(beta, tmp);
788 
789  /* alpha = 3*(x-delta)*(x+delta) */
790  felem_diff(ftmp, delta);
791  /* ftmp[i] < 2^57 + 2^58 + 2 < 2^59 */
792  felem_sum(ftmp2, delta);
793  /* ftmp2[i] < 2^57 + 2^57 = 2^58 */
794  felem_scalar(ftmp2, 3);
795  /* ftmp2[i] < 3 * 2^58 < 2^60 */
796  felem_mul(tmp, ftmp, ftmp2);
797  /* tmp[i] < 2^60 * 2^59 * 4 = 2^121 */
798  felem_reduce(alpha, tmp);
799 
800  /* x' = alpha^2 - 8*beta */
801  felem_square(tmp, alpha);
802  /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
803  felem_assign(ftmp, beta);
804  felem_scalar(ftmp, 8);
805  /* ftmp[i] < 8 * 2^57 = 2^60 */
806  felem_diff_128_64(tmp, ftmp);
807  /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */
808  felem_reduce(x_out, tmp);
809 
810  /* z' = (y + z)^2 - gamma - delta */
811  felem_sum(delta, gamma);
812  /* delta[i] < 2^57 + 2^57 = 2^58 */
813  felem_assign(ftmp, y_in);
814  felem_sum(ftmp, z_in);
815  /* ftmp[i] < 2^57 + 2^57 = 2^58 */
816  felem_square(tmp, ftmp);
817  /* tmp[i] < 4 * 2^58 * 2^58 = 2^118 */
818  felem_diff_128_64(tmp, delta);
819  /* tmp[i] < 2^118 + 2^64 + 8 < 2^119 */
820  felem_reduce(z_out, tmp);
821 
822  /* y' = alpha*(4*beta - x') - 8*gamma^2 */
823  felem_scalar(beta, 4);
824  /* beta[i] < 4 * 2^57 = 2^59 */
825  felem_diff(beta, x_out);
826  /* beta[i] < 2^59 + 2^58 + 2 < 2^60 */
827  felem_mul(tmp, alpha, beta);
828  /* tmp[i] < 4 * 2^57 * 2^60 = 2^119 */
829  felem_square(tmp2, gamma);
830  /* tmp2[i] < 4 * 2^57 * 2^57 = 2^116 */
831  widefelem_scalar(tmp2, 8);
832  /* tmp2[i] < 8 * 2^116 = 2^119 */
833  widefelem_diff(tmp, tmp2);
834  /* tmp[i] < 2^119 + 2^120 < 2^121 */
835  felem_reduce(y_out, tmp);
836  }
837 
838 /* Add two elliptic curve points:
839  * (X_1, Y_1, Z_1) + (X_2, Y_2, Z_2) = (X_3, Y_3, Z_3), where
840  * X_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1)^2 - (Z_1^2 * X_2 - Z_2^2 * X_1)^3 -
841  * 2 * Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^2
842  * 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) -
843  * Z_2^3 * Y_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^3
844  * Z_3 = (Z_1^2 * X_2 - Z_2^2 * X_1) * (Z_1 * Z_2)
845  *
846  * This runs faster if 'mixed' is set, which requires Z_2 = 1 or Z_2 = 0.
847  */
848 
849 /* This function is not entirely constant-time:
850  * it includes a branch for checking whether the two input points are equal,
851  * (while not equal to the point at infinity).
852  * This case never happens during single point multiplication,
853  * so there is no timing leak for ECDH or ECDSA signing. */
854 static void point_add(felem x3, felem y3, felem z3,
855  const felem x1, const felem y1, const felem z1,
856  const int mixed, const felem x2, const felem y2, const felem z2)
857  {
858  felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, x_out, y_out, z_out;
859  widefelem tmp, tmp2;
860  limb z1_is_zero, z2_is_zero, x_equal, y_equal;
861 
862  if (!mixed)
863  {
864  /* ftmp2 = z2^2 */
865  felem_square(tmp, z2);
866  felem_reduce(ftmp2, tmp);
867 
868  /* ftmp4 = z2^3 */
869  felem_mul(tmp, ftmp2, z2);
870  felem_reduce(ftmp4, tmp);
871 
872  /* ftmp4 = z2^3*y1 */
873  felem_mul(tmp2, ftmp4, y1);
874  felem_reduce(ftmp4, tmp2);
875 
876  /* ftmp2 = z2^2*x1 */
877  felem_mul(tmp2, ftmp2, x1);
878  felem_reduce(ftmp2, tmp2);
879  }
880  else
881  {
882  /* We'll assume z2 = 1 (special case z2 = 0 is handled later) */
883 
884  /* ftmp4 = z2^3*y1 */
885  felem_assign(ftmp4, y1);
886 
887  /* ftmp2 = z2^2*x1 */
888  felem_assign(ftmp2, x1);
889  }
890 
891  /* ftmp = z1^2 */
892  felem_square(tmp, z1);
893  felem_reduce(ftmp, tmp);
894 
895  /* ftmp3 = z1^3 */
896  felem_mul(tmp, ftmp, z1);
897  felem_reduce(ftmp3, tmp);
898 
899  /* tmp = z1^3*y2 */
900  felem_mul(tmp, ftmp3, y2);
901  /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
902 
903  /* ftmp3 = z1^3*y2 - z2^3*y1 */
904  felem_diff_128_64(tmp, ftmp4);
905  /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */
906  felem_reduce(ftmp3, tmp);
907 
908  /* tmp = z1^2*x2 */
909  felem_mul(tmp, ftmp, x2);
910  /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
911 
912  /* ftmp = z1^2*x2 - z2^2*x1 */
913  felem_diff_128_64(tmp, ftmp2);
914  /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */
915  felem_reduce(ftmp, tmp);
916 
917  /* the formulae are incorrect if the points are equal
918  * so we check for this and do doubling if this happens */
919  x_equal = felem_is_zero(ftmp);
920  y_equal = felem_is_zero(ftmp3);
921  z1_is_zero = felem_is_zero(z1);
922  z2_is_zero = felem_is_zero(z2);
923  /* In affine coordinates, (X_1, Y_1) == (X_2, Y_2) */
924  if (x_equal && y_equal && !z1_is_zero && !z2_is_zero)
925  {
926  point_double(x3, y3, z3, x1, y1, z1);
927  return;
928  }
929 
930  /* ftmp5 = z1*z2 */
931  if (!mixed)
932  {
933  felem_mul(tmp, z1, z2);
934  felem_reduce(ftmp5, tmp);
935  }
936  else
937  {
938  /* special case z2 = 0 is handled later */
939  felem_assign(ftmp5, z1);
940  }
941 
942  /* z_out = (z1^2*x2 - z2^2*x1)*(z1*z2) */
943  felem_mul(tmp, ftmp, ftmp5);
944  felem_reduce(z_out, tmp);
945 
946  /* ftmp = (z1^2*x2 - z2^2*x1)^2 */
947  felem_assign(ftmp5, ftmp);
948  felem_square(tmp, ftmp);
949  felem_reduce(ftmp, tmp);
950 
951  /* ftmp5 = (z1^2*x2 - z2^2*x1)^3 */
952  felem_mul(tmp, ftmp, ftmp5);
953  felem_reduce(ftmp5, tmp);
954 
955  /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */
956  felem_mul(tmp, ftmp2, ftmp);
957  felem_reduce(ftmp2, tmp);
958 
959  /* tmp = z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */
960  felem_mul(tmp, ftmp4, ftmp5);
961  /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
962 
963  /* tmp2 = (z1^3*y2 - z2^3*y1)^2 */
964  felem_square(tmp2, ftmp3);
965  /* tmp2[i] < 4 * 2^57 * 2^57 < 2^116 */
966 
967  /* tmp2 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 */
968  felem_diff_128_64(tmp2, ftmp5);
969  /* tmp2[i] < 2^116 + 2^64 + 8 < 2^117 */
970 
971  /* ftmp5 = 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */
972  felem_assign(ftmp5, ftmp2);
973  felem_scalar(ftmp5, 2);
974  /* ftmp5[i] < 2 * 2^57 = 2^58 */
975 
976  /* x_out = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 -
977  2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */
978  felem_diff_128_64(tmp2, ftmp5);
979  /* tmp2[i] < 2^117 + 2^64 + 8 < 2^118 */
980  felem_reduce(x_out, tmp2);
981 
982  /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out */
983  felem_diff(ftmp2, x_out);
984  /* ftmp2[i] < 2^57 + 2^58 + 2 < 2^59 */
985 
986  /* tmp2 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) */
987  felem_mul(tmp2, ftmp3, ftmp2);
988  /* tmp2[i] < 4 * 2^57 * 2^59 = 2^118 */
989 
990  /* y_out = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) -
991  z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */
992  widefelem_diff(tmp2, tmp);
993  /* tmp2[i] < 2^118 + 2^120 < 2^121 */
994  felem_reduce(y_out, tmp2);
995 
996  /* the result (x_out, y_out, z_out) is incorrect if one of the inputs is
997  * the point at infinity, so we need to check for this separately */
998 
999  /* if point 1 is at infinity, copy point 2 to output, and vice versa */
1000  copy_conditional(x_out, x2, z1_is_zero);
1001  copy_conditional(x_out, x1, z2_is_zero);
1002  copy_conditional(y_out, y2, z1_is_zero);
1003  copy_conditional(y_out, y1, z2_is_zero);
1004  copy_conditional(z_out, z2, z1_is_zero);
1005  copy_conditional(z_out, z1, z2_is_zero);
1006  felem_assign(x3, x_out);
1007  felem_assign(y3, y_out);
1008  felem_assign(z3, z_out);
1009  }
1010 
1011 /* select_point selects the |idx|th point from a precomputation table and
1012  * copies it to out. */
1013 static void select_point(const u64 idx, unsigned int size, const felem pre_comp[/*size*/][3], felem out[3])
1014  {
1015  unsigned i, j;
1016  limb *outlimbs = &out[0][0];
1017  memset(outlimbs, 0, 3 * sizeof(felem));
1018 
1019  for (i = 0; i < size; i++)
1020  {
1021  const limb *inlimbs = &pre_comp[i][0][0];
1022  u64 mask = i ^ idx;
1023  mask |= mask >> 4;
1024  mask |= mask >> 2;
1025  mask |= mask >> 1;
1026  mask &= 1;
1027  mask--;
1028  for (j = 0; j < 4 * 3; j++)
1029  outlimbs[j] |= inlimbs[j] & mask;
1030  }
1031  }
1032 
1033 /* get_bit returns the |i|th bit in |in| */
1034 static char get_bit(const felem_bytearray in, unsigned i)
1035  {
1036  if (i >= 224)
1037  return 0;
1038  return (in[i >> 3] >> (i & 7)) & 1;
1039  }
1040 
1041 /* Interleaved point multiplication using precomputed point multiples:
1042  * The small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[],
1043  * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple
1044  * of the generator, using certain (large) precomputed multiples in g_pre_comp.
1045  * Output point (X, Y, Z) is stored in x_out, y_out, z_out */
1046 static void batch_mul(felem x_out, felem y_out, felem z_out,
1047  const felem_bytearray scalars[], const unsigned num_points, const u8 *g_scalar,
1048  const int mixed, const felem pre_comp[][17][3], const felem g_pre_comp[2][16][3])
1049  {
1050  int i, skip;
1051  unsigned num;
1052  unsigned gen_mul = (g_scalar != NULL);
1053  felem nq[3], tmp[4];
1054  u64 bits;
1055  u8 sign, digit;
1056 
1057  /* set nq to the point at infinity */
1058  memset(nq, 0, 3 * sizeof(felem));
1059 
1060  /* Loop over all scalars msb-to-lsb, interleaving additions
1061  * of multiples of the generator (two in each of the last 28 rounds)
1062  * and additions of other points multiples (every 5th round).
1063  */
1064  skip = 1; /* save two point operations in the first round */
1065  for (i = (num_points ? 220 : 27); i >= 0; --i)
1066  {
1067  /* double */
1068  if (!skip)
1069  point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]);
1070 
1071  /* add multiples of the generator */
1072  if (gen_mul && (i <= 27))
1073  {
1074  /* first, look 28 bits upwards */
1075  bits = get_bit(g_scalar, i + 196) << 3;
1076  bits |= get_bit(g_scalar, i + 140) << 2;
1077  bits |= get_bit(g_scalar, i + 84) << 1;
1078  bits |= get_bit(g_scalar, i + 28);
1079  /* select the point to add, in constant time */
1080  select_point(bits, 16, g_pre_comp[1], tmp);
1081 
1082  if (!skip)
1083  {
1084  point_add(nq[0], nq[1], nq[2],
1085  nq[0], nq[1], nq[2],
1086  1 /* mixed */, tmp[0], tmp[1], tmp[2]);
1087  }
1088  else
1089  {
1090  memcpy(nq, tmp, 3 * sizeof(felem));
1091  skip = 0;
1092  }
1093 
1094  /* second, look at the current position */
1095  bits = get_bit(g_scalar, i + 168) << 3;
1096  bits |= get_bit(g_scalar, i + 112) << 2;
1097  bits |= get_bit(g_scalar, i + 56) << 1;
1098  bits |= get_bit(g_scalar, i);
1099  /* select the point to add, in constant time */
1100  select_point(bits, 16, g_pre_comp[0], tmp);
1101  point_add(nq[0], nq[1], nq[2],
1102  nq[0], nq[1], nq[2],
1103  1 /* mixed */, tmp[0], tmp[1], tmp[2]);
1104  }
1105 
1106  /* do other additions every 5 doublings */
1107  if (num_points && (i % 5 == 0))
1108  {
1109  /* loop over all scalars */
1110  for (num = 0; num < num_points; ++num)
1111  {
1112  bits = get_bit(scalars[num], i + 4) << 5;
1113  bits |= get_bit(scalars[num], i + 3) << 4;
1114  bits |= get_bit(scalars[num], i + 2) << 3;
1115  bits |= get_bit(scalars[num], i + 1) << 2;
1116  bits |= get_bit(scalars[num], i) << 1;
1117  bits |= get_bit(scalars[num], i - 1);
1118  ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits);
1119 
1120  /* select the point to add or subtract */
1121  select_point(digit, 17, pre_comp[num], tmp);
1122  felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the negative point */
1123  copy_conditional(tmp[1], tmp[3], sign);
1124 
1125  if (!skip)
1126  {
1127  point_add(nq[0], nq[1], nq[2],
1128  nq[0], nq[1], nq[2],
1129  mixed, tmp[0], tmp[1], tmp[2]);
1130  }
1131  else
1132  {
1133  memcpy(nq, tmp, 3 * sizeof(felem));
1134  skip = 0;
1135  }
1136  }
1137  }
1138  }
1139  felem_assign(x_out, nq[0]);
1140  felem_assign(y_out, nq[1]);
1141  felem_assign(z_out, nq[2]);
1142  }
1143 
1144 /******************************************************************************/
1145 /* FUNCTIONS TO MANAGE PRECOMPUTATION
1146  */
1147 
1148 static NISTP224_PRE_COMP *nistp224_pre_comp_new()
1149  {
1150  NISTP224_PRE_COMP *ret = NULL;
1151  ret = (NISTP224_PRE_COMP *) OPENSSL_malloc(sizeof *ret);
1152  if (!ret)
1153  {
1154  ECerr(EC_F_NISTP224_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
1155  return ret;
1156  }
1157  memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp));
1158  ret->references = 1;
1159  return ret;
1160  }
1161 
1162 static void *nistp224_pre_comp_dup(void *src_)
1163  {
1164  NISTP224_PRE_COMP *src = src_;
1165 
1166  /* no need to actually copy, these objects never change! */
1167  CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
1168 
1169  return src_;
1170  }
1171 
1172 static void nistp224_pre_comp_free(void *pre_)
1173  {
1174  int i;
1175  NISTP224_PRE_COMP *pre = pre_;
1176 
1177  if (!pre)
1178  return;
1179 
1180  i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1181  if (i > 0)
1182  return;
1183 
1184  OPENSSL_free(pre);
1185  }
1186 
1187 static void nistp224_pre_comp_clear_free(void *pre_)
1188  {
1189  int i;
1190  NISTP224_PRE_COMP *pre = pre_;
1191 
1192  if (!pre)
1193  return;
1194 
1195  i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1196  if (i > 0)
1197  return;
1198 
1199  OPENSSL_cleanse(pre, sizeof *pre);
1200  OPENSSL_free(pre);
1201  }
1202 
1203 /******************************************************************************/
1204 /* OPENSSL EC_METHOD FUNCTIONS
1205  */
1206 
1207 int ec_GFp_nistp224_group_init(EC_GROUP *group)
1208  {
1209  int ret;
1210  ret = ec_GFp_simple_group_init(group);
1211  group->a_is_minus3 = 1;
1212  return ret;
1213  }
1214 
1215 int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p,
1216  const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1217  {
1218  int ret = 0;
1219  BN_CTX *new_ctx = NULL;
1220  BIGNUM *curve_p, *curve_a, *curve_b;
1221 
1222  if (ctx == NULL)
1223  if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0;
1224  BN_CTX_start(ctx);
1225  if (((curve_p = BN_CTX_get(ctx)) == NULL) ||
1226  ((curve_a = BN_CTX_get(ctx)) == NULL) ||
1227  ((curve_b = BN_CTX_get(ctx)) == NULL)) goto err;
1228  BN_bin2bn(nistp224_curve_params[0], sizeof(felem_bytearray), curve_p);
1229  BN_bin2bn(nistp224_curve_params[1], sizeof(felem_bytearray), curve_a);
1230  BN_bin2bn(nistp224_curve_params[2], sizeof(felem_bytearray), curve_b);
1231  if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) ||
1232  (BN_cmp(curve_b, b)))
1233  {
1234  ECerr(EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE,
1235  EC_R_WRONG_CURVE_PARAMETERS);
1236  goto err;
1237  }
1238  group->field_mod_func = BN_nist_mod_224;
1239  ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx);
1240 err:
1241  BN_CTX_end(ctx);
1242  if (new_ctx != NULL)
1243  BN_CTX_free(new_ctx);
1244  return ret;
1245  }
1246 
1247 /* Takes the Jacobian coordinates (X, Y, Z) of a point and returns
1248  * (X', Y') = (X/Z^2, Y/Z^3) */
1249 int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group,
1250  const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
1251  {
1252  felem z1, z2, x_in, y_in, x_out, y_out;
1253  widefelem tmp;
1254 
1255  if (EC_POINT_is_at_infinity(group, point))
1256  {
1257  ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES,
1258  EC_R_POINT_AT_INFINITY);
1259  return 0;
1260  }
1261  if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) ||
1262  (!BN_to_felem(z1, &point->Z))) return 0;
1263  felem_inv(z2, z1);
1264  felem_square(tmp, z2); felem_reduce(z1, tmp);
1265  felem_mul(tmp, x_in, z1); felem_reduce(x_in, tmp);
1266  felem_contract(x_out, x_in);
1267  if (x != NULL)
1268  {
1269  if (!felem_to_BN(x, x_out)) {
1270  ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES,
1271  ERR_R_BN_LIB);
1272  return 0;
1273  }
1274  }
1275  felem_mul(tmp, z1, z2); felem_reduce(z1, tmp);
1276  felem_mul(tmp, y_in, z1); felem_reduce(y_in, tmp);
1277  felem_contract(y_out, y_in);
1278  if (y != NULL)
1279  {
1280  if (!felem_to_BN(y, y_out)) {
1281  ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES,
1282  ERR_R_BN_LIB);
1283  return 0;
1284  }
1285  }
1286  return 1;
1287  }
1288 
1289 static void make_points_affine(size_t num, felem points[/*num*/][3], felem tmp_felems[/*num+1*/])
1290  {
1291  /* Runs in constant time, unless an input is the point at infinity
1292  * (which normally shouldn't happen). */
1293  ec_GFp_nistp_points_make_affine_internal(
1294  num,
1295  points,
1296  sizeof(felem),
1297  tmp_felems,
1298  (void (*)(void *)) felem_one,
1299  (int (*)(const void *)) felem_is_zero_int,
1300  (void (*)(void *, const void *)) felem_assign,
1301  (void (*)(void *, const void *)) felem_square_reduce,
1302  (void (*)(void *, const void *, const void *)) felem_mul_reduce,
1303  (void (*)(void *, const void *)) felem_inv,
1304  (void (*)(void *, const void *)) felem_contract);
1305  }
1306 
1307 /* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values
1308  * Result is stored in r (r can equal one of the inputs). */
1309 int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r,
1310  const BIGNUM *scalar, size_t num, const EC_POINT *points[],
1311  const BIGNUM *scalars[], BN_CTX *ctx)
1312  {
1313  int ret = 0;
1314  int j;
1315  unsigned i;
1316  int mixed = 0;
1317  BN_CTX *new_ctx = NULL;
1318  BIGNUM *x, *y, *z, *tmp_scalar;
1319  felem_bytearray g_secret;
1320  felem_bytearray *secrets = NULL;
1321  felem (*pre_comp)[17][3] = NULL;
1322  felem *tmp_felems = NULL;
1323  felem_bytearray tmp;
1324  unsigned num_bytes;
1325  int have_pre_comp = 0;
1326  size_t num_points = num;
1327  felem x_in, y_in, z_in, x_out, y_out, z_out;
1328  NISTP224_PRE_COMP *pre = NULL;
1329  const felem (*g_pre_comp)[16][3] = NULL;
1330  EC_POINT *generator = NULL;
1331  const EC_POINT *p = NULL;
1332  const BIGNUM *p_scalar = NULL;
1333 
1334  if (ctx == NULL)
1335  if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0;
1336  BN_CTX_start(ctx);
1337  if (((x = BN_CTX_get(ctx)) == NULL) ||
1338  ((y = BN_CTX_get(ctx)) == NULL) ||
1339  ((z = BN_CTX_get(ctx)) == NULL) ||
1340  ((tmp_scalar = BN_CTX_get(ctx)) == NULL))
1341  goto err;
1342 
1343  if (scalar != NULL)
1344  {
1345  pre = EC_EX_DATA_get_data(group->extra_data,
1346  nistp224_pre_comp_dup, nistp224_pre_comp_free,
1347  nistp224_pre_comp_clear_free);
1348  if (pre)
1349  /* we have precomputation, try to use it */
1350  g_pre_comp = (const felem (*)[16][3]) pre->g_pre_comp;
1351  else
1352  /* try to use the standard precomputation */
1353  g_pre_comp = &gmul[0];
1354  generator = EC_POINT_new(group);
1355  if (generator == NULL)
1356  goto err;
1357  /* get the generator from precomputation */
1358  if (!felem_to_BN(x, g_pre_comp[0][1][0]) ||
1359  !felem_to_BN(y, g_pre_comp[0][1][1]) ||
1360  !felem_to_BN(z, g_pre_comp[0][1][2]))
1361  {
1362  ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB);
1363  goto err;
1364  }
1365  if (!EC_POINT_set_Jprojective_coordinates_GFp(group,
1366  generator, x, y, z, ctx))
1367  goto err;
1368  if (0 == EC_POINT_cmp(group, generator, group->generator, ctx))
1369  /* precomputation matches generator */
1370  have_pre_comp = 1;
1371  else
1372  /* we don't have valid precomputation:
1373  * treat the generator as a random point */
1374  num_points = num_points + 1;
1375  }
1376 
1377  if (num_points > 0)
1378  {
1379  if (num_points >= 3)
1380  {
1381  /* unless we precompute multiples for just one or two points,
1382  * converting those into affine form is time well spent */
1383  mixed = 1;
1384  }
1385  secrets = OPENSSL_malloc(num_points * sizeof(felem_bytearray));
1386  pre_comp = OPENSSL_malloc(num_points * 17 * 3 * sizeof(felem));
1387  if (mixed)
1388  tmp_felems = OPENSSL_malloc((num_points * 17 + 1) * sizeof(felem));
1389  if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_felems == NULL)))
1390  {
1391  ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1392  goto err;
1393  }
1394 
1395  /* we treat NULL scalars as 0, and NULL points as points at infinity,
1396  * i.e., they contribute nothing to the linear combination */
1397  memset(secrets, 0, num_points * sizeof(felem_bytearray));
1398  memset(pre_comp, 0, num_points * 17 * 3 * sizeof(felem));
1399  for (i = 0; i < num_points; ++i)
1400  {
1401  if (i == num)
1402  /* the generator */
1403  {
1404  p = EC_GROUP_get0_generator(group);
1405  p_scalar = scalar;
1406  }
1407  else
1408  /* the i^th point */
1409  {
1410  p = points[i];
1411  p_scalar = scalars[i];
1412  }
1413  if ((p_scalar != NULL) && (p != NULL))
1414  {
1415  /* reduce scalar to 0 <= scalar < 2^224 */
1416  if ((BN_num_bits(p_scalar) > 224) || (BN_is_negative(p_scalar)))
1417  {
1418  /* this is an unusual input, and we don't guarantee
1419  * constant-timeness */
1420  if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx))
1421  {
1422  ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB);
1423  goto err;
1424  }
1425  num_bytes = BN_bn2bin(tmp_scalar, tmp);
1426  }
1427  else
1428  num_bytes = BN_bn2bin(p_scalar, tmp);
1429  flip_endian(secrets[i], tmp, num_bytes);
1430  /* precompute multiples */
1431  if ((!BN_to_felem(x_out, &p->X)) ||
1432  (!BN_to_felem(y_out, &p->Y)) ||
1433  (!BN_to_felem(z_out, &p->Z))) goto err;
1434  felem_assign(pre_comp[i][1][0], x_out);
1435  felem_assign(pre_comp[i][1][1], y_out);
1436  felem_assign(pre_comp[i][1][2], z_out);
1437  for (j = 2; j <= 16; ++j)
1438  {
1439  if (j & 1)
1440  {
1441  point_add(
1442  pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2],
1443  pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2],
1444  0, pre_comp[i][j-1][0], pre_comp[i][j-1][1], pre_comp[i][j-1][2]);
1445  }
1446  else
1447  {
1448  point_double(
1449  pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2],
1450  pre_comp[i][j/2][0], pre_comp[i][j/2][1], pre_comp[i][j/2][2]);
1451  }
1452  }
1453  }
1454  }
1455  if (mixed)
1456  make_points_affine(num_points * 17, pre_comp[0], tmp_felems);
1457  }
1458 
1459  /* the scalar for the generator */
1460  if ((scalar != NULL) && (have_pre_comp))
1461  {
1462  memset(g_secret, 0, sizeof g_secret);
1463  /* reduce scalar to 0 <= scalar < 2^224 */
1464  if ((BN_num_bits(scalar) > 224) || (BN_is_negative(scalar)))
1465  {
1466  /* this is an unusual input, and we don't guarantee
1467  * constant-timeness */
1468  if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx))
1469  {
1470  ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB);
1471  goto err;
1472  }
1473  num_bytes = BN_bn2bin(tmp_scalar, tmp);
1474  }
1475  else
1476  num_bytes = BN_bn2bin(scalar, tmp);
1477  flip_endian(g_secret, tmp, num_bytes);
1478  /* do the multiplication with generator precomputation*/
1479  batch_mul(x_out, y_out, z_out,
1480  (const felem_bytearray (*)) secrets, num_points,
1481  g_secret,
1482  mixed, (const felem (*)[17][3]) pre_comp,
1483  g_pre_comp);
1484  }
1485  else
1486  /* do the multiplication without generator precomputation */
1487  batch_mul(x_out, y_out, z_out,
1488  (const felem_bytearray (*)) secrets, num_points,
1489  NULL, mixed, (const felem (*)[17][3]) pre_comp, NULL);
1490  /* reduce the output to its unique minimal representation */
1491  felem_contract(x_in, x_out);
1492  felem_contract(y_in, y_out);
1493  felem_contract(z_in, z_out);
1494  if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) ||
1495  (!felem_to_BN(z, z_in)))
1496  {
1497  ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB);
1498  goto err;
1499  }
1500  ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx);
1501 
1502 err:
1503  BN_CTX_end(ctx);
1504  if (generator != NULL)
1505  EC_POINT_free(generator);
1506  if (new_ctx != NULL)
1507  BN_CTX_free(new_ctx);
1508  if (secrets != NULL)
1509  OPENSSL_free(secrets);
1510  if (pre_comp != NULL)
1511  OPENSSL_free(pre_comp);
1512  if (tmp_felems != NULL)
1513  OPENSSL_free(tmp_felems);
1514  return ret;
1515  }
1516 
1517 int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
1518  {
1519  int ret = 0;
1520  NISTP224_PRE_COMP *pre = NULL;
1521  int i, j;
1522  BN_CTX *new_ctx = NULL;
1523  BIGNUM *x, *y;
1524  EC_POINT *generator = NULL;
1525  felem tmp_felems[32];
1526 
1527  /* throw away old precomputation */
1528  EC_EX_DATA_free_data(&group->extra_data, nistp224_pre_comp_dup,
1529  nistp224_pre_comp_free, nistp224_pre_comp_clear_free);
1530  if (ctx == NULL)
1531  if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0;
1532  BN_CTX_start(ctx);
1533  if (((x = BN_CTX_get(ctx)) == NULL) ||
1534  ((y = BN_CTX_get(ctx)) == NULL))
1535  goto err;
1536  /* get the generator */
1537  if (group->generator == NULL) goto err;
1538  generator = EC_POINT_new(group);
1539  if (generator == NULL)
1540  goto err;
1541  BN_bin2bn(nistp224_curve_params[3], sizeof (felem_bytearray), x);
1542  BN_bin2bn(nistp224_curve_params[4], sizeof (felem_bytearray), y);
1543  if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx))
1544  goto err;
1545  if ((pre = nistp224_pre_comp_new()) == NULL)
1546  goto err;
1547  /* if the generator is the standard one, use built-in precomputation */
1548  if (0 == EC_POINT_cmp(group, generator, group->generator, ctx))
1549  {
1550  memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp));
1551  ret = 1;
1552  goto err;
1553  }
1554  if ((!BN_to_felem(pre->g_pre_comp[0][1][0], &group->generator->X)) ||
1555  (!BN_to_felem(pre->g_pre_comp[0][1][1], &group->generator->Y)) ||
1556  (!BN_to_felem(pre->g_pre_comp[0][1][2], &group->generator->Z)))
1557  goto err;
1558  /* compute 2^56*G, 2^112*G, 2^168*G for the first table,
1559  * 2^28*G, 2^84*G, 2^140*G, 2^196*G for the second one
1560  */
1561  for (i = 1; i <= 8; i <<= 1)
1562  {
1563  point_double(
1564  pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2],
1565  pre->g_pre_comp[0][i][0], pre->g_pre_comp[0][i][1], pre->g_pre_comp[0][i][2]);
1566  for (j = 0; j < 27; ++j)
1567  {
1568  point_double(
1569  pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2],
1570  pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]);
1571  }
1572  if (i == 8)
1573  break;
1574  point_double(
1575  pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2],
1576  pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]);
1577  for (j = 0; j < 27; ++j)
1578  {
1579  point_double(
1580  pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2],
1581  pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2]);
1582  }
1583  }
1584  for (i = 0; i < 2; i++)
1585  {
1586  /* g_pre_comp[i][0] is the point at infinity */
1587  memset(pre->g_pre_comp[i][0], 0, sizeof(pre->g_pre_comp[i][0]));
1588  /* the remaining multiples */
1589  /* 2^56*G + 2^112*G resp. 2^84*G + 2^140*G */
1590  point_add(
1591  pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1],
1592  pre->g_pre_comp[i][6][2], pre->g_pre_comp[i][4][0],
1593  pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2],
1594  0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1],
1595  pre->g_pre_comp[i][2][2]);
1596  /* 2^56*G + 2^168*G resp. 2^84*G + 2^196*G */
1597  point_add(
1598  pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1],
1599  pre->g_pre_comp[i][10][2], pre->g_pre_comp[i][8][0],
1600  pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2],
1601  0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1],
1602  pre->g_pre_comp[i][2][2]);
1603  /* 2^112*G + 2^168*G resp. 2^140*G + 2^196*G */
1604  point_add(
1605  pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1],
1606  pre->g_pre_comp[i][12][2], pre->g_pre_comp[i][8][0],
1607  pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2],
1608  0, pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1],
1609  pre->g_pre_comp[i][4][2]);
1610  /* 2^56*G + 2^112*G + 2^168*G resp. 2^84*G + 2^140*G + 2^196*G */
1611  point_add(
1612  pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1],
1613  pre->g_pre_comp[i][14][2], pre->g_pre_comp[i][12][0],
1614  pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2],
1615  0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1],
1616  pre->g_pre_comp[i][2][2]);
1617  for (j = 1; j < 8; ++j)
1618  {
1619  /* odd multiples: add G resp. 2^28*G */
1620  point_add(
1621  pre->g_pre_comp[i][2*j+1][0], pre->g_pre_comp[i][2*j+1][1],
1622  pre->g_pre_comp[i][2*j+1][2], pre->g_pre_comp[i][2*j][0],
1623  pre->g_pre_comp[i][2*j][1], pre->g_pre_comp[i][2*j][2],
1624  0, pre->g_pre_comp[i][1][0], pre->g_pre_comp[i][1][1],
1625  pre->g_pre_comp[i][1][2]);
1626  }
1627  }
1628  make_points_affine(31, &(pre->g_pre_comp[0][1]), tmp_felems);
1629 
1630  if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp224_pre_comp_dup,
1631  nistp224_pre_comp_free, nistp224_pre_comp_clear_free))
1632  goto err;
1633  ret = 1;
1634  pre = NULL;
1635  err:
1636  BN_CTX_end(ctx);
1637  if (generator != NULL)
1638  EC_POINT_free(generator);
1639  if (new_ctx != NULL)
1640  BN_CTX_free(new_ctx);
1641  if (pre)
1642  nistp224_pre_comp_free(pre);
1643  return ret;
1644  }
1645 
1646 int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group)
1647  {
1648  if (EC_EX_DATA_get_data(group->extra_data, nistp224_pre_comp_dup,
1649  nistp224_pre_comp_free, nistp224_pre_comp_clear_free)
1650  != NULL)
1651  return 1;
1652  else
1653  return 0;
1654  }
1655 
1656 #else
1657 static void *dummy=&dummy;
1658 #endif
Generated on Thu Jan 10 2013 09:53:36 for OpenSSL by   doxygen 1.8.2