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-rw-r--r--src/lib/libcrypto/ec/ecp_nistp521.c1607
1 files changed, 854 insertions, 753 deletions
diff --git a/src/lib/libcrypto/ec/ecp_nistp521.c b/src/lib/libcrypto/ec/ecp_nistp521.c
index c34c38b7e8..f5b72a4c0d 100644
--- a/src/lib/libcrypto/ec/ecp_nistp521.c
+++ b/src/lib/libcrypto/ec/ecp_nistp521.c
@@ -133,46 +133,50 @@ static const limb bottom58bits = 0x3ffffffffffffff;
133 133
134/* bin66_to_felem takes a little-endian byte array and converts it into felem 134/* bin66_to_felem takes a little-endian byte array and converts it into felem
135 * form. This assumes that the CPU is little-endian. */ 135 * form. This assumes that the CPU is little-endian. */
136static void bin66_to_felem(felem out, const u8 in[66]) 136static void
137 { 137bin66_to_felem(felem out, const u8 in[66])
138 out[0] = (*((limb*) &in[0])) & bottom58bits; 138{
139 out[1] = (*((limb*) &in[7]) >> 2) & bottom58bits; 139 out[0] = (*((limb *) & in[0])) & bottom58bits;
140 out[2] = (*((limb*) &in[14]) >> 4) & bottom58bits; 140 out[1] = (*((limb *) & in[7]) >> 2) & bottom58bits;
141 out[3] = (*((limb*) &in[21]) >> 6) & bottom58bits; 141 out[2] = (*((limb *) & in[14]) >> 4) & bottom58bits;
142 out[4] = (*((limb*) &in[29])) & bottom58bits; 142 out[3] = (*((limb *) & in[21]) >> 6) & bottom58bits;
143 out[5] = (*((limb*) &in[36]) >> 2) & bottom58bits; 143 out[4] = (*((limb *) & in[29])) & bottom58bits;
144 out[6] = (*((limb*) &in[43]) >> 4) & bottom58bits; 144 out[5] = (*((limb *) & in[36]) >> 2) & bottom58bits;
145 out[7] = (*((limb*) &in[50]) >> 6) & bottom58bits; 145 out[6] = (*((limb *) & in[43]) >> 4) & bottom58bits;
146 out[8] = (*((limb*) &in[58])) & bottom57bits; 146 out[7] = (*((limb *) & in[50]) >> 6) & bottom58bits;
147 } 147 out[8] = (*((limb *) & in[58])) & bottom57bits;
148}
148 149
149/* felem_to_bin66 takes an felem and serialises into a little endian, 66 byte 150/* felem_to_bin66 takes an felem and serialises into a little endian, 66 byte
150 * array. This assumes that the CPU is little-endian. */ 151 * array. This assumes that the CPU is little-endian. */
151static void felem_to_bin66(u8 out[66], const felem in) 152static void
152 { 153felem_to_bin66(u8 out[66], const felem in)
154{
153 memset(out, 0, 66); 155 memset(out, 0, 66);
154 (*((limb*) &out[0])) = in[0]; 156 (*((limb *) & out[0])) = in[0];
155 (*((limb*) &out[7])) |= in[1] << 2; 157 (*((limb *) & out[7])) |= in[1] << 2;
156 (*((limb*) &out[14])) |= in[2] << 4; 158 (*((limb *) & out[14])) |= in[2] << 4;
157 (*((limb*) &out[21])) |= in[3] << 6; 159 (*((limb *) & out[21])) |= in[3] << 6;
158 (*((limb*) &out[29])) = in[4]; 160 (*((limb *) & out[29])) = in[4];
159 (*((limb*) &out[36])) |= in[5] << 2; 161 (*((limb *) & out[36])) |= in[5] << 2;
160 (*((limb*) &out[43])) |= in[6] << 4; 162 (*((limb *) & out[43])) |= in[6] << 4;
161 (*((limb*) &out[50])) |= in[7] << 6; 163 (*((limb *) & out[50])) |= in[7] << 6;
162 (*((limb*) &out[58])) = in[8]; 164 (*((limb *) & out[58])) = in[8];
163 } 165}
164 166
165/* To preserve endianness when using BN_bn2bin and BN_bin2bn */ 167/* To preserve endianness when using BN_bn2bin and BN_bin2bn */
166static void flip_endian(u8 *out, const u8 *in, unsigned len) 168static void
167 { 169flip_endian(u8 * out, const u8 * in, unsigned len)
170{
168 unsigned i; 171 unsigned i;
169 for (i = 0; i < len; ++i) 172 for (i = 0; i < len; ++i)
170 out[i] = in[len-1-i]; 173 out[i] = in[len - 1 - i];
171 } 174}
172 175
173/* BN_to_felem converts an OpenSSL BIGNUM into an felem */ 176/* BN_to_felem converts an OpenSSL BIGNUM into an felem */
174static int BN_to_felem(felem out, const BIGNUM *bn) 177static int
175 { 178BN_to_felem(felem out, const BIGNUM * bn)
179{
176 felem_bytearray b_in; 180 felem_bytearray b_in;
177 felem_bytearray b_out; 181 felem_bytearray b_out;
178 unsigned num_bytes; 182 unsigned num_bytes;
@@ -180,37 +184,37 @@ static int BN_to_felem(felem out, const BIGNUM *bn)
180 /* BN_bn2bin eats leading zeroes */ 184 /* BN_bn2bin eats leading zeroes */
181 memset(b_out, 0, sizeof b_out); 185 memset(b_out, 0, sizeof b_out);
182 num_bytes = BN_num_bytes(bn); 186 num_bytes = BN_num_bytes(bn);
183 if (num_bytes > sizeof b_out) 187 if (num_bytes > sizeof b_out) {
184 {
185 ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); 188 ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE);
186 return 0; 189 return 0;
187 } 190 }
188 if (BN_is_negative(bn)) 191 if (BN_is_negative(bn)) {
189 {
190 ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); 192 ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE);
191 return 0; 193 return 0;
192 } 194 }
193 num_bytes = BN_bn2bin(bn, b_in); 195 num_bytes = BN_bn2bin(bn, b_in);
194 flip_endian(b_out, b_in, num_bytes); 196 flip_endian(b_out, b_in, num_bytes);
195 bin66_to_felem(out, b_out); 197 bin66_to_felem(out, b_out);
196 return 1; 198 return 1;
197 } 199}
198 200
199/* felem_to_BN converts an felem into an OpenSSL BIGNUM */ 201/* felem_to_BN converts an felem into an OpenSSL BIGNUM */
200static BIGNUM *felem_to_BN(BIGNUM *out, const felem in) 202static BIGNUM *
201 { 203felem_to_BN(BIGNUM * out, const felem in)
204{
202 felem_bytearray b_in, b_out; 205 felem_bytearray b_in, b_out;
203 felem_to_bin66(b_in, in); 206 felem_to_bin66(b_in, in);
204 flip_endian(b_out, b_in, sizeof b_out); 207 flip_endian(b_out, b_in, sizeof b_out);
205 return BN_bin2bn(b_out, sizeof b_out, out); 208 return BN_bin2bn(b_out, sizeof b_out, out);
206 } 209}
207 210
208 211
209/* Field operations 212/* Field operations
210 * ---------------- */ 213 * ---------------- */
211 214
212static void felem_one(felem out) 215static void
213 { 216felem_one(felem out)
217{
214 out[0] = 1; 218 out[0] = 1;
215 out[1] = 0; 219 out[1] = 0;
216 out[2] = 0; 220 out[2] = 0;
@@ -220,10 +224,11 @@ static void felem_one(felem out)
220 out[6] = 0; 224 out[6] = 0;
221 out[7] = 0; 225 out[7] = 0;
222 out[8] = 0; 226 out[8] = 0;
223 } 227}
224 228
225static void felem_assign(felem out, const felem in) 229static void
226 { 230felem_assign(felem out, const felem in)
231{
227 out[0] = in[0]; 232 out[0] = in[0];
228 out[1] = in[1]; 233 out[1] = in[1];
229 out[2] = in[2]; 234 out[2] = in[2];
@@ -233,11 +238,12 @@ static void felem_assign(felem out, const felem in)
233 out[6] = in[6]; 238 out[6] = in[6];
234 out[7] = in[7]; 239 out[7] = in[7];
235 out[8] = in[8]; 240 out[8] = in[8];
236 } 241}
237 242
238/* felem_sum64 sets out = out + in. */ 243/* felem_sum64 sets out = out + in. */
239static void felem_sum64(felem out, const felem in) 244static void
240 { 245felem_sum64(felem out, const felem in)
246{
241 out[0] += in[0]; 247 out[0] += in[0];
242 out[1] += in[1]; 248 out[1] += in[1];
243 out[2] += in[2]; 249 out[2] += in[2];
@@ -247,11 +253,12 @@ static void felem_sum64(felem out, const felem in)
247 out[6] += in[6]; 253 out[6] += in[6];
248 out[7] += in[7]; 254 out[7] += in[7];
249 out[8] += in[8]; 255 out[8] += in[8];
250 } 256}
251 257
252/* felem_scalar sets out = in * scalar */ 258/* felem_scalar sets out = in * scalar */
253static void felem_scalar(felem out, const felem in, limb scalar) 259static void
254 { 260felem_scalar(felem out, const felem in, limb scalar)
261{
255 out[0] = in[0] * scalar; 262 out[0] = in[0] * scalar;
256 out[1] = in[1] * scalar; 263 out[1] = in[1] * scalar;
257 out[2] = in[2] * scalar; 264 out[2] = in[2] * scalar;
@@ -261,11 +268,12 @@ static void felem_scalar(felem out, const felem in, limb scalar)
261 out[6] = in[6] * scalar; 268 out[6] = in[6] * scalar;
262 out[7] = in[7] * scalar; 269 out[7] = in[7] * scalar;
263 out[8] = in[8] * scalar; 270 out[8] = in[8] * scalar;
264 } 271}
265 272
266/* felem_scalar64 sets out = out * scalar */ 273/* felem_scalar64 sets out = out * scalar */
267static void felem_scalar64(felem out, limb scalar) 274static void
268 { 275felem_scalar64(felem out, limb scalar)
276{
269 out[0] *= scalar; 277 out[0] *= scalar;
270 out[1] *= scalar; 278 out[1] *= scalar;
271 out[2] *= scalar; 279 out[2] *= scalar;
@@ -275,11 +283,12 @@ static void felem_scalar64(felem out, limb scalar)
275 out[6] *= scalar; 283 out[6] *= scalar;
276 out[7] *= scalar; 284 out[7] *= scalar;
277 out[8] *= scalar; 285 out[8] *= scalar;
278 } 286}
279 287
280/* felem_scalar128 sets out = out * scalar */ 288/* felem_scalar128 sets out = out * scalar */
281static void felem_scalar128(largefelem out, limb scalar) 289static void
282 { 290felem_scalar128(largefelem out, limb scalar)
291{
283 out[0] *= scalar; 292 out[0] *= scalar;
284 out[1] *= scalar; 293 out[1] *= scalar;
285 out[2] *= scalar; 294 out[2] *= scalar;
@@ -289,7 +298,7 @@ static void felem_scalar128(largefelem out, limb scalar)
289 out[6] *= scalar; 298 out[6] *= scalar;
290 out[7] *= scalar; 299 out[7] *= scalar;
291 out[8] *= scalar; 300 out[8] *= scalar;
292 } 301}
293 302
294/* felem_neg sets |out| to |-in| 303/* felem_neg sets |out| to |-in|
295 * On entry: 304 * On entry:
@@ -297,11 +306,12 @@ static void felem_scalar128(largefelem out, limb scalar)
297 * On exit: 306 * On exit:
298 * out[i] < 2^62 307 * out[i] < 2^62
299 */ 308 */
300static void felem_neg(felem out, const felem in) 309static void
301 { 310felem_neg(felem out, const felem in)
311{
302 /* In order to prevent underflow, we subtract from 0 mod p. */ 312 /* In order to prevent underflow, we subtract from 0 mod p. */
303 static const limb two62m3 = (((limb)1) << 62) - (((limb)1) << 5); 313 static const limb two62m3 = (((limb) 1) << 62) - (((limb) 1) << 5);
304 static const limb two62m2 = (((limb)1) << 62) - (((limb)1) << 4); 314 static const limb two62m2 = (((limb) 1) << 62) - (((limb) 1) << 4);
305 315
306 out[0] = two62m3 - in[0]; 316 out[0] = two62m3 - in[0];
307 out[1] = two62m2 - in[1]; 317 out[1] = two62m2 - in[1];
@@ -312,7 +322,7 @@ static void felem_neg(felem out, const felem in)
312 out[6] = two62m2 - in[6]; 322 out[6] = two62m2 - in[6];
313 out[7] = two62m2 - in[7]; 323 out[7] = two62m2 - in[7];
314 out[8] = two62m2 - in[8]; 324 out[8] = two62m2 - in[8];
315 } 325}
316 326
317/* felem_diff64 subtracts |in| from |out| 327/* felem_diff64 subtracts |in| from |out|
318 * On entry: 328 * On entry:
@@ -320,11 +330,12 @@ static void felem_neg(felem out, const felem in)
320 * On exit: 330 * On exit:
321 * out[i] < out[i] + 2^62 331 * out[i] < out[i] + 2^62
322 */ 332 */
323static void felem_diff64(felem out, const felem in) 333static void
324 { 334felem_diff64(felem out, const felem in)
335{
325 /* In order to prevent underflow, we add 0 mod p before subtracting. */ 336 /* In order to prevent underflow, we add 0 mod p before subtracting. */
326 static const limb two62m3 = (((limb)1) << 62) - (((limb)1) << 5); 337 static const limb two62m3 = (((limb) 1) << 62) - (((limb) 1) << 5);
327 static const limb two62m2 = (((limb)1) << 62) - (((limb)1) << 4); 338 static const limb two62m2 = (((limb) 1) << 62) - (((limb) 1) << 4);
328 339
329 out[0] += two62m3 - in[0]; 340 out[0] += two62m3 - in[0];
330 out[1] += two62m2 - in[1]; 341 out[1] += two62m2 - in[1];
@@ -335,7 +346,7 @@ static void felem_diff64(felem out, const felem in)
335 out[6] += two62m2 - in[6]; 346 out[6] += two62m2 - in[6];
336 out[7] += two62m2 - in[7]; 347 out[7] += two62m2 - in[7];
337 out[8] += two62m2 - in[8]; 348 out[8] += two62m2 - in[8];
338 } 349}
339 350
340/* felem_diff_128_64 subtracts |in| from |out| 351/* felem_diff_128_64 subtracts |in| from |out|
341 * On entry: 352 * On entry:
@@ -343,11 +354,12 @@ static void felem_diff64(felem out, const felem in)
343 * On exit: 354 * On exit:
344 * out[i] < out[i] + 2^63 355 * out[i] < out[i] + 2^63
345 */ 356 */
346static void felem_diff_128_64(largefelem out, const felem in) 357static void
347 { 358felem_diff_128_64(largefelem out, const felem in)
359{
348 /* In order to prevent underflow, we add 0 mod p before subtracting. */ 360 /* In order to prevent underflow, we add 0 mod p before subtracting. */
349 static const limb two63m6 = (((limb)1) << 62) - (((limb)1) << 5); 361 static const limb two63m6 = (((limb) 1) << 62) - (((limb) 1) << 5);
350 static const limb two63m5 = (((limb)1) << 62) - (((limb)1) << 4); 362 static const limb two63m5 = (((limb) 1) << 62) - (((limb) 1) << 4);
351 363
352 out[0] += two63m6 - in[0]; 364 out[0] += two63m6 - in[0];
353 out[1] += two63m5 - in[1]; 365 out[1] += two63m5 - in[1];
@@ -358,7 +370,7 @@ static void felem_diff_128_64(largefelem out, const felem in)
358 out[6] += two63m5 - in[6]; 370 out[6] += two63m5 - in[6];
359 out[7] += two63m5 - in[7]; 371 out[7] += two63m5 - in[7];
360 out[8] += two63m5 - in[8]; 372 out[8] += two63m5 - in[8];
361 } 373}
362 374
363/* felem_diff_128_64 subtracts |in| from |out| 375/* felem_diff_128_64 subtracts |in| from |out|
364 * On entry: 376 * On entry:
@@ -366,11 +378,12 @@ static void felem_diff_128_64(largefelem out, const felem in)
366 * On exit: 378 * On exit:
367 * out[i] < out[i] + 2^127 - 2^69 379 * out[i] < out[i] + 2^127 - 2^69
368 */ 380 */
369static void felem_diff128(largefelem out, const largefelem in) 381static void
370 { 382felem_diff128(largefelem out, const largefelem in)
383{
371 /* In order to prevent underflow, we add 0 mod p before subtracting. */ 384 /* In order to prevent underflow, we add 0 mod p before subtracting. */
372 static const uint128_t two127m70 = (((uint128_t)1) << 127) - (((uint128_t)1) << 70); 385 static const uint128_t two127m70 = (((uint128_t) 1) << 127) - (((uint128_t) 1) << 70);
373 static const uint128_t two127m69 = (((uint128_t)1) << 127) - (((uint128_t)1) << 69); 386 static const uint128_t two127m69 = (((uint128_t) 1) << 127) - (((uint128_t) 1) << 69);
374 387
375 out[0] += (two127m70 - in[0]); 388 out[0] += (two127m70 - in[0]);
376 out[1] += (two127m69 - in[1]); 389 out[1] += (two127m69 - in[1]);
@@ -381,7 +394,7 @@ static void felem_diff128(largefelem out, const largefelem in)
381 out[6] += (two127m69 - in[6]); 394 out[6] += (two127m69 - in[6]);
382 out[7] += (two127m69 - in[7]); 395 out[7] += (two127m69 - in[7]);
383 out[8] += (two127m69 - in[8]); 396 out[8] += (two127m69 - in[8]);
384 } 397}
385 398
386/* felem_square sets |out| = |in|^2 399/* felem_square sets |out| = |in|^2
387 * On entry: 400 * On entry:
@@ -389,90 +402,92 @@ static void felem_diff128(largefelem out, const largefelem in)
389 * On exit: 402 * On exit:
390 * out[i] < 17 * max(in[i]) * max(in[i]) 403 * out[i] < 17 * max(in[i]) * max(in[i])
391 */ 404 */
392static void felem_square(largefelem out, const felem in) 405static void
393 { 406felem_square(largefelem out, const felem in)
407{
394 felem inx2, inx4; 408 felem inx2, inx4;
395 felem_scalar(inx2, in, 2); 409 felem_scalar(inx2, in, 2);
396 felem_scalar(inx4, in, 4); 410 felem_scalar(inx4, in, 4);
397 411
398 /* We have many cases were we want to do 412 /*
399 * in[x] * in[y] + 413 * We have many cases were we want to do in[x] * in[y] + in[y] *
400 * in[y] * in[x] 414 * in[x] This is obviously just 2 * in[x] * in[y] However, rather
401 * This is obviously just 415 * than do the doubling on the 128 bit result, we double one of the
402 * 2 * in[x] * in[y] 416 * inputs to the multiplication by reading from |inx2|
403 * However, rather than do the doubling on the 128 bit result, we 417 */
404 * double one of the inputs to the multiplication by reading from
405 * |inx2| */
406 418
407 out[0] = ((uint128_t) in[0]) * in[0]; 419 out[0] = ((uint128_t) in[0]) * in[0];
408 out[1] = ((uint128_t) in[0]) * inx2[1]; 420 out[1] = ((uint128_t) in[0]) * inx2[1];
409 out[2] = ((uint128_t) in[0]) * inx2[2] + 421 out[2] = ((uint128_t) in[0]) * inx2[2] +
410 ((uint128_t) in[1]) * in[1]; 422 ((uint128_t) in[1]) * in[1];
411 out[3] = ((uint128_t) in[0]) * inx2[3] + 423 out[3] = ((uint128_t) in[0]) * inx2[3] +
412 ((uint128_t) in[1]) * inx2[2]; 424 ((uint128_t) in[1]) * inx2[2];
413 out[4] = ((uint128_t) in[0]) * inx2[4] + 425 out[4] = ((uint128_t) in[0]) * inx2[4] +
414 ((uint128_t) in[1]) * inx2[3] + 426 ((uint128_t) in[1]) * inx2[3] +
415 ((uint128_t) in[2]) * in[2]; 427 ((uint128_t) in[2]) * in[2];
416 out[5] = ((uint128_t) in[0]) * inx2[5] + 428 out[5] = ((uint128_t) in[0]) * inx2[5] +
417 ((uint128_t) in[1]) * inx2[4] + 429 ((uint128_t) in[1]) * inx2[4] +
418 ((uint128_t) in[2]) * inx2[3]; 430 ((uint128_t) in[2]) * inx2[3];
419 out[6] = ((uint128_t) in[0]) * inx2[6] + 431 out[6] = ((uint128_t) in[0]) * inx2[6] +
420 ((uint128_t) in[1]) * inx2[5] + 432 ((uint128_t) in[1]) * inx2[5] +
421 ((uint128_t) in[2]) * inx2[4] + 433 ((uint128_t) in[2]) * inx2[4] +
422 ((uint128_t) in[3]) * in[3]; 434 ((uint128_t) in[3]) * in[3];
423 out[7] = ((uint128_t) in[0]) * inx2[7] + 435 out[7] = ((uint128_t) in[0]) * inx2[7] +
424 ((uint128_t) in[1]) * inx2[6] + 436 ((uint128_t) in[1]) * inx2[6] +
425 ((uint128_t) in[2]) * inx2[5] + 437 ((uint128_t) in[2]) * inx2[5] +
426 ((uint128_t) in[3]) * inx2[4]; 438 ((uint128_t) in[3]) * inx2[4];
427 out[8] = ((uint128_t) in[0]) * inx2[8] + 439 out[8] = ((uint128_t) in[0]) * inx2[8] +
428 ((uint128_t) in[1]) * inx2[7] + 440 ((uint128_t) in[1]) * inx2[7] +
429 ((uint128_t) in[2]) * inx2[6] + 441 ((uint128_t) in[2]) * inx2[6] +
430 ((uint128_t) in[3]) * inx2[5] + 442 ((uint128_t) in[3]) * inx2[5] +
431 ((uint128_t) in[4]) * in[4]; 443 ((uint128_t) in[4]) * in[4];
432 444
433 /* The remaining limbs fall above 2^521, with the first falling at 445 /*
446 * The remaining limbs fall above 2^521, with the first falling at
434 * 2^522. They correspond to locations one bit up from the limbs 447 * 2^522. They correspond to locations one bit up from the limbs
435 * produced above so we would have to multiply by two to align them. 448 * produced above so we would have to multiply by two to align them.
436 * Again, rather than operate on the 128-bit result, we double one of 449 * Again, rather than operate on the 128-bit result, we double one of
437 * the inputs to the multiplication. If we want to double for both this 450 * the inputs to the multiplication. If we want to double for both
438 * reason, and the reason above, then we end up multiplying by four. */ 451 * this reason, and the reason above, then we end up multiplying by
452 * four.
453 */
439 454
440 /* 9 */ 455 /* 9 */
441 out[0] += ((uint128_t) in[1]) * inx4[8] + 456 out[0] += ((uint128_t) in[1]) * inx4[8] +
442 ((uint128_t) in[2]) * inx4[7] + 457 ((uint128_t) in[2]) * inx4[7] +
443 ((uint128_t) in[3]) * inx4[6] + 458 ((uint128_t) in[3]) * inx4[6] +
444 ((uint128_t) in[4]) * inx4[5]; 459 ((uint128_t) in[4]) * inx4[5];
445 460
446 /* 10 */ 461 /* 10 */
447 out[1] += ((uint128_t) in[2]) * inx4[8] + 462 out[1] += ((uint128_t) in[2]) * inx4[8] +
448 ((uint128_t) in[3]) * inx4[7] + 463 ((uint128_t) in[3]) * inx4[7] +
449 ((uint128_t) in[4]) * inx4[6] + 464 ((uint128_t) in[4]) * inx4[6] +
450 ((uint128_t) in[5]) * inx2[5]; 465 ((uint128_t) in[5]) * inx2[5];
451 466
452 /* 11 */ 467 /* 11 */
453 out[2] += ((uint128_t) in[3]) * inx4[8] + 468 out[2] += ((uint128_t) in[3]) * inx4[8] +
454 ((uint128_t) in[4]) * inx4[7] + 469 ((uint128_t) in[4]) * inx4[7] +
455 ((uint128_t) in[5]) * inx4[6]; 470 ((uint128_t) in[5]) * inx4[6];
456 471
457 /* 12 */ 472 /* 12 */
458 out[3] += ((uint128_t) in[4]) * inx4[8] + 473 out[3] += ((uint128_t) in[4]) * inx4[8] +
459 ((uint128_t) in[5]) * inx4[7] + 474 ((uint128_t) in[5]) * inx4[7] +
460 ((uint128_t) in[6]) * inx2[6]; 475 ((uint128_t) in[6]) * inx2[6];
461 476
462 /* 13 */ 477 /* 13 */
463 out[4] += ((uint128_t) in[5]) * inx4[8] + 478 out[4] += ((uint128_t) in[5]) * inx4[8] +
464 ((uint128_t) in[6]) * inx4[7]; 479 ((uint128_t) in[6]) * inx4[7];
465 480
466 /* 14 */ 481 /* 14 */
467 out[5] += ((uint128_t) in[6]) * inx4[8] + 482 out[5] += ((uint128_t) in[6]) * inx4[8] +
468 ((uint128_t) in[7]) * inx2[7]; 483 ((uint128_t) in[7]) * inx2[7];
469 484
470 /* 15 */ 485 /* 15 */
471 out[6] += ((uint128_t) in[7]) * inx4[8]; 486 out[6] += ((uint128_t) in[7]) * inx4[8];
472 487
473 /* 16 */ 488 /* 16 */
474 out[7] += ((uint128_t) in[8]) * inx2[8]; 489 out[7] += ((uint128_t) in[8]) * inx2[8];
475 } 490}
476 491
477/* felem_mul sets |out| = |in1| * |in2| 492/* felem_mul sets |out| = |in1| * |in2|
478 * On entry: 493 * On entry:
@@ -481,111 +496,112 @@ static void felem_square(largefelem out, const felem in)
481 * On exit: 496 * On exit:
482 * out[i] < 17 * max(in1[i]) * max(in2[i]) 497 * out[i] < 17 * max(in1[i]) * max(in2[i])
483 */ 498 */
484static void felem_mul(largefelem out, const felem in1, const felem in2) 499static void
485 { 500felem_mul(largefelem out, const felem in1, const felem in2)
501{
486 felem in2x2; 502 felem in2x2;
487 felem_scalar(in2x2, in2, 2); 503 felem_scalar(in2x2, in2, 2);
488 504
489 out[0] = ((uint128_t) in1[0]) * in2[0]; 505 out[0] = ((uint128_t) in1[0]) * in2[0];
490 506
491 out[1] = ((uint128_t) in1[0]) * in2[1] + 507 out[1] = ((uint128_t) in1[0]) * in2[1] +
492 ((uint128_t) in1[1]) * in2[0]; 508 ((uint128_t) in1[1]) * in2[0];
493 509
494 out[2] = ((uint128_t) in1[0]) * in2[2] + 510 out[2] = ((uint128_t) in1[0]) * in2[2] +
495 ((uint128_t) in1[1]) * in2[1] + 511 ((uint128_t) in1[1]) * in2[1] +
496 ((uint128_t) in1[2]) * in2[0]; 512 ((uint128_t) in1[2]) * in2[0];
497 513
498 out[3] = ((uint128_t) in1[0]) * in2[3] + 514 out[3] = ((uint128_t) in1[0]) * in2[3] +
499 ((uint128_t) in1[1]) * in2[2] + 515 ((uint128_t) in1[1]) * in2[2] +
500 ((uint128_t) in1[2]) * in2[1] + 516 ((uint128_t) in1[2]) * in2[1] +
501 ((uint128_t) in1[3]) * in2[0]; 517 ((uint128_t) in1[3]) * in2[0];
502 518
503 out[4] = ((uint128_t) in1[0]) * in2[4] + 519 out[4] = ((uint128_t) in1[0]) * in2[4] +
504 ((uint128_t) in1[1]) * in2[3] + 520 ((uint128_t) in1[1]) * in2[3] +
505 ((uint128_t) in1[2]) * in2[2] + 521 ((uint128_t) in1[2]) * in2[2] +
506 ((uint128_t) in1[3]) * in2[1] + 522 ((uint128_t) in1[3]) * in2[1] +
507 ((uint128_t) in1[4]) * in2[0]; 523 ((uint128_t) in1[4]) * in2[0];
508 524
509 out[5] = ((uint128_t) in1[0]) * in2[5] + 525 out[5] = ((uint128_t) in1[0]) * in2[5] +
510 ((uint128_t) in1[1]) * in2[4] + 526 ((uint128_t) in1[1]) * in2[4] +
511 ((uint128_t) in1[2]) * in2[3] + 527 ((uint128_t) in1[2]) * in2[3] +
512 ((uint128_t) in1[3]) * in2[2] + 528 ((uint128_t) in1[3]) * in2[2] +
513 ((uint128_t) in1[4]) * in2[1] + 529 ((uint128_t) in1[4]) * in2[1] +
514 ((uint128_t) in1[5]) * in2[0]; 530 ((uint128_t) in1[5]) * in2[0];
515 531
516 out[6] = ((uint128_t) in1[0]) * in2[6] + 532 out[6] = ((uint128_t) in1[0]) * in2[6] +
517 ((uint128_t) in1[1]) * in2[5] + 533 ((uint128_t) in1[1]) * in2[5] +
518 ((uint128_t) in1[2]) * in2[4] + 534 ((uint128_t) in1[2]) * in2[4] +
519 ((uint128_t) in1[3]) * in2[3] + 535 ((uint128_t) in1[3]) * in2[3] +
520 ((uint128_t) in1[4]) * in2[2] + 536 ((uint128_t) in1[4]) * in2[2] +
521 ((uint128_t) in1[5]) * in2[1] + 537 ((uint128_t) in1[5]) * in2[1] +
522 ((uint128_t) in1[6]) * in2[0]; 538 ((uint128_t) in1[6]) * in2[0];
523 539
524 out[7] = ((uint128_t) in1[0]) * in2[7] + 540 out[7] = ((uint128_t) in1[0]) * in2[7] +
525 ((uint128_t) in1[1]) * in2[6] + 541 ((uint128_t) in1[1]) * in2[6] +
526 ((uint128_t) in1[2]) * in2[5] + 542 ((uint128_t) in1[2]) * in2[5] +
527 ((uint128_t) in1[3]) * in2[4] + 543 ((uint128_t) in1[3]) * in2[4] +
528 ((uint128_t) in1[4]) * in2[3] + 544 ((uint128_t) in1[4]) * in2[3] +
529 ((uint128_t) in1[5]) * in2[2] + 545 ((uint128_t) in1[5]) * in2[2] +
530 ((uint128_t) in1[6]) * in2[1] + 546 ((uint128_t) in1[6]) * in2[1] +
531 ((uint128_t) in1[7]) * in2[0]; 547 ((uint128_t) in1[7]) * in2[0];
532 548
533 out[8] = ((uint128_t) in1[0]) * in2[8] + 549 out[8] = ((uint128_t) in1[0]) * in2[8] +
534 ((uint128_t) in1[1]) * in2[7] + 550 ((uint128_t) in1[1]) * in2[7] +
535 ((uint128_t) in1[2]) * in2[6] + 551 ((uint128_t) in1[2]) * in2[6] +
536 ((uint128_t) in1[3]) * in2[5] + 552 ((uint128_t) in1[3]) * in2[5] +
537 ((uint128_t) in1[4]) * in2[4] + 553 ((uint128_t) in1[4]) * in2[4] +
538 ((uint128_t) in1[5]) * in2[3] + 554 ((uint128_t) in1[5]) * in2[3] +
539 ((uint128_t) in1[6]) * in2[2] + 555 ((uint128_t) in1[6]) * in2[2] +
540 ((uint128_t) in1[7]) * in2[1] + 556 ((uint128_t) in1[7]) * in2[1] +
541 ((uint128_t) in1[8]) * in2[0]; 557 ((uint128_t) in1[8]) * in2[0];
542 558
543 /* See comment in felem_square about the use of in2x2 here */ 559 /* See comment in felem_square about the use of in2x2 here */
544 560
545 out[0] += ((uint128_t) in1[1]) * in2x2[8] + 561 out[0] += ((uint128_t) in1[1]) * in2x2[8] +
546 ((uint128_t) in1[2]) * in2x2[7] + 562 ((uint128_t) in1[2]) * in2x2[7] +
547 ((uint128_t) in1[3]) * in2x2[6] + 563 ((uint128_t) in1[3]) * in2x2[6] +
548 ((uint128_t) in1[4]) * in2x2[5] + 564 ((uint128_t) in1[4]) * in2x2[5] +
549 ((uint128_t) in1[5]) * in2x2[4] + 565 ((uint128_t) in1[5]) * in2x2[4] +
550 ((uint128_t) in1[6]) * in2x2[3] + 566 ((uint128_t) in1[6]) * in2x2[3] +
551 ((uint128_t) in1[7]) * in2x2[2] + 567 ((uint128_t) in1[7]) * in2x2[2] +
552 ((uint128_t) in1[8]) * in2x2[1]; 568 ((uint128_t) in1[8]) * in2x2[1];
553 569
554 out[1] += ((uint128_t) in1[2]) * in2x2[8] + 570 out[1] += ((uint128_t) in1[2]) * in2x2[8] +
555 ((uint128_t) in1[3]) * in2x2[7] + 571 ((uint128_t) in1[3]) * in2x2[7] +
556 ((uint128_t) in1[4]) * in2x2[6] + 572 ((uint128_t) in1[4]) * in2x2[6] +
557 ((uint128_t) in1[5]) * in2x2[5] + 573 ((uint128_t) in1[5]) * in2x2[5] +
558 ((uint128_t) in1[6]) * in2x2[4] + 574 ((uint128_t) in1[6]) * in2x2[4] +
559 ((uint128_t) in1[7]) * in2x2[3] + 575 ((uint128_t) in1[7]) * in2x2[3] +
560 ((uint128_t) in1[8]) * in2x2[2]; 576 ((uint128_t) in1[8]) * in2x2[2];
561 577
562 out[2] += ((uint128_t) in1[3]) * in2x2[8] + 578 out[2] += ((uint128_t) in1[3]) * in2x2[8] +
563 ((uint128_t) in1[4]) * in2x2[7] + 579 ((uint128_t) in1[4]) * in2x2[7] +
564 ((uint128_t) in1[5]) * in2x2[6] + 580 ((uint128_t) in1[5]) * in2x2[6] +
565 ((uint128_t) in1[6]) * in2x2[5] + 581 ((uint128_t) in1[6]) * in2x2[5] +
566 ((uint128_t) in1[7]) * in2x2[4] + 582 ((uint128_t) in1[7]) * in2x2[4] +
567 ((uint128_t) in1[8]) * in2x2[3]; 583 ((uint128_t) in1[8]) * in2x2[3];
568 584
569 out[3] += ((uint128_t) in1[4]) * in2x2[8] + 585 out[3] += ((uint128_t) in1[4]) * in2x2[8] +
570 ((uint128_t) in1[5]) * in2x2[7] + 586 ((uint128_t) in1[5]) * in2x2[7] +
571 ((uint128_t) in1[6]) * in2x2[6] + 587 ((uint128_t) in1[6]) * in2x2[6] +
572 ((uint128_t) in1[7]) * in2x2[5] + 588 ((uint128_t) in1[7]) * in2x2[5] +
573 ((uint128_t) in1[8]) * in2x2[4]; 589 ((uint128_t) in1[8]) * in2x2[4];
574 590
575 out[4] += ((uint128_t) in1[5]) * in2x2[8] + 591 out[4] += ((uint128_t) in1[5]) * in2x2[8] +
576 ((uint128_t) in1[6]) * in2x2[7] + 592 ((uint128_t) in1[6]) * in2x2[7] +
577 ((uint128_t) in1[7]) * in2x2[6] + 593 ((uint128_t) in1[7]) * in2x2[6] +
578 ((uint128_t) in1[8]) * in2x2[5]; 594 ((uint128_t) in1[8]) * in2x2[5];
579 595
580 out[5] += ((uint128_t) in1[6]) * in2x2[8] + 596 out[5] += ((uint128_t) in1[6]) * in2x2[8] +
581 ((uint128_t) in1[7]) * in2x2[7] + 597 ((uint128_t) in1[7]) * in2x2[7] +
582 ((uint128_t) in1[8]) * in2x2[6]; 598 ((uint128_t) in1[8]) * in2x2[6];
583 599
584 out[6] += ((uint128_t) in1[7]) * in2x2[8] + 600 out[6] += ((uint128_t) in1[7]) * in2x2[8] +
585 ((uint128_t) in1[8]) * in2x2[7]; 601 ((uint128_t) in1[8]) * in2x2[7];
586 602
587 out[7] += ((uint128_t) in1[8]) * in2x2[8]; 603 out[7] += ((uint128_t) in1[8]) * in2x2[8];
588 } 604}
589 605
590static const limb bottom52bits = 0xfffffffffffff; 606static const limb bottom52bits = 0xfffffffffffff;
591 607
@@ -595,8 +611,9 @@ static const limb bottom52bits = 0xfffffffffffff;
595 * On exit: 611 * On exit:
596 * out[i] < 2^59 + 2^14 612 * out[i] < 2^59 + 2^14
597 */ 613 */
598static void felem_reduce(felem out, const largefelem in) 614static void
599 { 615felem_reduce(felem out, const largefelem in)
616{
600 u64 overflow1, overflow2; 617 u64 overflow1, overflow2;
601 618
602 out[0] = ((limb) in[0]) & bottom58bits; 619 out[0] = ((limb) in[0]) & bottom58bits;
@@ -613,8 +630,9 @@ static void felem_reduce(felem out, const largefelem in)
613 630
614 out[1] += ((limb) in[0]) >> 58; 631 out[1] += ((limb) in[0]) >> 58;
615 out[1] += (((limb) (in[0] >> 64)) & bottom52bits) << 6; 632 out[1] += (((limb) (in[0] >> 64)) & bottom52bits) << 6;
616 /* out[1] < 2^58 + 2^6 + 2^58 633 /*
617 * = 2^59 + 2^6 */ 634 * out[1] < 2^58 + 2^6 + 2^58 = 2^59 + 2^6
635 */
618 out[2] += ((limb) (in[0] >> 64)) >> 52; 636 out[2] += ((limb) (in[0] >> 64)) >> 52;
619 637
620 out[2] += ((limb) in[1]) >> 58; 638 out[2] += ((limb) in[1]) >> 58;
@@ -643,39 +661,43 @@ static void felem_reduce(felem out, const largefelem in)
643 661
644 out[8] += ((limb) in[7]) >> 58; 662 out[8] += ((limb) in[7]) >> 58;
645 out[8] += (((limb) (in[7] >> 64)) & bottom52bits) << 6; 663 out[8] += (((limb) (in[7] >> 64)) & bottom52bits) << 6;
646 /* out[x > 1] < 2^58 + 2^6 + 2^58 + 2^12 664 /*
647 * < 2^59 + 2^13 */ 665 * out[x > 1] < 2^58 + 2^6 + 2^58 + 2^12 < 2^59 + 2^13
666 */
648 overflow1 = ((limb) (in[7] >> 64)) >> 52; 667 overflow1 = ((limb) (in[7] >> 64)) >> 52;
649 668
650 overflow1 += ((limb) in[8]) >> 58; 669 overflow1 += ((limb) in[8]) >> 58;
651 overflow1 += (((limb) (in[8] >> 64)) & bottom52bits) << 6; 670 overflow1 += (((limb) (in[8] >> 64)) & bottom52bits) << 6;
652 overflow2 = ((limb) (in[8] >> 64)) >> 52; 671 overflow2 = ((limb) (in[8] >> 64)) >> 52;
653 672
654 overflow1 <<= 1; /* overflow1 < 2^13 + 2^7 + 2^59 */ 673 overflow1 <<= 1; /* overflow1 < 2^13 + 2^7 + 2^59 */
655 overflow2 <<= 1; /* overflow2 < 2^13 */ 674 overflow2 <<= 1; /* overflow2 < 2^13 */
656 675
657 out[0] += overflow1; /* out[0] < 2^60 */ 676 out[0] += overflow1; /* out[0] < 2^60 */
658 out[1] += overflow2; /* out[1] < 2^59 + 2^6 + 2^13 */ 677 out[1] += overflow2; /* out[1] < 2^59 + 2^6 + 2^13 */
659 678
660 out[1] += out[0] >> 58; out[0] &= bottom58bits; 679 out[1] += out[0] >> 58;
661 /* out[0] < 2^58 680 out[0] &= bottom58bits;
662 * out[1] < 2^59 + 2^6 + 2^13 + 2^2 681 /*
663 * < 2^59 + 2^14 */ 682 * out[0] < 2^58 out[1] < 2^59 + 2^6 + 2^13 + 2^2 < 2^59 + 2^14
664 } 683 */
684}
665 685
666static void felem_square_reduce(felem out, const felem in) 686static void
667 { 687felem_square_reduce(felem out, const felem in)
688{
668 largefelem tmp; 689 largefelem tmp;
669 felem_square(tmp, in); 690 felem_square(tmp, in);
670 felem_reduce(out, tmp); 691 felem_reduce(out, tmp);
671 } 692}
672 693
673static void felem_mul_reduce(felem out, const felem in1, const felem in2) 694static void
674 { 695felem_mul_reduce(felem out, const felem in1, const felem in2)
696{
675 largefelem tmp; 697 largefelem tmp;
676 felem_mul(tmp, in1, in2); 698 felem_mul(tmp, in1, in2);
677 felem_reduce(out, tmp); 699 felem_reduce(out, tmp);
678 } 700}
679 701
680/* felem_inv calculates |out| = |in|^{-1} 702/* felem_inv calculates |out| = |in|^{-1}
681 * 703 *
@@ -684,117 +706,153 @@ static void felem_mul_reduce(felem out, const felem in1, const felem in2)
684 * a^{p-1} = 1 (mod p) 706 * a^{p-1} = 1 (mod p)
685 * a^{p-2} = a^{-1} (mod p) 707 * a^{p-2} = a^{-1} (mod p)
686 */ 708 */
687static void felem_inv(felem out, const felem in) 709static void
688 { 710felem_inv(felem out, const felem in)
711{
689 felem ftmp, ftmp2, ftmp3, ftmp4; 712 felem ftmp, ftmp2, ftmp3, ftmp4;
690 largefelem tmp; 713 largefelem tmp;
691 unsigned i; 714 unsigned i;
692 715
693 felem_square(tmp, in); felem_reduce(ftmp, tmp); /* 2^1 */ 716 felem_square(tmp, in);
694 felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^2 - 2^0 */ 717 felem_reduce(ftmp, tmp);/* 2^1 */
718 felem_mul(tmp, in, ftmp);
719 felem_reduce(ftmp, tmp);/* 2^2 - 2^0 */
695 felem_assign(ftmp2, ftmp); 720 felem_assign(ftmp2, ftmp);
696 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2^1 */ 721 felem_square(tmp, ftmp);
697 felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2^0 */ 722 felem_reduce(ftmp, tmp);/* 2^3 - 2^1 */
698 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^4 - 2^1 */ 723 felem_mul(tmp, in, ftmp);
724 felem_reduce(ftmp, tmp);/* 2^3 - 2^0 */
725 felem_square(tmp, ftmp);
726 felem_reduce(ftmp, tmp);/* 2^4 - 2^1 */
699 727
700 felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp); /* 2^3 - 2^1 */ 728 felem_square(tmp, ftmp2);
701 felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^4 - 2^2 */ 729 felem_reduce(ftmp3, tmp); /* 2^3 - 2^1 */
702 felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^4 - 2^0 */ 730 felem_square(tmp, ftmp3);
731 felem_reduce(ftmp3, tmp); /* 2^4 - 2^2 */
732 felem_mul(tmp, ftmp3, ftmp2);
733 felem_reduce(ftmp3, tmp); /* 2^4 - 2^0 */
703 734
704 felem_assign(ftmp2, ftmp3); 735 felem_assign(ftmp2, ftmp3);
705 felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^5 - 2^1 */ 736 felem_square(tmp, ftmp3);
706 felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^6 - 2^2 */ 737 felem_reduce(ftmp3, tmp); /* 2^5 - 2^1 */
707 felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^7 - 2^3 */ 738 felem_square(tmp, ftmp3);
708 felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^8 - 2^4 */ 739 felem_reduce(ftmp3, tmp); /* 2^6 - 2^2 */
740 felem_square(tmp, ftmp3);
741 felem_reduce(ftmp3, tmp); /* 2^7 - 2^3 */
742 felem_square(tmp, ftmp3);
743 felem_reduce(ftmp3, tmp); /* 2^8 - 2^4 */
709 felem_assign(ftmp4, ftmp3); 744 felem_assign(ftmp4, ftmp3);
710 felem_mul(tmp, ftmp3, ftmp); felem_reduce(ftmp4, tmp); /* 2^8 - 2^1 */ 745 felem_mul(tmp, ftmp3, ftmp);
711 felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp); /* 2^9 - 2^2 */ 746 felem_reduce(ftmp4, tmp); /* 2^8 - 2^1 */
712 felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^8 - 2^0 */ 747 felem_square(tmp, ftmp4);
748 felem_reduce(ftmp4, tmp); /* 2^9 - 2^2 */
749 felem_mul(tmp, ftmp3, ftmp2);
750 felem_reduce(ftmp3, tmp); /* 2^8 - 2^0 */
713 felem_assign(ftmp2, ftmp3); 751 felem_assign(ftmp2, ftmp3);
714 752
715 for (i = 0; i < 8; i++) 753 for (i = 0; i < 8; i++) {
716 { 754 felem_square(tmp, ftmp3);
717 felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^16 - 2^8 */ 755 felem_reduce(ftmp3, tmp); /* 2^16 - 2^8 */
718 } 756 }
719 felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^16 - 2^0 */ 757 felem_mul(tmp, ftmp3, ftmp2);
758 felem_reduce(ftmp3, tmp); /* 2^16 - 2^0 */
720 felem_assign(ftmp2, ftmp3); 759 felem_assign(ftmp2, ftmp3);
721 760
722 for (i = 0; i < 16; i++) 761 for (i = 0; i < 16; i++) {
723 { 762 felem_square(tmp, ftmp3);
724 felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^32 - 2^16 */ 763 felem_reduce(ftmp3, tmp); /* 2^32 - 2^16 */
725 } 764 }
726 felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^32 - 2^0 */ 765 felem_mul(tmp, ftmp3, ftmp2);
766 felem_reduce(ftmp3, tmp); /* 2^32 - 2^0 */
727 felem_assign(ftmp2, ftmp3); 767 felem_assign(ftmp2, ftmp3);
728 768
729 for (i = 0; i < 32; i++) 769 for (i = 0; i < 32; i++) {
730 { 770 felem_square(tmp, ftmp3);
731 felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^64 - 2^32 */ 771 felem_reduce(ftmp3, tmp); /* 2^64 - 2^32 */
732 } 772 }
733 felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^64 - 2^0 */ 773 felem_mul(tmp, ftmp3, ftmp2);
774 felem_reduce(ftmp3, tmp); /* 2^64 - 2^0 */
734 felem_assign(ftmp2, ftmp3); 775 felem_assign(ftmp2, ftmp3);
735 776
736 for (i = 0; i < 64; i++) 777 for (i = 0; i < 64; i++) {
737 { 778 felem_square(tmp, ftmp3);
738 felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^128 - 2^64 */ 779 felem_reduce(ftmp3, tmp); /* 2^128 - 2^64 */
739 } 780 }
740 felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^128 - 2^0 */ 781 felem_mul(tmp, ftmp3, ftmp2);
782 felem_reduce(ftmp3, tmp); /* 2^128 - 2^0 */
741 felem_assign(ftmp2, ftmp3); 783 felem_assign(ftmp2, ftmp3);
742 784
743 for (i = 0; i < 128; i++) 785 for (i = 0; i < 128; i++) {
744 { 786 felem_square(tmp, ftmp3);
745 felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^256 - 2^128 */ 787 felem_reduce(ftmp3, tmp); /* 2^256 - 2^128 */
746 } 788 }
747 felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^256 - 2^0 */ 789 felem_mul(tmp, ftmp3, ftmp2);
790 felem_reduce(ftmp3, tmp); /* 2^256 - 2^0 */
748 felem_assign(ftmp2, ftmp3); 791 felem_assign(ftmp2, ftmp3);
749 792
750 for (i = 0; i < 256; i++) 793 for (i = 0; i < 256; i++) {
751 { 794 felem_square(tmp, ftmp3);
752 felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^512 - 2^256 */ 795 felem_reduce(ftmp3, tmp); /* 2^512 - 2^256 */
753 } 796 }
754 felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^512 - 2^0 */ 797 felem_mul(tmp, ftmp3, ftmp2);
798 felem_reduce(ftmp3, tmp); /* 2^512 - 2^0 */
755 799
756 for (i = 0; i < 9; i++) 800 for (i = 0; i < 9; i++) {
757 { 801 felem_square(tmp, ftmp3);
758 felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^521 - 2^9 */ 802 felem_reduce(ftmp3, tmp); /* 2^521 - 2^9 */
759 } 803 }
760 felem_mul(tmp, ftmp3, ftmp4); felem_reduce(ftmp3, tmp); /* 2^512 - 2^2 */ 804 felem_mul(tmp, ftmp3, ftmp4);
761 felem_mul(tmp, ftmp3, in); felem_reduce(out, tmp); /* 2^512 - 3 */ 805 felem_reduce(ftmp3, tmp); /* 2^512 - 2^2 */
806 felem_mul(tmp, ftmp3, in);
807 felem_reduce(out, tmp); /* 2^512 - 3 */
762} 808}
763 809
764/* This is 2^521-1, expressed as an felem */ 810/* This is 2^521-1, expressed as an felem */
765static const felem kPrime = 811static const felem kPrime =
766 { 812{
767 0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff, 813 0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff,
768 0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff, 814 0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff,
769 0x03ffffffffffffff, 0x03ffffffffffffff, 0x01ffffffffffffff 815 0x03ffffffffffffff, 0x03ffffffffffffff, 0x01ffffffffffffff
770 }; 816};
771 817
772/* felem_is_zero returns a limb with all bits set if |in| == 0 (mod p) and 0 818/* felem_is_zero returns a limb with all bits set if |in| == 0 (mod p) and 0
773 * otherwise. 819 * otherwise.
774 * On entry: 820 * On entry:
775 * in[i] < 2^59 + 2^14 821 * in[i] < 2^59 + 2^14
776 */ 822 */
777static limb felem_is_zero(const felem in) 823static limb
778 { 824felem_is_zero(const felem in)
825{
779 felem ftmp; 826 felem ftmp;
780 limb is_zero, is_p; 827 limb is_zero, is_p;
781 felem_assign(ftmp, in); 828 felem_assign(ftmp, in);
782 829
783 ftmp[0] += ftmp[8] >> 57; ftmp[8] &= bottom57bits; 830 ftmp[0] += ftmp[8] >> 57;
831 ftmp[8] &= bottom57bits;
784 /* ftmp[8] < 2^57 */ 832 /* ftmp[8] < 2^57 */
785 ftmp[1] += ftmp[0] >> 58; ftmp[0] &= bottom58bits; 833 ftmp[1] += ftmp[0] >> 58;
786 ftmp[2] += ftmp[1] >> 58; ftmp[1] &= bottom58bits; 834 ftmp[0] &= bottom58bits;
787 ftmp[3] += ftmp[2] >> 58; ftmp[2] &= bottom58bits; 835 ftmp[2] += ftmp[1] >> 58;
788 ftmp[4] += ftmp[3] >> 58; ftmp[3] &= bottom58bits; 836 ftmp[1] &= bottom58bits;
789 ftmp[5] += ftmp[4] >> 58; ftmp[4] &= bottom58bits; 837 ftmp[3] += ftmp[2] >> 58;
790 ftmp[6] += ftmp[5] >> 58; ftmp[5] &= bottom58bits; 838 ftmp[2] &= bottom58bits;
791 ftmp[7] += ftmp[6] >> 58; ftmp[6] &= bottom58bits; 839 ftmp[4] += ftmp[3] >> 58;
792 ftmp[8] += ftmp[7] >> 58; ftmp[7] &= bottom58bits; 840 ftmp[3] &= bottom58bits;
841 ftmp[5] += ftmp[4] >> 58;
842 ftmp[4] &= bottom58bits;
843 ftmp[6] += ftmp[5] >> 58;
844 ftmp[5] &= bottom58bits;
845 ftmp[7] += ftmp[6] >> 58;
846 ftmp[6] &= bottom58bits;
847 ftmp[8] += ftmp[7] >> 58;
848 ftmp[7] &= bottom58bits;
793 /* ftmp[8] < 2^57 + 4 */ 849 /* ftmp[8] < 2^57 + 4 */
794 850
795 /* The ninth limb of 2*(2^521-1) is 0x03ffffffffffffff, which is 851 /*
796 * greater than our bound for ftmp[8]. Therefore we only have to check 852 * The ninth limb of 2*(2^521-1) is 0x03ffffffffffffff, which is
797 * if the zero is zero or 2^521-1. */ 853 * greater than our bound for ftmp[8]. Therefore we only have to
854 * check if the zero is zero or 2^521-1.
855 */
798 856
799 is_zero = 0; 857 is_zero = 0;
800 is_zero |= ftmp[0]; 858 is_zero |= ftmp[0];
@@ -808,8 +866,10 @@ static limb felem_is_zero(const felem in)
808 is_zero |= ftmp[8]; 866 is_zero |= ftmp[8];
809 867
810 is_zero--; 868 is_zero--;
811 /* We know that ftmp[i] < 2^63, therefore the only way that the top bit 869 /*
812 * can be set is if is_zero was 0 before the decrement. */ 870 * We know that ftmp[i] < 2^63, therefore the only way that the top
871 * bit can be set is if is_zero was 0 before the decrement.
872 */
813 is_zero = ((s64) is_zero) >> 63; 873 is_zero = ((s64) is_zero) >> 63;
814 874
815 is_p = ftmp[0] ^ kPrime[0]; 875 is_p = ftmp[0] ^ kPrime[0];
@@ -827,41 +887,57 @@ static limb felem_is_zero(const felem in)
827 887
828 is_zero |= is_p; 888 is_zero |= is_p;
829 return is_zero; 889 return is_zero;
830 } 890}
831 891
832static int felem_is_zero_int(const felem in) 892static int
833 { 893felem_is_zero_int(const felem in)
834 return (int) (felem_is_zero(in) & ((limb)1)); 894{
835 } 895 return (int) (felem_is_zero(in) & ((limb) 1));
896}
836 897
837/* felem_contract converts |in| to its unique, minimal representation. 898/* felem_contract converts |in| to its unique, minimal representation.
838 * On entry: 899 * On entry:
839 * in[i] < 2^59 + 2^14 900 * in[i] < 2^59 + 2^14
840 */ 901 */
841static void felem_contract(felem out, const felem in) 902static void
842 { 903felem_contract(felem out, const felem in)
904{
843 limb is_p, is_greater, sign; 905 limb is_p, is_greater, sign;
844 static const limb two58 = ((limb)1) << 58; 906 static const limb two58 = ((limb) 1) << 58;
845 907
846 felem_assign(out, in); 908 felem_assign(out, in);
847 909
848 out[0] += out[8] >> 57; out[8] &= bottom57bits; 910 out[0] += out[8] >> 57;
911 out[8] &= bottom57bits;
849 /* out[8] < 2^57 */ 912 /* out[8] < 2^57 */
850 out[1] += out[0] >> 58; out[0] &= bottom58bits; 913 out[1] += out[0] >> 58;
851 out[2] += out[1] >> 58; out[1] &= bottom58bits; 914 out[0] &= bottom58bits;
852 out[3] += out[2] >> 58; out[2] &= bottom58bits; 915 out[2] += out[1] >> 58;
853 out[4] += out[3] >> 58; out[3] &= bottom58bits; 916 out[1] &= bottom58bits;
854 out[5] += out[4] >> 58; out[4] &= bottom58bits; 917 out[3] += out[2] >> 58;
855 out[6] += out[5] >> 58; out[5] &= bottom58bits; 918 out[2] &= bottom58bits;
856 out[7] += out[6] >> 58; out[6] &= bottom58bits; 919 out[4] += out[3] >> 58;
857 out[8] += out[7] >> 58; out[7] &= bottom58bits; 920 out[3] &= bottom58bits;
921 out[5] += out[4] >> 58;
922 out[4] &= bottom58bits;
923 out[6] += out[5] >> 58;
924 out[5] &= bottom58bits;
925 out[7] += out[6] >> 58;
926 out[6] &= bottom58bits;
927 out[8] += out[7] >> 58;
928 out[7] &= bottom58bits;
858 /* out[8] < 2^57 + 4 */ 929 /* out[8] < 2^57 + 4 */
859 930
860 /* If the value is greater than 2^521-1 then we have to subtract 931 /*
932 * If the value is greater than 2^521-1 then we have to subtract
861 * 2^521-1 out. See the comments in felem_is_zero regarding why we 933 * 2^521-1 out. See the comments in felem_is_zero regarding why we
862 * don't test for other multiples of the prime. */ 934 * don't test for other multiples of the prime.
935 */
863 936
864 /* First, if |out| is equal to 2^521-1, we subtract it out to get zero. */ 937 /*
938 * First, if |out| is equal to 2^521-1, we subtract it out to get
939 * zero.
940 */
865 941
866 is_p = out[0] ^ kPrime[0]; 942 is_p = out[0] ^ kPrime[0];
867 is_p |= out[1] ^ kPrime[1]; 943 is_p |= out[1] ^ kPrime[1];
@@ -895,8 +971,10 @@ static void felem_contract(felem out, const felem in)
895 out[7] &= is_p; 971 out[7] &= is_p;
896 out[8] &= is_p; 972 out[8] &= is_p;
897 973
898 /* In order to test that |out| >= 2^521-1 we need only test if out[8] 974 /*
899 * >> 57 is greater than zero as (2^521-1) + x >= 2^522 */ 975 * In order to test that |out| >= 2^521-1 we need only test if out[8]
976 * >> 57 is greater than zero as (2^521-1) + x >= 2^522
977 */
900 is_greater = out[8] >> 57; 978 is_greater = out[8] >> 57;
901 is_greater |= is_greater << 32; 979 is_greater |= is_greater << 32;
902 is_greater |= is_greater << 16; 980 is_greater |= is_greater << 16;
@@ -917,18 +995,40 @@ static void felem_contract(felem out, const felem in)
917 out[8] -= kPrime[8] & is_greater; 995 out[8] -= kPrime[8] & is_greater;
918 996
919 /* Eliminate negative coefficients */ 997 /* Eliminate negative coefficients */
920 sign = -(out[0] >> 63); out[0] += (two58 & sign); out[1] -= (1 & sign); 998 sign = -(out[0] >> 63);
921 sign = -(out[1] >> 63); out[1] += (two58 & sign); out[2] -= (1 & sign); 999 out[0] += (two58 & sign);
922 sign = -(out[2] >> 63); out[2] += (two58 & sign); out[3] -= (1 & sign); 1000 out[1] -= (1 & sign);
923 sign = -(out[3] >> 63); out[3] += (two58 & sign); out[4] -= (1 & sign); 1001 sign = -(out[1] >> 63);
924 sign = -(out[4] >> 63); out[4] += (two58 & sign); out[5] -= (1 & sign); 1002 out[1] += (two58 & sign);
925 sign = -(out[0] >> 63); out[5] += (two58 & sign); out[6] -= (1 & sign); 1003 out[2] -= (1 & sign);
926 sign = -(out[6] >> 63); out[6] += (two58 & sign); out[7] -= (1 & sign); 1004 sign = -(out[2] >> 63);
927 sign = -(out[7] >> 63); out[7] += (two58 & sign); out[8] -= (1 & sign); 1005 out[2] += (two58 & sign);
928 sign = -(out[5] >> 63); out[5] += (two58 & sign); out[6] -= (1 & sign); 1006 out[3] -= (1 & sign);
929 sign = -(out[6] >> 63); out[6] += (two58 & sign); out[7] -= (1 & sign); 1007 sign = -(out[3] >> 63);
930 sign = -(out[7] >> 63); out[7] += (two58 & sign); out[8] -= (1 & sign); 1008 out[3] += (two58 & sign);
931 } 1009 out[4] -= (1 & sign);
1010 sign = -(out[4] >> 63);
1011 out[4] += (two58 & sign);
1012 out[5] -= (1 & sign);
1013 sign = -(out[0] >> 63);
1014 out[5] += (two58 & sign);
1015 out[6] -= (1 & sign);
1016 sign = -(out[6] >> 63);
1017 out[6] += (two58 & sign);
1018 out[7] -= (1 & sign);
1019 sign = -(out[7] >> 63);
1020 out[7] += (two58 & sign);
1021 out[8] -= (1 & sign);
1022 sign = -(out[5] >> 63);
1023 out[5] += (two58 & sign);
1024 out[6] -= (1 & sign);
1025 sign = -(out[6] >> 63);
1026 out[6] += (two58 & sign);
1027 out[7] -= (1 & sign);
1028 sign = -(out[7] >> 63);
1029 out[7] += (two58 & sign);
1030 out[8] -= (1 & sign);
1031}
932 1032
933/* Group operations 1033/* Group operations
934 * ---------------- 1034 * ----------------
@@ -946,8 +1046,8 @@ static void felem_contract(felem out, const felem in)
946 * while x_out == y_in is not (maybe this works, but it's not tested). */ 1046 * while x_out == y_in is not (maybe this works, but it's not tested). */
947static void 1047static void
948point_double(felem x_out, felem y_out, felem z_out, 1048point_double(felem x_out, felem y_out, felem z_out,
949 const felem x_in, const felem y_in, const felem z_in) 1049 const felem x_in, const felem y_in, const felem z_in)
950 { 1050{
951 largefelem tmp, tmp2; 1051 largefelem tmp, tmp2;
952 felem delta, gamma, beta, alpha, ftmp, ftmp2; 1052 felem delta, gamma, beta, alpha, ftmp, ftmp2;
953 1053
@@ -956,15 +1056,15 @@ point_double(felem x_out, felem y_out, felem z_out,
956 1056
957 /* delta = z^2 */ 1057 /* delta = z^2 */
958 felem_square(tmp, z_in); 1058 felem_square(tmp, z_in);
959 felem_reduce(delta, tmp); /* delta[i] < 2^59 + 2^14 */ 1059 felem_reduce(delta, tmp); /* delta[i] < 2^59 + 2^14 */
960 1060
961 /* gamma = y^2 */ 1061 /* gamma = y^2 */
962 felem_square(tmp, y_in); 1062 felem_square(tmp, y_in);
963 felem_reduce(gamma, tmp); /* gamma[i] < 2^59 + 2^14 */ 1063 felem_reduce(gamma, tmp); /* gamma[i] < 2^59 + 2^14 */
964 1064
965 /* beta = x*gamma */ 1065 /* beta = x*gamma */
966 felem_mul(tmp, x_in, gamma); 1066 felem_mul(tmp, x_in, gamma);
967 felem_reduce(beta, tmp); /* beta[i] < 2^59 + 2^14 */ 1067 felem_reduce(beta, tmp);/* beta[i] < 2^59 + 2^14 */
968 1068
969 /* alpha = 3*(x-delta)*(x+delta) */ 1069 /* alpha = 3*(x-delta)*(x+delta) */
970 felem_diff64(ftmp, delta); 1070 felem_diff64(ftmp, delta);
@@ -974,17 +1074,17 @@ point_double(felem x_out, felem y_out, felem z_out,
974 felem_scalar64(ftmp2, 3); 1074 felem_scalar64(ftmp2, 3);
975 /* ftmp2[i] < 3*2^60 + 3*2^15 */ 1075 /* ftmp2[i] < 3*2^60 + 3*2^15 */
976 felem_mul(tmp, ftmp, ftmp2); 1076 felem_mul(tmp, ftmp, ftmp2);
977 /* tmp[i] < 17(3*2^121 + 3*2^76) 1077 /*
978 * = 61*2^121 + 61*2^76 1078 * tmp[i] < 17(3*2^121 + 3*2^76) = 61*2^121 + 61*2^76 < 64*2^121 +
979 * < 64*2^121 + 64*2^76 1079 * 64*2^76 = 2^127 + 2^82 < 2^128
980 * = 2^127 + 2^82 1080 */
981 * < 2^128 */
982 felem_reduce(alpha, tmp); 1081 felem_reduce(alpha, tmp);
983 1082
984 /* x' = alpha^2 - 8*beta */ 1083 /* x' = alpha^2 - 8*beta */
985 felem_square(tmp, alpha); 1084 felem_square(tmp, alpha);
986 /* tmp[i] < 17*2^120 1085 /*
987 * < 2^125 */ 1086 * tmp[i] < 17*2^120 < 2^125
1087 */
988 felem_assign(ftmp, beta); 1088 felem_assign(ftmp, beta);
989 felem_scalar64(ftmp, 8); 1089 felem_scalar64(ftmp, 8);
990 /* ftmp[i] < 2^62 + 2^17 */ 1090 /* ftmp[i] < 2^62 + 2^17 */
@@ -999,8 +1099,9 @@ point_double(felem x_out, felem y_out, felem z_out,
999 felem_sum64(ftmp, z_in); 1099 felem_sum64(ftmp, z_in);
1000 /* ftmp[i] < 2^60 + 2^15 */ 1100 /* ftmp[i] < 2^60 + 2^15 */
1001 felem_square(tmp, ftmp); 1101 felem_square(tmp, ftmp);
1002 /* tmp[i] < 17(2^122) 1102 /*
1003 * < 2^127 */ 1103 * tmp[i] < 17(2^122) < 2^127
1104 */
1004 felem_diff_128_64(tmp, delta); 1105 felem_diff_128_64(tmp, delta);
1005 /* tmp[i] < 2^127 + 2^63 */ 1106 /* tmp[i] < 2^127 + 2^63 */
1006 felem_reduce(z_out, tmp); 1107 felem_reduce(z_out, tmp);
@@ -1011,36 +1112,39 @@ point_double(felem x_out, felem y_out, felem z_out,
1011 felem_diff64(beta, x_out); 1112 felem_diff64(beta, x_out);
1012 /* beta[i] < 2^61 + 2^60 + 2^16 */ 1113 /* beta[i] < 2^61 + 2^60 + 2^16 */
1013 felem_mul(tmp, alpha, beta); 1114 felem_mul(tmp, alpha, beta);
1014 /* tmp[i] < 17*((2^59 + 2^14)(2^61 + 2^60 + 2^16)) 1115 /*
1015 * = 17*(2^120 + 2^75 + 2^119 + 2^74 + 2^75 + 2^30) 1116 * tmp[i] < 17*((2^59 + 2^14)(2^61 + 2^60 + 2^16)) = 17*(2^120 + 2^75
1016 * = 17*(2^120 + 2^119 + 2^76 + 2^74 + 2^30) 1117 * + 2^119 + 2^74 + 2^75 + 2^30) = 17*(2^120 + 2^119 + 2^76 + 2^74 +
1017 * < 2^128 */ 1118 * 2^30) < 2^128
1119 */
1018 felem_square(tmp2, gamma); 1120 felem_square(tmp2, gamma);
1019 /* tmp2[i] < 17*(2^59 + 2^14)^2 1121 /*
1020 * = 17*(2^118 + 2^74 + 2^28) */ 1122 * tmp2[i] < 17*(2^59 + 2^14)^2 = 17*(2^118 + 2^74 + 2^28)
1123 */
1021 felem_scalar128(tmp2, 8); 1124 felem_scalar128(tmp2, 8);
1022 /* tmp2[i] < 8*17*(2^118 + 2^74 + 2^28) 1125 /*
1023 * = 2^125 + 2^121 + 2^81 + 2^77 + 2^35 + 2^31 1126 * tmp2[i] < 8*17*(2^118 + 2^74 + 2^28) = 2^125 + 2^121 + 2^81 + 2^77
1024 * < 2^126 */ 1127 * + 2^35 + 2^31 < 2^126
1128 */
1025 felem_diff128(tmp, tmp2); 1129 felem_diff128(tmp, tmp2);
1026 /* tmp[i] < 2^127 - 2^69 + 17(2^120 + 2^119 + 2^76 + 2^74 + 2^30) 1130 /*
1027 * = 2^127 + 2^124 + 2^122 + 2^120 + 2^118 + 2^80 + 2^78 + 2^76 + 1131 * tmp[i] < 2^127 - 2^69 + 17(2^120 + 2^119 + 2^76 + 2^74 + 2^30) =
1028 * 2^74 + 2^69 + 2^34 + 2^30 1132 * 2^127 + 2^124 + 2^122 + 2^120 + 2^118 + 2^80 + 2^78 + 2^76 + 2^74
1029 * < 2^128 */ 1133 * + 2^69 + 2^34 + 2^30 < 2^128
1134 */
1030 felem_reduce(y_out, tmp); 1135 felem_reduce(y_out, tmp);
1031 } 1136}
1032 1137
1033/* copy_conditional copies in to out iff mask is all ones. */ 1138/* copy_conditional copies in to out iff mask is all ones. */
1034static void 1139static void
1035copy_conditional(felem out, const felem in, limb mask) 1140copy_conditional(felem out, const felem in, limb mask)
1036 { 1141{
1037 unsigned i; 1142 unsigned i;
1038 for (i = 0; i < NLIMBS; ++i) 1143 for (i = 0; i < NLIMBS; ++i) {
1039 {
1040 const limb tmp = mask & (in[i] ^ out[i]); 1144 const limb tmp = mask & (in[i] ^ out[i]);
1041 out[i] ^= tmp; 1145 out[i] ^= tmp;
1042 }
1043 } 1146 }
1147}
1044 1148
1045/* point_add calcuates (x1, y1, z1) + (x2, y2, z2) 1149/* point_add calcuates (x1, y1, z1) + (x2, y2, z2)
1046 * 1150 *
@@ -1052,10 +1156,11 @@ copy_conditional(felem out, const felem in, limb mask)
1052 * are equal (while not equal to the point at infinity). This case never 1156 * are equal (while not equal to the point at infinity). This case never
1053 * happens during single point multiplication, so there is no timing leak for 1157 * happens during single point multiplication, so there is no timing leak for
1054 * ECDH or ECDSA signing. */ 1158 * ECDH or ECDSA signing. */
1055static void point_add(felem x3, felem y3, felem z3, 1159static void
1056 const felem x1, const felem y1, const felem z1, 1160point_add(felem x3, felem y3, felem z3,
1057 const int mixed, const felem x2, const felem y2, const felem z2) 1161 const felem x1, const felem y1, const felem z1,
1058 { 1162 const int mixed, const felem x2, const felem y2, const felem z2)
1163{
1059 felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, ftmp6, x_out, y_out, z_out; 1164 felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, ftmp6, x_out, y_out, z_out;
1060 largefelem tmp, tmp2; 1165 largefelem tmp, tmp2;
1061 limb x_equal, y_equal, z1_is_zero, z2_is_zero; 1166 limb x_equal, y_equal, z1_is_zero, z2_is_zero;
@@ -1067,8 +1172,7 @@ static void point_add(felem x3, felem y3, felem z3,
1067 felem_square(tmp, z1); 1172 felem_square(tmp, z1);
1068 felem_reduce(ftmp, tmp); 1173 felem_reduce(ftmp, tmp);
1069 1174
1070 if (!mixed) 1175 if (!mixed) {
1071 {
1072 /* ftmp2 = z2z2 = z2**2 */ 1176 /* ftmp2 = z2z2 = z2**2 */
1073 felem_square(tmp, z2); 1177 felem_square(tmp, z2);
1074 felem_reduce(ftmp2, tmp); 1178 felem_reduce(ftmp2, tmp);
@@ -1098,9 +1202,7 @@ static void point_add(felem x3, felem y3, felem z3,
1098 /* s1 = ftmp6 = y1 * z2**3 */ 1202 /* s1 = ftmp6 = y1 * z2**3 */
1099 felem_mul(tmp, y1, ftmp2); 1203 felem_mul(tmp, y1, ftmp2);
1100 felem_reduce(ftmp6, tmp); 1204 felem_reduce(ftmp6, tmp);
1101 } 1205 } else {
1102 else
1103 {
1104 /* We'll assume z2 = 1 (special case z2 = 0 is handled later) */ 1206 /* We'll assume z2 = 1 (special case z2 = 0 is handled later) */
1105 1207
1106 /* u1 = ftmp3 = x1*z2z2 */ 1208 /* u1 = ftmp3 = x1*z2z2 */
@@ -1111,7 +1213,7 @@ static void point_add(felem x3, felem y3, felem z3,
1111 1213
1112 /* s1 = ftmp6 = y1 * z2**3 */ 1214 /* s1 = ftmp6 = y1 * z2**3 */
1113 felem_assign(ftmp6, y1); 1215 felem_assign(ftmp6, y1);
1114 } 1216 }
1115 1217
1116 /* u2 = x2*z1z1 */ 1218 /* u2 = x2*z1z1 */
1117 felem_mul(tmp, x2, ftmp); 1219 felem_mul(tmp, x2, ftmp);
@@ -1144,12 +1246,10 @@ static void point_add(felem x3, felem y3, felem z3,
1144 felem_scalar64(ftmp5, 2); 1246 felem_scalar64(ftmp5, 2);
1145 /* ftmp5[i] < 2^61 */ 1247 /* ftmp5[i] < 2^61 */
1146 1248
1147 if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) 1249 if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) {
1148 {
1149 point_double(x3, y3, z3, x1, y1, z1); 1250 point_double(x3, y3, z3, x1, y1, z1);
1150 return; 1251 return;
1151 } 1252 }
1152
1153 /* I = ftmp = (2h)**2 */ 1253 /* I = ftmp = (2h)**2 */
1154 felem_assign(ftmp, ftmp4); 1254 felem_assign(ftmp, ftmp4);
1155 felem_scalar64(ftmp, 2); 1255 felem_scalar64(ftmp, 2);
@@ -1180,8 +1280,9 @@ static void point_add(felem x3, felem y3, felem z3,
1180 1280
1181 /* y_out = r(V-x_out) - 2 * s1 * J */ 1281 /* y_out = r(V-x_out) - 2 * s1 * J */
1182 felem_diff64(ftmp3, x_out); 1282 felem_diff64(ftmp3, x_out);
1183 /* ftmp3[i] < 2^60 + 2^60 1283 /*
1184 * = 2^61 */ 1284 * ftmp3[i] < 2^60 + 2^60 = 2^61
1285 */
1185 felem_mul(tmp, ftmp5, ftmp3); 1286 felem_mul(tmp, ftmp5, ftmp3);
1186 /* tmp[i] < 17*2^122 */ 1287 /* tmp[i] < 17*2^122 */
1187 felem_mul(tmp2, ftmp6, ftmp2); 1288 felem_mul(tmp2, ftmp6, ftmp2);
@@ -1189,9 +1290,10 @@ static void point_add(felem x3, felem y3, felem z3,
1189 felem_scalar128(tmp2, 2); 1290 felem_scalar128(tmp2, 2);
1190 /* tmp2[i] < 17*2^121 */ 1291 /* tmp2[i] < 17*2^121 */
1191 felem_diff128(tmp, tmp2); 1292 felem_diff128(tmp, tmp2);
1192 /* tmp[i] < 2^127 - 2^69 + 17*2^122 1293 /*
1193 * = 2^126 - 2^122 - 2^6 - 2^2 - 1 1294 * tmp[i] < 2^127 - 2^69 + 17*2^122 = 2^126 - 2^122 - 2^6 - 2^2 - 1 <
1194 * < 2^127 */ 1295 * 2^127
1296 */
1195 felem_reduce(y_out, tmp); 1297 felem_reduce(y_out, tmp);
1196 1298
1197 copy_conditional(x_out, x2, z1_is_zero); 1299 copy_conditional(x_out, x2, z1_is_zero);
@@ -1203,7 +1305,7 @@ static void point_add(felem x3, felem y3, felem z3,
1203 felem_assign(x3, x_out); 1305 felem_assign(x3, x_out);
1204 felem_assign(y3, y_out); 1306 felem_assign(y3, y_out);
1205 felem_assign(z3, z_out); 1307 felem_assign(z3, z_out);
1206 } 1308}
1207 1309
1208/* Base point pre computation 1310/* Base point pre computation
1209 * -------------------------- 1311 * --------------------------
@@ -1240,126 +1342,126 @@ static void point_add(felem x3, felem y3, felem z3,
1240 1342
1241/* gmul is the table of precomputed base points */ 1343/* gmul is the table of precomputed base points */
1242static const felem gmul[16][3] = 1344static const felem gmul[16][3] =
1243 {{{0, 0, 0, 0, 0, 0, 0, 0, 0}, 1345{{{0, 0, 0, 0, 0, 0, 0, 0, 0},
1244 {0, 0, 0, 0, 0, 0, 0, 0, 0}, 1346{0, 0, 0, 0, 0, 0, 0, 0, 0},
1245 {0, 0, 0, 0, 0, 0, 0, 0, 0}}, 1347{0, 0, 0, 0, 0, 0, 0, 0, 0}},
1246 {{0x017e7e31c2e5bd66, 0x022cf0615a90a6fe, 0x00127a2ffa8de334, 1348{{0x017e7e31c2e5bd66, 0x022cf0615a90a6fe, 0x00127a2ffa8de334,
1247 0x01dfbf9d64a3f877, 0x006b4d3dbaa14b5e, 0x014fed487e0a2bd8, 1349 0x01dfbf9d64a3f877, 0x006b4d3dbaa14b5e, 0x014fed487e0a2bd8,
1248 0x015b4429c6481390, 0x03a73678fb2d988e, 0x00c6858e06b70404}, 13500x015b4429c6481390, 0x03a73678fb2d988e, 0x00c6858e06b70404},
1249 {0x00be94769fd16650, 0x031c21a89cb09022, 0x039013fad0761353, 1351{0x00be94769fd16650, 0x031c21a89cb09022, 0x039013fad0761353,
1250 0x02657bd099031542, 0x03273e662c97ee72, 0x01e6d11a05ebef45, 1352 0x02657bd099031542, 0x03273e662c97ee72, 0x01e6d11a05ebef45,
1251 0x03d1bd998f544495, 0x03001172297ed0b1, 0x011839296a789a3b}, 13530x03d1bd998f544495, 0x03001172297ed0b1, 0x011839296a789a3b},
1252 {1, 0, 0, 0, 0, 0, 0, 0, 0}}, 1354{1, 0, 0, 0, 0, 0, 0, 0, 0}},
1253 {{0x0373faacbc875bae, 0x00f325023721c671, 0x00f666fd3dbde5ad, 1355{{0x0373faacbc875bae, 0x00f325023721c671, 0x00f666fd3dbde5ad,
1254 0x01a6932363f88ea7, 0x01fc6d9e13f9c47b, 0x03bcbffc2bbf734e, 1356 0x01a6932363f88ea7, 0x01fc6d9e13f9c47b, 0x03bcbffc2bbf734e,
1255 0x013ee3c3647f3a92, 0x029409fefe75d07d, 0x00ef9199963d85e5}, 13570x013ee3c3647f3a92, 0x029409fefe75d07d, 0x00ef9199963d85e5},
1256 {0x011173743ad5b178, 0x02499c7c21bf7d46, 0x035beaeabb8b1a58, 1358{0x011173743ad5b178, 0x02499c7c21bf7d46, 0x035beaeabb8b1a58,
1257 0x00f989c4752ea0a3, 0x0101e1de48a9c1a3, 0x01a20076be28ba6c, 1359 0x00f989c4752ea0a3, 0x0101e1de48a9c1a3, 0x01a20076be28ba6c,
1258 0x02f8052e5eb2de95, 0x01bfe8f82dea117c, 0x0160074d3c36ddb7}, 13600x02f8052e5eb2de95, 0x01bfe8f82dea117c, 0x0160074d3c36ddb7},
1259 {1, 0, 0, 0, 0, 0, 0, 0, 0}}, 1361{1, 0, 0, 0, 0, 0, 0, 0, 0}},
1260 {{0x012f3fc373393b3b, 0x03d3d6172f1419fa, 0x02adc943c0b86873, 1362{{0x012f3fc373393b3b, 0x03d3d6172f1419fa, 0x02adc943c0b86873,
1261 0x00d475584177952b, 0x012a4d1673750ee2, 0x00512517a0f13b0c, 1363 0x00d475584177952b, 0x012a4d1673750ee2, 0x00512517a0f13b0c,
1262 0x02b184671a7b1734, 0x0315b84236f1a50a, 0x00a4afc472edbdb9}, 13640x02b184671a7b1734, 0x0315b84236f1a50a, 0x00a4afc472edbdb9},
1263 {0x00152a7077f385c4, 0x03044007d8d1c2ee, 0x0065829d61d52b52, 1365{0x00152a7077f385c4, 0x03044007d8d1c2ee, 0x0065829d61d52b52,
1264 0x00494ff6b6631d0d, 0x00a11d94d5f06bcf, 0x02d2f89474d9282e, 1366 0x00494ff6b6631d0d, 0x00a11d94d5f06bcf, 0x02d2f89474d9282e,
1265 0x0241c5727c06eeb9, 0x0386928710fbdb9d, 0x01f883f727b0dfbe}, 13670x0241c5727c06eeb9, 0x0386928710fbdb9d, 0x01f883f727b0dfbe},
1266 {1, 0, 0, 0, 0, 0, 0, 0, 0}}, 1368{1, 0, 0, 0, 0, 0, 0, 0, 0}},
1267 {{0x019b0c3c9185544d, 0x006243a37c9d97db, 0x02ee3cbe030a2ad2, 1369{{0x019b0c3c9185544d, 0x006243a37c9d97db, 0x02ee3cbe030a2ad2,
1268 0x00cfdd946bb51e0d, 0x0271c00932606b91, 0x03f817d1ec68c561, 1370 0x00cfdd946bb51e0d, 0x0271c00932606b91, 0x03f817d1ec68c561,
1269 0x03f37009806a369c, 0x03c1f30baf184fd5, 0x01091022d6d2f065}, 13710x03f37009806a369c, 0x03c1f30baf184fd5, 0x01091022d6d2f065},
1270 {0x0292c583514c45ed, 0x0316fca51f9a286c, 0x00300af507c1489a, 1372{0x0292c583514c45ed, 0x0316fca51f9a286c, 0x00300af507c1489a,
1271 0x0295f69008298cf1, 0x02c0ed8274943d7b, 0x016509b9b47a431e, 1373 0x0295f69008298cf1, 0x02c0ed8274943d7b, 0x016509b9b47a431e,
1272 0x02bc9de9634868ce, 0x005b34929bffcb09, 0x000c1a0121681524}, 13740x02bc9de9634868ce, 0x005b34929bffcb09, 0x000c1a0121681524},
1273 {1, 0, 0, 0, 0, 0, 0, 0, 0}}, 1375{1, 0, 0, 0, 0, 0, 0, 0, 0}},
1274 {{0x0286abc0292fb9f2, 0x02665eee9805b3f7, 0x01ed7455f17f26d6, 1376{{0x0286abc0292fb9f2, 0x02665eee9805b3f7, 0x01ed7455f17f26d6,
1275 0x0346355b83175d13, 0x006284944cd0a097, 0x0191895bcdec5e51, 1377 0x0346355b83175d13, 0x006284944cd0a097, 0x0191895bcdec5e51,
1276 0x02e288370afda7d9, 0x03b22312bfefa67a, 0x01d104d3fc0613fe}, 13780x02e288370afda7d9, 0x03b22312bfefa67a, 0x01d104d3fc0613fe},
1277 {0x0092421a12f7e47f, 0x0077a83fa373c501, 0x03bd25c5f696bd0d, 1379{0x0092421a12f7e47f, 0x0077a83fa373c501, 0x03bd25c5f696bd0d,
1278 0x035c41e4d5459761, 0x01ca0d1742b24f53, 0x00aaab27863a509c, 1380 0x035c41e4d5459761, 0x01ca0d1742b24f53, 0x00aaab27863a509c,
1279 0x018b6de47df73917, 0x025c0b771705cd01, 0x01fd51d566d760a7}, 13810x018b6de47df73917, 0x025c0b771705cd01, 0x01fd51d566d760a7},
1280 {1, 0, 0, 0, 0, 0, 0, 0, 0}}, 1382{1, 0, 0, 0, 0, 0, 0, 0, 0}},
1281 {{0x01dd92ff6b0d1dbd, 0x039c5e2e8f8afa69, 0x0261ed13242c3b27, 1383{{0x01dd92ff6b0d1dbd, 0x039c5e2e8f8afa69, 0x0261ed13242c3b27,
1282 0x0382c6e67026e6a0, 0x01d60b10be2089f9, 0x03c15f3dce86723f, 1384 0x0382c6e67026e6a0, 0x01d60b10be2089f9, 0x03c15f3dce86723f,
1283 0x03c764a32d2a062d, 0x017307eac0fad056, 0x018207c0b96c5256}, 13850x03c764a32d2a062d, 0x017307eac0fad056, 0x018207c0b96c5256},
1284 {0x0196a16d60e13154, 0x03e6ce74c0267030, 0x00ddbf2b4e52a5aa, 1386{0x0196a16d60e13154, 0x03e6ce74c0267030, 0x00ddbf2b4e52a5aa,
1285 0x012738241bbf31c8, 0x00ebe8dc04685a28, 0x024c2ad6d380d4a2, 1387 0x012738241bbf31c8, 0x00ebe8dc04685a28, 0x024c2ad6d380d4a2,
1286 0x035ee062a6e62d0e, 0x0029ed74af7d3a0f, 0x00eef32aec142ebd}, 13880x035ee062a6e62d0e, 0x0029ed74af7d3a0f, 0x00eef32aec142ebd},
1287 {1, 0, 0, 0, 0, 0, 0, 0, 0}}, 1389{1, 0, 0, 0, 0, 0, 0, 0, 0}},
1288 {{0x00c31ec398993b39, 0x03a9f45bcda68253, 0x00ac733c24c70890, 1390{{0x00c31ec398993b39, 0x03a9f45bcda68253, 0x00ac733c24c70890,
1289 0x00872b111401ff01, 0x01d178c23195eafb, 0x03bca2c816b87f74, 1391 0x00872b111401ff01, 0x01d178c23195eafb, 0x03bca2c816b87f74,
1290 0x0261a9af46fbad7a, 0x0324b2a8dd3d28f9, 0x00918121d8f24e23}, 13920x0261a9af46fbad7a, 0x0324b2a8dd3d28f9, 0x00918121d8f24e23},
1291 {0x032bc8c1ca983cd7, 0x00d869dfb08fc8c6, 0x01693cb61fce1516, 1393{0x032bc8c1ca983cd7, 0x00d869dfb08fc8c6, 0x01693cb61fce1516,
1292 0x012a5ea68f4e88a8, 0x010869cab88d7ae3, 0x009081ad277ceee1, 1394 0x012a5ea68f4e88a8, 0x010869cab88d7ae3, 0x009081ad277ceee1,
1293 0x033a77166d064cdc, 0x03955235a1fb3a95, 0x01251a4a9b25b65e}, 13950x033a77166d064cdc, 0x03955235a1fb3a95, 0x01251a4a9b25b65e},
1294 {1, 0, 0, 0, 0, 0, 0, 0, 0}}, 1396{1, 0, 0, 0, 0, 0, 0, 0, 0}},
1295 {{0x00148a3a1b27f40b, 0x0123186df1b31fdc, 0x00026e7beaad34ce, 1397{{0x00148a3a1b27f40b, 0x0123186df1b31fdc, 0x00026e7beaad34ce,
1296 0x01db446ac1d3dbba, 0x0299c1a33437eaec, 0x024540610183cbb7, 1398 0x01db446ac1d3dbba, 0x0299c1a33437eaec, 0x024540610183cbb7,
1297 0x0173bb0e9ce92e46, 0x02b937e43921214b, 0x01ab0436a9bf01b5}, 13990x0173bb0e9ce92e46, 0x02b937e43921214b, 0x01ab0436a9bf01b5},
1298 {0x0383381640d46948, 0x008dacbf0e7f330f, 0x03602122bcc3f318, 1400{0x0383381640d46948, 0x008dacbf0e7f330f, 0x03602122bcc3f318,
1299 0x01ee596b200620d6, 0x03bd0585fda430b3, 0x014aed77fd123a83, 1401 0x01ee596b200620d6, 0x03bd0585fda430b3, 0x014aed77fd123a83,
1300 0x005ace749e52f742, 0x0390fe041da2b842, 0x0189a8ceb3299242}, 14020x005ace749e52f742, 0x0390fe041da2b842, 0x0189a8ceb3299242},
1301 {1, 0, 0, 0, 0, 0, 0, 0, 0}}, 1403{1, 0, 0, 0, 0, 0, 0, 0, 0}},
1302 {{0x012a19d6b3282473, 0x00c0915918b423ce, 0x023a954eb94405ae, 1404{{0x012a19d6b3282473, 0x00c0915918b423ce, 0x023a954eb94405ae,
1303 0x00529f692be26158, 0x0289fa1b6fa4b2aa, 0x0198ae4ceea346ef, 1405 0x00529f692be26158, 0x0289fa1b6fa4b2aa, 0x0198ae4ceea346ef,
1304 0x0047d8cdfbdedd49, 0x00cc8c8953f0f6b8, 0x001424abbff49203}, 14060x0047d8cdfbdedd49, 0x00cc8c8953f0f6b8, 0x001424abbff49203},
1305 {0x0256732a1115a03a, 0x0351bc38665c6733, 0x03f7b950fb4a6447, 1407{0x0256732a1115a03a, 0x0351bc38665c6733, 0x03f7b950fb4a6447,
1306 0x000afffa94c22155, 0x025763d0a4dab540, 0x000511e92d4fc283, 1408 0x000afffa94c22155, 0x025763d0a4dab540, 0x000511e92d4fc283,
1307 0x030a7e9eda0ee96c, 0x004c3cd93a28bf0a, 0x017edb3a8719217f}, 14090x030a7e9eda0ee96c, 0x004c3cd93a28bf0a, 0x017edb3a8719217f},
1308 {1, 0, 0, 0, 0, 0, 0, 0, 0}}, 1410{1, 0, 0, 0, 0, 0, 0, 0, 0}},
1309 {{0x011de5675a88e673, 0x031d7d0f5e567fbe, 0x0016b2062c970ae5, 1411{{0x011de5675a88e673, 0x031d7d0f5e567fbe, 0x0016b2062c970ae5,
1310 0x03f4a2be49d90aa7, 0x03cef0bd13822866, 0x03f0923dcf774a6c, 1412 0x03f4a2be49d90aa7, 0x03cef0bd13822866, 0x03f0923dcf774a6c,
1311 0x0284bebc4f322f72, 0x016ab2645302bb2c, 0x01793f95dace0e2a}, 14130x0284bebc4f322f72, 0x016ab2645302bb2c, 0x01793f95dace0e2a},
1312 {0x010646e13527a28f, 0x01ca1babd59dc5e7, 0x01afedfd9a5595df, 1414{0x010646e13527a28f, 0x01ca1babd59dc5e7, 0x01afedfd9a5595df,
1313 0x01f15785212ea6b1, 0x0324e5d64f6ae3f4, 0x02d680f526d00645, 1415 0x01f15785212ea6b1, 0x0324e5d64f6ae3f4, 0x02d680f526d00645,
1314 0x0127920fadf627a7, 0x03b383f75df4f684, 0x0089e0057e783b0a}, 14160x0127920fadf627a7, 0x03b383f75df4f684, 0x0089e0057e783b0a},
1315 {1, 0, 0, 0, 0, 0, 0, 0, 0}}, 1417{1, 0, 0, 0, 0, 0, 0, 0, 0}},
1316 {{0x00f334b9eb3c26c6, 0x0298fdaa98568dce, 0x01c2d24843a82292, 1418{{0x00f334b9eb3c26c6, 0x0298fdaa98568dce, 0x01c2d24843a82292,
1317 0x020bcb24fa1b0711, 0x02cbdb3d2b1875e6, 0x0014907598f89422, 1419 0x020bcb24fa1b0711, 0x02cbdb3d2b1875e6, 0x0014907598f89422,
1318 0x03abe3aa43b26664, 0x02cbf47f720bc168, 0x0133b5e73014b79b}, 14200x03abe3aa43b26664, 0x02cbf47f720bc168, 0x0133b5e73014b79b},
1319 {0x034aab5dab05779d, 0x00cdc5d71fee9abb, 0x0399f16bd4bd9d30, 1421{0x034aab5dab05779d, 0x00cdc5d71fee9abb, 0x0399f16bd4bd9d30,
1320 0x03582fa592d82647, 0x02be1cdfb775b0e9, 0x0034f7cea32e94cb, 1422 0x03582fa592d82647, 0x02be1cdfb775b0e9, 0x0034f7cea32e94cb,
1321 0x0335a7f08f56f286, 0x03b707e9565d1c8b, 0x0015c946ea5b614f}, 14230x0335a7f08f56f286, 0x03b707e9565d1c8b, 0x0015c946ea5b614f},
1322 {1, 0, 0, 0, 0, 0, 0, 0, 0}}, 1424{1, 0, 0, 0, 0, 0, 0, 0, 0}},
1323 {{0x024676f6cff72255, 0x00d14625cac96378, 0x00532b6008bc3767, 1425{{0x024676f6cff72255, 0x00d14625cac96378, 0x00532b6008bc3767,
1324 0x01fc16721b985322, 0x023355ea1b091668, 0x029de7afdc0317c3, 1426 0x01fc16721b985322, 0x023355ea1b091668, 0x029de7afdc0317c3,
1325 0x02fc8a7ca2da037c, 0x02de1217d74a6f30, 0x013f7173175b73bf}, 14270x02fc8a7ca2da037c, 0x02de1217d74a6f30, 0x013f7173175b73bf},
1326 {0x0344913f441490b5, 0x0200f9e272b61eca, 0x0258a246b1dd55d2, 1428{0x0344913f441490b5, 0x0200f9e272b61eca, 0x0258a246b1dd55d2,
1327 0x03753db9ea496f36, 0x025e02937a09c5ef, 0x030cbd3d14012692, 1429 0x03753db9ea496f36, 0x025e02937a09c5ef, 0x030cbd3d14012692,
1328 0x01793a67e70dc72a, 0x03ec1d37048a662e, 0x006550f700c32a8d}, 14300x01793a67e70dc72a, 0x03ec1d37048a662e, 0x006550f700c32a8d},
1329 {1, 0, 0, 0, 0, 0, 0, 0, 0}}, 1431{1, 0, 0, 0, 0, 0, 0, 0, 0}},
1330 {{0x00d3f48a347eba27, 0x008e636649b61bd8, 0x00d3b93716778fb3, 1432{{0x00d3f48a347eba27, 0x008e636649b61bd8, 0x00d3b93716778fb3,
1331 0x004d1915757bd209, 0x019d5311a3da44e0, 0x016d1afcbbe6aade, 1433 0x004d1915757bd209, 0x019d5311a3da44e0, 0x016d1afcbbe6aade,
1332 0x0241bf5f73265616, 0x0384672e5d50d39b, 0x005009fee522b684}, 14340x0241bf5f73265616, 0x0384672e5d50d39b, 0x005009fee522b684},
1333 {0x029b4fab064435fe, 0x018868ee095bbb07, 0x01ea3d6936cc92b8, 1435{0x029b4fab064435fe, 0x018868ee095bbb07, 0x01ea3d6936cc92b8,
1334 0x000608b00f78a2f3, 0x02db911073d1c20f, 0x018205938470100a, 1436 0x000608b00f78a2f3, 0x02db911073d1c20f, 0x018205938470100a,
1335 0x01f1e4964cbe6ff2, 0x021a19a29eed4663, 0x01414485f42afa81}, 14370x01f1e4964cbe6ff2, 0x021a19a29eed4663, 0x01414485f42afa81},
1336 {1, 0, 0, 0, 0, 0, 0, 0, 0}}, 1438{1, 0, 0, 0, 0, 0, 0, 0, 0}},
1337 {{0x01612b3a17f63e34, 0x03813992885428e6, 0x022b3c215b5a9608, 1439{{0x01612b3a17f63e34, 0x03813992885428e6, 0x022b3c215b5a9608,
1338 0x029b4057e19f2fcb, 0x0384059a587af7e6, 0x02d6400ace6fe610, 1440 0x029b4057e19f2fcb, 0x0384059a587af7e6, 0x02d6400ace6fe610,
1339 0x029354d896e8e331, 0x00c047ee6dfba65e, 0x0037720542e9d49d}, 14410x029354d896e8e331, 0x00c047ee6dfba65e, 0x0037720542e9d49d},
1340 {0x02ce9eed7c5e9278, 0x0374ed703e79643b, 0x01316c54c4072006, 1442{0x02ce9eed7c5e9278, 0x0374ed703e79643b, 0x01316c54c4072006,
1341 0x005aaa09054b2ee8, 0x002824000c840d57, 0x03d4eba24771ed86, 1443 0x005aaa09054b2ee8, 0x002824000c840d57, 0x03d4eba24771ed86,
1342 0x0189c50aabc3bdae, 0x0338c01541e15510, 0x00466d56e38eed42}, 14440x0189c50aabc3bdae, 0x0338c01541e15510, 0x00466d56e38eed42},
1343 {1, 0, 0, 0, 0, 0, 0, 0, 0}}, 1445{1, 0, 0, 0, 0, 0, 0, 0, 0}},
1344 {{0x007efd8330ad8bd6, 0x02465ed48047710b, 0x0034c6606b215e0c, 1446{{0x007efd8330ad8bd6, 0x02465ed48047710b, 0x0034c6606b215e0c,
1345 0x016ae30c53cbf839, 0x01fa17bd37161216, 0x018ead4e61ce8ab9, 1447 0x016ae30c53cbf839, 0x01fa17bd37161216, 0x018ead4e61ce8ab9,
1346 0x005482ed5f5dee46, 0x037543755bba1d7f, 0x005e5ac7e70a9d0f}, 14480x005482ed5f5dee46, 0x037543755bba1d7f, 0x005e5ac7e70a9d0f},
1347 {0x0117e1bb2fdcb2a2, 0x03deea36249f40c4, 0x028d09b4a6246cb7, 1449{0x0117e1bb2fdcb2a2, 0x03deea36249f40c4, 0x028d09b4a6246cb7,
1348 0x03524b8855bcf756, 0x023d7d109d5ceb58, 0x0178e43e3223ef9c, 1450 0x03524b8855bcf756, 0x023d7d109d5ceb58, 0x0178e43e3223ef9c,
1349 0x0154536a0c6e966a, 0x037964d1286ee9fe, 0x0199bcd90e125055}, 14510x0154536a0c6e966a, 0x037964d1286ee9fe, 0x0199bcd90e125055},
1350 {1, 0, 0, 0, 0, 0, 0, 0, 0}}}; 1452{1, 0, 0, 0, 0, 0, 0, 0, 0}}};
1351 1453
1352/* select_point selects the |idx|th point from a precomputation table and 1454/* select_point selects the |idx|th point from a precomputation table and
1353 * copies it to out. */ 1455 * copies it to out. */
1354static void select_point(const limb idx, unsigned int size, const felem pre_comp[/* size */][3], 1456static void
1355 felem out[3]) 1457select_point(const limb idx, unsigned int size, const felem pre_comp[ /* size */ ][3],
1356 { 1458 felem out[3])
1459{
1357 unsigned i, j; 1460 unsigned i, j;
1358 limb *outlimbs = &out[0][0]; 1461 limb *outlimbs = &out[0][0];
1359 memset(outlimbs, 0, 3 * sizeof(felem)); 1462 memset(outlimbs, 0, 3 * sizeof(felem));
1360 1463
1361 for (i = 0; i < size; i++) 1464 for (i = 0; i < size; i++) {
1362 {
1363 const limb *inlimbs = &pre_comp[i][0][0]; 1465 const limb *inlimbs = &pre_comp[i][0][0];
1364 limb mask = i ^ idx; 1466 limb mask = i ^ idx;
1365 mask |= mask >> 4; 1467 mask |= mask >> 4;
@@ -1369,26 +1471,28 @@ static void select_point(const limb idx, unsigned int size, const felem pre_comp
1369 mask--; 1471 mask--;
1370 for (j = 0; j < NLIMBS * 3; j++) 1472 for (j = 0; j < NLIMBS * 3; j++)
1371 outlimbs[j] |= inlimbs[j] & mask; 1473 outlimbs[j] |= inlimbs[j] & mask;
1372 }
1373 } 1474 }
1475}
1374 1476
1375/* get_bit returns the |i|th bit in |in| */ 1477/* get_bit returns the |i|th bit in |in| */
1376static char get_bit(const felem_bytearray in, int i) 1478static char
1377 { 1479get_bit(const felem_bytearray in, int i)
1480{
1378 if (i < 0) 1481 if (i < 0)
1379 return 0; 1482 return 0;
1380 return (in[i >> 3] >> (i & 7)) & 1; 1483 return (in[i >> 3] >> (i & 7)) & 1;
1381 } 1484}
1382 1485
1383/* Interleaved point multiplication using precomputed point multiples: 1486/* Interleaved point multiplication using precomputed point multiples:
1384 * The small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[], 1487 * The small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[],
1385 * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple 1488 * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple
1386 * of the generator, using certain (large) precomputed multiples in g_pre_comp. 1489 * of the generator, using certain (large) precomputed multiples in g_pre_comp.
1387 * Output point (X, Y, Z) is stored in x_out, y_out, z_out */ 1490 * Output point (X, Y, Z) is stored in x_out, y_out, z_out */
1388static void batch_mul(felem x_out, felem y_out, felem z_out, 1491static void
1389 const felem_bytearray scalars[], const unsigned num_points, const u8 *g_scalar, 1492batch_mul(felem x_out, felem y_out, felem z_out,
1390 const int mixed, const felem pre_comp[][17][3], const felem g_pre_comp[16][3]) 1493 const felem_bytearray scalars[], const unsigned num_points, const u8 * g_scalar,
1391 { 1494 const int mixed, const felem pre_comp[][17][3], const felem g_pre_comp[16][3])
1495{
1392 int i, skip; 1496 int i, skip;
1393 unsigned num, gen_mul = (g_scalar != NULL); 1497 unsigned num, gen_mul = (g_scalar != NULL);
1394 felem nq[3], tmp[4]; 1498 felem nq[3], tmp[4];
@@ -1398,48 +1502,41 @@ static void batch_mul(felem x_out, felem y_out, felem z_out,
1398 /* set nq to the point at infinity */ 1502 /* set nq to the point at infinity */
1399 memset(nq, 0, 3 * sizeof(felem)); 1503 memset(nq, 0, 3 * sizeof(felem));
1400 1504
1401 /* Loop over all scalars msb-to-lsb, interleaving additions 1505 /*
1402 * of multiples of the generator (last quarter of rounds) 1506 * Loop over all scalars msb-to-lsb, interleaving additions of
1403 * and additions of other points multiples (every 5th round). 1507 * multiples of the generator (last quarter of rounds) and additions
1508 * of other points multiples (every 5th round).
1404 */ 1509 */
1405 skip = 1; /* save two point operations in the first round */ 1510 skip = 1; /* save two point operations in the first
1406 for (i = (num_points ? 520 : 130); i >= 0; --i) 1511 * round */
1407 { 1512 for (i = (num_points ? 520 : 130); i >= 0; --i) {
1408 /* double */ 1513 /* double */
1409 if (!skip) 1514 if (!skip)
1410 point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); 1515 point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]);
1411 1516
1412 /* add multiples of the generator */ 1517 /* add multiples of the generator */
1413 if (gen_mul && (i <= 130)) 1518 if (gen_mul && (i <= 130)) {
1414 {
1415 bits = get_bit(g_scalar, i + 390) << 3; 1519 bits = get_bit(g_scalar, i + 390) << 3;
1416 if (i < 130) 1520 if (i < 130) {
1417 {
1418 bits |= get_bit(g_scalar, i + 260) << 2; 1521 bits |= get_bit(g_scalar, i + 260) << 2;
1419 bits |= get_bit(g_scalar, i + 130) << 1; 1522 bits |= get_bit(g_scalar, i + 130) << 1;
1420 bits |= get_bit(g_scalar, i); 1523 bits |= get_bit(g_scalar, i);
1421 } 1524 }
1422 /* select the point to add, in constant time */ 1525 /* select the point to add, in constant time */
1423 select_point(bits, 16, g_pre_comp, tmp); 1526 select_point(bits, 16, g_pre_comp, tmp);
1424 if (!skip) 1527 if (!skip) {
1425 {
1426 point_add(nq[0], nq[1], nq[2], 1528 point_add(nq[0], nq[1], nq[2],
1427 nq[0], nq[1], nq[2], 1529 nq[0], nq[1], nq[2],
1428 1 /* mixed */, tmp[0], tmp[1], tmp[2]); 1530 1 /* mixed */ , tmp[0], tmp[1], tmp[2]);
1429 } 1531 } else {
1430 else
1431 {
1432 memcpy(nq, tmp, 3 * sizeof(felem)); 1532 memcpy(nq, tmp, 3 * sizeof(felem));
1433 skip = 0; 1533 skip = 0;
1434 }
1435 } 1534 }
1436 1535 }
1437 /* do other additions every 5 doublings */ 1536 /* do other additions every 5 doublings */
1438 if (num_points && (i % 5 == 0)) 1537 if (num_points && (i % 5 == 0)) {
1439 {
1440 /* loop over all scalars */ 1538 /* loop over all scalars */
1441 for (num = 0; num < num_points; ++num) 1539 for (num = 0; num < num_points; ++num) {
1442 {
1443 bits = get_bit(scalars[num], i + 4) << 5; 1540 bits = get_bit(scalars[num], i + 4) << 5;
1444 bits |= get_bit(scalars[num], i + 3) << 4; 1541 bits |= get_bit(scalars[num], i + 3) << 4;
1445 bits |= get_bit(scalars[num], i + 2) << 3; 1542 bits |= get_bit(scalars[num], i + 2) << 3;
@@ -1448,29 +1545,30 @@ static void batch_mul(felem x_out, felem y_out, felem z_out,
1448 bits |= get_bit(scalars[num], i - 1); 1545 bits |= get_bit(scalars[num], i - 1);
1449 ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); 1546 ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits);
1450 1547
1451 /* select the point to add or subtract, in constant time */ 1548 /*
1549 * select the point to add or subtract, in
1550 * constant time
1551 */
1452 select_point(digit, 17, pre_comp[num], tmp); 1552 select_point(digit, 17, pre_comp[num], tmp);
1453 felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the negative point */ 1553 felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the
1554 * negative point */
1454 copy_conditional(tmp[1], tmp[3], (-(limb) sign)); 1555 copy_conditional(tmp[1], tmp[3], (-(limb) sign));
1455 1556
1456 if (!skip) 1557 if (!skip) {
1457 {
1458 point_add(nq[0], nq[1], nq[2], 1558 point_add(nq[0], nq[1], nq[2],
1459 nq[0], nq[1], nq[2], 1559 nq[0], nq[1], nq[2],
1460 mixed, tmp[0], tmp[1], tmp[2]); 1560 mixed, tmp[0], tmp[1], tmp[2]);
1461 } 1561 } else {
1462 else
1463 {
1464 memcpy(nq, tmp, 3 * sizeof(felem)); 1562 memcpy(nq, tmp, 3 * sizeof(felem));
1465 skip = 0; 1563 skip = 0;
1466 }
1467 } 1564 }
1468 } 1565 }
1469 } 1566 }
1567 }
1470 felem_assign(x_out, nq[0]); 1568 felem_assign(x_out, nq[0]);
1471 felem_assign(y_out, nq[1]); 1569 felem_assign(y_out, nq[1]);
1472 felem_assign(z_out, nq[2]); 1570 felem_assign(z_out, nq[2]);
1473 } 1571}
1474 1572
1475 1573
1476/* Precomputation for the group generator. */ 1574/* Precomputation for the group generator. */
@@ -1493,20 +1591,20 @@ EC_GFp_nistp521_method(void)
1493 .group_get_curve = ec_GFp_simple_group_get_curve, 1591 .group_get_curve = ec_GFp_simple_group_get_curve,
1494 .group_get_degree = ec_GFp_simple_group_get_degree, 1592 .group_get_degree = ec_GFp_simple_group_get_degree,
1495 .group_check_discriminant = 1593 .group_check_discriminant =
1496 ec_GFp_simple_group_check_discriminant, 1594 ec_GFp_simple_group_check_discriminant,
1497 .point_init = ec_GFp_simple_point_init, 1595 .point_init = ec_GFp_simple_point_init,
1498 .point_finish = ec_GFp_simple_point_finish, 1596 .point_finish = ec_GFp_simple_point_finish,
1499 .point_clear_finish = ec_GFp_simple_point_clear_finish, 1597 .point_clear_finish = ec_GFp_simple_point_clear_finish,
1500 .point_copy = ec_GFp_simple_point_copy, 1598 .point_copy = ec_GFp_simple_point_copy,
1501 .point_set_to_infinity = ec_GFp_simple_point_set_to_infinity, 1599 .point_set_to_infinity = ec_GFp_simple_point_set_to_infinity,
1502 .point_set_Jprojective_coordinates_GFp = 1600 .point_set_Jprojective_coordinates_GFp =
1503 ec_GFp_simple_set_Jprojective_coordinates_GFp, 1601 ec_GFp_simple_set_Jprojective_coordinates_GFp,
1504 .point_get_Jprojective_coordinates_GFp = 1602 .point_get_Jprojective_coordinates_GFp =
1505 ec_GFp_simple_get_Jprojective_coordinates_GFp, 1603 ec_GFp_simple_get_Jprojective_coordinates_GFp,
1506 .point_set_affine_coordinates = 1604 .point_set_affine_coordinates =
1507 ec_GFp_simple_point_set_affine_coordinates, 1605 ec_GFp_simple_point_set_affine_coordinates,
1508 .point_get_affine_coordinates = 1606 .point_get_affine_coordinates =
1509 ec_GFp_nistp521_point_get_affine_coordinates, 1607 ec_GFp_nistp521_point_get_affine_coordinates,
1510 .add = ec_GFp_simple_add, 1608 .add = ec_GFp_simple_add,
1511 .dbl = ec_GFp_simple_dbl, 1609 .dbl = ec_GFp_simple_dbl,
1512 .invert = ec_GFp_simple_invert, 1610 .invert = ec_GFp_simple_invert,
@@ -1530,32 +1628,34 @@ EC_GFp_nistp521_method(void)
1530/* FUNCTIONS TO MANAGE PRECOMPUTATION 1628/* FUNCTIONS TO MANAGE PRECOMPUTATION
1531 */ 1629 */
1532 1630
1533static NISTP521_PRE_COMP *nistp521_pre_comp_new() 1631static NISTP521_PRE_COMP *
1534 { 1632nistp521_pre_comp_new()
1633{
1535 NISTP521_PRE_COMP *ret = NULL; 1634 NISTP521_PRE_COMP *ret = NULL;
1536 ret = (NISTP521_PRE_COMP *)malloc(sizeof(NISTP521_PRE_COMP)); 1635 ret = (NISTP521_PRE_COMP *) malloc(sizeof(NISTP521_PRE_COMP));
1537 if (!ret) 1636 if (!ret) {
1538 {
1539 ECerr(EC_F_NISTP521_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); 1637 ECerr(EC_F_NISTP521_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
1540 return ret; 1638 return ret;
1541 } 1639 }
1542 memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp)); 1640 memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp));
1543 ret->references = 1; 1641 ret->references = 1;
1544 return ret; 1642 return ret;
1545 } 1643}
1546 1644
1547static void *nistp521_pre_comp_dup(void *src_) 1645static void *
1548 { 1646nistp521_pre_comp_dup(void *src_)
1647{
1549 NISTP521_PRE_COMP *src = src_; 1648 NISTP521_PRE_COMP *src = src_;
1550 1649
1551 /* no need to actually copy, these objects never change! */ 1650 /* no need to actually copy, these objects never change! */
1552 CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); 1651 CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
1553 1652
1554 return src_; 1653 return src_;
1555 } 1654}
1556 1655
1557static void nistp521_pre_comp_free(void *pre_) 1656static void
1558 { 1657nistp521_pre_comp_free(void *pre_)
1658{
1559 int i; 1659 int i;
1560 NISTP521_PRE_COMP *pre = pre_; 1660 NISTP521_PRE_COMP *pre = pre_;
1561 1661
@@ -1567,10 +1667,11 @@ static void nistp521_pre_comp_free(void *pre_)
1567 return; 1667 return;
1568 1668
1569 free(pre); 1669 free(pre);
1570 } 1670}
1571 1671
1572static void nistp521_pre_comp_clear_free(void *pre_) 1672static void
1573 { 1673nistp521_pre_comp_clear_free(void *pre_)
1674{
1574 int i; 1675 int i;
1575 NISTP521_PRE_COMP *pre = pre_; 1676 NISTP521_PRE_COMP *pre = pre_;
1576 1677
@@ -1583,43 +1684,46 @@ static void nistp521_pre_comp_clear_free(void *pre_)
1583 1684
1584 OPENSSL_cleanse(pre, sizeof(*pre)); 1685 OPENSSL_cleanse(pre, sizeof(*pre));
1585 free(pre); 1686 free(pre);
1586 } 1687}
1587 1688
1588/******************************************************************************/ 1689/******************************************************************************/
1589/* OPENSSL EC_METHOD FUNCTIONS 1690/* OPENSSL EC_METHOD FUNCTIONS
1590 */ 1691 */
1591 1692
1592int ec_GFp_nistp521_group_init(EC_GROUP *group) 1693int
1593 { 1694ec_GFp_nistp521_group_init(EC_GROUP * group)
1695{
1594 int ret; 1696 int ret;
1595 ret = ec_GFp_simple_group_init(group); 1697 ret = ec_GFp_simple_group_init(group);
1596 group->a_is_minus3 = 1; 1698 group->a_is_minus3 = 1;
1597 return ret; 1699 return ret;
1598 } 1700}
1599 1701
1600int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p, 1702int
1601 const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) 1703ec_GFp_nistp521_group_set_curve(EC_GROUP * group, const BIGNUM * p,
1602 { 1704 const BIGNUM * a, const BIGNUM * b, BN_CTX * ctx)
1705{
1603 int ret = 0; 1706 int ret = 0;
1604 BN_CTX *new_ctx = NULL; 1707 BN_CTX *new_ctx = NULL;
1605 BIGNUM *curve_p, *curve_a, *curve_b; 1708 BIGNUM *curve_p, *curve_a, *curve_b;
1606 1709
1607 if (ctx == NULL) 1710 if (ctx == NULL)
1608 if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; 1711 if ((ctx = new_ctx = BN_CTX_new()) == NULL)
1712 return 0;
1609 BN_CTX_start(ctx); 1713 BN_CTX_start(ctx);
1610 if (((curve_p = BN_CTX_get(ctx)) == NULL) || 1714 if (((curve_p = BN_CTX_get(ctx)) == NULL) ||
1611 ((curve_a = BN_CTX_get(ctx)) == NULL) || 1715 ((curve_a = BN_CTX_get(ctx)) == NULL) ||
1612 ((curve_b = BN_CTX_get(ctx)) == NULL)) goto err; 1716 ((curve_b = BN_CTX_get(ctx)) == NULL))
1717 goto err;
1613 BN_bin2bn(nistp521_curve_params[0], sizeof(felem_bytearray), curve_p); 1718 BN_bin2bn(nistp521_curve_params[0], sizeof(felem_bytearray), curve_p);
1614 BN_bin2bn(nistp521_curve_params[1], sizeof(felem_bytearray), curve_a); 1719 BN_bin2bn(nistp521_curve_params[1], sizeof(felem_bytearray), curve_a);
1615 BN_bin2bn(nistp521_curve_params[2], sizeof(felem_bytearray), curve_b); 1720 BN_bin2bn(nistp521_curve_params[2], sizeof(felem_bytearray), curve_b);
1616 if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || 1721 if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) ||
1617 (BN_cmp(curve_b, b))) 1722 (BN_cmp(curve_b, b))) {
1618 {
1619 ECerr(EC_F_EC_GFP_NISTP521_GROUP_SET_CURVE, 1723 ECerr(EC_F_EC_GFP_NISTP521_GROUP_SET_CURVE,
1620 EC_R_WRONG_CURVE_PARAMETERS); 1724 EC_R_WRONG_CURVE_PARAMETERS);
1621 goto err; 1725 goto err;
1622 } 1726 }
1623 group->field_mod_func = BN_nist_mod_521; 1727 group->field_mod_func = BN_nist_mod_521;
1624 ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); 1728 ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx);
1625err: 1729err:
@@ -1627,74 +1731,79 @@ err:
1627 if (new_ctx != NULL) 1731 if (new_ctx != NULL)
1628 BN_CTX_free(new_ctx); 1732 BN_CTX_free(new_ctx);
1629 return ret; 1733 return ret;
1630 } 1734}
1631 1735
1632/* Takes the Jacobian coordinates (X, Y, Z) of a point and returns 1736/* Takes the Jacobian coordinates (X, Y, Z) of a point and returns
1633 * (X', Y') = (X/Z^2, Y/Z^3) */ 1737 * (X', Y') = (X/Z^2, Y/Z^3) */
1634int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group, 1738int
1635 const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) 1739ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP * group,
1636 { 1740 const EC_POINT * point, BIGNUM * x, BIGNUM * y, BN_CTX * ctx)
1741{
1637 felem z1, z2, x_in, y_in, x_out, y_out; 1742 felem z1, z2, x_in, y_in, x_out, y_out;
1638 largefelem tmp; 1743 largefelem tmp;
1639 1744
1640 if (EC_POINT_is_at_infinity(group, point)) 1745 if (EC_POINT_is_at_infinity(group, point)) {
1641 {
1642 ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES, 1746 ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES,
1643 EC_R_POINT_AT_INFINITY); 1747 EC_R_POINT_AT_INFINITY);
1644 return 0; 1748 return 0;
1645 } 1749 }
1646 if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) || 1750 if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) ||
1647 (!BN_to_felem(z1, &point->Z))) return 0; 1751 (!BN_to_felem(z1, &point->Z)))
1752 return 0;
1648 felem_inv(z2, z1); 1753 felem_inv(z2, z1);
1649 felem_square(tmp, z2); felem_reduce(z1, tmp); 1754 felem_square(tmp, z2);
1650 felem_mul(tmp, x_in, z1); felem_reduce(x_in, tmp); 1755 felem_reduce(z1, tmp);
1756 felem_mul(tmp, x_in, z1);
1757 felem_reduce(x_in, tmp);
1651 felem_contract(x_out, x_in); 1758 felem_contract(x_out, x_in);
1652 if (x != NULL) 1759 if (x != NULL) {
1653 { 1760 if (!felem_to_BN(x, x_out)) {
1654 if (!felem_to_BN(x, x_out))
1655 {
1656 ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES, ERR_R_BN_LIB); 1761 ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES, ERR_R_BN_LIB);
1657 return 0; 1762 return 0;
1658 }
1659 } 1763 }
1660 felem_mul(tmp, z1, z2); felem_reduce(z1, tmp); 1764 }
1661 felem_mul(tmp, y_in, z1); felem_reduce(y_in, tmp); 1765 felem_mul(tmp, z1, z2);
1766 felem_reduce(z1, tmp);
1767 felem_mul(tmp, y_in, z1);
1768 felem_reduce(y_in, tmp);
1662 felem_contract(y_out, y_in); 1769 felem_contract(y_out, y_in);
1663 if (y != NULL) 1770 if (y != NULL) {
1664 { 1771 if (!felem_to_BN(y, y_out)) {
1665 if (!felem_to_BN(y, y_out))
1666 {
1667 ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES, ERR_R_BN_LIB); 1772 ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES, ERR_R_BN_LIB);
1668 return 0; 1773 return 0;
1669 }
1670 } 1774 }
1671 return 1;
1672 } 1775 }
1776 return 1;
1777}
1673 1778
1674static void make_points_affine(size_t num, felem points[/* num */][3], felem tmp_felems[/* num+1 */]) 1779static void
1675 { 1780make_points_affine(size_t num, felem points[ /* num */ ][3], felem tmp_felems[ /* num+1 */ ])
1676 /* Runs in constant time, unless an input is the point at infinity 1781{
1677 * (which normally shouldn't happen). */ 1782 /*
1783 * Runs in constant time, unless an input is the point at infinity
1784 * (which normally shouldn't happen).
1785 */
1678 ec_GFp_nistp_points_make_affine_internal( 1786 ec_GFp_nistp_points_make_affine_internal(
1679 num, 1787 num,
1680 points, 1788 points,
1681 sizeof(felem), 1789 sizeof(felem),
1682 tmp_felems, 1790 tmp_felems,
1683 (void (*)(void *)) felem_one, 1791 (void (*) (void *)) felem_one,
1684 (int (*)(const void *)) felem_is_zero_int, 1792 (int (*) (const void *)) felem_is_zero_int,
1685 (void (*)(void *, const void *)) felem_assign, 1793 (void (*) (void *, const void *)) felem_assign,
1686 (void (*)(void *, const void *)) felem_square_reduce, 1794 (void (*) (void *, const void *)) felem_square_reduce,
1687 (void (*)(void *, const void *, const void *)) felem_mul_reduce, 1795 (void (*) (void *, const void *, const void *)) felem_mul_reduce,
1688 (void (*)(void *, const void *)) felem_inv, 1796 (void (*) (void *, const void *)) felem_inv,
1689 (void (*)(void *, const void *)) felem_contract); 1797 (void (*) (void *, const void *)) felem_contract);
1690 } 1798}
1691 1799
1692/* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values 1800/* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values
1693 * Result is stored in r (r can equal one of the inputs). */ 1801 * Result is stored in r (r can equal one of the inputs). */
1694int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r, 1802int
1695 const BIGNUM *scalar, size_t num, const EC_POINT *points[], 1803ec_GFp_nistp521_points_mul(const EC_GROUP * group, EC_POINT * r,
1696 const BIGNUM *scalars[], BN_CTX *ctx) 1804 const BIGNUM * scalar, size_t num, const EC_POINT * points[],
1697 { 1805 const BIGNUM * scalars[], BN_CTX * ctx)
1806{
1698 int ret = 0; 1807 int ret = 0;
1699 int j; 1808 int j;
1700 int mixed = 0; 1809 int mixed = 0;
@@ -1702,7 +1811,7 @@ int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r,
1702 BIGNUM *x, *y, *z, *tmp_scalar; 1811 BIGNUM *x, *y, *z, *tmp_scalar;
1703 felem_bytearray g_secret; 1812 felem_bytearray g_secret;
1704 felem_bytearray *secrets = NULL; 1813 felem_bytearray *secrets = NULL;
1705 felem (*pre_comp)[17][3] = NULL; 1814 felem(*pre_comp)[17][3] = NULL;
1706 felem *tmp_felems = NULL; 1815 felem *tmp_felems = NULL;
1707 felem_bytearray tmp; 1816 felem_bytearray tmp;
1708 unsigned i, num_bytes; 1817 unsigned i, num_bytes;
@@ -1710,178 +1819,170 @@ int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r,
1710 size_t num_points = num; 1819 size_t num_points = num;
1711 felem x_in, y_in, z_in, x_out, y_out, z_out; 1820 felem x_in, y_in, z_in, x_out, y_out, z_out;
1712 NISTP521_PRE_COMP *pre = NULL; 1821 NISTP521_PRE_COMP *pre = NULL;
1713 felem (*g_pre_comp)[3] = NULL; 1822 felem(*g_pre_comp)[3] = NULL;
1714 EC_POINT *generator = NULL; 1823 EC_POINT *generator = NULL;
1715 const EC_POINT *p = NULL; 1824 const EC_POINT *p = NULL;
1716 const BIGNUM *p_scalar = NULL; 1825 const BIGNUM *p_scalar = NULL;
1717 1826
1718 if (ctx == NULL) 1827 if (ctx == NULL)
1719 if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; 1828 if ((ctx = new_ctx = BN_CTX_new()) == NULL)
1829 return 0;
1720 BN_CTX_start(ctx); 1830 BN_CTX_start(ctx);
1721 if (((x = BN_CTX_get(ctx)) == NULL) || 1831 if (((x = BN_CTX_get(ctx)) == NULL) ||
1722 ((y = BN_CTX_get(ctx)) == NULL) || 1832 ((y = BN_CTX_get(ctx)) == NULL) ||
1723 ((z = BN_CTX_get(ctx)) == NULL) || 1833 ((z = BN_CTX_get(ctx)) == NULL) ||
1724 ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) 1834 ((tmp_scalar = BN_CTX_get(ctx)) == NULL))
1725 goto err; 1835 goto err;
1726 1836
1727 if (scalar != NULL) 1837 if (scalar != NULL) {
1728 {
1729 pre = EC_EX_DATA_get_data(group->extra_data, 1838 pre = EC_EX_DATA_get_data(group->extra_data,
1730 nistp521_pre_comp_dup, nistp521_pre_comp_free, 1839 nistp521_pre_comp_dup, nistp521_pre_comp_free,
1731 nistp521_pre_comp_clear_free); 1840 nistp521_pre_comp_clear_free);
1732 if (pre) 1841 if (pre)
1733 /* we have precomputation, try to use it */ 1842 /* we have precomputation, try to use it */
1734 g_pre_comp = &pre->g_pre_comp[0]; 1843 g_pre_comp = &pre->g_pre_comp[0];
1735 else 1844 else
1736 /* try to use the standard precomputation */ 1845 /* try to use the standard precomputation */
1737 g_pre_comp = (felem (*)[3]) gmul; 1846 g_pre_comp = (felem(*)[3]) gmul;
1738 generator = EC_POINT_new(group); 1847 generator = EC_POINT_new(group);
1739 if (generator == NULL) 1848 if (generator == NULL)
1740 goto err; 1849 goto err;
1741 /* get the generator from precomputation */ 1850 /* get the generator from precomputation */
1742 if (!felem_to_BN(x, g_pre_comp[1][0]) || 1851 if (!felem_to_BN(x, g_pre_comp[1][0]) ||
1743 !felem_to_BN(y, g_pre_comp[1][1]) || 1852 !felem_to_BN(y, g_pre_comp[1][1]) ||
1744 !felem_to_BN(z, g_pre_comp[1][2])) 1853 !felem_to_BN(z, g_pre_comp[1][2])) {
1745 {
1746 ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB); 1854 ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB);
1747 goto err; 1855 goto err;
1748 } 1856 }
1749 if (!EC_POINT_set_Jprojective_coordinates_GFp(group, 1857 if (!EC_POINT_set_Jprojective_coordinates_GFp(group,
1750 generator, x, y, z, ctx)) 1858 generator, x, y, z, ctx))
1751 goto err; 1859 goto err;
1752 if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) 1860 if (0 == EC_POINT_cmp(group, generator, group->generator, ctx))
1753 /* precomputation matches generator */ 1861 /* precomputation matches generator */
1754 have_pre_comp = 1; 1862 have_pre_comp = 1;
1755 else 1863 else
1756 /* we don't have valid precomputation: 1864 /*
1757 * treat the generator as a random point */ 1865 * we don't have valid precomputation: treat the
1866 * generator as a random point
1867 */
1758 num_points++; 1868 num_points++;
1759 } 1869 }
1760 1870 if (num_points > 0) {
1761 if (num_points > 0) 1871 if (num_points >= 2) {
1762 { 1872 /*
1763 if (num_points >= 2) 1873 * unless we precompute multiples for just one point,
1764 { 1874 * converting those into affine form is time well
1765 /* unless we precompute multiples for just one point, 1875 * spent
1766 * converting those into affine form is time well spent */ 1876 */
1767 mixed = 1; 1877 mixed = 1;
1768 } 1878 }
1769 secrets = malloc(num_points * sizeof(felem_bytearray)); 1879 secrets = malloc(num_points * sizeof(felem_bytearray));
1770 pre_comp = malloc(num_points * 17 * 3 * sizeof(felem)); 1880 pre_comp = malloc(num_points * 17 * 3 * sizeof(felem));
1771 if (mixed) 1881 if (mixed)
1772 tmp_felems = malloc((num_points * 17 + 1) * sizeof(felem)); 1882 tmp_felems = malloc((num_points * 17 + 1) * sizeof(felem));
1773 if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_felems == NULL))) 1883 if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_felems == NULL))) {
1774 {
1775 ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_MALLOC_FAILURE); 1884 ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1776 goto err; 1885 goto err;
1777 } 1886 }
1778 1887 /*
1779 /* we treat NULL scalars as 0, and NULL points as points at infinity, 1888 * we treat NULL scalars as 0, and NULL points as points at
1780 * i.e., they contribute nothing to the linear combination */ 1889 * infinity, i.e., they contribute nothing to the linear
1890 * combination
1891 */
1781 memset(secrets, 0, num_points * sizeof(felem_bytearray)); 1892 memset(secrets, 0, num_points * sizeof(felem_bytearray));
1782 memset(pre_comp, 0, num_points * 17 * 3 * sizeof(felem)); 1893 memset(pre_comp, 0, num_points * 17 * 3 * sizeof(felem));
1783 for (i = 0; i < num_points; ++i) 1894 for (i = 0; i < num_points; ++i) {
1784 {
1785 if (i == num) 1895 if (i == num)
1786 /* we didn't have a valid precomputation, so we pick 1896 /*
1787 * the generator */ 1897 * we didn't have a valid precomputation, so
1788 { 1898 * we pick the generator
1899 */
1900 {
1789 p = EC_GROUP_get0_generator(group); 1901 p = EC_GROUP_get0_generator(group);
1790 p_scalar = scalar; 1902 p_scalar = scalar;
1791 } 1903 } else
1792 else
1793 /* the i^th point */ 1904 /* the i^th point */
1794 { 1905 {
1795 p = points[i]; 1906 p = points[i];
1796 p_scalar = scalars[i]; 1907 p_scalar = scalars[i];
1797 } 1908 }
1798 if ((p_scalar != NULL) && (p != NULL)) 1909 if ((p_scalar != NULL) && (p != NULL)) {
1799 {
1800 /* reduce scalar to 0 <= scalar < 2^521 */ 1910 /* reduce scalar to 0 <= scalar < 2^521 */
1801 if ((BN_num_bits(p_scalar) > 521) || (BN_is_negative(p_scalar))) 1911 if ((BN_num_bits(p_scalar) > 521) || (BN_is_negative(p_scalar))) {
1802 { 1912 /*
1803 /* this is an unusual input, and we don't guarantee 1913 * this is an unusual input, and we
1804 * constant-timeness */ 1914 * don't guarantee constant-timeness
1805 if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) 1915 */
1806 { 1916 if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) {
1807 ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB); 1917 ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB);
1808 goto err; 1918 goto err;
1809 }
1810 num_bytes = BN_bn2bin(tmp_scalar, tmp);
1811 } 1919 }
1812 else 1920 num_bytes = BN_bn2bin(tmp_scalar, tmp);
1921 } else
1813 num_bytes = BN_bn2bin(p_scalar, tmp); 1922 num_bytes = BN_bn2bin(p_scalar, tmp);
1814 flip_endian(secrets[i], tmp, num_bytes); 1923 flip_endian(secrets[i], tmp, num_bytes);
1815 /* precompute multiples */ 1924 /* precompute multiples */
1816 if ((!BN_to_felem(x_out, &p->X)) || 1925 if ((!BN_to_felem(x_out, &p->X)) ||
1817 (!BN_to_felem(y_out, &p->Y)) || 1926 (!BN_to_felem(y_out, &p->Y)) ||
1818 (!BN_to_felem(z_out, &p->Z))) goto err; 1927 (!BN_to_felem(z_out, &p->Z)))
1928 goto err;
1819 memcpy(pre_comp[i][1][0], x_out, sizeof(felem)); 1929 memcpy(pre_comp[i][1][0], x_out, sizeof(felem));
1820 memcpy(pre_comp[i][1][1], y_out, sizeof(felem)); 1930 memcpy(pre_comp[i][1][1], y_out, sizeof(felem));
1821 memcpy(pre_comp[i][1][2], z_out, sizeof(felem)); 1931 memcpy(pre_comp[i][1][2], z_out, sizeof(felem));
1822 for (j = 2; j <= 16; ++j) 1932 for (j = 2; j <= 16; ++j) {
1823 { 1933 if (j & 1) {
1824 if (j & 1)
1825 {
1826 point_add( 1934 point_add(
1827 pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], 1935 pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2],
1828 pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2], 1936 pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2],
1829 0, pre_comp[i][j-1][0], pre_comp[i][j-1][1], pre_comp[i][j-1][2]); 1937 0, pre_comp[i][j - 1][0], pre_comp[i][j - 1][1], pre_comp[i][j - 1][2]);
1830 } 1938 } else {
1831 else
1832 {
1833 point_double( 1939 point_double(
1834 pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], 1940 pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2],
1835 pre_comp[i][j/2][0], pre_comp[i][j/2][1], pre_comp[i][j/2][2]); 1941 pre_comp[i][j / 2][0], pre_comp[i][j / 2][1], pre_comp[i][j / 2][2]);
1836 }
1837 } 1942 }
1838 } 1943 }
1839 } 1944 }
1945 }
1840 if (mixed) 1946 if (mixed)
1841 make_points_affine(num_points * 17, pre_comp[0], tmp_felems); 1947 make_points_affine(num_points * 17, pre_comp[0], tmp_felems);
1842 } 1948 }
1843
1844 /* the scalar for the generator */ 1949 /* the scalar for the generator */
1845 if ((scalar != NULL) && (have_pre_comp)) 1950 if ((scalar != NULL) && (have_pre_comp)) {
1846 {
1847 memset(g_secret, 0, sizeof(g_secret)); 1951 memset(g_secret, 0, sizeof(g_secret));
1848 /* reduce scalar to 0 <= scalar < 2^521 */ 1952 /* reduce scalar to 0 <= scalar < 2^521 */
1849 if ((BN_num_bits(scalar) > 521) || (BN_is_negative(scalar))) 1953 if ((BN_num_bits(scalar) > 521) || (BN_is_negative(scalar))) {
1850 { 1954 /*
1851 /* this is an unusual input, and we don't guarantee 1955 * this is an unusual input, and we don't guarantee
1852 * constant-timeness */ 1956 * constant-timeness
1853 if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) 1957 */
1854 { 1958 if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) {
1855 ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB); 1959 ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB);
1856 goto err; 1960 goto err;
1857 }
1858 num_bytes = BN_bn2bin(tmp_scalar, tmp);
1859 } 1961 }
1860 else 1962 num_bytes = BN_bn2bin(tmp_scalar, tmp);
1963 } else
1861 num_bytes = BN_bn2bin(scalar, tmp); 1964 num_bytes = BN_bn2bin(scalar, tmp);
1862 flip_endian(g_secret, tmp, num_bytes); 1965 flip_endian(g_secret, tmp, num_bytes);
1863 /* do the multiplication with generator precomputation*/ 1966 /* do the multiplication with generator precomputation */
1864 batch_mul(x_out, y_out, z_out, 1967 batch_mul(x_out, y_out, z_out,
1865 (const felem_bytearray (*)) secrets, num_points, 1968 (const felem_bytearray(*)) secrets, num_points,
1866 g_secret, 1969 g_secret,
1867 mixed, (const felem (*)[17][3]) pre_comp, 1970 mixed, (const felem(*)[17][3]) pre_comp,
1868 (const felem (*)[3]) g_pre_comp); 1971 (const felem(*)[3]) g_pre_comp);
1869 } 1972 } else
1870 else
1871 /* do the multiplication without generator precomputation */ 1973 /* do the multiplication without generator precomputation */
1872 batch_mul(x_out, y_out, z_out, 1974 batch_mul(x_out, y_out, z_out,
1873 (const felem_bytearray (*)) secrets, num_points, 1975 (const felem_bytearray(*)) secrets, num_points,
1874 NULL, mixed, (const felem (*)[17][3]) pre_comp, NULL); 1976 NULL, mixed, (const felem(*)[17][3]) pre_comp, NULL);
1875 /* reduce the output to its unique minimal representation */ 1977 /* reduce the output to its unique minimal representation */
1876 felem_contract(x_in, x_out); 1978 felem_contract(x_in, x_out);
1877 felem_contract(y_in, y_out); 1979 felem_contract(y_in, y_out);
1878 felem_contract(z_in, z_out); 1980 felem_contract(z_in, z_out);
1879 if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) || 1981 if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) ||
1880 (!felem_to_BN(z, z_in))) 1982 (!felem_to_BN(z, z_in))) {
1881 {
1882 ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB); 1983 ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB);
1883 goto err; 1984 goto err;
1884 } 1985 }
1885 ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); 1986 ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx);
1886 1987
1887err: 1988err:
@@ -1897,10 +1998,11 @@ err:
1897 if (tmp_felems != NULL) 1998 if (tmp_felems != NULL)
1898 free(tmp_felems); 1999 free(tmp_felems);
1899 return ret; 2000 return ret;
1900 } 2001}
1901 2002
1902int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx) 2003int
1903 { 2004ec_GFp_nistp521_precompute_mult(EC_GROUP * group, BN_CTX * ctx)
2005{
1904 int ret = 0; 2006 int ret = 0;
1905 NISTP521_PRE_COMP *pre = NULL; 2007 NISTP521_PRE_COMP *pre = NULL;
1906 int i, j; 2008 int i, j;
@@ -1911,95 +2013,93 @@ int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
1911 2013
1912 /* throw away old precomputation */ 2014 /* throw away old precomputation */
1913 EC_EX_DATA_free_data(&group->extra_data, nistp521_pre_comp_dup, 2015 EC_EX_DATA_free_data(&group->extra_data, nistp521_pre_comp_dup,
1914 nistp521_pre_comp_free, nistp521_pre_comp_clear_free); 2016 nistp521_pre_comp_free, nistp521_pre_comp_clear_free);
1915 if (ctx == NULL) 2017 if (ctx == NULL)
1916 if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; 2018 if ((ctx = new_ctx = BN_CTX_new()) == NULL)
2019 return 0;
1917 BN_CTX_start(ctx); 2020 BN_CTX_start(ctx);
1918 if (((x = BN_CTX_get(ctx)) == NULL) || 2021 if (((x = BN_CTX_get(ctx)) == NULL) ||
1919 ((y = BN_CTX_get(ctx)) == NULL)) 2022 ((y = BN_CTX_get(ctx)) == NULL))
1920 goto err; 2023 goto err;
1921 /* get the generator */ 2024 /* get the generator */
1922 if (group->generator == NULL) goto err; 2025 if (group->generator == NULL)
2026 goto err;
1923 generator = EC_POINT_new(group); 2027 generator = EC_POINT_new(group);
1924 if (generator == NULL) 2028 if (generator == NULL)
1925 goto err; 2029 goto err;
1926 BN_bin2bn(nistp521_curve_params[3], sizeof (felem_bytearray), x); 2030 BN_bin2bn(nistp521_curve_params[3], sizeof(felem_bytearray), x);
1927 BN_bin2bn(nistp521_curve_params[4], sizeof (felem_bytearray), y); 2031 BN_bin2bn(nistp521_curve_params[4], sizeof(felem_bytearray), y);
1928 if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx)) 2032 if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx))
1929 goto err; 2033 goto err;
1930 if ((pre = nistp521_pre_comp_new()) == NULL) 2034 if ((pre = nistp521_pre_comp_new()) == NULL)
1931 goto err; 2035 goto err;
1932 /* if the generator is the standard one, use built-in precomputation */ 2036 /* if the generator is the standard one, use built-in precomputation */
1933 if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) 2037 if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) {
1934 {
1935 memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); 2038 memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp));
1936 ret = 1; 2039 ret = 1;
1937 goto err; 2040 goto err;
1938 } 2041 }
1939 if ((!BN_to_felem(pre->g_pre_comp[1][0], &group->generator->X)) || 2042 if ((!BN_to_felem(pre->g_pre_comp[1][0], &group->generator->X)) ||
1940 (!BN_to_felem(pre->g_pre_comp[1][1], &group->generator->Y)) || 2043 (!BN_to_felem(pre->g_pre_comp[1][1], &group->generator->Y)) ||
1941 (!BN_to_felem(pre->g_pre_comp[1][2], &group->generator->Z))) 2044 (!BN_to_felem(pre->g_pre_comp[1][2], &group->generator->Z)))
1942 goto err; 2045 goto err;
1943 /* compute 2^130*G, 2^260*G, 2^390*G */ 2046 /* compute 2^130*G, 2^260*G, 2^390*G */
1944 for (i = 1; i <= 4; i <<= 1) 2047 for (i = 1; i <= 4; i <<= 1) {
1945 { 2048 point_double(pre->g_pre_comp[2 * i][0], pre->g_pre_comp[2 * i][1],
1946 point_double(pre->g_pre_comp[2*i][0], pre->g_pre_comp[2*i][1], 2049 pre->g_pre_comp[2 * i][2], pre->g_pre_comp[i][0],
1947 pre->g_pre_comp[2*i][2], pre->g_pre_comp[i][0], 2050 pre->g_pre_comp[i][1], pre->g_pre_comp[i][2]);
1948 pre->g_pre_comp[i][1], pre->g_pre_comp[i][2]); 2051 for (j = 0; j < 129; ++j) {
1949 for (j = 0; j < 129; ++j) 2052 point_double(pre->g_pre_comp[2 * i][0],
1950 { 2053 pre->g_pre_comp[2 * i][1],
1951 point_double(pre->g_pre_comp[2*i][0], 2054 pre->g_pre_comp[2 * i][2],
1952 pre->g_pre_comp[2*i][1], 2055 pre->g_pre_comp[2 * i][0],
1953 pre->g_pre_comp[2*i][2], 2056 pre->g_pre_comp[2 * i][1],
1954 pre->g_pre_comp[2*i][0], 2057 pre->g_pre_comp[2 * i][2]);
1955 pre->g_pre_comp[2*i][1],
1956 pre->g_pre_comp[2*i][2]);
1957 }
1958 } 2058 }
2059 }
1959 /* g_pre_comp[0] is the point at infinity */ 2060 /* g_pre_comp[0] is the point at infinity */
1960 memset(pre->g_pre_comp[0], 0, sizeof(pre->g_pre_comp[0])); 2061 memset(pre->g_pre_comp[0], 0, sizeof(pre->g_pre_comp[0]));
1961 /* the remaining multiples */ 2062 /* the remaining multiples */
1962 /* 2^130*G + 2^260*G */ 2063 /* 2^130*G + 2^260*G */
1963 point_add(pre->g_pre_comp[6][0], pre->g_pre_comp[6][1], 2064 point_add(pre->g_pre_comp[6][0], pre->g_pre_comp[6][1],
1964 pre->g_pre_comp[6][2], pre->g_pre_comp[4][0], 2065 pre->g_pre_comp[6][2], pre->g_pre_comp[4][0],
1965 pre->g_pre_comp[4][1], pre->g_pre_comp[4][2], 2066 pre->g_pre_comp[4][1], pre->g_pre_comp[4][2],
1966 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], 2067 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1],
1967 pre->g_pre_comp[2][2]); 2068 pre->g_pre_comp[2][2]);
1968 /* 2^130*G + 2^390*G */ 2069 /* 2^130*G + 2^390*G */
1969 point_add(pre->g_pre_comp[10][0], pre->g_pre_comp[10][1], 2070 point_add(pre->g_pre_comp[10][0], pre->g_pre_comp[10][1],
1970 pre->g_pre_comp[10][2], pre->g_pre_comp[8][0], 2071 pre->g_pre_comp[10][2], pre->g_pre_comp[8][0],
1971 pre->g_pre_comp[8][1], pre->g_pre_comp[8][2], 2072 pre->g_pre_comp[8][1], pre->g_pre_comp[8][2],
1972 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], 2073 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1],
1973 pre->g_pre_comp[2][2]); 2074 pre->g_pre_comp[2][2]);
1974 /* 2^260*G + 2^390*G */ 2075 /* 2^260*G + 2^390*G */
1975 point_add(pre->g_pre_comp[12][0], pre->g_pre_comp[12][1], 2076 point_add(pre->g_pre_comp[12][0], pre->g_pre_comp[12][1],
1976 pre->g_pre_comp[12][2], pre->g_pre_comp[8][0], 2077 pre->g_pre_comp[12][2], pre->g_pre_comp[8][0],
1977 pre->g_pre_comp[8][1], pre->g_pre_comp[8][2], 2078 pre->g_pre_comp[8][1], pre->g_pre_comp[8][2],
1978 0, pre->g_pre_comp[4][0], pre->g_pre_comp[4][1], 2079 0, pre->g_pre_comp[4][0], pre->g_pre_comp[4][1],
1979 pre->g_pre_comp[4][2]); 2080 pre->g_pre_comp[4][2]);
1980 /* 2^130*G + 2^260*G + 2^390*G */ 2081 /* 2^130*G + 2^260*G + 2^390*G */
1981 point_add(pre->g_pre_comp[14][0], pre->g_pre_comp[14][1], 2082 point_add(pre->g_pre_comp[14][0], pre->g_pre_comp[14][1],
1982 pre->g_pre_comp[14][2], pre->g_pre_comp[12][0], 2083 pre->g_pre_comp[14][2], pre->g_pre_comp[12][0],
1983 pre->g_pre_comp[12][1], pre->g_pre_comp[12][2], 2084 pre->g_pre_comp[12][1], pre->g_pre_comp[12][2],
1984 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], 2085 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1],
1985 pre->g_pre_comp[2][2]); 2086 pre->g_pre_comp[2][2]);
1986 for (i = 1; i < 8; ++i) 2087 for (i = 1; i < 8; ++i) {
1987 {
1988 /* odd multiples: add G */ 2088 /* odd multiples: add G */
1989 point_add(pre->g_pre_comp[2*i+1][0], pre->g_pre_comp[2*i+1][1], 2089 point_add(pre->g_pre_comp[2 * i + 1][0], pre->g_pre_comp[2 * i + 1][1],
1990 pre->g_pre_comp[2*i+1][2], pre->g_pre_comp[2*i][0], 2090 pre->g_pre_comp[2 * i + 1][2], pre->g_pre_comp[2 * i][0],
1991 pre->g_pre_comp[2*i][1], pre->g_pre_comp[2*i][2], 2091 pre->g_pre_comp[2 * i][1], pre->g_pre_comp[2 * i][2],
1992 0, pre->g_pre_comp[1][0], pre->g_pre_comp[1][1], 2092 0, pre->g_pre_comp[1][0], pre->g_pre_comp[1][1],
1993 pre->g_pre_comp[1][2]); 2093 pre->g_pre_comp[1][2]);
1994 } 2094 }
1995 make_points_affine(15, &(pre->g_pre_comp[1]), tmp_felems); 2095 make_points_affine(15, &(pre->g_pre_comp[1]), tmp_felems);
1996 2096
1997 if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp521_pre_comp_dup, 2097 if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp521_pre_comp_dup,
1998 nistp521_pre_comp_free, nistp521_pre_comp_clear_free)) 2098 nistp521_pre_comp_free, nistp521_pre_comp_clear_free))
1999 goto err; 2099 goto err;
2000 ret = 1; 2100 ret = 1;
2001 pre = NULL; 2101 pre = NULL;
2002 err: 2102err:
2003 BN_CTX_end(ctx); 2103 BN_CTX_end(ctx);
2004 if (generator != NULL) 2104 if (generator != NULL)
2005 EC_POINT_free(generator); 2105 EC_POINT_free(generator);
@@ -2008,18 +2108,19 @@ int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
2008 if (pre) 2108 if (pre)
2009 nistp521_pre_comp_free(pre); 2109 nistp521_pre_comp_free(pre);
2010 return ret; 2110 return ret;
2011 } 2111}
2012 2112
2013int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group) 2113int
2014 { 2114ec_GFp_nistp521_have_precompute_mult(const EC_GROUP * group)
2115{
2015 if (EC_EX_DATA_get_data(group->extra_data, nistp521_pre_comp_dup, 2116 if (EC_EX_DATA_get_data(group->extra_data, nistp521_pre_comp_dup,
2016 nistp521_pre_comp_free, nistp521_pre_comp_clear_free) 2117 nistp521_pre_comp_free, nistp521_pre_comp_clear_free)
2017 != NULL) 2118 != NULL)
2018 return 1; 2119 return 1;
2019 else 2120 else
2020 return 0; 2121 return 0;
2021 } 2122}
2022 2123
2023#else 2124#else
2024static void *dummy=&dummy; 2125static void *dummy = &dummy;
2025#endif 2126#endif