diff options
Diffstat (limited to '')
-rw-r--r-- | src/lib/libcrypto/ec/ecp_nistp521.c | 1607 |
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. */ |
136 | static void bin66_to_felem(felem out, const u8 in[66]) | 136 | static void |
137 | { | 137 | bin66_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. */ |
151 | static void felem_to_bin66(u8 out[66], const felem in) | 152 | static void |
152 | { | 153 | felem_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 */ |
166 | static void flip_endian(u8 *out, const u8 *in, unsigned len) | 168 | static void |
167 | { | 169 | flip_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 */ |
174 | static int BN_to_felem(felem out, const BIGNUM *bn) | 177 | static int |
175 | { | 178 | BN_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 */ |
200 | static BIGNUM *felem_to_BN(BIGNUM *out, const felem in) | 202 | static BIGNUM * |
201 | { | 203 | felem_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 | ||
212 | static void felem_one(felem out) | 215 | static void |
213 | { | 216 | felem_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 | ||
225 | static void felem_assign(felem out, const felem in) | 229 | static void |
226 | { | 230 | felem_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. */ |
239 | static void felem_sum64(felem out, const felem in) | 244 | static void |
240 | { | 245 | felem_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 */ |
253 | static void felem_scalar(felem out, const felem in, limb scalar) | 259 | static void |
254 | { | 260 | felem_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 */ |
267 | static void felem_scalar64(felem out, limb scalar) | 274 | static void |
268 | { | 275 | felem_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 */ |
281 | static void felem_scalar128(largefelem out, limb scalar) | 289 | static void |
282 | { | 290 | felem_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 | */ |
300 | static void felem_neg(felem out, const felem in) | 309 | static void |
301 | { | 310 | felem_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 | */ |
323 | static void felem_diff64(felem out, const felem in) | 333 | static void |
324 | { | 334 | felem_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 | */ |
346 | static void felem_diff_128_64(largefelem out, const felem in) | 357 | static void |
347 | { | 358 | felem_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 | */ |
369 | static void felem_diff128(largefelem out, const largefelem in) | 381 | static void |
370 | { | 382 | felem_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 | */ |
392 | static void felem_square(largefelem out, const felem in) | 405 | static void |
393 | { | 406 | felem_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 | */ |
484 | static void felem_mul(largefelem out, const felem in1, const felem in2) | 499 | static void |
485 | { | 500 | felem_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 | ||
590 | static const limb bottom52bits = 0xfffffffffffff; | 606 | static 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 | */ |
598 | static void felem_reduce(felem out, const largefelem in) | 614 | static void |
599 | { | 615 | felem_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 | ||
666 | static void felem_square_reduce(felem out, const felem in) | 686 | static void |
667 | { | 687 | felem_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 | ||
673 | static void felem_mul_reduce(felem out, const felem in1, const felem in2) | 694 | static void |
674 | { | 695 | felem_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 | */ |
687 | static void felem_inv(felem out, const felem in) | 709 | static void |
688 | { | 710 | felem_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 */ |
765 | static const felem kPrime = | 811 | static 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 | */ |
777 | static limb felem_is_zero(const felem in) | 823 | static limb |
778 | { | 824 | felem_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 | ||
832 | static int felem_is_zero_int(const felem in) | 892 | static int |
833 | { | 893 | felem_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 | */ |
841 | static void felem_contract(felem out, const felem in) | 902 | static void |
842 | { | 903 | felem_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). */ |
947 | static void | 1047 | static void |
948 | point_double(felem x_out, felem y_out, felem z_out, | 1048 | point_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. */ |
1034 | static void | 1139 | static void |
1035 | copy_conditional(felem out, const felem in, limb mask) | 1140 | copy_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. */ |
1055 | static void point_add(felem x3, felem y3, felem z3, | 1159 | static void |
1056 | const felem x1, const felem y1, const felem z1, | 1160 | point_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 */ |
1242 | static const felem gmul[16][3] = | 1344 | static 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}, | 1350 | 0x015b4429c6481390, 0x03a73678fb2d988e, 0x00c6858e06b70404}, |
1249 | {0x00be94769fd16650, 0x031c21a89cb09022, 0x039013fad0761353, | 1351 | {0x00be94769fd16650, 0x031c21a89cb09022, 0x039013fad0761353, |
1250 | 0x02657bd099031542, 0x03273e662c97ee72, 0x01e6d11a05ebef45, | 1352 | 0x02657bd099031542, 0x03273e662c97ee72, 0x01e6d11a05ebef45, |
1251 | 0x03d1bd998f544495, 0x03001172297ed0b1, 0x011839296a789a3b}, | 1353 | 0x03d1bd998f544495, 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}, | 1357 | 0x013ee3c3647f3a92, 0x029409fefe75d07d, 0x00ef9199963d85e5}, |
1256 | {0x011173743ad5b178, 0x02499c7c21bf7d46, 0x035beaeabb8b1a58, | 1358 | {0x011173743ad5b178, 0x02499c7c21bf7d46, 0x035beaeabb8b1a58, |
1257 | 0x00f989c4752ea0a3, 0x0101e1de48a9c1a3, 0x01a20076be28ba6c, | 1359 | 0x00f989c4752ea0a3, 0x0101e1de48a9c1a3, 0x01a20076be28ba6c, |
1258 | 0x02f8052e5eb2de95, 0x01bfe8f82dea117c, 0x0160074d3c36ddb7}, | 1360 | 0x02f8052e5eb2de95, 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}, | 1364 | 0x02b184671a7b1734, 0x0315b84236f1a50a, 0x00a4afc472edbdb9}, |
1263 | {0x00152a7077f385c4, 0x03044007d8d1c2ee, 0x0065829d61d52b52, | 1365 | {0x00152a7077f385c4, 0x03044007d8d1c2ee, 0x0065829d61d52b52, |
1264 | 0x00494ff6b6631d0d, 0x00a11d94d5f06bcf, 0x02d2f89474d9282e, | 1366 | 0x00494ff6b6631d0d, 0x00a11d94d5f06bcf, 0x02d2f89474d9282e, |
1265 | 0x0241c5727c06eeb9, 0x0386928710fbdb9d, 0x01f883f727b0dfbe}, | 1367 | 0x0241c5727c06eeb9, 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}, | 1371 | 0x03f37009806a369c, 0x03c1f30baf184fd5, 0x01091022d6d2f065}, |
1270 | {0x0292c583514c45ed, 0x0316fca51f9a286c, 0x00300af507c1489a, | 1372 | {0x0292c583514c45ed, 0x0316fca51f9a286c, 0x00300af507c1489a, |
1271 | 0x0295f69008298cf1, 0x02c0ed8274943d7b, 0x016509b9b47a431e, | 1373 | 0x0295f69008298cf1, 0x02c0ed8274943d7b, 0x016509b9b47a431e, |
1272 | 0x02bc9de9634868ce, 0x005b34929bffcb09, 0x000c1a0121681524}, | 1374 | 0x02bc9de9634868ce, 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}, | 1378 | 0x02e288370afda7d9, 0x03b22312bfefa67a, 0x01d104d3fc0613fe}, |
1277 | {0x0092421a12f7e47f, 0x0077a83fa373c501, 0x03bd25c5f696bd0d, | 1379 | {0x0092421a12f7e47f, 0x0077a83fa373c501, 0x03bd25c5f696bd0d, |
1278 | 0x035c41e4d5459761, 0x01ca0d1742b24f53, 0x00aaab27863a509c, | 1380 | 0x035c41e4d5459761, 0x01ca0d1742b24f53, 0x00aaab27863a509c, |
1279 | 0x018b6de47df73917, 0x025c0b771705cd01, 0x01fd51d566d760a7}, | 1381 | 0x018b6de47df73917, 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}, | 1385 | 0x03c764a32d2a062d, 0x017307eac0fad056, 0x018207c0b96c5256}, |
1284 | {0x0196a16d60e13154, 0x03e6ce74c0267030, 0x00ddbf2b4e52a5aa, | 1386 | {0x0196a16d60e13154, 0x03e6ce74c0267030, 0x00ddbf2b4e52a5aa, |
1285 | 0x012738241bbf31c8, 0x00ebe8dc04685a28, 0x024c2ad6d380d4a2, | 1387 | 0x012738241bbf31c8, 0x00ebe8dc04685a28, 0x024c2ad6d380d4a2, |
1286 | 0x035ee062a6e62d0e, 0x0029ed74af7d3a0f, 0x00eef32aec142ebd}, | 1388 | 0x035ee062a6e62d0e, 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}, | 1392 | 0x0261a9af46fbad7a, 0x0324b2a8dd3d28f9, 0x00918121d8f24e23}, |
1291 | {0x032bc8c1ca983cd7, 0x00d869dfb08fc8c6, 0x01693cb61fce1516, | 1393 | {0x032bc8c1ca983cd7, 0x00d869dfb08fc8c6, 0x01693cb61fce1516, |
1292 | 0x012a5ea68f4e88a8, 0x010869cab88d7ae3, 0x009081ad277ceee1, | 1394 | 0x012a5ea68f4e88a8, 0x010869cab88d7ae3, 0x009081ad277ceee1, |
1293 | 0x033a77166d064cdc, 0x03955235a1fb3a95, 0x01251a4a9b25b65e}, | 1395 | 0x033a77166d064cdc, 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}, | 1399 | 0x0173bb0e9ce92e46, 0x02b937e43921214b, 0x01ab0436a9bf01b5}, |
1298 | {0x0383381640d46948, 0x008dacbf0e7f330f, 0x03602122bcc3f318, | 1400 | {0x0383381640d46948, 0x008dacbf0e7f330f, 0x03602122bcc3f318, |
1299 | 0x01ee596b200620d6, 0x03bd0585fda430b3, 0x014aed77fd123a83, | 1401 | 0x01ee596b200620d6, 0x03bd0585fda430b3, 0x014aed77fd123a83, |
1300 | 0x005ace749e52f742, 0x0390fe041da2b842, 0x0189a8ceb3299242}, | 1402 | 0x005ace749e52f742, 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}, | 1406 | 0x0047d8cdfbdedd49, 0x00cc8c8953f0f6b8, 0x001424abbff49203}, |
1305 | {0x0256732a1115a03a, 0x0351bc38665c6733, 0x03f7b950fb4a6447, | 1407 | {0x0256732a1115a03a, 0x0351bc38665c6733, 0x03f7b950fb4a6447, |
1306 | 0x000afffa94c22155, 0x025763d0a4dab540, 0x000511e92d4fc283, | 1408 | 0x000afffa94c22155, 0x025763d0a4dab540, 0x000511e92d4fc283, |
1307 | 0x030a7e9eda0ee96c, 0x004c3cd93a28bf0a, 0x017edb3a8719217f}, | 1409 | 0x030a7e9eda0ee96c, 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}, | 1413 | 0x0284bebc4f322f72, 0x016ab2645302bb2c, 0x01793f95dace0e2a}, |
1312 | {0x010646e13527a28f, 0x01ca1babd59dc5e7, 0x01afedfd9a5595df, | 1414 | {0x010646e13527a28f, 0x01ca1babd59dc5e7, 0x01afedfd9a5595df, |
1313 | 0x01f15785212ea6b1, 0x0324e5d64f6ae3f4, 0x02d680f526d00645, | 1415 | 0x01f15785212ea6b1, 0x0324e5d64f6ae3f4, 0x02d680f526d00645, |
1314 | 0x0127920fadf627a7, 0x03b383f75df4f684, 0x0089e0057e783b0a}, | 1416 | 0x0127920fadf627a7, 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}, | 1420 | 0x03abe3aa43b26664, 0x02cbf47f720bc168, 0x0133b5e73014b79b}, |
1319 | {0x034aab5dab05779d, 0x00cdc5d71fee9abb, 0x0399f16bd4bd9d30, | 1421 | {0x034aab5dab05779d, 0x00cdc5d71fee9abb, 0x0399f16bd4bd9d30, |
1320 | 0x03582fa592d82647, 0x02be1cdfb775b0e9, 0x0034f7cea32e94cb, | 1422 | 0x03582fa592d82647, 0x02be1cdfb775b0e9, 0x0034f7cea32e94cb, |
1321 | 0x0335a7f08f56f286, 0x03b707e9565d1c8b, 0x0015c946ea5b614f}, | 1423 | 0x0335a7f08f56f286, 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}, | 1427 | 0x02fc8a7ca2da037c, 0x02de1217d74a6f30, 0x013f7173175b73bf}, |
1326 | {0x0344913f441490b5, 0x0200f9e272b61eca, 0x0258a246b1dd55d2, | 1428 | {0x0344913f441490b5, 0x0200f9e272b61eca, 0x0258a246b1dd55d2, |
1327 | 0x03753db9ea496f36, 0x025e02937a09c5ef, 0x030cbd3d14012692, | 1429 | 0x03753db9ea496f36, 0x025e02937a09c5ef, 0x030cbd3d14012692, |
1328 | 0x01793a67e70dc72a, 0x03ec1d37048a662e, 0x006550f700c32a8d}, | 1430 | 0x01793a67e70dc72a, 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}, | 1434 | 0x0241bf5f73265616, 0x0384672e5d50d39b, 0x005009fee522b684}, |
1333 | {0x029b4fab064435fe, 0x018868ee095bbb07, 0x01ea3d6936cc92b8, | 1435 | {0x029b4fab064435fe, 0x018868ee095bbb07, 0x01ea3d6936cc92b8, |
1334 | 0x000608b00f78a2f3, 0x02db911073d1c20f, 0x018205938470100a, | 1436 | 0x000608b00f78a2f3, 0x02db911073d1c20f, 0x018205938470100a, |
1335 | 0x01f1e4964cbe6ff2, 0x021a19a29eed4663, 0x01414485f42afa81}, | 1437 | 0x01f1e4964cbe6ff2, 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}, | 1441 | 0x029354d896e8e331, 0x00c047ee6dfba65e, 0x0037720542e9d49d}, |
1340 | {0x02ce9eed7c5e9278, 0x0374ed703e79643b, 0x01316c54c4072006, | 1442 | {0x02ce9eed7c5e9278, 0x0374ed703e79643b, 0x01316c54c4072006, |
1341 | 0x005aaa09054b2ee8, 0x002824000c840d57, 0x03d4eba24771ed86, | 1443 | 0x005aaa09054b2ee8, 0x002824000c840d57, 0x03d4eba24771ed86, |
1342 | 0x0189c50aabc3bdae, 0x0338c01541e15510, 0x00466d56e38eed42}, | 1444 | 0x0189c50aabc3bdae, 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}, | 1448 | 0x005482ed5f5dee46, 0x037543755bba1d7f, 0x005e5ac7e70a9d0f}, |
1347 | {0x0117e1bb2fdcb2a2, 0x03deea36249f40c4, 0x028d09b4a6246cb7, | 1449 | {0x0117e1bb2fdcb2a2, 0x03deea36249f40c4, 0x028d09b4a6246cb7, |
1348 | 0x03524b8855bcf756, 0x023d7d109d5ceb58, 0x0178e43e3223ef9c, | 1450 | 0x03524b8855bcf756, 0x023d7d109d5ceb58, 0x0178e43e3223ef9c, |
1349 | 0x0154536a0c6e966a, 0x037964d1286ee9fe, 0x0199bcd90e125055}, | 1451 | 0x0154536a0c6e966a, 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. */ |
1354 | static void select_point(const limb idx, unsigned int size, const felem pre_comp[/* size */][3], | 1456 | static void |
1355 | felem out[3]) | 1457 | select_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| */ |
1376 | static char get_bit(const felem_bytearray in, int i) | 1478 | static char |
1377 | { | 1479 | get_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 */ |
1388 | static void batch_mul(felem x_out, felem y_out, felem z_out, | 1491 | static void |
1389 | const felem_bytearray scalars[], const unsigned num_points, const u8 *g_scalar, | 1492 | batch_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 | ||
1533 | static NISTP521_PRE_COMP *nistp521_pre_comp_new() | 1631 | static NISTP521_PRE_COMP * |
1534 | { | 1632 | nistp521_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 | ||
1547 | static void *nistp521_pre_comp_dup(void *src_) | 1645 | static void * |
1548 | { | 1646 | nistp521_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 | ||
1557 | static void nistp521_pre_comp_free(void *pre_) | 1656 | static void |
1558 | { | 1657 | nistp521_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 | ||
1572 | static void nistp521_pre_comp_clear_free(void *pre_) | 1672 | static void |
1573 | { | 1673 | nistp521_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 | ||
1592 | int ec_GFp_nistp521_group_init(EC_GROUP *group) | 1693 | int |
1593 | { | 1694 | ec_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 | ||
1600 | int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p, | 1702 | int |
1601 | const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) | 1703 | ec_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); |
1625 | err: | 1729 | err: |
@@ -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) */ |
1634 | int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group, | 1738 | int |
1635 | const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) | 1739 | ec_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 | ||
1674 | static void make_points_affine(size_t num, felem points[/* num */][3], felem tmp_felems[/* num+1 */]) | 1779 | static void |
1675 | { | 1780 | make_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). */ |
1694 | int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r, | 1802 | int |
1695 | const BIGNUM *scalar, size_t num, const EC_POINT *points[], | 1803 | ec_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 | ||
1887 | err: | 1988 | err: |
@@ -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 | ||
1902 | int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx) | 2003 | int |
1903 | { | 2004 | ec_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: | 2102 | err: |
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 | ||
2013 | int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group) | 2113 | int |
2014 | { | 2114 | ec_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 |
2024 | static void *dummy=&dummy; | 2125 | static void *dummy = &dummy; |
2025 | #endif | 2126 | #endif |