31 extern const char DONNA64_FNAME[] = __FILE__;
33 #if defined(CRYPTOPP_CURVE25519_64BIT) 37 ANONYMOUS_NAMESPACE_BEGIN
40 using CryptoPP::word64;
45 inline word64 U8TO64_LE(
const byte* p)
50 inline void U64TO8_LE(byte* p, word64 w)
55 ANONYMOUS_NAMESPACE_END
58 NAMESPACE_BEGIN(Donna)
59 NAMESPACE_BEGIN(X25519)
60 ANONYMOUS_NAMESPACE_BEGIN
63 using CryptoPP::word32;
64 using CryptoPP::sword32;
65 using CryptoPP::word64;
66 using CryptoPP::sword64;
68 using CryptoPP::GetBlock;
72 using namespace CryptoPP::Donna::Arch64;
76 curve25519_copy(bignum25519 out,
const bignum25519 in) {
77 out[0] = in[0]; out[1] = in[1];
78 out[2] = in[2]; out[3] = in[3];
84 curve25519_add(bignum25519 out,
const bignum25519 a,
const bignum25519 b) {
94 curve25519_sub(bignum25519 out,
const bignum25519 a,
const bignum25519 b) {
95 out[0] = a[0] + two54m152 - b[0];
96 out[1] = a[1] + two54m8 - b[1];
97 out[2] = a[2] + two54m8 - b[2];
98 out[3] = a[3] + two54m8 - b[3];
99 out[4] = a[4] + two54m8 - b[4];
104 curve25519_scalar_product(bignum25519 out,
const bignum25519 in,
const word64 scalar) {
108 #if defined(CRYPTOPP_WORD128_AVAILABLE) 109 a = ((word128) in[0]) * scalar; out[0] = (word64)a & reduce_mask_51; c = (word64)(a >> 51);
110 a = ((word128) in[1]) * scalar + c; out[1] = (word64)a & reduce_mask_51; c = (word64)(a >> 51);
111 a = ((word128) in[2]) * scalar + c; out[2] = (word64)a & reduce_mask_51; c = (word64)(a >> 51);
112 a = ((word128) in[3]) * scalar + c; out[3] = (word64)a & reduce_mask_51; c = (word64)(a >> 51);
113 a = ((word128) in[4]) * scalar + c; out[4] = (word64)a & reduce_mask_51; c = (word64)(a >> 51);
116 mul64x64_128(a, in[0], scalar) out[0] = lo128(a) & reduce_mask_51; shr128(c, a, 51);
117 mul64x64_128(a, in[1], scalar) add128_64(a, c) out[1] = lo128(a) & reduce_mask_51; shr128(c, a, 51);
118 mul64x64_128(a, in[2], scalar) add128_64(a, c) out[2] = lo128(a) & reduce_mask_51; shr128(c, a, 51);
119 mul64x64_128(a, in[3], scalar) add128_64(a, c) out[3] = lo128(a) & reduce_mask_51; shr128(c, a, 51);
120 mul64x64_128(a, in[4], scalar) add128_64(a, c) out[4] = lo128(a) & reduce_mask_51; shr128(c, a, 51);
127 curve25519_mul(bignum25519 out,
const bignum25519 a,
const bignum25519 b) {
128 #if !defined(CRYPTOPP_WORD128_AVAILABLE) 132 word64 r0,r1,r2,r3,r4,s0,s1,s2,s3,s4,c;
134 r0 = b[0]; r1 = b[1]; r2 = b[2]; r3 = b[3]; r4 = b[4];
135 s0 = a[0]; s1 = a[1]; s2 = a[2]; s3 = a[3]; s4 = a[4];
137 #if defined(CRYPTOPP_WORD128_AVAILABLE) 138 t[0] = ((word128) r0) * s0;
139 t[1] = ((word128) r0) * s1 + ((word128) r1) * s0;
140 t[2] = ((word128) r0) * s2 + ((word128) r2) * s0 + ((word128) r1) * s1;
141 t[3] = ((word128) r0) * s3 + ((word128) r3) * s0 + ((word128) r1) * s2 + ((word128) r2) * s1;
142 t[4] = ((word128) r0) * s4 + ((word128) r4) * s0 + ((word128) r3) * s1 + ((word128) r1) * s3 + ((word128) r2) * s2;
144 mul64x64_128(t[0], r0, s0)
145 mul64x64_128(t[1], r0, s1) mul64x64_128(mul, r1, s0) add128(t[1], mul)
146 mul64x64_128(t[2], r0, s2) mul64x64_128(mul, r2, s0) add128(t[2], mul) mul64x64_128(mul, r1, s1) add128(t[2], mul)
147 mul64x64_128(t[3], r0, s3) mul64x64_128(mul, r3, s0) add128(t[3], mul) mul64x64_128(mul, r1, s2) add128(t[3], mul) mul64x64_128(mul, r2, s1) add128(t[3], mul)
148 mul64x64_128(t[4], r0, s4) mul64x64_128(mul, r4, s0) add128(t[4], mul) mul64x64_128(mul, r3, s1) add128(t[4], mul) mul64x64_128(mul, r1, s3) add128(t[4], mul) mul64x64_128(mul, r2, s2) add128(t[4], mul)
151 r1 *= 19; r2 *= 19; r3 *= 19; r4 *= 19;
153 #if defined(CRYPTOPP_WORD128_AVAILABLE) 154 t[0] += ((word128) r4) * s1 + ((word128) r1) * s4 + ((word128) r2) * s3 + ((word128) r3) * s2;
155 t[1] += ((word128) r4) * s2 + ((word128) r2) * s4 + ((word128) r3) * s3;
156 t[2] += ((word128) r4) * s3 + ((word128) r3) * s4;
157 t[3] += ((word128) r4) * s4;
159 mul64x64_128(mul, r4, s1) add128(t[0], mul) mul64x64_128(mul, r1, s4) add128(t[0], mul) mul64x64_128(mul, r2, s3) add128(t[0], mul) mul64x64_128(mul, r3, s2) add128(t[0], mul)
160 mul64x64_128(mul, r4, s2) add128(t[1], mul) mul64x64_128(mul, r2, s4) add128(t[1], mul) mul64x64_128(mul, r3, s3) add128(t[1], mul)
161 mul64x64_128(mul, r4, s3) add128(t[2], mul) mul64x64_128(mul, r3, s4) add128(t[2], mul)
162 mul64x64_128(mul, r4, s4) add128(t[3], mul)
165 r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51);
166 add128_64(t[1], c) r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51);
167 add128_64(t[2], c) r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51);
168 add128_64(t[3], c) r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51);
169 add128_64(t[4], c) r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51);
170 r0 += c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51;
173 out[0] = r0; out[1] = r1; out[2] = r2; out[3] = r3; out[4] = r4;
178 curve25519_square_times(bignum25519 out,
const bignum25519 in, word64 count) {
179 #if !defined(CRYPTOPP_WORD128_AVAILABLE) 183 word64 r0,r1,r2,r3,r4,c;
184 word64 d0,d1,d2,d4,d419;
186 r0 = in[0]; r1 = in[1]; r2 = in[2]; r3 = in[3]; r4 = in[4];
189 d0 = r0 * 2; d1 = r1 * 2;
191 d419 = r4 * 19; d4 = d419 * 2;
193 #if defined(CRYPTOPP_WORD128_AVAILABLE) 194 t[0] = ((word128) r0) * r0 + ((word128) d4) * r1 + (((word128) d2) * (r3 ));
195 t[1] = ((word128) d0) * r1 + ((word128) d4) * r2 + (((word128) r3) * (r3 * 19));
196 t[2] = ((word128) d0) * r2 + ((word128) r1) * r1 + (((word128) d4) * (r3 ));
197 t[3] = ((word128) d0) * r3 + ((word128) d1) * r2 + (((word128) r4) * (d419 ));
198 t[4] = ((word128) d0) * r4 + ((word128) d1) * r3 + (((word128) r2) * (r2 ));
200 mul64x64_128(t[0], r0, r0) mul64x64_128(mul, d4, r1) add128(t[0], mul) mul64x64_128(mul, d2, r3) add128(t[0], mul)
201 mul64x64_128(t[1], d0, r1) mul64x64_128(mul, d4, r2) add128(t[1], mul) mul64x64_128(mul, r3, r3 * 19) add128(t[1], mul)
202 mul64x64_128(t[2], d0, r2) mul64x64_128(mul, r1, r1) add128(t[2], mul) mul64x64_128(mul, d4, r3) add128(t[2], mul)
203 mul64x64_128(t[3], d0, r3) mul64x64_128(mul, d1, r2) add128(t[3], mul) mul64x64_128(mul, r4, d419) add128(t[3], mul)
204 mul64x64_128(t[4], d0, r4) mul64x64_128(mul, d1, r3) add128(t[4], mul) mul64x64_128(mul, r2, r2) add128(t[4], mul)
207 r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51);
208 add128_64(t[1], c) r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51);
209 add128_64(t[2], c) r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51);
210 add128_64(t[3], c) r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51);
211 add128_64(t[4], c) r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51);
212 r0 += c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51;
216 out[0] = r0; out[1] = r1; out[2] = r2; out[3] = r3; out[4] = r4;
220 curve25519_square(bignum25519 out,
const bignum25519 in) {
221 #if !defined(CRYPTOPP_WORD128_AVAILABLE) 225 word64 r0,r1,r2,r3,r4,c;
226 word64 d0,d1,d2,d4,d419;
228 r0 = in[0]; r1 = in[1]; r2 = in[2]; r3 = in[3]; r4 = in[4];
230 d0 = r0 * 2; d1 = r1 * 2;
232 d419 = r4 * 19; d4 = d419 * 2;
234 #if defined(CRYPTOPP_WORD128_AVAILABLE) 235 t[0] = ((word128) r0) * r0 + ((word128) d4) * r1 + (((word128) d2) * (r3 ));
236 t[1] = ((word128) d0) * r1 + ((word128) d4) * r2 + (((word128) r3) * (r3 * 19));
237 t[2] = ((word128) d0) * r2 + ((word128) r1) * r1 + (((word128) d4) * (r3 ));
238 t[3] = ((word128) d0) * r3 + ((word128) d1) * r2 + (((word128) r4) * (d419 ));
239 t[4] = ((word128) d0) * r4 + ((word128) d1) * r3 + (((word128) r2) * (r2 ));
241 mul64x64_128(t[0], r0, r0) mul64x64_128(mul, d4, r1) add128(t[0], mul) mul64x64_128(mul, d2, r3) add128(t[0], mul)
242 mul64x64_128(t[1], d0, r1) mul64x64_128(mul, d4, r2) add128(t[1], mul) mul64x64_128(mul, r3, r3 * 19) add128(t[1], mul)
243 mul64x64_128(t[2], d0, r2) mul64x64_128(mul, r1, r1) add128(t[2], mul) mul64x64_128(mul, d4, r3) add128(t[2], mul)
244 mul64x64_128(t[3], d0, r3) mul64x64_128(mul, d1, r2) add128(t[3], mul) mul64x64_128(mul, r4, d419) add128(t[3], mul)
245 mul64x64_128(t[4], d0, r4) mul64x64_128(mul, d1, r3) add128(t[4], mul) mul64x64_128(mul, r2, r2) add128(t[4], mul)
248 r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51);
249 add128_64(t[1], c) r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51);
250 add128_64(t[2], c) r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51);
251 add128_64(t[3], c) r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51);
252 add128_64(t[4], c) r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51);
253 r0 += c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51;
256 out[0] = r0; out[1] = r1; out[2] = r2; out[3] = r3; out[4] = r4;
261 curve25519_expand(bignum25519 out,
const byte *in) {
264 block(x0)(x1)(x2)(x3);
266 out[0] = x0 & reduce_mask_51; x0 = (x0 >> 51) | (x1 << 13);
267 out[1] = x0 & reduce_mask_51; x1 = (x1 >> 38) | (x2 << 26);
268 out[2] = x1 & reduce_mask_51; x2 = (x2 >> 25) | (x3 << 39);
269 out[3] = x2 & reduce_mask_51; x3 = (x3 >> 12);
270 out[4] = x3 & reduce_mask_51;
277 curve25519_contract(byte *out,
const bignum25519 input) {
287 #define curve25519_contract_carry() \ 288 t[1] += t[0] >> 51; t[0] &= reduce_mask_51; \ 289 t[2] += t[1] >> 51; t[1] &= reduce_mask_51; \ 290 t[3] += t[2] >> 51; t[2] &= reduce_mask_51; \ 291 t[4] += t[3] >> 51; t[3] &= reduce_mask_51; 293 #define curve25519_contract_carry_full() curve25519_contract_carry() \ 294 t[0] += 19 * (t[4] >> 51); t[4] &= reduce_mask_51; 296 #define curve25519_contract_carry_final() curve25519_contract_carry() \ 297 t[4] &= reduce_mask_51; 299 curve25519_contract_carry_full()
300 curve25519_contract_carry_full()
305 curve25519_contract_carry_full()
308 t[0] += 0x8000000000000 - 19;
309 t[1] += 0x8000000000000 - 1;
310 t[2] += 0x8000000000000 - 1;
311 t[3] += 0x8000000000000 - 1;
312 t[4] += 0x8000000000000 - 1;
315 curve25519_contract_carry_final()
317 #define write51full(n,shift) \ 318 f = ((t[n] >> shift) | (t[n+1] << (51 - shift))); \ 319 for (i = 0; i < 8; i++, f >>= 8) *out++ = (byte)f; 320 #define write51(n) write51full(n,13*n) 327 #undef curve25519_contract_carry 328 #undef curve25519_contract_carry_full 329 #undef curve25519_contract_carry_final 338 curve25519_swap_conditional(bignum25519 x, bignum25519 qpx, word64 iswap) {
339 const word64 swap = (word64)(-(sword64)iswap);
340 word64 x0,x1,x2,x3,x4;
342 x0 = swap & (x[0] ^ qpx[0]); x[0] ^= x0; qpx[0] ^= x0;
343 x1 = swap & (x[1] ^ qpx[1]); x[1] ^= x1; qpx[1] ^= x1;
344 x2 = swap & (x[2] ^ qpx[2]); x[2] ^= x2; qpx[2] ^= x2;
345 x3 = swap & (x[3] ^ qpx[3]); x[3] ^= x3; qpx[3] ^= x3;
346 x4 = swap & (x[4] ^ qpx[4]); x[4] ^= x4; qpx[4] ^= x4;
354 curve25519_pow_two5mtwo0_two250mtwo0(bignum25519 b) {
355 ALIGN(16) bignum25519 t0,c;
358 curve25519_square_times(t0, b, 5);
359 curve25519_mul(b, t0, b);
360 curve25519_square_times(t0, b, 10);
361 curve25519_mul(c, t0, b);
362 curve25519_square_times(t0, c, 20);
363 curve25519_mul(t0, t0, c);
364 curve25519_square_times(t0, t0, 10);
365 curve25519_mul(b, t0, b);
366 curve25519_square_times(t0, b, 50);
367 curve25519_mul(c, t0, b);
368 curve25519_square_times(t0, c, 100);
369 curve25519_mul(t0, t0, c);
370 curve25519_square_times(t0, t0, 50);
371 curve25519_mul(b, t0, b);
378 curve25519_recip(bignum25519 out, const bignum25519 z) {
379 ALIGN(16) bignum25519 a, t0, b;
381 curve25519_square(a, z);
382 curve25519_square_times(t0, a, 2);
383 curve25519_mul(b, t0, z);
384 curve25519_mul(a, b, a);
385 curve25519_square(t0, a);
386 curve25519_mul(b, t0, b);
387 curve25519_pow_two5mtwo0_two250mtwo0(b);
388 curve25519_square_times(b, b, 5);
389 curve25519_mul(out, b, a);
392 ANONYMOUS_NAMESPACE_END
400 NAMESPACE_BEGIN(Donna)
401 NAMESPACE_BEGIN(Ed25519)
402 ANONYMOUS_NAMESPACE_BEGIN
416 using namespace
CryptoPP::Donna::Arch64;
420 curve25519_copy(bignum25519 out, const bignum25519 in) {
421 out[0] = in[0]; out[1] = in[1];
422 out[2] = in[2]; out[3] = in[3];
428 curve25519_add(bignum25519 out,
const bignum25519 a,
const bignum25519 b) {
429 out[0] = a[0] + b[0]; out[1] = a[1] + b[1];
430 out[2] = a[2] + b[2]; out[3] = a[3] + b[3];
431 out[4] = a[4] + b[4];
436 curve25519_add_after_basic(bignum25519 out,
const bignum25519 a,
const bignum25519 b) {
437 out[0] = a[0] + b[0]; out[1] = a[1] + b[1];
438 out[2] = a[2] + b[2]; out[3] = a[3] + b[3];
439 out[4] = a[4] + b[4];
443 curve25519_add_reduce(bignum25519 out,
const bignum25519 a,
const bignum25519 b) {
445 out[0] = a[0] + b[0] ; c = (out[0] >> 51); out[0] &= reduce_mask_51;
446 out[1] = a[1] + b[1] + c; c = (out[1] >> 51); out[1] &= reduce_mask_51;
447 out[2] = a[2] + b[2] + c; c = (out[2] >> 51); out[2] &= reduce_mask_51;
448 out[3] = a[3] + b[3] + c; c = (out[3] >> 51); out[3] &= reduce_mask_51;
449 out[4] = a[4] + b[4] + c; c = (out[4] >> 51); out[4] &= reduce_mask_51;
455 curve25519_sub(bignum25519 out,
const bignum25519 a,
const bignum25519 b) {
456 out[0] = a[0] + twoP0 - b[0];
457 out[1] = a[1] + twoP1234 - b[1];
458 out[2] = a[2] + twoP1234 - b[2];
459 out[3] = a[3] + twoP1234 - b[3];
460 out[4] = a[4] + twoP1234 - b[4];
465 curve25519_sub_after_basic(bignum25519 out,
const bignum25519 a,
const bignum25519 b) {
466 out[0] = a[0] + fourP0 - b[0];
467 out[1] = a[1] + fourP1234 - b[1];
468 out[2] = a[2] + fourP1234 - b[2];
469 out[3] = a[3] + fourP1234 - b[3];
470 out[4] = a[4] + fourP1234 - b[4];
474 curve25519_sub_reduce(bignum25519 out,
const bignum25519 a,
const bignum25519 b) {
476 out[0] = a[0] + fourP0 - b[0] ; c = (out[0] >> 51); out[0] &= reduce_mask_51;
477 out[1] = a[1] + fourP1234 - b[1] + c; c = (out[1] >> 51); out[1] &= reduce_mask_51;
478 out[2] = a[2] + fourP1234 - b[2] + c; c = (out[2] >> 51); out[2] &= reduce_mask_51;
479 out[3] = a[3] + fourP1234 - b[3] + c; c = (out[3] >> 51); out[3] &= reduce_mask_51;
480 out[4] = a[4] + fourP1234 - b[4] + c; c = (out[4] >> 51); out[4] &= reduce_mask_51;
486 curve25519_neg(bignum25519 out,
const bignum25519 a) {
488 out[0] = twoP0 - a[0] ; c = (out[0] >> 51); out[0] &= reduce_mask_51;
489 out[1] = twoP1234 - a[1] + c; c = (out[1] >> 51); out[1] &= reduce_mask_51;
490 out[2] = twoP1234 - a[2] + c; c = (out[2] >> 51); out[2] &= reduce_mask_51;
491 out[3] = twoP1234 - a[3] + c; c = (out[3] >> 51); out[3] &= reduce_mask_51;
492 out[4] = twoP1234 - a[4] + c; c = (out[4] >> 51); out[4] &= reduce_mask_51;
498 curve25519_mul(bignum25519 out,
const bignum25519 in2,
const bignum25519 in) {
499 #if !defined(CRYPTOPP_WORD128_AVAILABLE) 503 word64 r0,r1,r2,r3,r4,s0,s1,s2,s3,s4,c;
505 r0 = in[0]; r1 = in[1];
506 r2 = in[2]; r3 = in[3];
509 s0 = in2[0]; s1 = in2[1];
510 s2 = in2[2]; s3 = in2[3];
513 #if defined(CRYPTOPP_WORD128_AVAILABLE) 514 t[0] = ((word128) r0) * s0;
515 t[1] = ((word128) r0) * s1 + ((word128) r1) * s0;
516 t[2] = ((word128) r0) * s2 + ((word128) r2) * s0 + ((word128) r1) * s1;
517 t[3] = ((word128) r0) * s3 + ((word128) r3) * s0 + ((word128) r1) * s2 + ((word128) r2) * s1;
518 t[4] = ((word128) r0) * s4 + ((word128) r4) * s0 + ((word128) r3) * s1 + ((word128) r1) * s3 + ((word128) r2) * s2;
520 mul64x64_128(t[0], r0, s0)
521 mul64x64_128(t[1], r0, s1) mul64x64_128(mul, r1, s0) add128(t[1], mul)
522 mul64x64_128(t[2], r0, s2) mul64x64_128(mul, r2, s0) add128(t[2], mul) mul64x64_128(mul, r1, s1) add128(t[2], mul)
523 mul64x64_128(t[3], r0, s3) mul64x64_128(mul, r3, s0) add128(t[3], mul) mul64x64_128(mul, r1, s2) add128(t[3], mul) mul64x64_128(mul, r2, s1) add128(t[3], mul)
524 mul64x64_128(t[4], r0, s4) mul64x64_128(mul, r4, s0) add128(t[4], mul) mul64x64_128(mul, r3, s1) add128(t[4], mul) mul64x64_128(mul, r1, s3) add128(t[4], mul) mul64x64_128(mul, r2, s2) add128(t[4], mul)
530 #if defined(CRYPTOPP_WORD128_AVAILABLE) 531 t[0] += ((word128) r4) * s1 + ((word128) r1) * s4 + ((word128) r2) * s3 + ((word128) r3) * s2;
532 t[1] += ((word128) r4) * s2 + ((word128) r2) * s4 + ((word128) r3) * s3;
533 t[2] += ((word128) r4) * s3 + ((word128) r3) * s4;
534 t[3] += ((word128) r4) * s4;
536 mul64x64_128(mul, r4, s1) add128(t[0], mul) mul64x64_128(mul, r1, s4) add128(t[0], mul) mul64x64_128(mul, r2, s3) add128(t[0], mul) mul64x64_128(mul, r3, s2) add128(t[0], mul)
537 mul64x64_128(mul, r4, s2) add128(t[1], mul) mul64x64_128(mul, r2, s4) add128(t[1], mul) mul64x64_128(mul, r3, s3) add128(t[1], mul)
538 mul64x64_128(mul, r4, s3) add128(t[2], mul) mul64x64_128(mul, r3, s4) add128(t[2], mul)
539 mul64x64_128(mul, r4, s4) add128(t[3], mul)
542 r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51);
543 add128_64(t[1], c) r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51);
544 add128_64(t[2], c) r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51);
545 add128_64(t[3], c) r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51);
546 add128_64(t[4], c) r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51);
547 r0 += c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51;
550 out[0] = r0; out[1] = r1;
551 out[2] = r2; out[3] = r3;
556 curve25519_mul_noinline(bignum25519 out,
const bignum25519 in2,
const bignum25519 in) {
557 curve25519_mul(out, in2, in);
562 curve25519_square_times(bignum25519 out,
const bignum25519 in, word64 count) {
563 #if !defined(CRYPTOPP_WORD128_AVAILABLE) 567 word64 r0,r1,r2,r3,r4,c;
568 word64 d0,d1,d2,d4,d419;
570 r0 = in[0]; r1 = in[1];
571 r2 = in[2]; r3 = in[3];
581 #if defined(CRYPTOPP_WORD128_AVAILABLE) 582 t[0] = ((word128) r0) * r0 + ((word128) d4) * r1 + (((word128) d2) * (r3 ));
583 t[1] = ((word128) d0) * r1 + ((word128) d4) * r2 + (((word128) r3) * (r3 * 19));
584 t[2] = ((word128) d0) * r2 + ((word128) r1) * r1 + (((word128) d4) * (r3 ));
585 t[3] = ((word128) d0) * r3 + ((word128) d1) * r2 + (((word128) r4) * (d419 ));
586 t[4] = ((word128) d0) * r4 + ((word128) d1) * r3 + (((word128) r2) * (r2 ));
588 mul64x64_128(t[0], r0, r0) mul64x64_128(mul, d4, r1) add128(t[0], mul) mul64x64_128(mul, d2, r3) add128(t[0], mul)
589 mul64x64_128(t[1], d0, r1) mul64x64_128(mul, d4, r2) add128(t[1], mul) mul64x64_128(mul, r3, r3 * 19) add128(t[1], mul)
590 mul64x64_128(t[2], d0, r2) mul64x64_128(mul, r1, r1) add128(t[2], mul) mul64x64_128(mul, d4, r3) add128(t[2], mul)
591 mul64x64_128(t[3], d0, r3) mul64x64_128(mul, d1, r2) add128(t[3], mul) mul64x64_128(mul, r4, d419) add128(t[3], mul)
592 mul64x64_128(t[4], d0, r4) mul64x64_128(mul, d1, r3) add128(t[4], mul) mul64x64_128(mul, r2, r2) add128(t[4], mul)
595 r0 = lo128(t[0]) & reduce_mask_51;
596 r1 = lo128(t[1]) & reduce_mask_51; shl128(c, t[0], 13); r1 += c;
597 r2 = lo128(t[2]) & reduce_mask_51; shl128(c, t[1], 13); r2 += c;
598 r3 = lo128(t[3]) & reduce_mask_51; shl128(c, t[2], 13); r3 += c;
599 r4 = lo128(t[4]) & reduce_mask_51; shl128(c, t[3], 13); r4 += c;
600 shl128(c, t[4], 13); r0 += c * 19;
601 c = r0 >> 51; r0 &= reduce_mask_51;
602 r1 += c ; c = r1 >> 51; r1 &= reduce_mask_51;
603 r2 += c ; c = r2 >> 51; r2 &= reduce_mask_51;
604 r3 += c ; c = r3 >> 51; r3 &= reduce_mask_51;
605 r4 += c ; c = r4 >> 51; r4 &= reduce_mask_51;
609 out[0] = r0; out[1] = r1;
610 out[2] = r2; out[3] = r3;
615 curve25519_square(bignum25519 out,
const bignum25519 in) {
616 #if !defined(CRYPTOPP_WORD128_AVAILABLE) 620 word64 r0,r1,r2,r3,r4,c;
621 word64 d0,d1,d2,d4,d419;
623 r0 = in[0]; r1 = in[1];
624 r2 = in[2]; r3 = in[3];
627 d0 = r0 * 2; d1 = r1 * 2;
632 #if defined(CRYPTOPP_WORD128_AVAILABLE) 633 t[0] = ((word128) r0) * r0 + ((word128) d4) * r1 + (((word128) d2) * (r3 ));
634 t[1] = ((word128) d0) * r1 + ((word128) d4) * r2 + (((word128) r3) * (r3 * 19));
635 t[2] = ((word128) d0) * r2 + ((word128) r1) * r1 + (((word128) d4) * (r3 ));
636 t[3] = ((word128) d0) * r3 + ((word128) d1) * r2 + (((word128) r4) * (d419 ));
637 t[4] = ((word128) d0) * r4 + ((word128) d1) * r3 + (((word128) r2) * (r2 ));
639 mul64x64_128(t[0], r0, r0) mul64x64_128(mul, d4, r1) add128(t[0], mul) mul64x64_128(mul, d2, r3) add128(t[0], mul)
640 mul64x64_128(t[1], d0, r1) mul64x64_128(mul, d4, r2) add128(t[1], mul) mul64x64_128(mul, r3, r3 * 19) add128(t[1], mul)
641 mul64x64_128(t[2], d0, r2) mul64x64_128(mul, r1, r1) add128(t[2], mul) mul64x64_128(mul, d4, r3) add128(t[2], mul)
642 mul64x64_128(t[3], d0, r3) mul64x64_128(mul, d1, r2) add128(t[3], mul) mul64x64_128(mul, r4, d419) add128(t[3], mul)
643 mul64x64_128(t[4], d0, r4) mul64x64_128(mul, d1, r3) add128(t[4], mul) mul64x64_128(mul, r2, r2) add128(t[4], mul)
646 r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51);
647 add128_64(t[1], c) r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51);
648 add128_64(t[2], c) r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51);
649 add128_64(t[3], c) r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51);
650 add128_64(t[4], c) r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51);
651 r0 += c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51;
654 out[0] = r0; out[1] = r1;
655 out[2] = r2; out[3] = r3;
661 curve25519_expand(bignum25519 out,
const byte *in) {
664 block(x0)(x1)(x2)(x3);
666 out[0] = x0 & reduce_mask_51; x0 = (x0 >> 51) | (x1 << 13);
667 out[1] = x0 & reduce_mask_51; x1 = (x1 >> 38) | (x2 << 26);
668 out[2] = x1 & reduce_mask_51; x2 = (x2 >> 25) | (x3 << 39);
669 out[3] = x2 & reduce_mask_51; x3 = (x3 >> 12);
670 out[4] = x3 & reduce_mask_51;
677 curve25519_contract(byte *out,
const bignum25519 input) {
687 #define curve25519_contract_carry() \ 688 t[1] += t[0] >> 51; t[0] &= reduce_mask_51; \ 689 t[2] += t[1] >> 51; t[1] &= reduce_mask_51; \ 690 t[3] += t[2] >> 51; t[2] &= reduce_mask_51; \ 691 t[4] += t[3] >> 51; t[3] &= reduce_mask_51; 693 #define curve25519_contract_carry_full() curve25519_contract_carry() \ 694 t[0] += 19 * (t[4] >> 51); t[4] &= reduce_mask_51; 696 #define curve25519_contract_carry_final() curve25519_contract_carry() \ 697 t[4] &= reduce_mask_51; 699 curve25519_contract_carry_full()
700 curve25519_contract_carry_full()
705 curve25519_contract_carry_full()
708 t[0] += (reduce_mask_51 + 1) - 19;
709 t[1] += (reduce_mask_51 + 1) - 1;
710 t[2] += (reduce_mask_51 + 1) - 1;
711 t[3] += (reduce_mask_51 + 1) - 1;
712 t[4] += (reduce_mask_51 + 1) - 1;
715 curve25519_contract_carry_final()
717 #define write51full(n,shift) \ 718 f = ((t[n] >> shift) | (t[n+1] << (51 - shift))); \ 719 for (i = 0; i < 8; i++, f >>= 8) *out++ = (byte)f; 720 #define write51(n) write51full(n,13*n) 727 #if !defined(ED25519_GCC_64BIT_CHOOSE) 731 curve25519_move_conditional_bytes(uint8_t out[96],
const uint8_t in[96], word64 flag) {
732 const word64 nb = flag - 1, b = ~nb;
733 const word64 *inq = (
const word64 *)in;
734 word64 *outq = (word64 *)out;
735 outq[0] = (outq[0] & nb) | (inq[0] & b);
736 outq[1] = (outq[1] & nb) | (inq[1] & b);
737 outq[2] = (outq[2] & nb) | (inq[2] & b);
738 outq[3] = (outq[3] & nb) | (inq[3] & b);
739 outq[4] = (outq[4] & nb) | (inq[4] & b);
740 outq[5] = (outq[5] & nb) | (inq[5] & b);
741 outq[6] = (outq[6] & nb) | (inq[6] & b);
742 outq[7] = (outq[7] & nb) | (inq[7] & b);
743 outq[8] = (outq[8] & nb) | (inq[8] & b);
744 outq[9] = (outq[9] & nb) | (inq[9] & b);
745 outq[10] = (outq[10] & nb) | (inq[10] & b);
746 outq[11] = (outq[11] & nb) | (inq[11] & b);
751 curve25519_swap_conditional(bignum25519 a, bignum25519 b, word64 iswap) {
752 const word64 swap = (word64)(-(int64_t)iswap);
753 word64 x0,x1,x2,x3,x4;
755 x0 = swap & (a[0] ^ b[0]); a[0] ^= x0; b[0] ^= x0;
756 x1 = swap & (a[1] ^ b[1]); a[1] ^= x1; b[1] ^= x1;
757 x2 = swap & (a[2] ^ b[2]); a[2] ^= x2; b[2] ^= x2;
758 x3 = swap & (a[3] ^ b[3]); a[3] ^= x3; b[3] ^= x3;
759 x4 = swap & (a[4] ^ b[4]); a[4] ^= x4; b[4] ^= x4;
767 ed25519_hash(byte *hash,
const byte *in,
size_t inlen) {
772 ed25519_extsk(hash_512bits extsk,
const byte sk[32]) {
773 ed25519_hash(extsk, sk, 32);
780 ed25519_hram(hash_512bits hram,
const byte RS[64],
const byte pk[32],
const unsigned char *m,
size_t mlen) {
788 bignum256modm_element_t
789 lt_modm(bignum256modm_element_t a, bignum256modm_element_t b) {
790 return (a - b) >> 63;
794 reduce256_modm(bignum256modm r) {
796 bignum256modm_element_t b = 0, pb, mask;
800 pb += modm_m[0]; b = lt_modm(r[0], pb); t[0] = (r[0] - pb + (b << 56)); pb = b;
801 pb += modm_m[1]; b = lt_modm(r[1], pb); t[1] = (r[1] - pb + (b << 56)); pb = b;
802 pb += modm_m[2]; b = lt_modm(r[2], pb); t[2] = (r[2] - pb + (b << 56)); pb = b;
803 pb += modm_m[3]; b = lt_modm(r[3], pb); t[3] = (r[3] - pb + (b << 56)); pb = b;
804 pb += modm_m[4]; b = lt_modm(r[4], pb); t[4] = (r[4] - pb + (b << 32));
809 r[0] ^= mask & (r[0] ^ t[0]);
810 r[1] ^= mask & (r[1] ^ t[1]);
811 r[2] ^= mask & (r[2] ^ t[2]);
812 r[3] ^= mask & (r[3] ^ t[3]);
813 r[4] ^= mask & (r[4] ^ t[4]);
817 barrett_reduce256_modm(bignum256modm r,
const bignum256modm q1,
const bignum256modm r1) {
818 bignum256modm q3, r2;
820 bignum256modm_element_t f, b, pb;
825 mul64x64_128(c, modm_mu[0], q1[3]) mul64x64_128(mul, modm_mu[3], q1[0]) add128(c, mul) mul64x64_128(mul, modm_mu[1], q1[2]) add128(c, mul) mul64x64_128(mul, modm_mu[2], q1[1]) add128(c, mul) shr128(f, c, 56);
826 mul64x64_128(c, modm_mu[0], q1[4]) add128_64(c, f) mul64x64_128(mul, modm_mu[4], q1[0]) add128(c, mul) mul64x64_128(mul, modm_mu[3], q1[1]) add128(c, mul) mul64x64_128(mul, modm_mu[1], q1[3]) add128(c, mul) mul64x64_128(mul, modm_mu[2], q1[2]) add128(c, mul)
827 f = lo128(c); q3[0] = (f >> 40) & 0xffff; shr128(f, c, 56);
828 mul64x64_128(c, modm_mu[4], q1[1]) add128_64(c, f) mul64x64_128(mul, modm_mu[1], q1[4]) add128(c, mul) mul64x64_128(mul, modm_mu[2], q1[3]) add128(c, mul) mul64x64_128(mul, modm_mu[3], q1[2]) add128(c, mul)
829 f = lo128(c); q3[0] |= (f << 16) & 0xffffffffffffff; q3[1] = (f >> 40) & 0xffff; shr128(f, c, 56);
830 mul64x64_128(c, modm_mu[4], q1[2]) add128_64(c, f) mul64x64_128(mul, modm_mu[2], q1[4]) add128(c, mul) mul64x64_128(mul, modm_mu[3], q1[3]) add128(c, mul)
831 f = lo128(c); q3[1] |= (f << 16) & 0xffffffffffffff; q3[2] = (f >> 40) & 0xffff; shr128(f, c, 56);
832 mul64x64_128(c, modm_mu[4], q1[3]) add128_64(c, f) mul64x64_128(mul, modm_mu[3], q1[4]) add128(c, mul)
833 f = lo128(c); q3[2] |= (f << 16) & 0xffffffffffffff; q3[3] = (f >> 40) & 0xffff; shr128(f, c, 56);
834 mul64x64_128(c, modm_mu[4], q1[4]) add128_64(c, f)
835 f = lo128(c); q3[3] |= (f << 16) & 0xffffffffffffff; q3[4] = (f >> 40) & 0xffff; shr128(f, c, 56);
838 mul64x64_128(c, modm_m[0], q3[0])
839 r2[0] = lo128(c) & 0xffffffffffffff; shr128(f, c, 56);
840 mul64x64_128(c, modm_m[0], q3[1]) add128_64(c, f) mul64x64_128(mul, modm_m[1], q3[0]) add128(c, mul)
841 r2[1] = lo128(c) & 0xffffffffffffff; shr128(f, c, 56);
842 mul64x64_128(c, modm_m[0], q3[2]) add128_64(c, f) mul64x64_128(mul, modm_m[2], q3[0]) add128(c, mul) mul64x64_128(mul, modm_m[1], q3[1]) add128(c, mul)
843 r2[2] = lo128(c) & 0xffffffffffffff; shr128(f, c, 56);
844 mul64x64_128(c, modm_m[0], q3[3]) add128_64(c, f) mul64x64_128(mul, modm_m[3], q3[0]) add128(c, mul) mul64x64_128(mul, modm_m[1], q3[2]) add128(c, mul) mul64x64_128(mul, modm_m[2], q3[1]) add128(c, mul)
845 r2[3] = lo128(c) & 0xffffffffffffff; shr128(f, c, 56);
846 mul64x64_128(c, modm_m[0], q3[4]) add128_64(c, f) mul64x64_128(mul, modm_m[4], q3[0]) add128(c, mul) mul64x64_128(mul, modm_m[3], q3[1]) add128(c, mul) mul64x64_128(mul, modm_m[1], q3[3]) add128(c, mul) mul64x64_128(mul, modm_m[2], q3[2]) add128(c, mul)
847 r2[4] = lo128(c) & 0x0000ffffffffff;
850 pb += r2[0]; b = lt_modm(r1[0], pb); r[0] = (r1[0] - pb + (b << 56)); pb = b;
851 pb += r2[1]; b = lt_modm(r1[1], pb); r[1] = (r1[1] - pb + (b << 56)); pb = b;
852 pb += r2[2]; b = lt_modm(r1[2], pb); r[2] = (r1[2] - pb + (b << 56)); pb = b;
853 pb += r2[3]; b = lt_modm(r1[3], pb); r[3] = (r1[3] - pb + (b << 56)); pb = b;
854 pb += r2[4]; b = lt_modm(r1[4], pb); r[4] = (r1[4] - pb + (b << 40));
862 add256_modm(bignum256modm r,
const bignum256modm x,
const bignum256modm y) {
863 bignum256modm_element_t c;
865 c = x[0] + y[0]; r[0] = c & 0xffffffffffffff; c >>= 56;
866 c += x[1] + y[1]; r[1] = c & 0xffffffffffffff; c >>= 56;
867 c += x[2] + y[2]; r[2] = c & 0xffffffffffffff; c >>= 56;
868 c += x[3] + y[3]; r[3] = c & 0xffffffffffffff; c >>= 56;
869 c += x[4] + y[4]; r[4] = c;
875 mul256_modm(bignum256modm r,
const bignum256modm x,
const bignum256modm y) {
876 bignum256modm q1, r1;
878 bignum256modm_element_t f;
880 mul64x64_128(c, x[0], y[0])
881 f = lo128(c); r1[0] = f & 0xffffffffffffff; shr128(f, c, 56);
882 mul64x64_128(c, x[0], y[1]) add128_64(c, f) mul64x64_128(mul, x[1], y[0]) add128(c, mul)
883 f = lo128(c); r1[1] = f & 0xffffffffffffff; shr128(f, c, 56);
884 mul64x64_128(c, x[0], y[2]) add128_64(c, f) mul64x64_128(mul, x[2], y[0]) add128(c, mul) mul64x64_128(mul, x[1], y[1]) add128(c, mul)
885 f = lo128(c); r1[2] = f & 0xffffffffffffff; shr128(f, c, 56);
886 mul64x64_128(c, x[0], y[3]) add128_64(c, f) mul64x64_128(mul, x[3], y[0]) add128(c, mul) mul64x64_128(mul, x[1], y[2]) add128(c, mul) mul64x64_128(mul, x[2], y[1]) add128(c, mul)
887 f = lo128(c); r1[3] = f & 0xffffffffffffff; shr128(f, c, 56);
888 mul64x64_128(c, x[0], y[4]) add128_64(c, f) mul64x64_128(mul, x[4], y[0]) add128(c, mul) mul64x64_128(mul, x[3], y[1]) add128(c, mul) mul64x64_128(mul, x[1], y[3]) add128(c, mul) mul64x64_128(mul, x[2], y[2]) add128(c, mul)
889 f = lo128(c); r1[4] = f & 0x0000ffffffffff; q1[0] = (f >> 24) & 0xffffffff; shr128(f, c, 56);
890 mul64x64_128(c, x[4], y[1]) add128_64(c, f) mul64x64_128(mul, x[1], y[4]) add128(c, mul) mul64x64_128(mul, x[2], y[3]) add128(c, mul) mul64x64_128(mul, x[3], y[2]) add128(c, mul)
891 f = lo128(c); q1[0] |= (f << 32) & 0xffffffffffffff; q1[1] = (f >> 24) & 0xffffffff; shr128(f, c, 56);
892 mul64x64_128(c, x[4], y[2]) add128_64(c, f) mul64x64_128(mul, x[2], y[4]) add128(c, mul) mul64x64_128(mul, x[3], y[3]) add128(c, mul)
893 f = lo128(c); q1[1] |= (f << 32) & 0xffffffffffffff; q1[2] = (f >> 24) & 0xffffffff; shr128(f, c, 56);
894 mul64x64_128(c, x[4], y[3]) add128_64(c, f) mul64x64_128(mul, x[3], y[4]) add128(c, mul)
895 f = lo128(c); q1[2] |= (f << 32) & 0xffffffffffffff; q1[3] = (f >> 24) & 0xffffffff; shr128(f, c, 56);
896 mul64x64_128(c, x[4], y[4]) add128_64(c, f)
897 f = lo128(c); q1[3] |= (f << 32) & 0xffffffffffffff; q1[4] = (f >> 24) & 0xffffffff; shr128(f, c, 56);
900 barrett_reduce256_modm(r, q1, r1);
904 expand256_modm(bignum256modm out,
const byte *in,
size_t len) {
906 bignum256modm_element_t x[16];
909 memcpy(work, in, len);
910 x[0] = U8TO64_LE(work + 0);
911 x[1] = U8TO64_LE(work + 8);
912 x[2] = U8TO64_LE(work + 16);
913 x[3] = U8TO64_LE(work + 24);
914 x[4] = U8TO64_LE(work + 32);
915 x[5] = U8TO64_LE(work + 40);
916 x[6] = U8TO64_LE(work + 48);
917 x[7] = U8TO64_LE(work + 56);
920 out[0] = ( x[0]) & 0xffffffffffffff;
921 out[1] = ((x[ 0] >> 56) | (x[ 1] << 8)) & 0xffffffffffffff;
922 out[2] = ((x[ 1] >> 48) | (x[ 2] << 16)) & 0xffffffffffffff;
923 out[3] = ((x[ 2] >> 40) | (x[ 3] << 24)) & 0xffffffffffffff;
924 out[4] = ((x[ 3] >> 32) | (x[ 4] << 32)) & 0x0000ffffffffff;
931 q1[0] = ((x[ 3] >> 56) | (x[ 4] << 8)) & 0xffffffffffffff;
932 q1[1] = ((x[ 4] >> 48) | (x[ 5] << 16)) & 0xffffffffffffff;
933 q1[2] = ((x[ 5] >> 40) | (x[ 6] << 24)) & 0xffffffffffffff;
934 q1[3] = ((x[ 6] >> 32) | (x[ 7] << 32)) & 0xffffffffffffff;
935 q1[4] = ((x[ 7] >> 24) );
937 barrett_reduce256_modm(out, q1, out);
941 expand_raw256_modm(bignum256modm out,
const byte in[32]) {
942 bignum256modm_element_t x[4];
944 x[0] = U8TO64_LE(in + 0);
945 x[1] = U8TO64_LE(in + 8);
946 x[2] = U8TO64_LE(in + 16);
947 x[3] = U8TO64_LE(in + 24);
949 out[0] = ( x[0]) & 0xffffffffffffff;
950 out[1] = ((x[ 0] >> 56) | (x[ 1] << 8)) & 0xffffffffffffff;
951 out[2] = ((x[ 1] >> 48) | (x[ 2] << 16)) & 0xffffffffffffff;
952 out[3] = ((x[ 2] >> 40) | (x[ 3] << 24)) & 0xffffffffffffff;
953 out[4] = ((x[ 3] >> 32) ) & 0x000000ffffffff;
957 contract256_modm(byte out[32],
const bignum256modm in) {
958 U64TO8_LE(out + 0, (in[0] ) | (in[1] << 56));
959 U64TO8_LE(out + 8, (in[1] >> 8) | (in[2] << 48));
960 U64TO8_LE(out + 16, (in[2] >> 16) | (in[3] << 40));
961 U64TO8_LE(out + 24, (in[3] >> 24) | (in[4] << 32));
965 contract256_window4_modm(
signed char r[64],
const bignum256modm in) {
967 signed char *quads = r;
968 bignum256modm_element_t i, j, v, m;
970 for (i = 0; i < 5; i++) {
972 m = (i == 4) ? 8 : 14;
973 for (j = 0; j < m; j++) {
981 for(i = 0; i < 63; i++) {
983 r[i+1] += (r[i] >> 4);
986 r[i] -= (carry << 4);
992 contract256_slidingwindow_modm(
signed char r[256],
const bignum256modm s,
int windowsize) {
994 int m = (1 << (windowsize - 1)) - 1, soplen = 256;
995 signed char *bits = r;
996 bignum256modm_element_t v;
999 for (i = 0; i < 4; i++) {
1001 for (j = 0; j < 56; j++, v >>= 1)
1005 for (j = 0; j < 32; j++, v >>= 1)
1009 for (j = 0; j < soplen; j++) {
1013 for (b = 1; (b < (soplen - j)) && (b <= 6); b++) {
1014 if ((r[j] + (r[j + b] << b)) <= m) {
1015 r[j] += r[j + b] << b;
1017 }
else if ((r[j] - (r[j + b] << b)) >= -m) {
1018 r[j] -= r[j + b] << b;
1019 for (k = j + b; k < soplen; k++) {
1026 }
else if (r[j + b]) {
1038 curve25519_pow_two5mtwo0_two250mtwo0(bignum25519 b) {
1039 ALIGN(16) bignum25519 t0,c;
1042 curve25519_square_times(t0, b, 5);
1043 curve25519_mul_noinline(b, t0, b);
1044 curve25519_square_times(t0, b, 10);
1045 curve25519_mul_noinline(c, t0, b);
1046 curve25519_square_times(t0, c, 20);
1047 curve25519_mul_noinline(t0, t0, c);
1048 curve25519_square_times(t0, t0, 10);
1049 curve25519_mul_noinline(b, t0, b);
1050 curve25519_square_times(t0, b, 50);
1051 curve25519_mul_noinline(c, t0, b);
1052 curve25519_square_times(t0, c, 100);
1053 curve25519_mul_noinline(t0, t0, c);
1054 curve25519_square_times(t0, t0, 50);
1055 curve25519_mul_noinline(b, t0, b);
1062 curve25519_recip(bignum25519 out, const bignum25519 z) {
1063 ALIGN(16) bignum25519 a,t0,b;
1065 curve25519_square_times(a, z, 1);
1066 curve25519_square_times(t0, a, 2);
1067 curve25519_mul_noinline(b, t0, z);
1068 curve25519_mul_noinline(a, b, a);
1069 curve25519_square_times(t0, a, 1);
1070 curve25519_mul_noinline(b, t0, b);
1071 curve25519_pow_two5mtwo0_two250mtwo0(b);
1072 curve25519_square_times(b, b, 5);
1073 curve25519_mul_noinline(out, b, a);
1080 curve25519_pow_two252m3(bignum25519 two252m3, const bignum25519 z) {
1081 ALIGN(16) bignum25519 b,c,t0;
1083 curve25519_square_times(c, z, 1);
1084 curve25519_square_times(t0, c, 2);
1085 curve25519_mul_noinline(b, t0, z);
1086 curve25519_mul_noinline(c, b, c);
1087 curve25519_square_times(t0, c, 1);
1088 curve25519_mul_noinline(b, t0, b);
1089 curve25519_pow_two5mtwo0_two250mtwo0(b);
1090 curve25519_square_times(b, b, 2);
1091 curve25519_mul_noinline(two252m3, b, z);
1095 ge25519_p1p1_to_partial(ge25519 *r, const ge25519_p1p1 *p) {
1096 curve25519_mul(r->x, p->x, p->t);
1097 curve25519_mul(r->y, p->y, p->z);
1098 curve25519_mul(r->z, p->z, p->t);
1102 ge25519_p1p1_to_full(ge25519 *r,
const ge25519_p1p1 *p) {
1103 curve25519_mul(r->x, p->x, p->t);
1104 curve25519_mul(r->y, p->y, p->z);
1105 curve25519_mul(r->z, p->z, p->t);
1106 curve25519_mul(r->t, p->x, p->y);
1110 ge25519_full_to_pniels(ge25519_pniels *p,
const ge25519 *r) {
1111 curve25519_sub(p->ysubx, r->y, r->x);
1112 curve25519_add(p->xaddy, r->y, r->x);
1113 curve25519_copy(p->z, r->z);
1114 curve25519_mul(p->t2d, r->t, ge25519_ec2d);
1118 ge25519_add_p1p1(ge25519_p1p1 *r,
const ge25519 *p,
const ge25519 *q) {
1119 bignum25519 a,b,c,d,t,u;
1121 curve25519_sub(a, p->y, p->x);
1122 curve25519_add(b, p->y, p->x);
1123 curve25519_sub(t, q->y, q->x);
1124 curve25519_add(u, q->y, q->x);
1125 curve25519_mul(a, a, t);
1126 curve25519_mul(b, b, u);
1127 curve25519_mul(c, p->t, q->t);
1128 curve25519_mul(c, c, ge25519_ec2d);
1129 curve25519_mul(d, p->z, q->z);
1130 curve25519_add(d, d, d);
1131 curve25519_sub(r->x, b, a);
1132 curve25519_add(r->y, b, a);
1133 curve25519_add_after_basic(r->z, d, c);
1134 curve25519_sub_after_basic(r->t, d, c);
1138 ge25519_double_p1p1(ge25519_p1p1 *r,
const ge25519 *p) {
1141 curve25519_square(a, p->x);
1142 curve25519_square(b, p->y);
1143 curve25519_square(c, p->z);
1144 curve25519_add_reduce(c, c, c);
1145 curve25519_add(r->x, p->x, p->y);
1146 curve25519_square(r->x, r->x);
1147 curve25519_add(r->y, b, a);
1148 curve25519_sub(r->z, b, a);
1149 curve25519_sub_after_basic(r->x, r->x, r->y);
1150 curve25519_sub_after_basic(r->t, c, r->z);
1154 ge25519_nielsadd2_p1p1(ge25519_p1p1 *r,
const ge25519 *p,
const ge25519_niels *q, byte signbit) {
1155 const bignum25519 *qb = (
const bignum25519 *)q;
1156 bignum25519 *rb = (bignum25519 *)r;
1159 curve25519_sub(a, p->y, p->x);
1160 curve25519_add(b, p->y, p->x);
1161 curve25519_mul(a, a, qb[signbit]);
1162 curve25519_mul(r->x, b, qb[signbit^1]);
1163 curve25519_add(r->y, r->x, a);
1164 curve25519_sub(r->x, r->x, a);
1165 curve25519_mul(c, p->t, q->t2d);
1166 curve25519_add_reduce(r->t, p->z, p->z);
1167 curve25519_copy(r->z, r->t);
1168 curve25519_add(rb[2+signbit], rb[2+signbit], c);
1169 curve25519_sub(rb[2+(signbit^1)], rb[2+(signbit^1)], c);
1173 ge25519_pnielsadd_p1p1(ge25519_p1p1 *r,
const ge25519 *p,
const ge25519_pniels *q, byte signbit) {
1174 const bignum25519 *qb = (
const bignum25519 *)q;
1175 bignum25519 *rb = (bignum25519 *)r;
1178 curve25519_sub(a, p->y, p->x);
1179 curve25519_add(b, p->y, p->x);
1180 curve25519_mul(a, a, qb[signbit]);
1181 curve25519_mul(r->x, b, qb[signbit^1]);
1182 curve25519_add(r->y, r->x, a);
1183 curve25519_sub(r->x, r->x, a);
1184 curve25519_mul(c, p->t, q->t2d);
1185 curve25519_mul(r->t, p->z, q->z);
1186 curve25519_add_reduce(r->t, r->t, r->t);
1187 curve25519_copy(r->z, r->t);
1188 curve25519_add(rb[2+signbit], rb[2+signbit], c);
1189 curve25519_sub(rb[2+(signbit^1)], rb[2+(signbit^1)], c);
1193 ge25519_double_partial(ge25519 *r,
const ge25519 *p) {
1195 ge25519_double_p1p1(&t, p);
1196 ge25519_p1p1_to_partial(r, &t);
1200 ge25519_double(ge25519 *r,
const ge25519 *p) {
1202 ge25519_double_p1p1(&t, p);
1203 ge25519_p1p1_to_full(r, &t);
1207 ge25519_add(ge25519 *r,
const ge25519 *p,
const ge25519 *q) {
1209 ge25519_add_p1p1(&t, p, q);
1210 ge25519_p1p1_to_full(r, &t);
1214 ge25519_nielsadd2(ge25519 *r,
const ge25519_niels *q) {
1215 bignum25519 a,b,c,e,f,g,h;
1217 curve25519_sub(a, r->y, r->x);
1218 curve25519_add(b, r->y, r->x);
1219 curve25519_mul(a, a, q->ysubx);
1220 curve25519_mul(e, b, q->xaddy);
1221 curve25519_add(h, e, a);
1222 curve25519_sub(e, e, a);
1223 curve25519_mul(c, r->t, q->t2d);
1224 curve25519_add(f, r->z, r->z);
1225 curve25519_add_after_basic(g, f, c);
1226 curve25519_sub_after_basic(f, f, c);
1227 curve25519_mul(r->x, e, f);
1228 curve25519_mul(r->y, h, g);
1229 curve25519_mul(r->z, g, f);
1230 curve25519_mul(r->t, e, h);
1234 ge25519_pnielsadd(ge25519_pniels *r,
const ge25519 *p,
const ge25519_pniels *q) {
1235 bignum25519 a,b,c,x,y,z,t;
1237 curve25519_sub(a, p->y, p->x);
1238 curve25519_add(b, p->y, p->x);
1239 curve25519_mul(a, a, q->ysubx);
1240 curve25519_mul(x, b, q->xaddy);
1241 curve25519_add(y, x, a);
1242 curve25519_sub(x, x, a);
1243 curve25519_mul(c, p->t, q->t2d);
1244 curve25519_mul(t, p->z, q->z);
1245 curve25519_add(t, t, t);
1246 curve25519_add_after_basic(z, t, c);
1247 curve25519_sub_after_basic(t, t, c);
1248 curve25519_mul(r->xaddy, x, t);
1249 curve25519_mul(r->ysubx, y, z);
1250 curve25519_mul(r->z, z, t);
1251 curve25519_mul(r->t2d, x, y);
1252 curve25519_copy(y, r->ysubx);
1253 curve25519_sub(r->ysubx, r->ysubx, r->xaddy);
1254 curve25519_add(r->xaddy, r->xaddy, y);
1255 curve25519_mul(r->t2d, r->t2d, ge25519_ec2d);
1259 ge25519_pack(byte r[32],
const ge25519 *p) {
1260 bignum25519 tx, ty, zi;
1262 curve25519_recip(zi, p->z);
1263 curve25519_mul(tx, p->x, zi);
1264 curve25519_mul(ty, p->y, zi);
1265 curve25519_contract(r, ty);
1266 curve25519_contract(parity, tx);
1267 r[31] ^= ((parity[0] & 1) << 7);
1271 ed25519_verify(
const unsigned char *x,
const unsigned char *y,
size_t len) {
1272 size_t differentbits = 0;
1274 differentbits |= (*x++ ^ *y++);
1275 return (
int) (1 & ((differentbits - 1) >> 8));
1279 ge25519_unpack_negative_vartime(ge25519 *r,
const byte p[32]) {
1280 const byte zero[32] = {0};
1281 const bignum25519 one = {1};
1282 byte parity = p[31] >> 7;
1284 bignum25519 t, root, num, den, d3;
1286 curve25519_expand(r->y, p);
1287 curve25519_copy(r->z, one);
1288 curve25519_square(num, r->y);
1289 curve25519_mul(den, num, ge25519_ecd);
1290 curve25519_sub_reduce(num, num, r->z);
1291 curve25519_add(den, den, r->z);
1295 curve25519_square(t, den);
1296 curve25519_mul(d3, t, den);
1297 curve25519_square(r->x, d3);
1298 curve25519_mul(r->x, r->x, den);
1299 curve25519_mul(r->x, r->x, num);
1300 curve25519_pow_two252m3(r->x, r->x);
1303 curve25519_mul(r->x, r->x, d3);
1304 curve25519_mul(r->x, r->x, num);
1307 curve25519_square(t, r->x);
1308 curve25519_mul(t, t, den);
1309 curve25519_sub_reduce(root, t, num);
1310 curve25519_contract(check, root);
1311 if (!ed25519_verify(check, zero, 32)) {
1312 curve25519_add_reduce(t, t, num);
1313 curve25519_contract(check, t);
1314 if (!ed25519_verify(check, zero, 32))
1316 curve25519_mul(r->x, r->x, ge25519_sqrtneg1);
1319 curve25519_contract(check, r->x);
1320 if ((check[0] & 1) == parity) {
1321 curve25519_copy(t, r->x);
1322 curve25519_neg(r->x, t);
1324 curve25519_mul(r->t, r->x, r->y);
1330 ge25519_double_scalarmult_vartime(ge25519 *r,
const ge25519 *p1,
const bignum256modm s1,
const bignum256modm s2) {
1331 signed char slide1[256], slide2[256];
1332 ge25519_pniels pre1[S1_TABLE_SIZE];
1337 contract256_slidingwindow_modm(slide1, s1, S1_SWINDOWSIZE);
1338 contract256_slidingwindow_modm(slide2, s2, S2_SWINDOWSIZE);
1340 ge25519_double(&d1, p1);
1341 ge25519_full_to_pniels(pre1, p1);
1342 for (i = 0; i < S1_TABLE_SIZE - 1; i++)
1343 ge25519_pnielsadd(&pre1[i+1], &d1, &pre1[i]);
1346 memset(r, 0,
sizeof(ge25519));
1351 while ((i >= 0) && !(slide1[i] | slide2[i]))
1354 for (; i >= 0; i--) {
1355 ge25519_double_p1p1(&t, r);
1358 ge25519_p1p1_to_full(r, &t);
1359 ge25519_pnielsadd_p1p1(&t, r, &pre1[abs(slide1[i]) / 2], (byte)slide1[i] >> 7);
1363 ge25519_p1p1_to_full(r, &t);
1364 ge25519_nielsadd2_p1p1(&t, r, &ge25519_niels_sliding_multiples[abs(slide2[i]) / 2], (byte)slide2[i] >> 7);
1367 ge25519_p1p1_to_partial(r, &t);
1371 #if !defined(HAVE_GE25519_SCALARMULT_BASE_CHOOSE_NIELS) 1374 ge25519_windowb_equal(word32 b, word32 c) {
1375 return ((b ^ c) - 1) >> 31;
1379 ge25519_scalarmult_base_choose_niels(ge25519_niels *t,
const uint8_t table[256][96], word32 pos,
signed char b) {
1381 word32 sign = (word32)((byte)b >> 7);
1382 word32 mask = ~(sign - 1);
1383 word32 u = (b + mask) ^ mask;
1387 uint8_t packed[96] = {0};
1391 for (i = 0; i < 8; i++)
1392 curve25519_move_conditional_bytes(packed, table[(pos * 8) + i], ge25519_windowb_equal(u, i + 1));
1395 curve25519_expand(t->ysubx, packed + 0);
1396 curve25519_expand(t->xaddy, packed + 32);
1397 curve25519_expand(t->t2d , packed + 64);
1400 curve25519_swap_conditional(t->ysubx, t->xaddy, sign);
1401 curve25519_neg(neg, t->t2d);
1402 curve25519_swap_conditional(t->t2d, neg, sign);
1409 ge25519_scalarmult_base_niels(ge25519 *r,
const uint8_t basepoint_table[256][96],
const bignum256modm s) {
1414 contract256_window4_modm(b, s);
1416 ge25519_scalarmult_base_choose_niels(&t, basepoint_table, 0, b[1]);
1417 curve25519_sub_reduce(r->x, t.xaddy, t.ysubx);
1418 curve25519_add_reduce(r->y, t.xaddy, t.ysubx);
1419 memset(r->z, 0,
sizeof(bignum25519));
1420 curve25519_copy(r->t, t.t2d);
1422 for (i = 3; i < 64; i += 2) {
1423 ge25519_scalarmult_base_choose_niels(&t, basepoint_table, i / 2, b[i]);
1424 ge25519_nielsadd2(r, &t);
1426 ge25519_double_partial(r, r);
1427 ge25519_double_partial(r, r);
1428 ge25519_double_partial(r, r);
1429 ge25519_double(r, r);
1430 ge25519_scalarmult_base_choose_niels(&t, basepoint_table, 0, b[0]);
1431 curve25519_mul(t.t2d, t.t2d, ge25519_ecd);
1432 ge25519_nielsadd2(r, &t);
1433 for(i = 2; i < 64; i += 2) {
1434 ge25519_scalarmult_base_choose_niels(&t, basepoint_table, i / 2, b[i]);
1435 ge25519_nielsadd2(r, &t);
1439 ANONYMOUS_NAMESPACE_END
1447 NAMESPACE_BEGIN(Donna)
1449 int curve25519_mult_CXX(byte sharedKey[32],
const byte secretKey[32],
const byte othersKey[32])
1451 using namespace CryptoPP::Donna::X25519;
1454 for (
size_t i = 0;i < 32;++i)
1455 e[i] = secretKey[i];
1456 e[0] &= 0xf8; e[31] &= 0x7f; e[31] |= 0x40;
1458 bignum25519 nqpqx = {1}, nqpqz = {0}, nqz = {1}, nqx;
1459 bignum25519 q, qx, qpqx, qqx, zzz, zmone;
1460 size_t bit, lastbit;
1462 curve25519_expand(q, othersKey);
1463 curve25519_copy(nqx, q);
1470 for (
int i = 253; i >= 2; i--) {
1471 curve25519_add(qx, nqx, nqz);
1472 curve25519_sub(nqz, nqx, nqz);
1473 curve25519_add(qpqx, nqpqx, nqpqz);
1474 curve25519_sub(nqpqz, nqpqx, nqpqz);
1475 curve25519_mul(nqpqx, qpqx, nqz);
1476 curve25519_mul(nqpqz, qx, nqpqz);
1477 curve25519_add(qqx, nqpqx, nqpqz);
1478 curve25519_sub(nqpqz, nqpqx, nqpqz);
1479 curve25519_square(nqpqz, nqpqz);
1480 curve25519_square(nqpqx, qqx);
1481 curve25519_mul(nqpqz, nqpqz, q);
1482 curve25519_square(qx, qx);
1483 curve25519_square(nqz, nqz);
1484 curve25519_mul(nqx, qx, nqz);
1485 curve25519_sub(nqz, qx, nqz);
1486 curve25519_scalar_product(zzz, nqz, 121665);
1487 curve25519_add(zzz, zzz, qx);
1488 curve25519_mul(nqz, nqz, zzz);
1490 bit = (e[i/8] >> (i & 7)) & 1;
1491 curve25519_swap_conditional(nqx, nqpqx, bit ^ lastbit);
1492 curve25519_swap_conditional(nqz, nqpqz, bit ^ lastbit);
1497 for (
int i = 0; i < 3; i++) {
1498 curve25519_add(qx, nqx, nqz);
1499 curve25519_sub(nqz, nqx, nqz);
1500 curve25519_square(qx, qx);
1501 curve25519_square(nqz, nqz);
1502 curve25519_mul(nqx, qx, nqz);
1503 curve25519_sub(nqz, qx, nqz);
1504 curve25519_scalar_product(zzz, nqz, 121665);
1505 curve25519_add(zzz, zzz, qx);
1506 curve25519_mul(nqz, nqz, zzz);
1509 curve25519_recip(zmone, nqz);
1510 curve25519_mul(nqz, nqx, zmone);
1511 curve25519_contract(sharedKey, nqz);
1518 using namespace CryptoPP::Donna::X25519;
1520 #if (CRYPTOPP_CURVE25519_SSE2) 1522 return curve25519_mult_SSE2(publicKey, secretKey, basePoint);
1526 return curve25519_mult_CXX(publicKey, secretKey, basePoint);
1529 int curve25519_mult(byte sharedKey[32],
const byte secretKey[32],
const byte othersKey[32])
1531 #if (CRYPTOPP_CURVE25519_SSE2) 1533 return curve25519_mult_SSE2(sharedKey, secretKey, othersKey);
1537 return curve25519_mult_CXX(sharedKey, secretKey, othersKey);
1546 NAMESPACE_BEGIN(Donna)
1549 ed25519_publickey_CXX(byte publicKey[32],
const byte secretKey[32])
1551 using namespace CryptoPP::Donna::Ed25519;
1554 ALIGN(16) ge25519 A;
1558 ed25519_extsk(extsk, secretKey);
1559 expand256_modm(a, extsk, 32);
1560 ge25519_scalarmult_base_niels(&A, ge25519_niels_base_multiples, a);
1561 ge25519_pack(publicKey, &A);
1569 return ed25519_publickey_CXX(publicKey, secretKey);
1573 ed25519_sign_CXX(
const byte *m,
size_t mlen,
const byte sk[32],
const byte pk[32], byte RS[64])
1575 using namespace CryptoPP::Donna::Ed25519;
1577 bignum256modm r, S, a;
1578 ALIGN(16) ge25519 R;
1579 hash_512bits extsk, hashr, hram;
1581 ed25519_extsk(extsk, sk);
1585 hash.Update(extsk + 32, 32);
1586 hash.Update(m, mlen);
1588 expand256_modm(r, hashr, 64);
1591 ge25519_scalarmult_base_niels(&R, ge25519_niels_base_multiples, r);
1592 ge25519_pack(RS, &R);
1595 ed25519_hram(hram, RS, pk, m, mlen);
1596 expand256_modm(S, hram, 64);
1599 expand256_modm(a, extsk, 32);
1600 mul256_modm(S, S, a);
1603 add256_modm(S, S, r);
1606 contract256_modm(RS + 32, S);
1611 ed25519_sign(const byte* message,
size_t messageLength, const byte secretKey[32],
1612 const byte publicKey[32], byte signature[64])
1614 return ed25519_sign_CXX(message, messageLength, secretKey, publicKey, signature);
1618 ed25519_sign_open_CXX(
const byte *m,
size_t mlen,
const byte pk[32],
const byte RS[64]) {
1620 using namespace CryptoPP::Donna::Ed25519;
1622 ALIGN(16) ge25519 R, A;
1624 bignum256modm hram, S;
1625 unsigned char checkR[32];
1627 if ((RS[63] & 224) || !ge25519_unpack_negative_vartime(&A, pk))
1631 ed25519_hram(hash, RS, pk, m, mlen);
1632 expand256_modm(hram, hash, 64);
1635 expand256_modm(S, RS + 32, 32);
1638 ge25519_double_scalarmult_vartime(&R, &A, hram, S);
1639 ge25519_pack(checkR, &R);
1642 return ed25519_verify(RS, checkR, 32) ? 0 : -1;
1646 ed25519_sign_open(const byte *message,
size_t messageLength, const byte publicKey[32], const byte signature[64])
1648 return ed25519_sign_open_CXX(message, messageLength, publicKey, signature);
1654 #endif // CRYPTOPP_CURVE25519_64BIT
Utility functions for the Crypto++ library.
void PutWord(bool assumeAligned, ByteOrder order, byte *block, T value, const byte *xorBlock=NULL)
Access a block of memory.
Converts an enumeration to a type suitable for use as a template parameter.
EnumToType< ByteOrder, LITTLE_ENDIAN_ORDER > LittleEndian
Provides a constant for LittleEndian.
Library configuration file.
void Update(const byte *input, size_t length)
Updates a hash with additional input.
byte order is little-endian
Classes and functions for secure memory allocations.
T GetWord(bool assumeAligned, ByteOrder order, const byte *block)
Access a block of memory.
int ed25519_sign(const byte *message, size_t messageLength, const byte secretKey[32], const byte publicKey[32], byte signature[64])
Creates a signature on a message.
int curve25519_mult(byte publicKey[32], const byte secretKey[32])
Generate a public key.
int ed25519_sign_open(const byte *message, size_t messageLength, const byte publicKey[32], const byte signature[64])
Verifies a signature on a message.
Fixed size stack-based SecBlock.
Functions for CPU features and intrinsics.
Classes for SHA-1 and SHA-2 family of message digests.
bool HasSSE2()
Determines SSE2 availability.
Access a block of memory.
Crypto++ library namespace.
int ed25519_publickey(byte publicKey[32], const byte secretKey[32])
Creates a public key from a secret key.