33 #if CRYPTOPP_GCC_DIAGNOSTIC_AVAILABLE 34 # pragma GCC diagnostic ignored "-Wunused-function" 38 extern const char DONNA64_FNAME[] = __FILE__;
40 #if defined(CRYPTOPP_CURVE25519_64BIT) 44 ANONYMOUS_NAMESPACE_BEGIN
47 using CryptoPP::word64;
52 inline word64 U8TO64_LE(
const byte* p)
57 inline void U64TO8_LE(byte* p, word64 w)
62 ANONYMOUS_NAMESPACE_END
65 NAMESPACE_BEGIN(Donna)
66 NAMESPACE_BEGIN(X25519)
67 ANONYMOUS_NAMESPACE_BEGIN
70 using CryptoPP::word32;
71 using CryptoPP::sword32;
72 using CryptoPP::word64;
73 using CryptoPP::sword64;
75 using CryptoPP::GetBlock;
79 using namespace CryptoPP::Donna::Arch64;
83 curve25519_copy(bignum25519 out,
const bignum25519 in) {
84 out[0] = in[0]; out[1] = in[1];
85 out[2] = in[2]; out[3] = in[3];
91 curve25519_add(bignum25519 out,
const bignum25519 a,
const bignum25519 b) {
101 curve25519_sub(bignum25519 out,
const bignum25519 a,
const bignum25519 b) {
102 out[0] = a[0] + two54m152 - b[0];
103 out[1] = a[1] + two54m8 - b[1];
104 out[2] = a[2] + two54m8 - b[2];
105 out[3] = a[3] + two54m8 - b[3];
106 out[4] = a[4] + two54m8 - b[4];
111 curve25519_scalar_product(bignum25519 out,
const bignum25519 in,
const word64 scalar) {
115 #if defined(CRYPTOPP_WORD128_AVAILABLE) 116 a = ((word128) in[0]) * scalar; out[0] = (word64)a & reduce_mask_51; c = (word64)(a >> 51);
117 a = ((word128) in[1]) * scalar + c; out[1] = (word64)a & reduce_mask_51; c = (word64)(a >> 51);
118 a = ((word128) in[2]) * scalar + c; out[2] = (word64)a & reduce_mask_51; c = (word64)(a >> 51);
119 a = ((word128) in[3]) * scalar + c; out[3] = (word64)a & reduce_mask_51; c = (word64)(a >> 51);
120 a = ((word128) in[4]) * scalar + c; out[4] = (word64)a & reduce_mask_51; c = (word64)(a >> 51);
123 mul64x64_128(a, in[0], scalar) out[0] = lo128(a) & reduce_mask_51; shr128(c, a, 51);
124 mul64x64_128(a, in[1], scalar) add128_64(a, c) out[1] = lo128(a) & reduce_mask_51; shr128(c, a, 51);
125 mul64x64_128(a, in[2], scalar) add128_64(a, c) out[2] = lo128(a) & reduce_mask_51; shr128(c, a, 51);
126 mul64x64_128(a, in[3], scalar) add128_64(a, c) out[3] = lo128(a) & reduce_mask_51; shr128(c, a, 51);
127 mul64x64_128(a, in[4], scalar) add128_64(a, c) out[4] = lo128(a) & reduce_mask_51; shr128(c, a, 51);
134 curve25519_mul(bignum25519 out,
const bignum25519 a,
const bignum25519 b) {
135 #if !defined(CRYPTOPP_WORD128_AVAILABLE) 139 word64 r0,r1,r2,r3,r4,s0,s1,s2,s3,s4,c;
141 r0 = b[0]; r1 = b[1]; r2 = b[2]; r3 = b[3]; r4 = b[4];
142 s0 = a[0]; s1 = a[1]; s2 = a[2]; s3 = a[3]; s4 = a[4];
144 #if defined(CRYPTOPP_WORD128_AVAILABLE) 145 t[0] = ((word128) r0) * s0;
146 t[1] = ((word128) r0) * s1 + ((word128) r1) * s0;
147 t[2] = ((word128) r0) * s2 + ((word128) r2) * s0 + ((word128) r1) * s1;
148 t[3] = ((word128) r0) * s3 + ((word128) r3) * s0 + ((word128) r1) * s2 + ((word128) r2) * s1;
149 t[4] = ((word128) r0) * s4 + ((word128) r4) * s0 + ((word128) r3) * s1 + ((word128) r1) * s3 + ((word128) r2) * s2;
151 mul64x64_128(t[0], r0, s0)
152 mul64x64_128(t[1], r0, s1) mul64x64_128(mul, r1, s0) add128(t[1], mul)
153 mul64x64_128(t[2], r0, s2) mul64x64_128(mul, r2, s0) add128(t[2], mul) mul64x64_128(mul, r1, s1) add128(t[2], mul)
154 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)
155 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)
158 r1 *= 19; r2 *= 19; r3 *= 19; r4 *= 19;
160 #if defined(CRYPTOPP_WORD128_AVAILABLE) 161 t[0] += ((word128) r4) * s1 + ((word128) r1) * s4 + ((word128) r2) * s3 + ((word128) r3) * s2;
162 t[1] += ((word128) r4) * s2 + ((word128) r2) * s4 + ((word128) r3) * s3;
163 t[2] += ((word128) r4) * s3 + ((word128) r3) * s4;
164 t[3] += ((word128) r4) * s4;
166 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)
167 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)
168 mul64x64_128(mul, r4, s3) add128(t[2], mul) mul64x64_128(mul, r3, s4) add128(t[2], mul)
169 mul64x64_128(mul, r4, s4) add128(t[3], mul)
172 r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51);
173 add128_64(t[1], c) r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51);
174 add128_64(t[2], c) r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51);
175 add128_64(t[3], c) r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51);
176 add128_64(t[4], c) r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51);
177 r0 += c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51;
180 out[0] = r0; out[1] = r1; out[2] = r2; out[3] = r3; out[4] = r4;
185 curve25519_square_times(bignum25519 out,
const bignum25519 in, word64 count) {
186 #if !defined(CRYPTOPP_WORD128_AVAILABLE) 190 word64 r0,r1,r2,r3,r4,c;
191 word64 d0,d1,d2,d4,d419;
193 r0 = in[0]; r1 = in[1]; r2 = in[2]; r3 = in[3]; r4 = in[4];
196 d0 = r0 * 2; d1 = r1 * 2;
198 d419 = r4 * 19; d4 = d419 * 2;
200 #if defined(CRYPTOPP_WORD128_AVAILABLE) 201 t[0] = ((word128) r0) * r0 + ((word128) d4) * r1 + (((word128) d2) * (r3 ));
202 t[1] = ((word128) d0) * r1 + ((word128) d4) * r2 + (((word128) r3) * (r3 * 19));
203 t[2] = ((word128) d0) * r2 + ((word128) r1) * r1 + (((word128) d4) * (r3 ));
204 t[3] = ((word128) d0) * r3 + ((word128) d1) * r2 + (((word128) r4) * (d419 ));
205 t[4] = ((word128) d0) * r4 + ((word128) d1) * r3 + (((word128) r2) * (r2 ));
207 mul64x64_128(t[0], r0, r0) mul64x64_128(mul, d4, r1) add128(t[0], mul) mul64x64_128(mul, d2, r3) add128(t[0], mul)
208 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)
209 mul64x64_128(t[2], d0, r2) mul64x64_128(mul, r1, r1) add128(t[2], mul) mul64x64_128(mul, d4, r3) add128(t[2], mul)
210 mul64x64_128(t[3], d0, r3) mul64x64_128(mul, d1, r2) add128(t[3], mul) mul64x64_128(mul, r4, d419) add128(t[3], mul)
211 mul64x64_128(t[4], d0, r4) mul64x64_128(mul, d1, r3) add128(t[4], mul) mul64x64_128(mul, r2, r2) add128(t[4], mul)
214 r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51);
215 add128_64(t[1], c) r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51);
216 add128_64(t[2], c) r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51);
217 add128_64(t[3], c) r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51);
218 add128_64(t[4], c) r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51);
219 r0 += c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51;
223 out[0] = r0; out[1] = r1; out[2] = r2; out[3] = r3; out[4] = r4;
227 curve25519_square(bignum25519 out,
const bignum25519 in) {
228 #if !defined(CRYPTOPP_WORD128_AVAILABLE) 232 word64 r0,r1,r2,r3,r4,c;
233 word64 d0,d1,d2,d4,d419;
235 r0 = in[0]; r1 = in[1]; r2 = in[2]; r3 = in[3]; r4 = in[4];
237 d0 = r0 * 2; d1 = r1 * 2;
239 d419 = r4 * 19; d4 = d419 * 2;
241 #if defined(CRYPTOPP_WORD128_AVAILABLE) 242 t[0] = ((word128) r0) * r0 + ((word128) d4) * r1 + (((word128) d2) * (r3 ));
243 t[1] = ((word128) d0) * r1 + ((word128) d4) * r2 + (((word128) r3) * (r3 * 19));
244 t[2] = ((word128) d0) * r2 + ((word128) r1) * r1 + (((word128) d4) * (r3 ));
245 t[3] = ((word128) d0) * r3 + ((word128) d1) * r2 + (((word128) r4) * (d419 ));
246 t[4] = ((word128) d0) * r4 + ((word128) d1) * r3 + (((word128) r2) * (r2 ));
248 mul64x64_128(t[0], r0, r0) mul64x64_128(mul, d4, r1) add128(t[0], mul) mul64x64_128(mul, d2, r3) add128(t[0], mul)
249 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)
250 mul64x64_128(t[2], d0, r2) mul64x64_128(mul, r1, r1) add128(t[2], mul) mul64x64_128(mul, d4, r3) add128(t[2], mul)
251 mul64x64_128(t[3], d0, r3) mul64x64_128(mul, d1, r2) add128(t[3], mul) mul64x64_128(mul, r4, d419) add128(t[3], mul)
252 mul64x64_128(t[4], d0, r4) mul64x64_128(mul, d1, r3) add128(t[4], mul) mul64x64_128(mul, r2, r2) add128(t[4], mul)
255 r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51);
256 add128_64(t[1], c) r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51);
257 add128_64(t[2], c) r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51);
258 add128_64(t[3], c) r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51);
259 add128_64(t[4], c) r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51);
260 r0 += c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51;
263 out[0] = r0; out[1] = r1; out[2] = r2; out[3] = r3; out[4] = r4;
268 curve25519_expand(bignum25519 out,
const byte *in) {
271 block(x0)(x1)(x2)(x3);
273 out[0] = x0 & reduce_mask_51; x0 = (x0 >> 51) | (x1 << 13);
274 out[1] = x0 & reduce_mask_51; x1 = (x1 >> 38) | (x2 << 26);
275 out[2] = x1 & reduce_mask_51; x2 = (x2 >> 25) | (x3 << 39);
276 out[3] = x2 & reduce_mask_51; x3 = (x3 >> 12);
277 out[4] = x3 & reduce_mask_51;
284 curve25519_contract(byte *out,
const bignum25519 input) {
294 #define curve25519_contract_carry() \ 295 t[1] += t[0] >> 51; t[0] &= reduce_mask_51; \ 296 t[2] += t[1] >> 51; t[1] &= reduce_mask_51; \ 297 t[3] += t[2] >> 51; t[2] &= reduce_mask_51; \ 298 t[4] += t[3] >> 51; t[3] &= reduce_mask_51; 300 #define curve25519_contract_carry_full() curve25519_contract_carry() \ 301 t[0] += 19 * (t[4] >> 51); t[4] &= reduce_mask_51; 303 #define curve25519_contract_carry_final() curve25519_contract_carry() \ 304 t[4] &= reduce_mask_51; 306 curve25519_contract_carry_full()
307 curve25519_contract_carry_full()
312 curve25519_contract_carry_full()
315 t[0] += 0x8000000000000 - 19;
316 t[1] += 0x8000000000000 - 1;
317 t[2] += 0x8000000000000 - 1;
318 t[3] += 0x8000000000000 - 1;
319 t[4] += 0x8000000000000 - 1;
322 curve25519_contract_carry_final()
324 #define write51full(n,shift) \ 325 f = ((t[n] >> shift) | (t[n+1] << (51 - shift))); \ 326 for (i = 0; i < 8; i++, f >>= 8) *out++ = (byte)f; 327 #define write51(n) write51full(n,13*n) 334 #undef curve25519_contract_carry 335 #undef curve25519_contract_carry_full 336 #undef curve25519_contract_carry_final 345 curve25519_swap_conditional(bignum25519 x, bignum25519 qpx, word64 iswap) {
346 const word64 swap = (word64)(-(sword64)iswap);
347 word64 x0,x1,x2,x3,x4;
349 x0 = swap & (x[0] ^ qpx[0]); x[0] ^= x0; qpx[0] ^= x0;
350 x1 = swap & (x[1] ^ qpx[1]); x[1] ^= x1; qpx[1] ^= x1;
351 x2 = swap & (x[2] ^ qpx[2]); x[2] ^= x2; qpx[2] ^= x2;
352 x3 = swap & (x[3] ^ qpx[3]); x[3] ^= x3; qpx[3] ^= x3;
353 x4 = swap & (x[4] ^ qpx[4]); x[4] ^= x4; qpx[4] ^= x4;
361 curve25519_pow_two5mtwo0_two250mtwo0(bignum25519 b) {
362 ALIGN(16) bignum25519 t0,c;
365 curve25519_square_times(t0, b, 5);
366 curve25519_mul(b, t0, b);
367 curve25519_square_times(t0, b, 10);
368 curve25519_mul(c, t0, b);
369 curve25519_square_times(t0, c, 20);
370 curve25519_mul(t0, t0, c);
371 curve25519_square_times(t0, t0, 10);
372 curve25519_mul(b, t0, b);
373 curve25519_square_times(t0, b, 50);
374 curve25519_mul(c, t0, b);
375 curve25519_square_times(t0, c, 100);
376 curve25519_mul(t0, t0, c);
377 curve25519_square_times(t0, t0, 50);
378 curve25519_mul(b, t0, b);
385 curve25519_recip(bignum25519 out, const bignum25519 z) {
386 ALIGN(16) bignum25519 a, t0, b;
388 curve25519_square(a, z);
389 curve25519_square_times(t0, a, 2);
390 curve25519_mul(b, t0, z);
391 curve25519_mul(a, b, a);
392 curve25519_square(t0, a);
393 curve25519_mul(b, t0, b);
394 curve25519_pow_two5mtwo0_two250mtwo0(b);
395 curve25519_square_times(b, b, 5);
396 curve25519_mul(out, b, a);
399 ANONYMOUS_NAMESPACE_END
407 NAMESPACE_BEGIN(Donna)
408 NAMESPACE_BEGIN(Ed25519)
409 ANONYMOUS_NAMESPACE_BEGIN
423 using namespace
CryptoPP::Donna::Arch64;
427 curve25519_copy(bignum25519 out, const bignum25519 in) {
428 out[0] = in[0]; out[1] = in[1];
429 out[2] = in[2]; out[3] = in[3];
435 curve25519_add(bignum25519 out,
const bignum25519 a,
const bignum25519 b) {
436 out[0] = a[0] + b[0]; out[1] = a[1] + b[1];
437 out[2] = a[2] + b[2]; out[3] = a[3] + b[3];
438 out[4] = a[4] + b[4];
443 curve25519_add_after_basic(bignum25519 out,
const bignum25519 a,
const bignum25519 b) {
444 out[0] = a[0] + b[0]; out[1] = a[1] + b[1];
445 out[2] = a[2] + b[2]; out[3] = a[3] + b[3];
446 out[4] = a[4] + b[4];
450 curve25519_add_reduce(bignum25519 out,
const bignum25519 a,
const bignum25519 b) {
452 out[0] = a[0] + b[0] ; c = (out[0] >> 51); out[0] &= reduce_mask_51;
453 out[1] = a[1] + b[1] + c; c = (out[1] >> 51); out[1] &= reduce_mask_51;
454 out[2] = a[2] + b[2] + c; c = (out[2] >> 51); out[2] &= reduce_mask_51;
455 out[3] = a[3] + b[3] + c; c = (out[3] >> 51); out[3] &= reduce_mask_51;
456 out[4] = a[4] + b[4] + c; c = (out[4] >> 51); out[4] &= reduce_mask_51;
462 curve25519_sub(bignum25519 out,
const bignum25519 a,
const bignum25519 b) {
463 out[0] = a[0] + twoP0 - b[0];
464 out[1] = a[1] + twoP1234 - b[1];
465 out[2] = a[2] + twoP1234 - b[2];
466 out[3] = a[3] + twoP1234 - b[3];
467 out[4] = a[4] + twoP1234 - b[4];
472 curve25519_sub_after_basic(bignum25519 out,
const bignum25519 a,
const bignum25519 b) {
473 out[0] = a[0] + fourP0 - b[0];
474 out[1] = a[1] + fourP1234 - b[1];
475 out[2] = a[2] + fourP1234 - b[2];
476 out[3] = a[3] + fourP1234 - b[3];
477 out[4] = a[4] + fourP1234 - b[4];
481 curve25519_sub_reduce(bignum25519 out,
const bignum25519 a,
const bignum25519 b) {
483 out[0] = a[0] + fourP0 - b[0] ; c = (out[0] >> 51); out[0] &= reduce_mask_51;
484 out[1] = a[1] + fourP1234 - b[1] + c; c = (out[1] >> 51); out[1] &= reduce_mask_51;
485 out[2] = a[2] + fourP1234 - b[2] + c; c = (out[2] >> 51); out[2] &= reduce_mask_51;
486 out[3] = a[3] + fourP1234 - b[3] + c; c = (out[3] >> 51); out[3] &= reduce_mask_51;
487 out[4] = a[4] + fourP1234 - b[4] + c; c = (out[4] >> 51); out[4] &= reduce_mask_51;
493 curve25519_neg(bignum25519 out,
const bignum25519 a) {
495 out[0] = twoP0 - a[0] ; c = (out[0] >> 51); out[0] &= reduce_mask_51;
496 out[1] = twoP1234 - a[1] + c; c = (out[1] >> 51); out[1] &= reduce_mask_51;
497 out[2] = twoP1234 - a[2] + c; c = (out[2] >> 51); out[2] &= reduce_mask_51;
498 out[3] = twoP1234 - a[3] + c; c = (out[3] >> 51); out[3] &= reduce_mask_51;
499 out[4] = twoP1234 - a[4] + c; c = (out[4] >> 51); out[4] &= reduce_mask_51;
505 curve25519_mul(bignum25519 out,
const bignum25519 in2,
const bignum25519 in) {
506 #if !defined(CRYPTOPP_WORD128_AVAILABLE) 510 word64 r0,r1,r2,r3,r4,s0,s1,s2,s3,s4,c;
512 r0 = in[0]; r1 = in[1];
513 r2 = in[2]; r3 = in[3];
516 s0 = in2[0]; s1 = in2[1];
517 s2 = in2[2]; s3 = in2[3];
520 #if defined(CRYPTOPP_WORD128_AVAILABLE) 521 t[0] = ((word128) r0) * s0;
522 t[1] = ((word128) r0) * s1 + ((word128) r1) * s0;
523 t[2] = ((word128) r0) * s2 + ((word128) r2) * s0 + ((word128) r1) * s1;
524 t[3] = ((word128) r0) * s3 + ((word128) r3) * s0 + ((word128) r1) * s2 + ((word128) r2) * s1;
525 t[4] = ((word128) r0) * s4 + ((word128) r4) * s0 + ((word128) r3) * s1 + ((word128) r1) * s3 + ((word128) r2) * s2;
527 mul64x64_128(t[0], r0, s0)
528 mul64x64_128(t[1], r0, s1) mul64x64_128(mul, r1, s0) add128(t[1], mul)
529 mul64x64_128(t[2], r0, s2) mul64x64_128(mul, r2, s0) add128(t[2], mul) mul64x64_128(mul, r1, s1) add128(t[2], mul)
530 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)
531 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)
537 #if defined(CRYPTOPP_WORD128_AVAILABLE) 538 t[0] += ((word128) r4) * s1 + ((word128) r1) * s4 + ((word128) r2) * s3 + ((word128) r3) * s2;
539 t[1] += ((word128) r4) * s2 + ((word128) r2) * s4 + ((word128) r3) * s3;
540 t[2] += ((word128) r4) * s3 + ((word128) r3) * s4;
541 t[3] += ((word128) r4) * s4;
543 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)
544 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)
545 mul64x64_128(mul, r4, s3) add128(t[2], mul) mul64x64_128(mul, r3, s4) add128(t[2], mul)
546 mul64x64_128(mul, r4, s4) add128(t[3], mul)
549 r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51);
550 add128_64(t[1], c) r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51);
551 add128_64(t[2], c) r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51);
552 add128_64(t[3], c) r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51);
553 add128_64(t[4], c) r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51);
554 r0 += c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51;
557 out[0] = r0; out[1] = r1;
558 out[2] = r2; out[3] = r3;
563 curve25519_mul_noinline(bignum25519 out,
const bignum25519 in2,
const bignum25519 in) {
564 curve25519_mul(out, in2, in);
569 curve25519_square_times(bignum25519 out,
const bignum25519 in, word64 count) {
570 #if !defined(CRYPTOPP_WORD128_AVAILABLE) 574 word64 r0,r1,r2,r3,r4,c;
575 word64 d0,d1,d2,d4,d419;
577 r0 = in[0]; r1 = in[1];
578 r2 = in[2]; r3 = in[3];
588 #if defined(CRYPTOPP_WORD128_AVAILABLE) 589 t[0] = ((word128) r0) * r0 + ((word128) d4) * r1 + (((word128) d2) * (r3 ));
590 t[1] = ((word128) d0) * r1 + ((word128) d4) * r2 + (((word128) r3) * (r3 * 19));
591 t[2] = ((word128) d0) * r2 + ((word128) r1) * r1 + (((word128) d4) * (r3 ));
592 t[3] = ((word128) d0) * r3 + ((word128) d1) * r2 + (((word128) r4) * (d419 ));
593 t[4] = ((word128) d0) * r4 + ((word128) d1) * r3 + (((word128) r2) * (r2 ));
595 mul64x64_128(t[0], r0, r0) mul64x64_128(mul, d4, r1) add128(t[0], mul) mul64x64_128(mul, d2, r3) add128(t[0], mul)
596 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)
597 mul64x64_128(t[2], d0, r2) mul64x64_128(mul, r1, r1) add128(t[2], mul) mul64x64_128(mul, d4, r3) add128(t[2], mul)
598 mul64x64_128(t[3], d0, r3) mul64x64_128(mul, d1, r2) add128(t[3], mul) mul64x64_128(mul, r4, d419) add128(t[3], mul)
599 mul64x64_128(t[4], d0, r4) mul64x64_128(mul, d1, r3) add128(t[4], mul) mul64x64_128(mul, r2, r2) add128(t[4], mul)
602 r0 = lo128(t[0]) & reduce_mask_51;
603 r1 = lo128(t[1]) & reduce_mask_51; shl128(c, t[0], 13); r1 += c;
604 r2 = lo128(t[2]) & reduce_mask_51; shl128(c, t[1], 13); r2 += c;
605 r3 = lo128(t[3]) & reduce_mask_51; shl128(c, t[2], 13); r3 += c;
606 r4 = lo128(t[4]) & reduce_mask_51; shl128(c, t[3], 13); r4 += c;
607 shl128(c, t[4], 13); r0 += c * 19;
608 c = r0 >> 51; r0 &= reduce_mask_51;
609 r1 += c ; c = r1 >> 51; r1 &= reduce_mask_51;
610 r2 += c ; c = r2 >> 51; r2 &= reduce_mask_51;
611 r3 += c ; c = r3 >> 51; r3 &= reduce_mask_51;
612 r4 += c ; c = r4 >> 51; r4 &= reduce_mask_51;
616 out[0] = r0; out[1] = r1;
617 out[2] = r2; out[3] = r3;
622 curve25519_square(bignum25519 out,
const bignum25519 in) {
623 #if !defined(CRYPTOPP_WORD128_AVAILABLE) 627 word64 r0,r1,r2,r3,r4,c;
628 word64 d0,d1,d2,d4,d419;
630 r0 = in[0]; r1 = in[1];
631 r2 = in[2]; r3 = in[3];
634 d0 = r0 * 2; d1 = r1 * 2;
639 #if defined(CRYPTOPP_WORD128_AVAILABLE) 640 t[0] = ((word128) r0) * r0 + ((word128) d4) * r1 + (((word128) d2) * (r3 ));
641 t[1] = ((word128) d0) * r1 + ((word128) d4) * r2 + (((word128) r3) * (r3 * 19));
642 t[2] = ((word128) d0) * r2 + ((word128) r1) * r1 + (((word128) d4) * (r3 ));
643 t[3] = ((word128) d0) * r3 + ((word128) d1) * r2 + (((word128) r4) * (d419 ));
644 t[4] = ((word128) d0) * r4 + ((word128) d1) * r3 + (((word128) r2) * (r2 ));
646 mul64x64_128(t[0], r0, r0) mul64x64_128(mul, d4, r1) add128(t[0], mul) mul64x64_128(mul, d2, r3) add128(t[0], mul)
647 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)
648 mul64x64_128(t[2], d0, r2) mul64x64_128(mul, r1, r1) add128(t[2], mul) mul64x64_128(mul, d4, r3) add128(t[2], mul)
649 mul64x64_128(t[3], d0, r3) mul64x64_128(mul, d1, r2) add128(t[3], mul) mul64x64_128(mul, r4, d419) add128(t[3], mul)
650 mul64x64_128(t[4], d0, r4) mul64x64_128(mul, d1, r3) add128(t[4], mul) mul64x64_128(mul, r2, r2) add128(t[4], mul)
653 r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51);
654 add128_64(t[1], c) r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51);
655 add128_64(t[2], c) r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51);
656 add128_64(t[3], c) r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51);
657 add128_64(t[4], c) r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51);
658 r0 += c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51;
661 out[0] = r0; out[1] = r1;
662 out[2] = r2; out[3] = r3;
668 curve25519_expand(bignum25519 out,
const byte *in) {
671 block(x0)(x1)(x2)(x3);
673 out[0] = x0 & reduce_mask_51; x0 = (x0 >> 51) | (x1 << 13);
674 out[1] = x0 & reduce_mask_51; x1 = (x1 >> 38) | (x2 << 26);
675 out[2] = x1 & reduce_mask_51; x2 = (x2 >> 25) | (x3 << 39);
676 out[3] = x2 & reduce_mask_51; x3 = (x3 >> 12);
677 out[4] = x3 & reduce_mask_51;
684 curve25519_contract(byte *out,
const bignum25519 input) {
694 #define curve25519_contract_carry() \ 695 t[1] += t[0] >> 51; t[0] &= reduce_mask_51; \ 696 t[2] += t[1] >> 51; t[1] &= reduce_mask_51; \ 697 t[3] += t[2] >> 51; t[2] &= reduce_mask_51; \ 698 t[4] += t[3] >> 51; t[3] &= reduce_mask_51; 700 #define curve25519_contract_carry_full() curve25519_contract_carry() \ 701 t[0] += 19 * (t[4] >> 51); t[4] &= reduce_mask_51; 703 #define curve25519_contract_carry_final() curve25519_contract_carry() \ 704 t[4] &= reduce_mask_51; 706 curve25519_contract_carry_full()
707 curve25519_contract_carry_full()
712 curve25519_contract_carry_full()
715 t[0] += (reduce_mask_51 + 1) - 19;
716 t[1] += (reduce_mask_51 + 1) - 1;
717 t[2] += (reduce_mask_51 + 1) - 1;
718 t[3] += (reduce_mask_51 + 1) - 1;
719 t[4] += (reduce_mask_51 + 1) - 1;
722 curve25519_contract_carry_final()
724 #define write51full(n,shift) \ 725 f = ((t[n] >> shift) | (t[n+1] << (51 - shift))); \ 726 for (i = 0; i < 8; i++, f >>= 8) *out++ = (byte)f; 727 #define write51(n) write51full(n,13*n) 734 #if !defined(ED25519_GCC_64BIT_CHOOSE) 738 curve25519_move_conditional_bytes(byte out[96],
const byte in[96], word64 flag) {
739 const word64 nb = flag - 1, b = ~nb;
740 const word64 *inq = (
const word64 *)in;
741 word64 *outq = (word64 *)out;
742 outq[0] = (outq[0] & nb) | (inq[0] & b);
743 outq[1] = (outq[1] & nb) | (inq[1] & b);
744 outq[2] = (outq[2] & nb) | (inq[2] & b);
745 outq[3] = (outq[3] & nb) | (inq[3] & b);
746 outq[4] = (outq[4] & nb) | (inq[4] & b);
747 outq[5] = (outq[5] & nb) | (inq[5] & b);
748 outq[6] = (outq[6] & nb) | (inq[6] & b);
749 outq[7] = (outq[7] & nb) | (inq[7] & b);
750 outq[8] = (outq[8] & nb) | (inq[8] & b);
751 outq[9] = (outq[9] & nb) | (inq[9] & b);
752 outq[10] = (outq[10] & nb) | (inq[10] & b);
753 outq[11] = (outq[11] & nb) | (inq[11] & b);
758 curve25519_swap_conditional(bignum25519 a, bignum25519 b, word64 iswap) {
759 const word64 swap = (word64)(-(sword64)iswap);
760 word64 x0,x1,x2,x3,x4;
762 x0 = swap & (a[0] ^ b[0]); a[0] ^= x0; b[0] ^= x0;
763 x1 = swap & (a[1] ^ b[1]); a[1] ^= x1; b[1] ^= x1;
764 x2 = swap & (a[2] ^ b[2]); a[2] ^= x2; b[2] ^= x2;
765 x3 = swap & (a[3] ^ b[3]); a[3] ^= x3; b[3] ^= x3;
766 x4 = swap & (a[4] ^ b[4]); a[4] ^= x4; b[4] ^= x4;
774 ed25519_hash(byte *hash,
const byte *in,
size_t inlen) {
779 ed25519_extsk(hash_512bits extsk,
const byte sk[32]) {
780 ed25519_hash(extsk, sk, 32);
790 while (stream.read((
char*)block.begin(), block.size()))
791 hash.
Update(block, block.size());
793 std::streamsize rem = stream.gcount();
801 ed25519_hram(hash_512bits hram,
const byte RS[64],
const byte pk[32],
const byte *m,
size_t mlen) {
810 ed25519_hram(hash_512bits hram,
const byte RS[64],
const byte pk[32], std::istream& stream) {
814 UpdateFromStream(hash, stream);
818 bignum256modm_element_t
819 lt_modm(bignum256modm_element_t a, bignum256modm_element_t b) {
820 return (a - b) >> 63;
824 reduce256_modm(bignum256modm r) {
826 bignum256modm_element_t b = 0, pb, mask;
830 pb += modm_m[0]; b = lt_modm(r[0], pb); t[0] = (r[0] - pb + (b << 56)); pb = b;
831 pb += modm_m[1]; b = lt_modm(r[1], pb); t[1] = (r[1] - pb + (b << 56)); pb = b;
832 pb += modm_m[2]; b = lt_modm(r[2], pb); t[2] = (r[2] - pb + (b << 56)); pb = b;
833 pb += modm_m[3]; b = lt_modm(r[3], pb); t[3] = (r[3] - pb + (b << 56)); pb = b;
834 pb += modm_m[4]; b = lt_modm(r[4], pb); t[4] = (r[4] - pb + (b << 32));
839 r[0] ^= mask & (r[0] ^ t[0]);
840 r[1] ^= mask & (r[1] ^ t[1]);
841 r[2] ^= mask & (r[2] ^ t[2]);
842 r[3] ^= mask & (r[3] ^ t[3]);
843 r[4] ^= mask & (r[4] ^ t[4]);
847 barrett_reduce256_modm(bignum256modm r,
const bignum256modm q1,
const bignum256modm r1) {
848 bignum256modm q3, r2;
850 bignum256modm_element_t f, b, pb;
855 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);
856 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)
857 f = lo128(c); q3[0] = (f >> 40) & 0xffff; shr128(f, c, 56);
858 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)
859 f = lo128(c); q3[0] |= (f << 16) & 0xffffffffffffff; q3[1] = (f >> 40) & 0xffff; shr128(f, c, 56);
860 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)
861 f = lo128(c); q3[1] |= (f << 16) & 0xffffffffffffff; q3[2] = (f >> 40) & 0xffff; shr128(f, c, 56);
862 mul64x64_128(c, modm_mu[4], q1[3]) add128_64(c, f) mul64x64_128(mul, modm_mu[3], q1[4]) add128(c, mul)
863 f = lo128(c); q3[2] |= (f << 16) & 0xffffffffffffff; q3[3] = (f >> 40) & 0xffff; shr128(f, c, 56);
864 mul64x64_128(c, modm_mu[4], q1[4]) add128_64(c, f)
865 f = lo128(c); q3[3] |= (f << 16) & 0xffffffffffffff; q3[4] = (f >> 40) & 0xffff; shr128(f, c, 56);
868 mul64x64_128(c, modm_m[0], q3[0])
869 r2[0] = lo128(c) & 0xffffffffffffff; shr128(f, c, 56);
870 mul64x64_128(c, modm_m[0], q3[1]) add128_64(c, f) mul64x64_128(mul, modm_m[1], q3[0]) add128(c, mul)
871 r2[1] = lo128(c) & 0xffffffffffffff; shr128(f, c, 56);
872 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)
873 r2[2] = lo128(c) & 0xffffffffffffff; shr128(f, c, 56);
874 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)
875 r2[3] = lo128(c) & 0xffffffffffffff; shr128(f, c, 56);
876 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)
877 r2[4] = lo128(c) & 0x0000ffffffffff;
880 pb += r2[0]; b = lt_modm(r1[0], pb); r[0] = (r1[0] - pb + (b << 56)); pb = b;
881 pb += r2[1]; b = lt_modm(r1[1], pb); r[1] = (r1[1] - pb + (b << 56)); pb = b;
882 pb += r2[2]; b = lt_modm(r1[2], pb); r[2] = (r1[2] - pb + (b << 56)); pb = b;
883 pb += r2[3]; b = lt_modm(r1[3], pb); r[3] = (r1[3] - pb + (b << 56)); pb = b;
884 pb += r2[4]; b = lt_modm(r1[4], pb); r[4] = (r1[4] - pb + (b << 40));
891 add256_modm(bignum256modm r,
const bignum256modm x,
const bignum256modm y) {
892 bignum256modm_element_t c;
894 c = x[0] + y[0]; r[0] = c & 0xffffffffffffff; c >>= 56;
895 c += x[1] + y[1]; r[1] = c & 0xffffffffffffff; c >>= 56;
896 c += x[2] + y[2]; r[2] = c & 0xffffffffffffff; c >>= 56;
897 c += x[3] + y[3]; r[3] = c & 0xffffffffffffff; c >>= 56;
898 c += x[4] + y[4]; r[4] = c;
904 mul256_modm(bignum256modm r,
const bignum256modm x,
const bignum256modm y) {
905 bignum256modm q1, r1;
907 bignum256modm_element_t f;
909 mul64x64_128(c, x[0], y[0])
910 f = lo128(c); r1[0] = f & 0xffffffffffffff; shr128(f, c, 56);
911 mul64x64_128(c, x[0], y[1]) add128_64(c, f) mul64x64_128(mul, x[1], y[0]) add128(c, mul)
912 f = lo128(c); r1[1] = f & 0xffffffffffffff; shr128(f, c, 56);
913 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)
914 f = lo128(c); r1[2] = f & 0xffffffffffffff; shr128(f, c, 56);
915 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)
916 f = lo128(c); r1[3] = f & 0xffffffffffffff; shr128(f, c, 56);
917 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)
918 f = lo128(c); r1[4] = f & 0x0000ffffffffff; q1[0] = (f >> 24) & 0xffffffff; shr128(f, c, 56);
919 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)
920 f = lo128(c); q1[0] |= (f << 32) & 0xffffffffffffff; q1[1] = (f >> 24) & 0xffffffff; shr128(f, c, 56);
921 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)
922 f = lo128(c); q1[1] |= (f << 32) & 0xffffffffffffff; q1[2] = (f >> 24) & 0xffffffff; shr128(f, c, 56);
923 mul64x64_128(c, x[4], y[3]) add128_64(c, f) mul64x64_128(mul, x[3], y[4]) add128(c, mul)
924 f = lo128(c); q1[2] |= (f << 32) & 0xffffffffffffff; q1[3] = (f >> 24) & 0xffffffff; shr128(f, c, 56);
925 mul64x64_128(c, x[4], y[4]) add128_64(c, f)
926 f = lo128(c); q1[3] |= (f << 32) & 0xffffffffffffff; q1[4] = (f >> 24) & 0xffffffff; shr128(f, c, 56);
929 barrett_reduce256_modm(r, q1, r1);
933 expand256_modm(bignum256modm out,
const byte *in,
size_t len) {
935 bignum256modm_element_t x[16];
938 memcpy(work, in, len);
939 x[0] = U8TO64_LE(work + 0);
940 x[1] = U8TO64_LE(work + 8);
941 x[2] = U8TO64_LE(work + 16);
942 x[3] = U8TO64_LE(work + 24);
943 x[4] = U8TO64_LE(work + 32);
944 x[5] = U8TO64_LE(work + 40);
945 x[6] = U8TO64_LE(work + 48);
946 x[7] = U8TO64_LE(work + 56);
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) | (x[ 4] << 32)) & 0x0000ffffffffff;
960 q1[0] = ((x[ 3] >> 56) | (x[ 4] << 8)) & 0xffffffffffffff;
961 q1[1] = ((x[ 4] >> 48) | (x[ 5] << 16)) & 0xffffffffffffff;
962 q1[2] = ((x[ 5] >> 40) | (x[ 6] << 24)) & 0xffffffffffffff;
963 q1[3] = ((x[ 6] >> 32) | (x[ 7] << 32)) & 0xffffffffffffff;
964 q1[4] = ((x[ 7] >> 24) );
966 barrett_reduce256_modm(out, q1, out);
970 expand_raw256_modm(bignum256modm out,
const byte in[32]) {
971 bignum256modm_element_t x[4];
973 x[0] = U8TO64_LE(in + 0);
974 x[1] = U8TO64_LE(in + 8);
975 x[2] = U8TO64_LE(in + 16);
976 x[3] = U8TO64_LE(in + 24);
978 out[0] = ( x[0]) & 0xffffffffffffff;
979 out[1] = ((x[ 0] >> 56) | (x[ 1] << 8)) & 0xffffffffffffff;
980 out[2] = ((x[ 1] >> 48) | (x[ 2] << 16)) & 0xffffffffffffff;
981 out[3] = ((x[ 2] >> 40) | (x[ 3] << 24)) & 0xffffffffffffff;
982 out[4] = ((x[ 3] >> 32) ) & 0x000000ffffffff;
986 contract256_modm(byte out[32],
const bignum256modm in) {
987 U64TO8_LE(out + 0, (in[0] ) | (in[1] << 56));
988 U64TO8_LE(out + 8, (in[1] >> 8) | (in[2] << 48));
989 U64TO8_LE(out + 16, (in[2] >> 16) | (in[3] << 40));
990 U64TO8_LE(out + 24, (in[3] >> 24) | (in[4] << 32));
994 contract256_window4_modm(
signed char r[64],
const bignum256modm in) {
996 signed char *quads = r;
997 bignum256modm_element_t i, j, v, m;
999 for (i = 0; i < 5; i++) {
1001 m = (i == 4) ? 8 : 14;
1002 for (j = 0; j < m; j++) {
1003 *quads++ = (v & 15);
1010 for(i = 0; i < 63; i++) {
1012 r[i+1] += (r[i] >> 4);
1014 carry = (r[i] >> 3);
1015 r[i] -= (carry << 4);
1021 contract256_slidingwindow_modm(
signed char r[256],
const bignum256modm s,
int windowsize) {
1023 int m = (1 << (windowsize - 1)) - 1, soplen = 256;
1024 signed char *bits = r;
1025 bignum256modm_element_t v;
1028 for (i = 0; i < 4; i++) {
1030 for (j = 0; j < 56; j++, v >>= 1)
1034 for (j = 0; j < 32; j++, v >>= 1)
1038 for (j = 0; j < soplen; j++) {
1042 for (b = 1; (b < (soplen - j)) && (b <= 6); b++) {
1043 if ((r[j] + (r[j + b] << b)) <= m) {
1044 r[j] += r[j + b] << b;
1046 }
else if ((r[j] - (r[j + b] << b)) >= -m) {
1047 r[j] -= r[j + b] << b;
1048 for (k = j + b; k < soplen; k++) {
1055 }
else if (r[j + b]) {
1067 curve25519_pow_two5mtwo0_two250mtwo0(bignum25519 b) {
1068 ALIGN(16) bignum25519 t0,c;
1071 curve25519_square_times(t0, b, 5);
1072 curve25519_mul_noinline(b, t0, b);
1073 curve25519_square_times(t0, b, 10);
1074 curve25519_mul_noinline(c, t0, b);
1075 curve25519_square_times(t0, c, 20);
1076 curve25519_mul_noinline(t0, t0, c);
1077 curve25519_square_times(t0, t0, 10);
1078 curve25519_mul_noinline(b, t0, b);
1079 curve25519_square_times(t0, b, 50);
1080 curve25519_mul_noinline(c, t0, b);
1081 curve25519_square_times(t0, c, 100);
1082 curve25519_mul_noinline(t0, t0, c);
1083 curve25519_square_times(t0, t0, 50);
1084 curve25519_mul_noinline(b, t0, b);
1091 curve25519_recip(bignum25519 out, const bignum25519 z) {
1092 ALIGN(16) bignum25519 a,t0,b;
1094 curve25519_square_times(a, z, 1);
1095 curve25519_square_times(t0, a, 2);
1096 curve25519_mul_noinline(b, t0, z);
1097 curve25519_mul_noinline(a, b, a);
1098 curve25519_square_times(t0, a, 1);
1099 curve25519_mul_noinline(b, t0, b);
1100 curve25519_pow_two5mtwo0_two250mtwo0(b);
1101 curve25519_square_times(b, b, 5);
1102 curve25519_mul_noinline(out, b, a);
1109 curve25519_pow_two252m3(bignum25519 two252m3, const bignum25519 z) {
1110 ALIGN(16) bignum25519 b,c,t0;
1112 curve25519_square_times(c, z, 1);
1113 curve25519_square_times(t0, c, 2);
1114 curve25519_mul_noinline(b, t0, z);
1115 curve25519_mul_noinline(c, b, c);
1116 curve25519_square_times(t0, c, 1);
1117 curve25519_mul_noinline(b, t0, b);
1118 curve25519_pow_two5mtwo0_two250mtwo0(b);
1119 curve25519_square_times(b, b, 2);
1120 curve25519_mul_noinline(two252m3, b, z);
1124 ge25519_p1p1_to_partial(ge25519 *r, const ge25519_p1p1 *p) {
1125 curve25519_mul(r->x, p->x, p->t);
1126 curve25519_mul(r->y, p->y, p->z);
1127 curve25519_mul(r->z, p->z, p->t);
1131 ge25519_p1p1_to_full(ge25519 *r,
const ge25519_p1p1 *p) {
1132 curve25519_mul(r->x, p->x, p->t);
1133 curve25519_mul(r->y, p->y, p->z);
1134 curve25519_mul(r->z, p->z, p->t);
1135 curve25519_mul(r->t, p->x, p->y);
1139 ge25519_full_to_pniels(ge25519_pniels *p,
const ge25519 *r) {
1140 curve25519_sub(p->ysubx, r->y, r->x);
1141 curve25519_add(p->xaddy, r->y, r->x);
1142 curve25519_copy(p->z, r->z);
1143 curve25519_mul(p->t2d, r->t, ge25519_ec2d);
1147 ge25519_add_p1p1(ge25519_p1p1 *r,
const ge25519 *p,
const ge25519 *q) {
1148 bignum25519 a,b,c,d,t,u;
1150 curve25519_sub(a, p->y, p->x);
1151 curve25519_add(b, p->y, p->x);
1152 curve25519_sub(t, q->y, q->x);
1153 curve25519_add(u, q->y, q->x);
1154 curve25519_mul(a, a, t);
1155 curve25519_mul(b, b, u);
1156 curve25519_mul(c, p->t, q->t);
1157 curve25519_mul(c, c, ge25519_ec2d);
1158 curve25519_mul(d, p->z, q->z);
1159 curve25519_add(d, d, d);
1160 curve25519_sub(r->x, b, a);
1161 curve25519_add(r->y, b, a);
1162 curve25519_add_after_basic(r->z, d, c);
1163 curve25519_sub_after_basic(r->t, d, c);
1167 ge25519_double_p1p1(ge25519_p1p1 *r,
const ge25519 *p) {
1170 curve25519_square(a, p->x);
1171 curve25519_square(b, p->y);
1172 curve25519_square(c, p->z);
1173 curve25519_add_reduce(c, c, c);
1174 curve25519_add(r->x, p->x, p->y);
1175 curve25519_square(r->x, r->x);
1176 curve25519_add(r->y, b, a);
1177 curve25519_sub(r->z, b, a);
1178 curve25519_sub_after_basic(r->x, r->x, r->y);
1179 curve25519_sub_after_basic(r->t, c, r->z);
1183 ge25519_nielsadd2_p1p1(ge25519_p1p1 *r,
const ge25519 *p,
const ge25519_niels *q, byte signbit) {
1184 const bignum25519 *qb = (
const bignum25519 *)q;
1185 bignum25519 *rb = (bignum25519 *)r;
1188 curve25519_sub(a, p->y, p->x);
1189 curve25519_add(b, p->y, p->x);
1190 curve25519_mul(a, a, qb[signbit]);
1191 curve25519_mul(r->x, b, qb[signbit^1]);
1192 curve25519_add(r->y, r->x, a);
1193 curve25519_sub(r->x, r->x, a);
1194 curve25519_mul(c, p->t, q->t2d);
1195 curve25519_add_reduce(r->t, p->z, p->z);
1196 curve25519_copy(r->z, r->t);
1197 curve25519_add(rb[2+signbit], rb[2+signbit], c);
1198 curve25519_sub(rb[2+(signbit^1)], rb[2+(signbit^1)], c);
1202 ge25519_pnielsadd_p1p1(ge25519_p1p1 *r,
const ge25519 *p,
const ge25519_pniels *q, byte signbit) {
1203 const bignum25519 *qb = (
const bignum25519 *)q;
1204 bignum25519 *rb = (bignum25519 *)r;
1207 curve25519_sub(a, p->y, p->x);
1208 curve25519_add(b, p->y, p->x);
1209 curve25519_mul(a, a, qb[signbit]);
1210 curve25519_mul(r->x, b, qb[signbit^1]);
1211 curve25519_add(r->y, r->x, a);
1212 curve25519_sub(r->x, r->x, a);
1213 curve25519_mul(c, p->t, q->t2d);
1214 curve25519_mul(r->t, p->z, q->z);
1215 curve25519_add_reduce(r->t, r->t, r->t);
1216 curve25519_copy(r->z, r->t);
1217 curve25519_add(rb[2+signbit], rb[2+signbit], c);
1218 curve25519_sub(rb[2+(signbit^1)], rb[2+(signbit^1)], c);
1222 ge25519_double_partial(ge25519 *r,
const ge25519 *p) {
1224 ge25519_double_p1p1(&t, p);
1225 ge25519_p1p1_to_partial(r, &t);
1229 ge25519_double(ge25519 *r,
const ge25519 *p) {
1231 ge25519_double_p1p1(&t, p);
1232 ge25519_p1p1_to_full(r, &t);
1236 ge25519_add(ge25519 *r,
const ge25519 *p,
const ge25519 *q) {
1238 ge25519_add_p1p1(&t, p, q);
1239 ge25519_p1p1_to_full(r, &t);
1243 ge25519_nielsadd2(ge25519 *r,
const ge25519_niels *q) {
1244 bignum25519 a,b,c,e,f,g,h;
1246 curve25519_sub(a, r->y, r->x);
1247 curve25519_add(b, r->y, r->x);
1248 curve25519_mul(a, a, q->ysubx);
1249 curve25519_mul(e, b, q->xaddy);
1250 curve25519_add(h, e, a);
1251 curve25519_sub(e, e, a);
1252 curve25519_mul(c, r->t, q->t2d);
1253 curve25519_add(f, r->z, r->z);
1254 curve25519_add_after_basic(g, f, c);
1255 curve25519_sub_after_basic(f, f, c);
1256 curve25519_mul(r->x, e, f);
1257 curve25519_mul(r->y, h, g);
1258 curve25519_mul(r->z, g, f);
1259 curve25519_mul(r->t, e, h);
1263 ge25519_pnielsadd(ge25519_pniels *r,
const ge25519 *p,
const ge25519_pniels *q) {
1264 bignum25519 a,b,c,x,y,z,t;
1266 curve25519_sub(a, p->y, p->x);
1267 curve25519_add(b, p->y, p->x);
1268 curve25519_mul(a, a, q->ysubx);
1269 curve25519_mul(x, b, q->xaddy);
1270 curve25519_add(y, x, a);
1271 curve25519_sub(x, x, a);
1272 curve25519_mul(c, p->t, q->t2d);
1273 curve25519_mul(t, p->z, q->z);
1274 curve25519_add(t, t, t);
1275 curve25519_add_after_basic(z, t, c);
1276 curve25519_sub_after_basic(t, t, c);
1277 curve25519_mul(r->xaddy, x, t);
1278 curve25519_mul(r->ysubx, y, z);
1279 curve25519_mul(r->z, z, t);
1280 curve25519_mul(r->t2d, x, y);
1281 curve25519_copy(y, r->ysubx);
1282 curve25519_sub(r->ysubx, r->ysubx, r->xaddy);
1283 curve25519_add(r->xaddy, r->xaddy, y);
1284 curve25519_mul(r->t2d, r->t2d, ge25519_ec2d);
1288 ge25519_pack(byte r[32],
const ge25519 *p) {
1289 bignum25519 tx, ty, zi;
1291 curve25519_recip(zi, p->z);
1292 curve25519_mul(tx, p->x, zi);
1293 curve25519_mul(ty, p->y, zi);
1294 curve25519_contract(r, ty);
1295 curve25519_contract(parity, tx);
1296 r[31] ^= ((parity[0] & 1) << 7);
1300 ed25519_verify(
const byte *x,
const byte *y,
size_t len) {
1301 size_t differentbits = 0;
1303 differentbits |= (*x++ ^ *y++);
1304 return (
int) (1 & ((differentbits - 1) >> 8));
1308 ge25519_unpack_negative_vartime(ge25519 *r,
const byte p[32]) {
1309 const byte zero[32] = {0};
1310 const bignum25519 one = {1};
1311 byte parity = p[31] >> 7;
1313 bignum25519 t, root, num, den, d3;
1315 curve25519_expand(r->y, p);
1316 curve25519_copy(r->z, one);
1317 curve25519_square(num, r->y);
1318 curve25519_mul(den, num, ge25519_ecd);
1319 curve25519_sub_reduce(num, num, r->z);
1320 curve25519_add(den, den, r->z);
1324 curve25519_square(t, den);
1325 curve25519_mul(d3, t, den);
1326 curve25519_square(r->x, d3);
1327 curve25519_mul(r->x, r->x, den);
1328 curve25519_mul(r->x, r->x, num);
1329 curve25519_pow_two252m3(r->x, r->x);
1332 curve25519_mul(r->x, r->x, d3);
1333 curve25519_mul(r->x, r->x, num);
1336 curve25519_square(t, r->x);
1337 curve25519_mul(t, t, den);
1338 curve25519_sub_reduce(root, t, num);
1339 curve25519_contract(check, root);
1340 if (!ed25519_verify(check, zero, 32)) {
1341 curve25519_add_reduce(t, t, num);
1342 curve25519_contract(check, t);
1343 if (!ed25519_verify(check, zero, 32))
1345 curve25519_mul(r->x, r->x, ge25519_sqrtneg1);
1348 curve25519_contract(check, r->x);
1349 if ((check[0] & 1) == parity) {
1350 curve25519_copy(t, r->x);
1351 curve25519_neg(r->x, t);
1353 curve25519_mul(r->t, r->x, r->y);
1359 ge25519_double_scalarmult_vartime(ge25519 *r,
const ge25519 *p1,
const bignum256modm s1,
const bignum256modm s2) {
1360 signed char slide1[256], slide2[256];
1361 ge25519_pniels pre1[S1_TABLE_SIZE];
1366 contract256_slidingwindow_modm(slide1, s1, S1_SWINDOWSIZE);
1367 contract256_slidingwindow_modm(slide2, s2, S2_SWINDOWSIZE);
1369 ge25519_double(&d1, p1);
1370 ge25519_full_to_pniels(pre1, p1);
1371 for (i = 0; i < S1_TABLE_SIZE - 1; i++)
1372 ge25519_pnielsadd(&pre1[i+1], &d1, &pre1[i]);
1375 memset(r, 0,
sizeof(ge25519));
1380 while ((i >= 0) && !(slide1[i] | slide2[i]))
1383 for (; i >= 0; i--) {
1384 ge25519_double_p1p1(&t, r);
1387 ge25519_p1p1_to_full(r, &t);
1388 ge25519_pnielsadd_p1p1(&t, r, &pre1[abs(slide1[i]) / 2], (byte)slide1[i] >> 7);
1392 ge25519_p1p1_to_full(r, &t);
1393 ge25519_nielsadd2_p1p1(&t, r, &ge25519_niels_sliding_multiples[abs(slide2[i]) / 2], (byte)slide2[i] >> 7);
1396 ge25519_p1p1_to_partial(r, &t);
1400 #if !defined(HAVE_GE25519_SCALARMULT_BASE_CHOOSE_NIELS) 1403 ge25519_windowb_equal(word32 b, word32 c) {
1404 return ((b ^ c) - 1) >> 31;
1408 ge25519_scalarmult_base_choose_niels(ge25519_niels *t,
const byte table[256][96], word32 pos,
signed char b) {
1410 word32 sign = (word32)((byte)b >> 7);
1411 word32 mask = ~(sign - 1);
1412 word32 u = (b + mask) ^ mask;
1416 byte packed[96] = {0};
1420 for (i = 0; i < 8; i++)
1421 curve25519_move_conditional_bytes(packed, table[(pos * 8) + i], ge25519_windowb_equal(u, i + 1));
1424 curve25519_expand(t->ysubx, packed + 0);
1425 curve25519_expand(t->xaddy, packed + 32);
1426 curve25519_expand(t->t2d , packed + 64);
1429 curve25519_swap_conditional(t->ysubx, t->xaddy, sign);
1430 curve25519_neg(neg, t->t2d);
1431 curve25519_swap_conditional(t->t2d, neg, sign);
1438 ge25519_scalarmult_base_niels(ge25519 *r,
const byte basepoint_table[256][96],
const bignum256modm s) {
1443 contract256_window4_modm(b, s);
1445 ge25519_scalarmult_base_choose_niels(&t, basepoint_table, 0, b[1]);
1446 curve25519_sub_reduce(r->x, t.xaddy, t.ysubx);
1447 curve25519_add_reduce(r->y, t.xaddy, t.ysubx);
1448 memset(r->z, 0,
sizeof(bignum25519));
1449 curve25519_copy(r->t, t.t2d);
1451 for (i = 3; i < 64; i += 2) {
1452 ge25519_scalarmult_base_choose_niels(&t, basepoint_table, i / 2, b[i]);
1453 ge25519_nielsadd2(r, &t);
1455 ge25519_double_partial(r, r);
1456 ge25519_double_partial(r, r);
1457 ge25519_double_partial(r, r);
1458 ge25519_double(r, r);
1459 ge25519_scalarmult_base_choose_niels(&t, basepoint_table, 0, b[0]);
1460 curve25519_mul(t.t2d, t.t2d, ge25519_ecd);
1461 ge25519_nielsadd2(r, &t);
1462 for(i = 2; i < 64; i += 2) {
1463 ge25519_scalarmult_base_choose_niels(&t, basepoint_table, i / 2, b[i]);
1464 ge25519_nielsadd2(r, &t);
1468 ANONYMOUS_NAMESPACE_END
1476 NAMESPACE_BEGIN(Donna)
1478 int curve25519_mult_CXX(byte sharedKey[32],
const byte secretKey[32],
const byte othersKey[32])
1480 using namespace CryptoPP::Donna::X25519;
1483 for (
size_t i = 0;i < 32;++i)
1484 e[i] = secretKey[i];
1485 e[0] &= 0xf8; e[31] &= 0x7f; e[31] |= 0x40;
1487 bignum25519 nqpqx = {1}, nqpqz = {0}, nqz = {1}, nqx;
1488 bignum25519 q, qx, qpqx, qqx, zzz, zmone;
1489 size_t bit, lastbit;
1491 curve25519_expand(q, othersKey);
1492 curve25519_copy(nqx, q);
1499 for (
int i = 253; i >= 2; i--) {
1500 curve25519_add(qx, nqx, nqz);
1501 curve25519_sub(nqz, nqx, nqz);
1502 curve25519_add(qpqx, nqpqx, nqpqz);
1503 curve25519_sub(nqpqz, nqpqx, nqpqz);
1504 curve25519_mul(nqpqx, qpqx, nqz);
1505 curve25519_mul(nqpqz, qx, nqpqz);
1506 curve25519_add(qqx, nqpqx, nqpqz);
1507 curve25519_sub(nqpqz, nqpqx, nqpqz);
1508 curve25519_square(nqpqz, nqpqz);
1509 curve25519_square(nqpqx, qqx);
1510 curve25519_mul(nqpqz, nqpqz, q);
1511 curve25519_square(qx, qx);
1512 curve25519_square(nqz, nqz);
1513 curve25519_mul(nqx, qx, nqz);
1514 curve25519_sub(nqz, qx, nqz);
1515 curve25519_scalar_product(zzz, nqz, 121665);
1516 curve25519_add(zzz, zzz, qx);
1517 curve25519_mul(nqz, nqz, zzz);
1519 bit = (e[i/8] >> (i & 7)) & 1;
1520 curve25519_swap_conditional(nqx, nqpqx, bit ^ lastbit);
1521 curve25519_swap_conditional(nqz, nqpqz, bit ^ lastbit);
1526 for (
int i = 0; i < 3; i++) {
1527 curve25519_add(qx, nqx, nqz);
1528 curve25519_sub(nqz, nqx, nqz);
1529 curve25519_square(qx, qx);
1530 curve25519_square(nqz, nqz);
1531 curve25519_mul(nqx, qx, nqz);
1532 curve25519_sub(nqz, qx, nqz);
1533 curve25519_scalar_product(zzz, nqz, 121665);
1534 curve25519_add(zzz, zzz, qx);
1535 curve25519_mul(nqz, nqz, zzz);
1538 curve25519_recip(zmone, nqz);
1539 curve25519_mul(nqz, nqx, zmone);
1540 curve25519_contract(sharedKey, nqz);
1547 using namespace CryptoPP::Donna::X25519;
1549 #if (CRYPTOPP_CURVE25519_SSE2) 1551 return curve25519_mult_SSE2(publicKey, secretKey, basePoint);
1555 return curve25519_mult_CXX(publicKey, secretKey, basePoint);
1558 int curve25519_mult(byte sharedKey[32],
const byte secretKey[32],
const byte othersKey[32])
1560 #if (CRYPTOPP_CURVE25519_SSE2) 1562 return curve25519_mult_SSE2(sharedKey, secretKey, othersKey);
1566 return curve25519_mult_CXX(sharedKey, secretKey, othersKey);
1575 NAMESPACE_BEGIN(Donna)
1578 ed25519_publickey_CXX(byte publicKey[32],
const byte secretKey[32])
1580 using namespace CryptoPP::Donna::Ed25519;
1583 ALIGN(16) ge25519 A;
1587 ed25519_extsk(extsk, secretKey);
1588 expand256_modm(a, extsk, 32);
1589 ge25519_scalarmult_base_niels(&A, ge25519_niels_base_multiples, a);
1590 ge25519_pack(publicKey, &A);
1598 return ed25519_publickey_CXX(publicKey, secretKey);
1602 ed25519_sign_CXX(std::istream& stream,
const byte sk[32],
const byte pk[32], byte RS[64])
1604 using namespace CryptoPP::Donna::Ed25519;
1606 bignum256modm r, S, a;
1607 ALIGN(16) ge25519 R;
1608 hash_512bits extsk, hashr, hram;
1614 std::streampos where = stream.tellg();
1616 ed25519_extsk(extsk, sk);
1620 hash.Update(extsk + 32, 32);
1621 UpdateFromStream(hash, stream);
1623 expand256_modm(r, hashr, 64);
1626 ge25519_scalarmult_base_niels(&R, ge25519_niels_base_multiples, r);
1627 ge25519_pack(RS, &R);
1631 stream.seekg(where);
1634 ed25519_hram(hram, RS, pk, stream);
1635 expand256_modm(S, hram, 64);
1638 expand256_modm(a, extsk, 32);
1639 mul256_modm(S, S, a);
1642 add256_modm(S, S, r);
1645 contract256_modm(RS + 32, S);
1650 ed25519_sign_CXX(const byte *m,
size_t mlen, const byte sk[32], const byte pk[32], byte RS[64])
1652 using namespace CryptoPP::Donna::Ed25519;
1654 bignum256modm r, S, a;
1655 ALIGN(16) ge25519 R;
1656 hash_512bits extsk, hashr, hram;
1658 ed25519_extsk(extsk, sk);
1662 hash.Update(extsk + 32, 32);
1663 hash.Update(m, mlen);
1665 expand256_modm(r, hashr, 64);
1668 ge25519_scalarmult_base_niels(&R, ge25519_niels_base_multiples, r);
1669 ge25519_pack(RS, &R);
1672 ed25519_hram(hram, RS, pk, m, mlen);
1673 expand256_modm(S, hram, 64);
1676 expand256_modm(a, extsk, 32);
1677 mul256_modm(S, S, a);
1680 add256_modm(S, S, r);
1683 contract256_modm(RS + 32, S);
1688 ed25519_sign(
std::istream& stream, const byte secretKey[32], const byte publicKey[32],
1691 return ed25519_sign_CXX(stream, secretKey, publicKey, signature);
1695 ed25519_sign(
const byte* message,
size_t messageLength,
const byte secretKey[32],
1696 const byte publicKey[32], byte signature[64])
1698 return ed25519_sign_CXX(message, messageLength, secretKey, publicKey, signature);
1702 ed25519_sign_open_CXX(
const byte *m,
size_t mlen,
const byte pk[32],
const byte RS[64]) {
1704 using namespace CryptoPP::Donna::Ed25519;
1706 ALIGN(16) ge25519 R, A;
1708 bignum256modm hram, S;
1711 if ((RS[63] & 224) || !ge25519_unpack_negative_vartime(&A, pk))
1715 ed25519_hram(hash, RS, pk, m, mlen);
1716 expand256_modm(hram, hash, 64);
1719 expand256_modm(S, RS + 32, 32);
1722 ge25519_double_scalarmult_vartime(&R, &A, hram, S);
1723 ge25519_pack(checkR, &R);
1726 return ed25519_verify(RS, checkR, 32) ? 0 : -1;
1730 ed25519_sign_open_CXX(
std::istream& stream, const byte pk[32], const byte RS[64]) {
1732 using namespace CryptoPP::Donna::Ed25519;
1734 ALIGN(16) ge25519 R, A;
1736 bignum256modm hram, S;
1739 if ((RS[63] & 224) || !ge25519_unpack_negative_vartime(&A, pk))
1743 ed25519_hram(hash, RS, pk, stream);
1744 expand256_modm(hram, hash, 64);
1747 expand256_modm(S, RS + 32, 32);
1750 ge25519_double_scalarmult_vartime(&R, &A, hram, S);
1751 ge25519_pack(checkR, &R);
1754 return ed25519_verify(RS, checkR, 32) ? 0 : -1;
1760 return ed25519_sign_open_CXX(stream, publicKey, signature);
1764 ed25519_sign_open(
const byte *message,
size_t messageLength,
const byte publicKey[32],
const byte signature[64])
1766 return ed25519_sign_open_CXX(message, messageLength, publicKey, signature);
1772 #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.