CoCalc -- donna

GitHub Repository: folium-app/Folium
Path: blob/a-new-beginning/SharedDependencies/Sources/cryptopp/donna_64.cpp
² views
1
// donna_64.cpp - written and placed in public domain by Jeffrey Walton
2
//                Crypto++ specific implementation wrapped around Andrew
3
//                Moon's public domain curve25519-donna and ed25519-donna,
4
//                https://github.com/floodyberry/curve25519-donna and
5
//                https://github.com/floodyberry/ed25519-donna.
6

7
// The curve25519 and ed25519 source files multiplex different repos and
8
// architectures using namespaces. The repos are Andrew Moon's
9
// curve25519-donna and ed25519-donna. The architectures are 32-bit, 64-bit
10
// and SSE. For example, 32-bit x25519 uses symbols from Donna::X25519 and
11
// Donna::Arch32.
12

13
// A fair amount of duplication happens below, but we could not directly
14
// use curve25519 for both x25519 and ed25519. A close examination reveals
15
// slight differences in the implementation. For example, look at the
16
// two curve25519_sub functions.
17

18
// If needed, see Moon's commit "Go back to ignoring 256th bit [sic]",
19
// https://github.com/floodyberry/curve25519-donna/commit/57a683d18721a658
20

21
#include "pch.h"
22

23
#include "config.h"
24
#include "donna.h"
25
#include "secblock.h"
26
#include "sha.h"
27
#include "misc.h"
28
#include "cpu.h"
29

30
#include <istream>
31
#include <sstream>
32

33
#if CRYPTOPP_GCC_DIAGNOSTIC_AVAILABLE
34
# pragma GCC diagnostic ignored "-Wunused-function"
35
#endif
36

37
#if CRYPTOPP_MSC_VERSION
38
# pragma warning(disable: 4244)
39
#endif
40

41
// Squash MS LNK4221 and libtool warnings
42
extern const char DONNA64_FNAME[] = __FILE__;
43

44
ANONYMOUS_NAMESPACE_BEGIN
45

46
// Can't use GetAlignmentOf<word64>() because of C++11 and constexpr
47
// Can use 'const unsigned int' because of MSVC 2013
48
#if (CRYPTOPP_BOOL_X86 || CRYPTOPP_BOOL_X32 || CRYPTOPP_BOOL_X64)
49
# define ALIGN_SPEC 16
50
#else
51
# define ALIGN_SPEC 8
52
#endif
53

54
ANONYMOUS_NAMESPACE_END
55

56
#if defined(CRYPTOPP_CURVE25519_64BIT)
57

58
#include "donna_64.h"
59

60
ANONYMOUS_NAMESPACE_BEGIN
61

62
using CryptoPP::byte;
63
using CryptoPP::word64;
64
using CryptoPP::GetWord;
65
using CryptoPP::PutWord;
66
using CryptoPP::LITTLE_ENDIAN_ORDER;
67

68
inline word64 U8TO64_LE(const byte* p)
69
{
70
    return GetWord<word64>(false, LITTLE_ENDIAN_ORDER, p);
71
}
72

73
inline void U64TO8_LE(byte* p, word64 w)
74
{
75
    PutWord(false, LITTLE_ENDIAN_ORDER, p, w);
76
}
77

78
ANONYMOUS_NAMESPACE_END
79

80
NAMESPACE_BEGIN(CryptoPP)
81
NAMESPACE_BEGIN(Donna)
82
NAMESPACE_BEGIN(X25519)
83
ANONYMOUS_NAMESPACE_BEGIN
84

85
using CryptoPP::byte;
86
using CryptoPP::word32;
87
using CryptoPP::sword32;
88
using CryptoPP::word64;
89
using CryptoPP::sword64;
90

91
using CryptoPP::GetBlock;
92
using CryptoPP::LittleEndian;
93

94
// Bring in all the symbols from the 64-bit header
95
using namespace CryptoPP::Donna::Arch64;
96

97
/* out = in */
98
inline void
99
curve25519_copy(bignum25519 out, const bignum25519 in) {
100
    out[0] = in[0]; out[1] = in[1];
101
    out[2] = in[2]; out[3] = in[3];
102
    out[4] = in[4];
103
}
104

105
/* out = a + b */
106
inline void
107
curve25519_add(bignum25519 out, const bignum25519 a, const bignum25519 b) {
108
    out[0] = a[0] + b[0];
109
    out[1] = a[1] + b[1];
110
    out[2] = a[2] + b[2];
111
    out[3] = a[3] + b[3];
112
    out[4] = a[4] + b[4];
113
}
114

115
/* out = a - b */
116
inline void
117
curve25519_sub(bignum25519 out, const bignum25519 a, const bignum25519 b) {
118
    out[0] = a[0] + two54m152 - b[0];
119
    out[1] = a[1] + two54m8 - b[1];
120
    out[2] = a[2] + two54m8 - b[2];
121
    out[3] = a[3] + two54m8 - b[3];
122
    out[4] = a[4] + two54m8 - b[4];
123
}
124

125
/* out = (in * scalar) */
126
inline void
127
curve25519_scalar_product(bignum25519 out, const bignum25519 in, const word64 scalar) {
128
  word128 a;
129
  word64 c;
130

131
#if defined(CRYPTOPP_WORD128_AVAILABLE)
132
    a = ((word128) in[0]) * scalar;     out[0] = (word64)a & reduce_mask_51; c = (word64)(a >> 51);
133
    a = ((word128) in[1]) * scalar + c; out[1] = (word64)a & reduce_mask_51; c = (word64)(a >> 51);
134
    a = ((word128) in[2]) * scalar + c; out[2] = (word64)a & reduce_mask_51; c = (word64)(a >> 51);
135
    a = ((word128) in[3]) * scalar + c; out[3] = (word64)a & reduce_mask_51; c = (word64)(a >> 51);
136
    a = ((word128) in[4]) * scalar + c; out[4] = (word64)a & reduce_mask_51; c = (word64)(a >> 51);
137
                                          out[0] += c * 19;
138
#else
139
    mul64x64_128(a, in[0], scalar)                  out[0] = lo128(a) & reduce_mask_51; shr128(c, a, 51);
140
    mul64x64_128(a, in[1], scalar) add128_64(a, c)  out[1] = lo128(a) & reduce_mask_51; shr128(c, a, 51);
141
    mul64x64_128(a, in[2], scalar) add128_64(a, c)  out[2] = lo128(a) & reduce_mask_51; shr128(c, a, 51);
142
    mul64x64_128(a, in[3], scalar) add128_64(a, c)  out[3] = lo128(a) & reduce_mask_51; shr128(c, a, 51);
143
    mul64x64_128(a, in[4], scalar) add128_64(a, c)  out[4] = lo128(a) & reduce_mask_51; shr128(c, a, 51);
144
                                                    out[0] += c * 19;
145
#endif
146
}
147

148
/* out = a * b */
149
inline void
150
curve25519_mul(bignum25519 out, const bignum25519 a, const bignum25519 b) {
151
#if !defined(CRYPTOPP_WORD128_AVAILABLE)
152
    word128 mul;
153
#endif
154
    word128 t[5];
155
    word64 r0,r1,r2,r3,r4,s0,s1,s2,s3,s4,c;
156

157
    r0 = b[0]; r1 = b[1]; r2 = b[2]; r3 = b[3]; r4 = b[4];
158
    s0 = a[0]; s1 = a[1]; s2 = a[2]; s3 = a[3]; s4 = a[4];
159

160
#if defined(CRYPTOPP_WORD128_AVAILABLE)
161
    t[0]  =  ((word128) r0) * s0;
162
    t[1]  =  ((word128) r0) * s1 + ((word128) r1) * s0;
163
    t[2]  =  ((word128) r0) * s2 + ((word128) r2) * s0 + ((word128) r1) * s1;
164
    t[3]  =  ((word128) r0) * s3 + ((word128) r3) * s0 + ((word128) r1) * s2 + ((word128) r2) * s1;
165
    t[4]  =  ((word128) r0) * s4 + ((word128) r4) * s0 + ((word128) r3) * s1 + ((word128) r1) * s3 + ((word128) r2) * s2;
166
#else
167
    mul64x64_128(t[0], r0, s0)
168
    mul64x64_128(t[1], r0, s1) mul64x64_128(mul, r1, s0) add128(t[1], mul)
169
    mul64x64_128(t[2], r0, s2) mul64x64_128(mul, r2, s0) add128(t[2], mul) mul64x64_128(mul, r1, s1) add128(t[2], mul)
170
    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)
171
    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)
172
#endif
173

174
    r1 *= 19; r2 *= 19; r3 *= 19; r4 *= 19;
175

176
#if defined(CRYPTOPP_WORD128_AVAILABLE)
177
    t[0] += ((word128) r4) * s1 + ((word128) r1) * s4 + ((word128) r2) * s3 + ((word128) r3) * s2;
178
    t[1] += ((word128) r4) * s2 + ((word128) r2) * s4 + ((word128) r3) * s3;
179
    t[2] += ((word128) r4) * s3 + ((word128) r3) * s4;
180
    t[3] += ((word128) r4) * s4;
181
#else
182
    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)
183
    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)
184
    mul64x64_128(mul, r4, s3) add128(t[2], mul) mul64x64_128(mul, r3, s4) add128(t[2], mul)
185
    mul64x64_128(mul, r4, s4) add128(t[3], mul)
186
#endif
187

188
                         r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51);
189
    add128_64(t[1], c)   r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51);
190
    add128_64(t[2], c)   r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51);
191
    add128_64(t[3], c)   r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51);
192
    add128_64(t[4], c)   r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51);
193
    r0 +=   c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51;
194
    r1 +=   c;
195

196
    out[0] = r0; out[1] = r1; out[2] = r2; out[3] = r3; out[4] = r4;
197
}
198

199
/* out = in^(2 * count) */
200
inline void
201
curve25519_square_times(bignum25519 out, const bignum25519 in, word64 count) {
202
#if !defined(CRYPTOPP_WORD128_AVAILABLE)
203
    word128 mul;
204
#endif
205
    word128 t[5];
206
    word64 r0,r1,r2,r3,r4,c;
207
    word64 d0,d1,d2,d4,d419;
208

209
    r0 = in[0]; r1 = in[1]; r2 = in[2]; r3 = in[3]; r4 = in[4];
210

211
    do {
212
        d0 = r0 * 2; d1 = r1 * 2;
213
        d2 = r2 * 2 * 19;
214
        d419 = r4 * 19; d4 = d419 * 2;
215

216
#if defined(CRYPTOPP_WORD128_AVAILABLE)
217
        t[0] = ((word128) r0) * r0 + ((word128) d4) * r1 + (((word128) d2) * (r3     ));
218
        t[1] = ((word128) d0) * r1 + ((word128) d4) * r2 + (((word128) r3) * (r3 * 19));
219
        t[2] = ((word128) d0) * r2 + ((word128) r1) * r1 + (((word128) d4) * (r3     ));
220
        t[3] = ((word128) d0) * r3 + ((word128) d1) * r2 + (((word128) r4) * (d419   ));
221
        t[4] = ((word128) d0) * r4 + ((word128) d1) * r3 + (((word128) r2) * (r2     ));
222
#else
223
        mul64x64_128(t[0], r0, r0) mul64x64_128(mul, d4, r1) add128(t[0], mul) mul64x64_128(mul, d2,      r3) add128(t[0], mul)
224
        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)
225
        mul64x64_128(t[2], d0, r2) mul64x64_128(mul, r1, r1) add128(t[2], mul) mul64x64_128(mul, d4,      r3) add128(t[2], mul)
226
        mul64x64_128(t[3], d0, r3) mul64x64_128(mul, d1, r2) add128(t[3], mul) mul64x64_128(mul, r4,    d419) add128(t[3], mul)
227
        mul64x64_128(t[4], d0, r4) mul64x64_128(mul, d1, r3) add128(t[4], mul) mul64x64_128(mul, r2,      r2) add128(t[4], mul)
228
#endif
229

230
                             r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51);
231
        add128_64(t[1], c)   r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51);
232
        add128_64(t[2], c)   r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51);
233
        add128_64(t[3], c)   r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51);
234
        add128_64(t[4], c)   r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51);
235
        r0 +=   c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51;
236
        r1 +=   c;
237
    } while(--count);
238

239
    out[0] = r0; out[1] = r1; out[2] = r2; out[3] = r3; out[4] = r4;
240
}
241

242
inline void
243
curve25519_square(bignum25519 out, const bignum25519 in) {
244
#if !defined(CRYPTOPP_WORD128_AVAILABLE)
245
    word128 mul;
246
#endif
247
    word128 t[5];
248
    word64 r0,r1,r2,r3,r4,c;
249
    word64 d0,d1,d2,d4,d419;
250

251
    r0 = in[0]; r1 = in[1]; r2 = in[2]; r3 = in[3]; r4 = in[4];
252

253
    d0 = r0 * 2; d1 = r1 * 2;
254
    d2 = r2 * 2 * 19;
255
    d419 = r4 * 19; d4 = d419 * 2;
256

257
#if defined(CRYPTOPP_WORD128_AVAILABLE)
258
    t[0] = ((word128) r0) * r0 + ((word128) d4) * r1 + (((word128) d2) * (r3     ));
259
    t[1] = ((word128) d0) * r1 + ((word128) d4) * r2 + (((word128) r3) * (r3 * 19));
260
    t[2] = ((word128) d0) * r2 + ((word128) r1) * r1 + (((word128) d4) * (r3     ));
261
    t[3] = ((word128) d0) * r3 + ((word128) d1) * r2 + (((word128) r4) * (d419   ));
262
    t[4] = ((word128) d0) * r4 + ((word128) d1) * r3 + (((word128) r2) * (r2     ));
263
#else
264
    mul64x64_128(t[0], r0, r0) mul64x64_128(mul, d4, r1) add128(t[0], mul) mul64x64_128(mul, d2,      r3) add128(t[0], mul)
265
    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)
266
    mul64x64_128(t[2], d0, r2) mul64x64_128(mul, r1, r1) add128(t[2], mul) mul64x64_128(mul, d4,      r3) add128(t[2], mul)
267
    mul64x64_128(t[3], d0, r3) mul64x64_128(mul, d1, r2) add128(t[3], mul) mul64x64_128(mul, r4,    d419) add128(t[3], mul)
268
    mul64x64_128(t[4], d0, r4) mul64x64_128(mul, d1, r3) add128(t[4], mul) mul64x64_128(mul, r2,      r2) add128(t[4], mul)
269
#endif
270

271
                         r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51);
272
    add128_64(t[1], c)   r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51);
273
    add128_64(t[2], c)   r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51);
274
    add128_64(t[3], c)   r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51);
275
    add128_64(t[4], c)   r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51);
276
    r0 +=   c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51;
277
    r1 +=   c;
278

279
    out[0] = r0; out[1] = r1; out[2] = r2; out[3] = r3; out[4] = r4;
280
}
281

282
/* Take a little-endian, 32-byte number and expand it into polynomial form */
283
inline void
284
curve25519_expand(bignum25519 out, const byte *in) {
285
    word64 x0,x1,x2,x3;
286
    GetBlock<word64, LittleEndian> block(in);
287
    block(x0)(x1)(x2)(x3);
288

289
    out[0] = x0 & reduce_mask_51; x0 = (x0 >> 51) | (x1 << 13);
290
    out[1] = x0 & reduce_mask_51; x1 = (x1 >> 38) | (x2 << 26);
291
    out[2] = x1 & reduce_mask_51; x2 = (x2 >> 25) | (x3 << 39);
292
    out[3] = x2 & reduce_mask_51; x3 = (x3 >> 12);
293
    out[4] = x3 & reduce_mask_51; /* ignore the top bit */
294
}
295

296
/* Take a fully reduced polynomial form number and contract it into a
297
 * little-endian, 32-byte array
298
 */
299
inline void
300
curve25519_contract(byte *out, const bignum25519 input) {
301
    word64 t[5];
302
    word64 f, i;
303

304
    t[0] = input[0];
305
    t[1] = input[1];
306
    t[2] = input[2];
307
    t[3] = input[3];
308
    t[4] = input[4];
309

310
    #define curve25519_contract_carry() \
311
        t[1] += t[0] >> 51; t[0] &= reduce_mask_51; \
312
        t[2] += t[1] >> 51; t[1] &= reduce_mask_51; \
313
        t[3] += t[2] >> 51; t[2] &= reduce_mask_51; \
314
        t[4] += t[3] >> 51; t[3] &= reduce_mask_51;
315

316
    #define curve25519_contract_carry_full() curve25519_contract_carry() \
317
        t[0] += 19 * (t[4] >> 51); t[4] &= reduce_mask_51;
318

319
    #define curve25519_contract_carry_final() curve25519_contract_carry() \
320
        t[4] &= reduce_mask_51;
321

322
    curve25519_contract_carry_full()
323
    curve25519_contract_carry_full()
324

325
    /* now t is between 0 and 2^255-1, properly carried. */
326
    /* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */
327
    t[0] += 19;
328
    curve25519_contract_carry_full()
329

330
    /* now between 19 and 2^255-1 in both cases, and offset by 19. */
331
    t[0] += 0x8000000000000 - 19;
332
    t[1] += 0x8000000000000 - 1;
333
    t[2] += 0x8000000000000 - 1;
334
    t[3] += 0x8000000000000 - 1;
335
    t[4] += 0x8000000000000 - 1;
336

337
    /* now between 2^255 and 2^256-20, and offset by 2^255. */
338
    curve25519_contract_carry_final()
339

340
    #define write51full(n,shift) \
341
        f = ((t[n] >> shift) | (t[n+1] << (51 - shift))); \
342
        for (i = 0; i < 8; i++, f >>= 8) *out++ = (byte)f;
343
    #define write51(n) write51full(n,13*n)
344

345
    write51(0)
346
    write51(1)
347
    write51(2)
348
    write51(3)
349

350
    #undef curve25519_contract_carry
351
    #undef curve25519_contract_carry_full
352
    #undef curve25519_contract_carry_final
353
    #undef write51full
354
    #undef write51
355
}
356

357
/*
358
 * Swap the contents of [qx] and [qpx] iff @swap is non-zero
359
 */
360
inline void
361
curve25519_swap_conditional(bignum25519 x, bignum25519 qpx, word64 iswap) {
362
    const word64 swap = (word64)(-(sword64)iswap);
363
    word64 x0,x1,x2,x3,x4;
364

365
    x0 = swap & (x[0] ^ qpx[0]); x[0] ^= x0; qpx[0] ^= x0;
366
    x1 = swap & (x[1] ^ qpx[1]); x[1] ^= x1; qpx[1] ^= x1;
367
    x2 = swap & (x[2] ^ qpx[2]); x[2] ^= x2; qpx[2] ^= x2;
368
    x3 = swap & (x[3] ^ qpx[3]); x[3] ^= x3; qpx[3] ^= x3;
369
    x4 = swap & (x[4] ^ qpx[4]); x[4] ^= x4; qpx[4] ^= x4;
370
}
371

372
/*
373
 * In:  b =   2^5 - 2^0
374
 * Out: b = 2^250 - 2^0
375
 */
376
void
377
curve25519_pow_two5mtwo0_two250mtwo0(bignum25519 b) {
378
    ALIGN(ALIGN_SPEC) bignum25519 t0,c;
379

380
    /* 2^5  - 2^0 */ /* b */
381
    /* 2^10 - 2^5 */ curve25519_square_times(t0, b, 5);
382
    /* 2^10 - 2^0 */ curve25519_mul(b, t0, b);
383
    /* 2^20 - 2^10 */ curve25519_square_times(t0, b, 10);
384
    /* 2^20 - 2^0 */ curve25519_mul(c, t0, b);
385
    /* 2^40 - 2^20 */ curve25519_square_times(t0, c, 20);
386
    /* 2^40 - 2^0 */ curve25519_mul(t0, t0, c);
387
    /* 2^50 - 2^10 */ curve25519_square_times(t0, t0, 10);
388
    /* 2^50 - 2^0 */ curve25519_mul(b, t0, b);
389
    /* 2^100 - 2^50 */ curve25519_square_times(t0, b, 50);
390
    /* 2^100 - 2^0 */ curve25519_mul(c, t0, b);
391
    /* 2^200 - 2^100 */ curve25519_square_times(t0, c, 100);
392
    /* 2^200 - 2^0 */ curve25519_mul(t0, t0, c);
393
    /* 2^250 - 2^50 */ curve25519_square_times(t0, t0, 50);
394
    /* 2^250 - 2^0 */ curve25519_mul(b, t0, b);
395
}
396

397
/*
398
 * z^(p - 2) = z(2^255 - 21)
399
 */
400
void
401
curve25519_recip(bignum25519 out, const bignum25519 z) {
402
    ALIGN(ALIGN_SPEC) bignum25519 a, t0, b;
403

404
    /* 2 */ curve25519_square(a, z); /* a = 2 */
405
    /* 8 */ curve25519_square_times(t0, a, 2);
406
    /* 9 */ curve25519_mul(b, t0, z); /* b = 9 */
407
    /* 11 */ curve25519_mul(a, b, a); /* a = 11 */
408
    /* 22 */ curve25519_square(t0, a);
409
    /* 2^5 - 2^0 = 31 */ curve25519_mul(b, t0, b);
410
    /* 2^250 - 2^0 */ curve25519_pow_two5mtwo0_two250mtwo0(b);
411
    /* 2^255 - 2^5 */ curve25519_square_times(b, b, 5);
412
    /* 2^255 - 21 */  curve25519_mul(out, b, a);
413
}
414

415
ANONYMOUS_NAMESPACE_END
416
NAMESPACE_END  // X25519
417
NAMESPACE_END  // Donna
418
NAMESPACE_END  // CryptoPP
419

420
//******************************* ed25519 *******************************//
421

422
NAMESPACE_BEGIN(CryptoPP)
423
NAMESPACE_BEGIN(Donna)
424
NAMESPACE_BEGIN(Ed25519)
425
ANONYMOUS_NAMESPACE_BEGIN
426

427
using CryptoPP::byte;
428
using CryptoPP::word32;
429
using CryptoPP::sword32;
430
using CryptoPP::word64;
431
using CryptoPP::sword64;
432

433
using CryptoPP::GetBlock;
434
using CryptoPP::LittleEndian;
435

436
using CryptoPP::SHA512;
437

438
// Bring in all the symbols from the 64-bit header
439
using namespace CryptoPP::Donna::Arch64;
440

441
/* out = in */
442
inline void
443
curve25519_copy(bignum25519 out, const bignum25519 in) {
444
    out[0] = in[0]; out[1] = in[1];
445
    out[2] = in[2]; out[3] = in[3];
446
    out[4] = in[4];
447
}
448

449
/* out = a + b */
450
inline void
451
curve25519_add(bignum25519 out, const bignum25519 a, const bignum25519 b) {
452
    out[0] = a[0] + b[0]; out[1] = a[1] + b[1];
453
    out[2] = a[2] + b[2]; out[3] = a[3] + b[3];
454
    out[4] = a[4] + b[4];
455
}
456

457
/* out = a + b, where a and/or b are the result of a basic op (add,sub) */
458
inline void
459
curve25519_add_after_basic(bignum25519 out, const bignum25519 a, const bignum25519 b) {
460
    out[0] = a[0] + b[0]; out[1] = a[1] + b[1];
461
    out[2] = a[2] + b[2]; out[3] = a[3] + b[3];
462
    out[4] = a[4] + b[4];
463
}
464

465
inline void
466
curve25519_add_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) {
467
    word64 c;
468
    out[0] = a[0] + b[0]    ; c = (out[0] >> 51); out[0] &= reduce_mask_51;
469
    out[1] = a[1] + b[1] + c; c = (out[1] >> 51); out[1] &= reduce_mask_51;
470
    out[2] = a[2] + b[2] + c; c = (out[2] >> 51); out[2] &= reduce_mask_51;
471
    out[3] = a[3] + b[3] + c; c = (out[3] >> 51); out[3] &= reduce_mask_51;
472
    out[4] = a[4] + b[4] + c; c = (out[4] >> 51); out[4] &= reduce_mask_51;
473
    out[0] += c * 19;
474
}
475

476
/* out = a - b */
477
inline void
478
curve25519_sub(bignum25519 out, const bignum25519 a, const bignum25519 b) {
479
    out[0] = a[0] + twoP0    - b[0];
480
    out[1] = a[1] + twoP1234 - b[1];
481
    out[2] = a[2] + twoP1234 - b[2];
482
    out[3] = a[3] + twoP1234 - b[3];
483
    out[4] = a[4] + twoP1234 - b[4];
484
}
485

486
/* out = a - b, where a and/or b are the result of a basic op (add,sub) */
487
inline void
488
curve25519_sub_after_basic(bignum25519 out, const bignum25519 a, const bignum25519 b) {
489
    out[0] = a[0] + fourP0    - b[0];
490
    out[1] = a[1] + fourP1234 - b[1];
491
    out[2] = a[2] + fourP1234 - b[2];
492
    out[3] = a[3] + fourP1234 - b[3];
493
    out[4] = a[4] + fourP1234 - b[4];
494
}
495

496
inline void
497
curve25519_sub_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) {
498
    word64 c;
499
    out[0] = a[0] + fourP0    - b[0]    ; c = (out[0] >> 51); out[0] &= reduce_mask_51;
500
    out[1] = a[1] + fourP1234 - b[1] + c; c = (out[1] >> 51); out[1] &= reduce_mask_51;
501
    out[2] = a[2] + fourP1234 - b[2] + c; c = (out[2] >> 51); out[2] &= reduce_mask_51;
502
    out[3] = a[3] + fourP1234 - b[3] + c; c = (out[3] >> 51); out[3] &= reduce_mask_51;
503
    out[4] = a[4] + fourP1234 - b[4] + c; c = (out[4] >> 51); out[4] &= reduce_mask_51;
504
    out[0] += c * 19;
505
}
506

507
/* out = -a */
508
inline void
509
curve25519_neg(bignum25519 out, const bignum25519 a) {
510
    word64 c;
511
    out[0] = twoP0    - a[0]    ; c = (out[0] >> 51); out[0] &= reduce_mask_51;
512
    out[1] = twoP1234 - a[1] + c; c = (out[1] >> 51); out[1] &= reduce_mask_51;
513
    out[2] = twoP1234 - a[2] + c; c = (out[2] >> 51); out[2] &= reduce_mask_51;
514
    out[3] = twoP1234 - a[3] + c; c = (out[3] >> 51); out[3] &= reduce_mask_51;
515
    out[4] = twoP1234 - a[4] + c; c = (out[4] >> 51); out[4] &= reduce_mask_51;
516
    out[0] += c * 19;
517
}
518

519
/* out = a * b */
520
inline void
521
curve25519_mul(bignum25519 out, const bignum25519 in2, const bignum25519 in) {
522
#if !defined(CRYPTOPP_WORD128_AVAILABLE)
523
    word128 mul;
524
#endif
525
    word128 t[5];
526
    word64 r0,r1,r2,r3,r4,s0,s1,s2,s3,s4,c;
527

528
    r0 = in[0]; r1 = in[1];
529
    r2 = in[2]; r3 = in[3];
530
    r4 = in[4];
531

532
    s0 = in2[0]; s1 = in2[1];
533
    s2 = in2[2]; s3 = in2[3];
534
    s4 = in2[4];
535

536
#if defined(CRYPTOPP_WORD128_AVAILABLE)
537
    t[0]  =  ((word128) r0) * s0;
538
    t[1]  =  ((word128) r0) * s1 + ((word128) r1) * s0;
539
    t[2]  =  ((word128) r0) * s2 + ((word128) r2) * s0 + ((word128) r1) * s1;
540
    t[3]  =  ((word128) r0) * s3 + ((word128) r3) * s0 + ((word128) r1) * s2 + ((word128) r2) * s1;
541
    t[4]  =  ((word128) r0) * s4 + ((word128) r4) * s0 + ((word128) r3) * s1 + ((word128) r1) * s3 + ((word128) r2) * s2;
542
#else
543
    mul64x64_128(t[0], r0, s0)
544
    mul64x64_128(t[1], r0, s1) mul64x64_128(mul, r1, s0) add128(t[1], mul)
545
    mul64x64_128(t[2], r0, s2) mul64x64_128(mul, r2, s0) add128(t[2], mul) mul64x64_128(mul, r1, s1) add128(t[2], mul)
546
    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)
547
    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)
548
#endif
549

550
    r1 *= 19; r2 *= 19;
551
    r3 *= 19; r4 *= 19;
552

553
#if defined(CRYPTOPP_WORD128_AVAILABLE)
554
    t[0] += ((word128) r4) * s1 + ((word128) r1) * s4 + ((word128) r2) * s3 + ((word128) r3) * s2;
555
    t[1] += ((word128) r4) * s2 + ((word128) r2) * s4 + ((word128) r3) * s3;
556
    t[2] += ((word128) r4) * s3 + ((word128) r3) * s4;
557
    t[3] += ((word128) r4) * s4;
558
#else
559
    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)
560
    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)
561
    mul64x64_128(mul, r4, s3) add128(t[2], mul) mul64x64_128(mul, r3, s4) add128(t[2], mul)
562
    mul64x64_128(mul, r4, s4) add128(t[3], mul)
563
#endif
564

565
                         r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51);
566
    add128_64(t[1], c)   r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51);
567
    add128_64(t[2], c)   r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51);
568
    add128_64(t[3], c)   r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51);
569
    add128_64(t[4], c)   r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51);
570
    r0 +=   c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51;
571
    r1 +=   c;
572

573
    out[0] = r0; out[1] = r1;
574
    out[2] = r2; out[3] = r3;
575
    out[4] = r4;
576
}
577

578
void
579
curve25519_mul_noinline(bignum25519 out, const bignum25519 in2, const bignum25519 in) {
580
    curve25519_mul(out, in2, in);
581
}
582

583
/* out = in^(2 * count) */
584
void
585
curve25519_square_times(bignum25519 out, const bignum25519 in, word64 count) {
586
#if !defined(CRYPTOPP_WORD128_AVAILABLE)
587
    word128 mul;
588
#endif
589
    word128 t[5];
590
    word64 r0,r1,r2,r3,r4,c;
591
    word64 d0,d1,d2,d4,d419;
592

593
    r0 = in[0]; r1 = in[1];
594
    r2 = in[2]; r3 = in[3];
595
    r4 = in[4];
596

597
    do {
598
        d0 = r0 * 2;
599
        d1 = r1 * 2;
600
        d2 = r2 * 2 * 19;
601
        d419 = r4 * 19;
602
        d4 = d419 * 2;
603

604
#if defined(CRYPTOPP_WORD128_AVAILABLE)
605
        t[0] = ((word128) r0) * r0 + ((word128) d4) * r1 + (((word128) d2) * (r3     ));
606
        t[1] = ((word128) d0) * r1 + ((word128) d4) * r2 + (((word128) r3) * (r3 * 19));
607
        t[2] = ((word128) d0) * r2 + ((word128) r1) * r1 + (((word128) d4) * (r3     ));
608
        t[3] = ((word128) d0) * r3 + ((word128) d1) * r2 + (((word128) r4) * (d419   ));
609
        t[4] = ((word128) d0) * r4 + ((word128) d1) * r3 + (((word128) r2) * (r2     ));
610
#else
611
        mul64x64_128(t[0], r0, r0) mul64x64_128(mul, d4, r1) add128(t[0], mul) mul64x64_128(mul, d2,      r3) add128(t[0], mul)
612
        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)
613
        mul64x64_128(t[2], d0, r2) mul64x64_128(mul, r1, r1) add128(t[2], mul) mul64x64_128(mul, d4,      r3) add128(t[2], mul)
614
        mul64x64_128(t[3], d0, r3) mul64x64_128(mul, d1, r2) add128(t[3], mul) mul64x64_128(mul, r4,    d419) add128(t[3], mul)
615
        mul64x64_128(t[4], d0, r4) mul64x64_128(mul, d1, r3) add128(t[4], mul) mul64x64_128(mul, r2,      r2) add128(t[4], mul)
616
#endif
617

618
        r0 = lo128(t[0]) & reduce_mask_51;
619
        r1 = lo128(t[1]) & reduce_mask_51; shl128(c, t[0], 13); r1 += c;
620
        r2 = lo128(t[2]) & reduce_mask_51; shl128(c, t[1], 13); r2 += c;
621
        r3 = lo128(t[3]) & reduce_mask_51; shl128(c, t[2], 13); r3 += c;
622
        r4 = lo128(t[4]) & reduce_mask_51; shl128(c, t[3], 13); r4 += c;
623
                                           shl128(c, t[4], 13); r0 += c * 19;
624
                       c = r0 >> 51; r0 &= reduce_mask_51;
625
        r1 += c     ;  c = r1 >> 51; r1 &= reduce_mask_51;
626
        r2 += c     ;  c = r2 >> 51; r2 &= reduce_mask_51;
627
        r3 += c     ;  c = r3 >> 51; r3 &= reduce_mask_51;
628
        r4 += c     ;  c = r4 >> 51; r4 &= reduce_mask_51;
629
        r0 += c * 19;
630
    } while(--count);
631

632
    out[0] = r0; out[1] = r1;
633
    out[2] = r2; out[3] = r3;
634
    out[4] = r4;
635
}
636

637
inline void
638
curve25519_square(bignum25519 out, const bignum25519 in) {
639
#if !defined(CRYPTOPP_WORD128_AVAILABLE)
640
    word128 mul;
641
#endif
642
    word128 t[5];
643
    word64 r0,r1,r2,r3,r4,c;
644
    word64 d0,d1,d2,d4,d419;
645

646
    r0 = in[0]; r1 = in[1];
647
    r2 = in[2]; r3 = in[3];
648
    r4 = in[4];
649

650
    d0 = r0 * 2; d1 = r1 * 2;
651
    d2 = r2 * 2 * 19;
652
    d419 = r4 * 19;
653
    d4 = d419 * 2;
654

655
#if defined(CRYPTOPP_WORD128_AVAILABLE)
656
    t[0] = ((word128) r0) * r0 + ((word128) d4) * r1 + (((word128) d2) * (r3     ));
657
    t[1] = ((word128) d0) * r1 + ((word128) d4) * r2 + (((word128) r3) * (r3 * 19));
658
    t[2] = ((word128) d0) * r2 + ((word128) r1) * r1 + (((word128) d4) * (r3     ));
659
    t[3] = ((word128) d0) * r3 + ((word128) d1) * r2 + (((word128) r4) * (d419   ));
660
    t[4] = ((word128) d0) * r4 + ((word128) d1) * r3 + (((word128) r2) * (r2     ));
661
#else
662
    mul64x64_128(t[0], r0, r0) mul64x64_128(mul, d4, r1) add128(t[0], mul) mul64x64_128(mul, d2,      r3) add128(t[0], mul)
663
    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)
664
    mul64x64_128(t[2], d0, r2) mul64x64_128(mul, r1, r1) add128(t[2], mul) mul64x64_128(mul, d4,      r3) add128(t[2], mul)
665
    mul64x64_128(t[3], d0, r3) mul64x64_128(mul, d1, r2) add128(t[3], mul) mul64x64_128(mul, r4,    d419) add128(t[3], mul)
666
    mul64x64_128(t[4], d0, r4) mul64x64_128(mul, d1, r3) add128(t[4], mul) mul64x64_128(mul, r2,      r2) add128(t[4], mul)
667
#endif
668

669
                         r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51);
670
    add128_64(t[1], c)   r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51);
671
    add128_64(t[2], c)   r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51);
672
    add128_64(t[3], c)   r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51);
673
    add128_64(t[4], c)   r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51);
674
    r0 +=   c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51;
675
    r1 +=   c;
676

677
    out[0] = r0; out[1] = r1;
678
    out[2] = r2; out[3] = r3;
679
    out[4] = r4;
680
}
681

682
/* Take a little-endian, 32-byte number and expand it into polynomial form */
683
inline void
684
curve25519_expand(bignum25519 out, const byte *in) {
685
    word64 x0,x1,x2,x3;
686
    GetBlock<word64, LittleEndian> block(in);
687
    block(x0)(x1)(x2)(x3);
688

689
    out[0] = x0 & reduce_mask_51; x0 = (x0 >> 51) | (x1 << 13);
690
    out[1] = x0 & reduce_mask_51; x1 = (x1 >> 38) | (x2 << 26);
691
    out[2] = x1 & reduce_mask_51; x2 = (x2 >> 25) | (x3 << 39);
692
    out[3] = x2 & reduce_mask_51; x3 = (x3 >> 12);
693
    out[4] = x3 & reduce_mask_51;
694
}
695

696
/* Take a fully reduced polynomial form number and contract it into a
697
 * little-endian, 32-byte array
698
 */
699
inline void
700
curve25519_contract(byte *out, const bignum25519 input) {
701
    word64 t[5];
702
    word64 f, i;
703

704
    t[0] = input[0];
705
    t[1] = input[1];
706
    t[2] = input[2];
707
    t[3] = input[3];
708
    t[4] = input[4];
709

710
    #define curve25519_contract_carry() \
711
        t[1] += t[0] >> 51; t[0] &= reduce_mask_51; \
712
        t[2] += t[1] >> 51; t[1] &= reduce_mask_51; \
713
        t[3] += t[2] >> 51; t[2] &= reduce_mask_51; \
714
        t[4] += t[3] >> 51; t[3] &= reduce_mask_51;
715

716
    #define curve25519_contract_carry_full() curve25519_contract_carry() \
717
        t[0] += 19 * (t[4] >> 51); t[4] &= reduce_mask_51;
718

719
    #define curve25519_contract_carry_final() curve25519_contract_carry() \
720
        t[4] &= reduce_mask_51;
721

722
    curve25519_contract_carry_full()
723
    curve25519_contract_carry_full()
724

725
    /* now t is between 0 and 2^255-1, properly carried. */
726
    /* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */
727
    t[0] += 19;
728
    curve25519_contract_carry_full()
729

730
    /* now between 19 and 2^255-1 in both cases, and offset by 19. */
731
    t[0] += (reduce_mask_51 + 1) - 19;
732
    t[1] += (reduce_mask_51 + 1) - 1;
733
    t[2] += (reduce_mask_51 + 1) - 1;
734
    t[3] += (reduce_mask_51 + 1) - 1;
735
    t[4] += (reduce_mask_51 + 1) - 1;
736

737
    /* now between 2^255 and 2^256-20, and offset by 2^255. */
738
    curve25519_contract_carry_final()
739

740
    #define write51full(n,shift) \
741
        f = ((t[n] >> shift) | (t[n+1] << (51 - shift))); \
742
        for (i = 0; i < 8; i++, f >>= 8) *out++ = (byte)f;
743
    #define write51(n) write51full(n,13*n)
744
    write51(0)
745
    write51(1)
746
    write51(2)
747
    write51(3)
748
}
749

750
#if !defined(ED25519_GCC_64BIT_CHOOSE)
751

752
/* out = (flag) ? in : out */
753
inline void
754
curve25519_move_conditional_bytes(byte out[96], const byte in[96], word64 flag)
755
{
756
    // TODO: enable this code path once we can test and benchmark it.
757
    // It is about 24 insns shorter, it avoids punning which may be UB,
758
    // and it is guaranteed constant time.
759
#if defined(__GNUC__) && defined(__x86_64__) && 0
760
    const word32 iter = 96/sizeof(word64);
761
    word64* outq = reinterpret_cast<word64*>(out);
762
    const word64* inq = reinterpret_cast<const word64*>(in);
763
    word64 idx=0, val;
764

765
    __asm__ __volatile__ (
766
        ".att_syntax                         ;\n"
767
        "cmpq     $0, %[flag]                ;\n"  // compare, set ZERO flag
768
        "movq     %[iter], %%rcx             ;\n"  // load iteration count
769
        "1:                                  ;\n"
770
        "  movq     (%[idx],%[out]), %[val]  ;\n"  // val = out[idx]
771
        "  cmovnzq  (%[idx],%[in]), %[val]   ;\n"  // copy in[idx] to val if NZ
772
        "  movq     %[val], (%[idx],%[out])  ;\n"  // out[idx] = val
773
        "  leaq     8(%[idx]), %[idx]        ;\n"  // increment index
774
        "  loopnz   1b                       ;\n"  // does not affect flags
775
        : [out] "+S" (outq), [in] "+D" (inq),
776
          [idx] "+b" (idx), [val] "=r" (val)
777
        : [flag] "g" (flag), [iter] "I" (iter)
778
        : "rcx", "memory", "cc"
779
    );
780
#else
781
    const word64 nb = flag - 1, b = ~nb;
782
    const word64 *inq = (const word64 *)(const void*)in;
783
    word64 *outq = (word64 *)(void *)out;
784
    outq[0] = (outq[0] & nb) | (inq[0] & b);
785
    outq[1] = (outq[1] & nb) | (inq[1] & b);
786
    outq[2] = (outq[2] & nb) | (inq[2] & b);
787
    outq[3] = (outq[3] & nb) | (inq[3] & b);
788
    outq[4] = (outq[4] & nb) | (inq[4] & b);
789
    outq[5] = (outq[5] & nb) | (inq[5] & b);
790
    outq[6] = (outq[6] & nb) | (inq[6] & b);
791
    outq[7] = (outq[7] & nb) | (inq[7] & b);
792
    outq[8] = (outq[8] & nb) | (inq[8] & b);
793
    outq[9] = (outq[9] & nb) | (inq[9] & b);
794
    outq[10] = (outq[10] & nb) | (inq[10] & b);
795
    outq[11] = (outq[11] & nb) | (inq[11] & b);
796
#endif
797
}
798

799
/* if (iswap) swap(a, b) */
800
inline void
801
curve25519_swap_conditional(bignum25519 a, bignum25519 b, word64 iswap) {
802
    const word64 swap = (word64)(-(sword64)iswap);
803
    word64 x0,x1,x2,x3,x4;
804

805
    x0 = swap & (a[0] ^ b[0]); a[0] ^= x0; b[0] ^= x0;
806
    x1 = swap & (a[1] ^ b[1]); a[1] ^= x1; b[1] ^= x1;
807
    x2 = swap & (a[2] ^ b[2]); a[2] ^= x2; b[2] ^= x2;
808
    x3 = swap & (a[3] ^ b[3]); a[3] ^= x3; b[3] ^= x3;
809
    x4 = swap & (a[4] ^ b[4]); a[4] ^= x4; b[4] ^= x4;
810
}
811

812
#endif /* ED25519_GCC_64BIT_CHOOSE */
813

814
// ************************************************************************************
815

816
inline void
817
ed25519_hash(byte *hash, const byte *in, size_t inlen) {
818
    SHA512().CalculateDigest(hash, in, inlen);
819
}
820

821
inline void
822
ed25519_extsk(hash_512bits extsk, const byte sk[32]) {
823
    ed25519_hash(extsk, sk, 32);
824
    extsk[0] &= 248;
825
    extsk[31] &= 127;
826
    extsk[31] |= 64;
827
}
828

829
void
830
UpdateFromStream(HashTransformation& hash, std::istream& stream)
831
{
832
    SecByteBlock block(4096);
833
    while (stream.read((char*)block.begin(), block.size()))
834
        hash.Update(block, block.size());
835

836
    std::streamsize rem = stream.gcount();
837
    if (rem)
838
        hash.Update(block, rem);
839

840
    block.SetMark(0);
841
}
842

843
void
844
ed25519_hram(hash_512bits hram, const byte RS[64], const byte pk[32], const byte *m, size_t mlen) {
845
    SHA512 hash;
846
    hash.Update(RS, 32);
847
    hash.Update(pk, 32);
848
    hash.Update(m, mlen);
849
    hash.Final(hram);
850
}
851

852
void
853
ed25519_hram(hash_512bits hram, const byte RS[64], const byte pk[32], std::istream& stream) {
854
    SHA512 hash;
855
    hash.Update(RS, 32);
856
    hash.Update(pk, 32);
857
    UpdateFromStream(hash, stream);
858
    hash.Final(hram);
859
}
860

861
bignum256modm_element_t
862
lt_modm(bignum256modm_element_t a, bignum256modm_element_t b) {
863
    return (a - b) >> 63;
864
}
865

866
void
867
reduce256_modm(bignum256modm r) {
868
    bignum256modm t;
869
    bignum256modm_element_t b = 0, pb, mask;
870

871
    /* t = r - m */
872
    pb = 0;
873
    pb += modm_m[0]; b = lt_modm(r[0], pb); t[0] = (r[0] - pb + (b << 56)); pb = b;
874
    pb += modm_m[1]; b = lt_modm(r[1], pb); t[1] = (r[1] - pb + (b << 56)); pb = b;
875
    pb += modm_m[2]; b = lt_modm(r[2], pb); t[2] = (r[2] - pb + (b << 56)); pb = b;
876
    pb += modm_m[3]; b = lt_modm(r[3], pb); t[3] = (r[3] - pb + (b << 56)); pb = b;
877
    pb += modm_m[4]; b = lt_modm(r[4], pb); t[4] = (r[4] - pb + (b << 32));
878

879
    /* keep r if r was smaller than m */
880
    mask = b - 1;
881

882
    r[0] ^= mask & (r[0] ^ t[0]);
883
    r[1] ^= mask & (r[1] ^ t[1]);
884
    r[2] ^= mask & (r[2] ^ t[2]);
885
    r[3] ^= mask & (r[3] ^ t[3]);
886
    r[4] ^= mask & (r[4] ^ t[4]);
887
}
888

889
void
890
barrett_reduce256_modm(bignum256modm r, const bignum256modm q1, const bignum256modm r1) {
891
    bignum256modm q3, r2;
892
    word128 c, mul;
893
    bignum256modm_element_t f, b, pb;
894

895
    /* q1 = x >> 248 = 264 bits = 5 56 bit elements
896
    q2 = mu * q1
897
    q3 = (q2 / 256(32+1)) = q2 / (2^8)^(32+1) = q2 >> 264 */
898
    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);
899
    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)
900
    f = lo128(c); q3[0] = (f >> 40) & 0xffff; shr128(f, c, 56);
901
    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)
902
    f = lo128(c); q3[0] |= (f << 16) & 0xffffffffffffff; q3[1] = (f >> 40) & 0xffff; shr128(f, c, 56);
903
    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)
904
    f = lo128(c); q3[1] |= (f << 16) & 0xffffffffffffff; q3[2] = (f >> 40) & 0xffff; shr128(f, c, 56);
905
    mul64x64_128(c, modm_mu[4], q1[3]) add128_64(c, f) mul64x64_128(mul, modm_mu[3], q1[4]) add128(c, mul)
906
    f = lo128(c); q3[2] |= (f << 16) & 0xffffffffffffff; q3[3] = (f >> 40) & 0xffff; shr128(f, c, 56);
907
    mul64x64_128(c, modm_mu[4], q1[4]) add128_64(c, f)
908
    f = lo128(c); q3[3] |= (f << 16) & 0xffffffffffffff; q3[4] = (f >> 40) & 0xffff; shr128(f, c, 56);
909
    q3[4] |= (f << 16);
910

911
    mul64x64_128(c, modm_m[0], q3[0])
912
    r2[0] = lo128(c) & 0xffffffffffffff; shr128(f, c, 56);
913
    mul64x64_128(c, modm_m[0], q3[1]) add128_64(c, f) mul64x64_128(mul, modm_m[1], q3[0]) add128(c, mul)
914
    r2[1] = lo128(c) & 0xffffffffffffff; shr128(f, c, 56);
915
    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)
916
    r2[2] = lo128(c) & 0xffffffffffffff; shr128(f, c, 56);
917
    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)
918
    r2[3] = lo128(c) & 0xffffffffffffff; shr128(f, c, 56);
919
    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)
920
    r2[4] = lo128(c) & 0x0000ffffffffff;
921

922
    pb = 0;
923
    pb += r2[0]; b = lt_modm(r1[0], pb); r[0] = (r1[0] - pb + (b << 56)); pb = b;
924
    pb += r2[1]; b = lt_modm(r1[1], pb); r[1] = (r1[1] - pb + (b << 56)); pb = b;
925
    pb += r2[2]; b = lt_modm(r1[2], pb); r[2] = (r1[2] - pb + (b << 56)); pb = b;
926
    pb += r2[3]; b = lt_modm(r1[3], pb); r[3] = (r1[3] - pb + (b << 56)); pb = b;
927
    pb += r2[4]; b = lt_modm(r1[4], pb); r[4] = (r1[4] - pb + (b << 40));
928

929
    reduce256_modm(r);
930
    reduce256_modm(r);
931
}
932

933
void
934
add256_modm(bignum256modm r, const bignum256modm x, const bignum256modm y) {
935
    bignum256modm_element_t c;
936

937
    c  = x[0] + y[0]; r[0] = c & 0xffffffffffffff; c >>= 56;
938
    c += x[1] + y[1]; r[1] = c & 0xffffffffffffff; c >>= 56;
939
    c += x[2] + y[2]; r[2] = c & 0xffffffffffffff; c >>= 56;
940
    c += x[3] + y[3]; r[3] = c & 0xffffffffffffff; c >>= 56;
941
    c += x[4] + y[4]; r[4] = c;
942

943
    reduce256_modm(r);
944
}
945

946
void
947
mul256_modm(bignum256modm r, const bignum256modm x, const bignum256modm y) {
948
    bignum256modm q1, r1;
949
    word128 c, mul;
950
    bignum256modm_element_t f;
951

952
    mul64x64_128(c, x[0], y[0])
953
    f = lo128(c); r1[0] = f & 0xffffffffffffff; shr128(f, c, 56);
954
    mul64x64_128(c, x[0], y[1]) add128_64(c, f) mul64x64_128(mul, x[1], y[0]) add128(c, mul)
955
    f = lo128(c); r1[1] = f & 0xffffffffffffff; shr128(f, c, 56);
956
    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)
957
    f = lo128(c); r1[2] = f & 0xffffffffffffff; shr128(f, c, 56);
958
    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)
959
    f = lo128(c); r1[3] = f & 0xffffffffffffff; shr128(f, c, 56);
960
    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)
961
    f = lo128(c); r1[4] = f & 0x0000ffffffffff; q1[0] = (f >> 24) & 0xffffffff; shr128(f, c, 56);
962
    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)
963
    f = lo128(c); q1[0] |= (f << 32) & 0xffffffffffffff; q1[1] = (f >> 24) & 0xffffffff; shr128(f, c, 56);
964
    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)
965
    f = lo128(c); q1[1] |= (f << 32) & 0xffffffffffffff; q1[2] = (f >> 24) & 0xffffffff; shr128(f, c, 56);
966
    mul64x64_128(c, x[4], y[3]) add128_64(c, f) mul64x64_128(mul, x[3], y[4]) add128(c, mul)
967
    f = lo128(c); q1[2] |= (f << 32) & 0xffffffffffffff; q1[3] = (f >> 24) & 0xffffffff; shr128(f, c, 56);
968
    mul64x64_128(c, x[4], y[4]) add128_64(c, f)
969
    f = lo128(c); q1[3] |= (f << 32) & 0xffffffffffffff; q1[4] = (f >> 24) & 0xffffffff; shr128(f, c, 56);
970
    q1[4] |= (f << 32);
971

972
    barrett_reduce256_modm(r, q1, r1);
973
}
974

975
void
976
expand256_modm(bignum256modm out, const byte *in, size_t len) {
977
    byte work[64] = {0};
978
    bignum256modm_element_t x[16];
979
    bignum256modm q1;
980

981
    std::memcpy(work, in, len);
982
    x[0] = U8TO64_LE(work +  0);
983
    x[1] = U8TO64_LE(work +  8);
984
    x[2] = U8TO64_LE(work + 16);
985
    x[3] = U8TO64_LE(work + 24);
986
    x[4] = U8TO64_LE(work + 32);
987
    x[5] = U8TO64_LE(work + 40);
988
    x[6] = U8TO64_LE(work + 48);
989
    x[7] = U8TO64_LE(work + 56);
990

991
    /* r1 = (x mod 256^(32+1)) = x mod (2^8)(31+1) = x & ((1 << 264) - 1) */
992
    out[0] = (                         x[0]) & 0xffffffffffffff;
993
    out[1] = ((x[ 0] >> 56) | (x[ 1] <<  8)) & 0xffffffffffffff;
994
    out[2] = ((x[ 1] >> 48) | (x[ 2] << 16)) & 0xffffffffffffff;
995
    out[3] = ((x[ 2] >> 40) | (x[ 3] << 24)) & 0xffffffffffffff;
996
    out[4] = ((x[ 3] >> 32) | (x[ 4] << 32)) & 0x0000ffffffffff;
997

998
    /* under 252 bits, no need to reduce */
999
    if (len < 32)
1000
        return;
1001

1002
    /* q1 = x >> 248 = 264 bits */
1003
    q1[0] = ((x[ 3] >> 56) | (x[ 4] <<  8)) & 0xffffffffffffff;
1004
    q1[1] = ((x[ 4] >> 48) | (x[ 5] << 16)) & 0xffffffffffffff;
1005
    q1[2] = ((x[ 5] >> 40) | (x[ 6] << 24)) & 0xffffffffffffff;
1006
    q1[3] = ((x[ 6] >> 32) | (x[ 7] << 32)) & 0xffffffffffffff;
1007
    q1[4] = ((x[ 7] >> 24)                );
1008

1009
    barrett_reduce256_modm(out, q1, out);
1010
}
1011

1012
void
1013
expand_raw256_modm(bignum256modm out, const byte in[32]) {
1014
    bignum256modm_element_t x[4];
1015

1016
    x[0] = U8TO64_LE(in +  0);
1017
    x[1] = U8TO64_LE(in +  8);
1018
    x[2] = U8TO64_LE(in + 16);
1019
    x[3] = U8TO64_LE(in + 24);
1020

1021
    out[0] = (                         x[0]) & 0xffffffffffffff;
1022
    out[1] = ((x[ 0] >> 56) | (x[ 1] <<  8)) & 0xffffffffffffff;
1023
    out[2] = ((x[ 1] >> 48) | (x[ 2] << 16)) & 0xffffffffffffff;
1024
    out[3] = ((x[ 2] >> 40) | (x[ 3] << 24)) & 0xffffffffffffff;
1025
    out[4] = ((x[ 3] >> 32)                ) & 0x000000ffffffff;
1026
}
1027

1028
void
1029
contract256_modm(byte out[32], const bignum256modm in) {
1030
    U64TO8_LE(out +  0, (in[0]      ) | (in[1] << 56));
1031
    U64TO8_LE(out +  8, (in[1] >>  8) | (in[2] << 48));
1032
    U64TO8_LE(out + 16, (in[2] >> 16) | (in[3] << 40));
1033
    U64TO8_LE(out + 24, (in[3] >> 24) | (in[4] << 32));
1034
}
1035

1036
void
1037
contract256_window4_modm(signed char r[64], const bignum256modm in) {
1038
    char carry;
1039
    signed char *quads = r;
1040
    bignum256modm_element_t i, j, v, m;
1041

1042
    for (i = 0; i < 5; i++) {
1043
        v = in[i];
1044
        m = (i == 4) ? 8 : 14;
1045
        for (j = 0; j < m; j++) {
1046
            *quads++ = (v & 15);
1047
            v >>= 4;
1048
        }
1049
    }
1050

1051
    /* making it signed */
1052
    carry = 0;
1053
    for(i = 0; i < 63; i++) {
1054
        r[i] += carry;
1055
        r[i+1] += (r[i] >> 4);
1056
        r[i] &= 15;
1057
        carry = (r[i] >> 3);
1058
        r[i] -= (carry << 4);
1059
    }
1060
    r[63] += carry;
1061
}
1062

1063
void
1064
contract256_slidingwindow_modm(signed char r[256], const bignum256modm s, int windowsize) {
1065
    int i,j,k,b;
1066
    int m = (1 << (windowsize - 1)) - 1, soplen = 256;
1067
    signed char *bits = r;
1068
    bignum256modm_element_t v;
1069

1070
    /* first put the binary expansion into r  */
1071
    for (i = 0; i < 4; i++) {
1072
        v = s[i];
1073
        for (j = 0; j < 56; j++, v >>= 1)
1074
            *bits++ = (v & 1);
1075
    }
1076
    v = s[4];
1077
    for (j = 0; j < 32; j++, v >>= 1)
1078
        *bits++ = (v & 1);
1079

1080
    /* Making it sliding window */
1081
    for (j = 0; j < soplen; j++) {
1082
        if (!r[j])
1083
            continue;
1084

1085
        for (b = 1; (b < (soplen - j)) && (b <= 6); b++) {
1086
            if ((r[j] + (r[j + b] << b)) <= m) {
1087
                r[j] += r[j + b] << b;
1088
                r[j + b] = 0;
1089
            } else if ((r[j] - (r[j + b] << b)) >= -m) {
1090
                r[j] -= r[j + b] << b;
1091
                for (k = j + b; k < soplen; k++) {
1092
                    if (!r[k]) {
1093
                        r[k] = 1;
1094
                        break;
1095
                    }
1096
                    r[k] = 0;
1097
                }
1098
            } else if (r[j + b]) {
1099
                break;
1100
            }
1101
        }
1102
    }
1103
}
1104

1105
/*
1106
 * In:  b =   2^5 - 2^0
1107
 * Out: b = 2^250 - 2^0
1108
 */
1109
void
1110
curve25519_pow_two5mtwo0_two250mtwo0(bignum25519 b) {
1111
    ALIGN(ALIGN_SPEC) bignum25519 t0,c;
1112

1113
    /* 2^5  - 2^0 */ /* b */
1114
    /* 2^10 - 2^5 */ curve25519_square_times(t0, b, 5);
1115
    /* 2^10 - 2^0 */ curve25519_mul_noinline(b, t0, b);
1116
    /* 2^20 - 2^10 */ curve25519_square_times(t0, b, 10);
1117
    /* 2^20 - 2^0 */ curve25519_mul_noinline(c, t0, b);
1118
    /* 2^40 - 2^20 */ curve25519_square_times(t0, c, 20);
1119
    /* 2^40 - 2^0 */ curve25519_mul_noinline(t0, t0, c);
1120
    /* 2^50 - 2^10 */ curve25519_square_times(t0, t0, 10);
1121
    /* 2^50 - 2^0 */ curve25519_mul_noinline(b, t0, b);
1122
    /* 2^100 - 2^50 */ curve25519_square_times(t0, b, 50);
1123
    /* 2^100 - 2^0 */ curve25519_mul_noinline(c, t0, b);
1124
    /* 2^200 - 2^100 */ curve25519_square_times(t0, c, 100);
1125
    /* 2^200 - 2^0 */ curve25519_mul_noinline(t0, t0, c);
1126
    /* 2^250 - 2^50 */ curve25519_square_times(t0, t0, 50);
1127
    /* 2^250 - 2^0 */ curve25519_mul_noinline(b, t0, b);
1128
}
1129

1130
/*
1131
 * z^(p - 2) = z(2^255 - 21)
1132
 */
1133
void
1134
curve25519_recip(bignum25519 out, const bignum25519 z) {
1135
    ALIGN(ALIGN_SPEC) bignum25519 a,t0,b;
1136

1137
    /* 2 */ curve25519_square_times(a, z, 1); /* a = 2 */
1138
    /* 8 */ curve25519_square_times(t0, a, 2);
1139
    /* 9 */ curve25519_mul_noinline(b, t0, z); /* b = 9 */
1140
    /* 11 */ curve25519_mul_noinline(a, b, a); /* a = 11 */
1141
    /* 22 */ curve25519_square_times(t0, a, 1);
1142
    /* 2^5 - 2^0 = 31 */ curve25519_mul_noinline(b, t0, b);
1143
    /* 2^250 - 2^0 */ curve25519_pow_two5mtwo0_two250mtwo0(b);
1144
    /* 2^255 - 2^5 */ curve25519_square_times(b, b, 5);
1145
    /* 2^255 - 21 */ curve25519_mul_noinline(out, b, a);
1146
}
1147

1148
/*
1149
 * z^((p-5)/8) = z^(2^252 - 3)
1150
 */
1151
void
1152
curve25519_pow_two252m3(bignum25519 two252m3, const bignum25519 z) {
1153
    ALIGN(ALIGN_SPEC) bignum25519 b,c,t0;
1154

1155
    /* 2 */ curve25519_square_times(c, z, 1); /* c = 2 */
1156
    /* 8 */ curve25519_square_times(t0, c, 2); /* t0 = 8 */
1157
    /* 9 */ curve25519_mul_noinline(b, t0, z); /* b = 9 */
1158
    /* 11 */ curve25519_mul_noinline(c, b, c); /* c = 11 */
1159
    /* 22 */ curve25519_square_times(t0, c, 1);
1160
    /* 2^5 - 2^0 = 31 */ curve25519_mul_noinline(b, t0, b);
1161
    /* 2^250 - 2^0 */ curve25519_pow_two5mtwo0_two250mtwo0(b);
1162
    /* 2^252 - 2^2 */ curve25519_square_times(b, b, 2);
1163
    /* 2^252 - 3 */ curve25519_mul_noinline(two252m3, b, z);
1164
}
1165

1166
inline void
1167
ge25519_p1p1_to_partial(ge25519 *r, const ge25519_p1p1 *p) {
1168
    curve25519_mul(r->x, p->x, p->t);
1169
    curve25519_mul(r->y, p->y, p->z);
1170
    curve25519_mul(r->z, p->z, p->t);
1171
}
1172

1173
inline void
1174
ge25519_p1p1_to_full(ge25519 *r, const ge25519_p1p1 *p) {
1175
    curve25519_mul(r->x, p->x, p->t);
1176
    curve25519_mul(r->y, p->y, p->z);
1177
    curve25519_mul(r->z, p->z, p->t);
1178
    curve25519_mul(r->t, p->x, p->y);
1179
}
1180

1181
void
1182
ge25519_full_to_pniels(ge25519_pniels *p, const ge25519 *r) {
1183
    curve25519_sub(p->ysubx, r->y, r->x);
1184
    curve25519_add(p->xaddy, r->y, r->x);
1185
    curve25519_copy(p->z, r->z);
1186
    curve25519_mul(p->t2d, r->t, ge25519_ec2d);
1187
}
1188

1189
void
1190
ge25519_add_p1p1(ge25519_p1p1 *r, const ge25519 *p, const ge25519 *q) {
1191
    bignum25519 a,b,c,d,t,u;
1192

1193
    curve25519_sub(a, p->y, p->x);
1194
    curve25519_add(b, p->y, p->x);
1195
    curve25519_sub(t, q->y, q->x);
1196
    curve25519_add(u, q->y, q->x);
1197
    curve25519_mul(a, a, t);
1198
    curve25519_mul(b, b, u);
1199
    curve25519_mul(c, p->t, q->t);
1200
    curve25519_mul(c, c, ge25519_ec2d);
1201
    curve25519_mul(d, p->z, q->z);
1202
    curve25519_add(d, d, d);
1203
    curve25519_sub(r->x, b, a);
1204
    curve25519_add(r->y, b, a);
1205
    curve25519_add_after_basic(r->z, d, c);
1206
    curve25519_sub_after_basic(r->t, d, c);
1207
}
1208

1209
void
1210
ge25519_double_p1p1(ge25519_p1p1 *r, const ge25519 *p) {
1211
    bignum25519 a,b,c;
1212

1213
    curve25519_square(a, p->x);
1214
    curve25519_square(b, p->y);
1215
    curve25519_square(c, p->z);
1216
    curve25519_add_reduce(c, c, c);
1217
    curve25519_add(r->x, p->x, p->y);
1218
    curve25519_square(r->x, r->x);
1219
    curve25519_add(r->y, b, a);
1220
    curve25519_sub(r->z, b, a);
1221
    curve25519_sub_after_basic(r->x, r->x, r->y);
1222
    curve25519_sub_after_basic(r->t, c, r->z);
1223
}
1224

1225
void
1226
ge25519_nielsadd2_p1p1(ge25519_p1p1 *r, const ge25519 *p, const ge25519_niels *q, byte signbit) {
1227
    const bignum25519 *qb = (const bignum25519 *)q;
1228
    bignum25519 *rb = (bignum25519 *)r;
1229
    bignum25519 a,b,c;
1230

1231
    curve25519_sub(a, p->y, p->x);
1232
    curve25519_add(b, p->y, p->x);
1233
    curve25519_mul(a, a, qb[signbit]); /* x for +, y for - */
1234
    curve25519_mul(r->x, b, qb[signbit^1]); /* y for +, x for - */
1235
    curve25519_add(r->y, r->x, a);
1236
    curve25519_sub(r->x, r->x, a);
1237
    curve25519_mul(c, p->t, q->t2d);
1238
    curve25519_add_reduce(r->t, p->z, p->z);
1239
    curve25519_copy(r->z, r->t);
1240
    curve25519_add(rb[2+signbit], rb[2+signbit], c); /* z for +, t for - */
1241
    curve25519_sub(rb[2+(signbit^1)], rb[2+(signbit^1)], c); /* t for +, z for - */
1242
}
1243

1244
void
1245
ge25519_pnielsadd_p1p1(ge25519_p1p1 *r, const ge25519 *p, const ge25519_pniels *q, byte signbit) {
1246
    const bignum25519 *qb = (const bignum25519 *)q;
1247
    bignum25519 *rb = (bignum25519 *)r;
1248
    bignum25519 a,b,c;
1249

1250
    curve25519_sub(a, p->y, p->x);
1251
    curve25519_add(b, p->y, p->x);
1252
    curve25519_mul(a, a, qb[signbit]); /* ysubx for +, xaddy for - */
1253
    curve25519_mul(r->x, b, qb[signbit^1]); /* xaddy for +, ysubx for - */
1254
    curve25519_add(r->y, r->x, a);
1255
    curve25519_sub(r->x, r->x, a);
1256
    curve25519_mul(c, p->t, q->t2d);
1257
    curve25519_mul(r->t, p->z, q->z);
1258
    curve25519_add_reduce(r->t, r->t, r->t);
1259
    curve25519_copy(r->z, r->t);
1260
    curve25519_add(rb[2+signbit], rb[2+signbit], c); /* z for +, t for - */
1261
    curve25519_sub(rb[2+(signbit^1)], rb[2+(signbit^1)], c); /* t for +, z for - */
1262
}
1263

1264
void
1265
ge25519_double_partial(ge25519 *r, const ge25519 *p) {
1266
    ge25519_p1p1 t;
1267
    ge25519_double_p1p1(&t, p);
1268
    ge25519_p1p1_to_partial(r, &t);
1269
}
1270

1271
void
1272
ge25519_double(ge25519 *r, const ge25519 *p) {
1273
    ge25519_p1p1 t;
1274
    ge25519_double_p1p1(&t, p);
1275
    ge25519_p1p1_to_full(r, &t);
1276
}
1277

1278
void
1279
ge25519_add(ge25519 *r, const ge25519 *p,  const ge25519 *q) {
1280
    ge25519_p1p1 t;
1281
    ge25519_add_p1p1(&t, p, q);
1282
    ge25519_p1p1_to_full(r, &t);
1283
}
1284

1285
void
1286
ge25519_nielsadd2(ge25519 *r, const ge25519_niels *q) {
1287
    bignum25519 a,b,c,e,f,g,h;
1288

1289
    curve25519_sub(a, r->y, r->x);
1290
    curve25519_add(b, r->y, r->x);
1291
    curve25519_mul(a, a, q->ysubx);
1292
    curve25519_mul(e, b, q->xaddy);
1293
    curve25519_add(h, e, a);
1294
    curve25519_sub(e, e, a);
1295
    curve25519_mul(c, r->t, q->t2d);
1296
    curve25519_add(f, r->z, r->z);
1297
    curve25519_add_after_basic(g, f, c);
1298
    curve25519_sub_after_basic(f, f, c);
1299
    curve25519_mul(r->x, e, f);
1300
    curve25519_mul(r->y, h, g);
1301
    curve25519_mul(r->z, g, f);
1302
    curve25519_mul(r->t, e, h);
1303
}
1304

1305
void
1306
ge25519_pnielsadd(ge25519_pniels *r, const ge25519 *p, const ge25519_pniels *q) {
1307
    bignum25519 a,b,c,x,y,z,t;
1308

1309
    curve25519_sub(a, p->y, p->x);
1310
    curve25519_add(b, p->y, p->x);
1311
    curve25519_mul(a, a, q->ysubx);
1312
    curve25519_mul(x, b, q->xaddy);
1313
    curve25519_add(y, x, a);
1314
    curve25519_sub(x, x, a);
1315
    curve25519_mul(c, p->t, q->t2d);
1316
    curve25519_mul(t, p->z, q->z);
1317
    curve25519_add(t, t, t);
1318
    curve25519_add_after_basic(z, t, c);
1319
    curve25519_sub_after_basic(t, t, c);
1320
    curve25519_mul(r->xaddy, x, t);
1321
    curve25519_mul(r->ysubx, y, z);
1322
    curve25519_mul(r->z, z, t);
1323
    curve25519_mul(r->t2d, x, y);
1324
    curve25519_copy(y, r->ysubx);
1325
    curve25519_sub(r->ysubx, r->ysubx, r->xaddy);
1326
    curve25519_add(r->xaddy, r->xaddy, y);
1327
    curve25519_mul(r->t2d, r->t2d, ge25519_ec2d);
1328
}
1329

1330
void
1331
ge25519_pack(byte r[32], const ge25519 *p) {
1332
    bignum25519 tx, ty, zi;
1333
    byte parity[32];
1334
    curve25519_recip(zi, p->z);
1335
    curve25519_mul(tx, p->x, zi);
1336
    curve25519_mul(ty, p->y, zi);
1337
    curve25519_contract(r, ty);
1338
    curve25519_contract(parity, tx);
1339
    r[31] ^= ((parity[0] & 1) << 7);
1340
}
1341

1342
int
1343
ed25519_verify(const byte *x, const byte *y, size_t len) {
1344
    size_t differentbits = 0;
1345
    while (len--)
1346
        differentbits |= (*x++ ^ *y++);
1347
    return (int) (1 & ((differentbits - 1) >> 8));
1348
}
1349

1350
int
1351
ge25519_unpack_negative_vartime(ge25519 *r, const byte p[32]) {
1352
    const byte zero[32] = {0};
1353
    const bignum25519 one = {1};
1354
    byte parity = p[31] >> 7;
1355
    byte check[32];
1356
    bignum25519 t, root, num, den, d3;
1357

1358
    curve25519_expand(r->y, p);
1359
    curve25519_copy(r->z, one);
1360
    curve25519_square(num, r->y); /* x = y^2 */
1361
    curve25519_mul(den, num, ge25519_ecd); /* den = dy^2 */
1362
    curve25519_sub_reduce(num, num, r->z); /* x = y^1 - 1 */
1363
    curve25519_add(den, den, r->z); /* den = dy^2 + 1 */
1364

1365
    /* Computation of sqrt(num/den) */
1366
    /* 1.: computation of num^((p-5)/8)*den^((7p-35)/8) = (num*den^7)^((p-5)/8) */
1367
    curve25519_square(t, den);
1368
    curve25519_mul(d3, t, den);
1369
    curve25519_square(r->x, d3);
1370
    curve25519_mul(r->x, r->x, den);
1371
    curve25519_mul(r->x, r->x, num);
1372
    curve25519_pow_two252m3(r->x, r->x);
1373

1374
    /* 2. computation of r->x = num * den^3 * (num*den^7)^((p-5)/8) */
1375
    curve25519_mul(r->x, r->x, d3);
1376
    curve25519_mul(r->x, r->x, num);
1377

1378
    /* 3. Check if either of the roots works: */
1379
    curve25519_square(t, r->x);
1380
    curve25519_mul(t, t, den);
1381
    curve25519_sub_reduce(root, t, num);
1382
    curve25519_contract(check, root);
1383
    if (!ed25519_verify(check, zero, 32)) {
1384
        curve25519_add_reduce(t, t, num);
1385
        curve25519_contract(check, t);
1386
        if (!ed25519_verify(check, zero, 32))
1387
            return 0;
1388
        curve25519_mul(r->x, r->x, ge25519_sqrtneg1);
1389
    }
1390

1391
    curve25519_contract(check, r->x);
1392
    if ((check[0] & 1) == parity) {
1393
        curve25519_copy(t, r->x);
1394
        curve25519_neg(r->x, t);
1395
    }
1396
    curve25519_mul(r->t, r->x, r->y);
1397
    return 1;
1398
}
1399

1400
/* computes [s1]p1 + [s2]basepoint */
1401
void
1402
ge25519_double_scalarmult_vartime(ge25519 *r, const ge25519 *p1, const bignum256modm s1, const bignum256modm s2) {
1403
    signed char slide1[256], slide2[256];
1404
    ge25519_pniels pre1[S1_TABLE_SIZE];
1405
    ge25519 d1;
1406
    ge25519_p1p1 t;
1407
    sword32 i;
1408

1409
    contract256_slidingwindow_modm(slide1, s1, S1_SWINDOWSIZE);
1410
    contract256_slidingwindow_modm(slide2, s2, S2_SWINDOWSIZE);
1411

1412
    ge25519_double(&d1, p1);
1413
    ge25519_full_to_pniels(pre1, p1);
1414
    for (i = 0; i < S1_TABLE_SIZE - 1; i++)
1415
            ge25519_pnielsadd(&pre1[i+1], &d1, &pre1[i]);
1416

1417
    /* set neutral */
1418
    std::memset(r, 0, sizeof(ge25519));
1419
    r->y[0] = 1;
1420
    r->z[0] = 1;
1421

1422
    i = 255;
1423
    while ((i >= 0) && !(slide1[i] | slide2[i]))
1424
        i--;
1425

1426
    for (; i >= 0; i--) {
1427
        ge25519_double_p1p1(&t, r);
1428

1429
        if (slide1[i]) {
1430
            ge25519_p1p1_to_full(r, &t);
1431
            ge25519_pnielsadd_p1p1(&t, r, &pre1[abs(slide1[i]) / 2], (byte)slide1[i] >> 7);
1432
        }
1433

1434
        if (slide2[i]) {
1435
            ge25519_p1p1_to_full(r, &t);
1436
            ge25519_nielsadd2_p1p1(&t, r, &ge25519_niels_sliding_multiples[abs(slide2[i]) / 2], (byte)slide2[i] >> 7);
1437
        }
1438

1439
        ge25519_p1p1_to_partial(r, &t);
1440
    }
1441
}
1442

1443
#if !defined(HAVE_GE25519_SCALARMULT_BASE_CHOOSE_NIELS)
1444

1445
word32
1446
ge25519_windowb_equal(word32 b, word32 c) {
1447
    return ((b ^ c) - 1) >> 31;
1448
}
1449

1450
void
1451
ge25519_scalarmult_base_choose_niels(ge25519_niels *t, const byte table[256][96], word32 pos, signed char b) {
1452
    bignum25519 neg;
1453
    word32 sign = (word32)((byte)b >> 7);
1454
    word32 mask = ~(sign - 1);
1455
    word32 u = (b + mask) ^ mask;
1456
    word32 i;
1457

1458
    /* ysubx, xaddy, t2d in packed form. initialize to ysubx = 1, xaddy = 1, t2d = 0 */
1459
    byte packed[96] = {0};
1460
    packed[0] = 1;
1461
    packed[32] = 1;
1462

1463
    for (i = 0; i < 8; i++)
1464
        curve25519_move_conditional_bytes(packed, table[(pos * 8) + i], ge25519_windowb_equal(u, i + 1));
1465

1466
    /* expand in to t */
1467
    curve25519_expand(t->ysubx, packed +  0);
1468
    curve25519_expand(t->xaddy, packed + 32);
1469
    curve25519_expand(t->t2d  , packed + 64);
1470

1471
    /* adjust for sign */
1472
    curve25519_swap_conditional(t->ysubx, t->xaddy, sign);
1473
    curve25519_neg(neg, t->t2d);
1474
    curve25519_swap_conditional(t->t2d, neg, sign);
1475
}
1476

1477
#endif /* HAVE_GE25519_SCALARMULT_BASE_CHOOSE_NIELS */
1478

1479
/* computes [s]basepoint */
1480
void
1481
ge25519_scalarmult_base_niels(ge25519 *r, const byte basepoint_table[256][96], const bignum256modm s) {
1482
    signed char b[64];
1483
    word32 i;
1484
    ge25519_niels t;
1485

1486
    contract256_window4_modm(b, s);
1487

1488
    ge25519_scalarmult_base_choose_niels(&t, basepoint_table, 0, b[1]);
1489
    curve25519_sub_reduce(r->x, t.xaddy, t.ysubx);
1490
    curve25519_add_reduce(r->y, t.xaddy, t.ysubx);
1491
    std::memset(r->z, 0, sizeof(bignum25519));
1492
    curve25519_copy(r->t, t.t2d);
1493
    r->z[0] = 2;
1494
    for (i = 3; i < 64; i += 2) {
1495
        ge25519_scalarmult_base_choose_niels(&t, basepoint_table, i / 2, b[i]);
1496
        ge25519_nielsadd2(r, &t);
1497
    }
1498
    ge25519_double_partial(r, r);
1499
    ge25519_double_partial(r, r);
1500
    ge25519_double_partial(r, r);
1501
    ge25519_double(r, r);
1502
    ge25519_scalarmult_base_choose_niels(&t, basepoint_table, 0, b[0]);
1503
    curve25519_mul(t.t2d, t.t2d, ge25519_ecd);
1504
    ge25519_nielsadd2(r, &t);
1505
    for(i = 2; i < 64; i += 2) {
1506
        ge25519_scalarmult_base_choose_niels(&t, basepoint_table, i / 2, b[i]);
1507
        ge25519_nielsadd2(r, &t);
1508
    }
1509
}
1510

1511
ANONYMOUS_NAMESPACE_END
1512
NAMESPACE_END  // Ed25519
1513
NAMESPACE_END  // Donna
1514
NAMESPACE_END  // CryptoPP
1515

1516
//***************************** curve25519 *****************************//
1517

1518
NAMESPACE_BEGIN(CryptoPP)
1519
NAMESPACE_BEGIN(Donna)
1520

1521
int curve25519_mult_CXX(byte sharedKey[32], const byte secretKey[32], const byte othersKey[32])
1522
{
1523
    using namespace CryptoPP::Donna::X25519;
1524

1525
    FixedSizeSecBlock<byte, 32> e;
1526
    for (size_t i = 0;i < 32;++i)
1527
        e[i] = secretKey[i];
1528
    e[0] &= 0xf8; e[31] &= 0x7f; e[31] |= 0x40;
1529

1530
    bignum25519 nqpqx = {1}, nqpqz = {0}, nqz = {1}, nqx;
1531
    bignum25519 q, qx, qpqx, qqx, zzz, zmone;
1532
    size_t bit, lastbit;
1533

1534
    curve25519_expand(q, othersKey);
1535
    curve25519_copy(nqx, q);
1536

1537
    /* bit 255 is always 0, and bit 254 is always 1, so skip bit 255 and
1538
       start pre-swapped on bit 254 */
1539
    lastbit = 1;
1540

1541
    /* we are doing bits 254..3 in the loop, but are swapping in bits 253..2 */
1542
    for (int i = 253; i >= 2; i--) {
1543
        curve25519_add(qx, nqx, nqz);
1544
        curve25519_sub(nqz, nqx, nqz);
1545
        curve25519_add(qpqx, nqpqx, nqpqz);
1546
        curve25519_sub(nqpqz, nqpqx, nqpqz);
1547
        curve25519_mul(nqpqx, qpqx, nqz);
1548
        curve25519_mul(nqpqz, qx, nqpqz);
1549
        curve25519_add(qqx, nqpqx, nqpqz);
1550
        curve25519_sub(nqpqz, nqpqx, nqpqz);
1551
        curve25519_square(nqpqz, nqpqz);
1552
        curve25519_square(nqpqx, qqx);
1553
        curve25519_mul(nqpqz, nqpqz, q);
1554
        curve25519_square(qx, qx);
1555
        curve25519_square(nqz, nqz);
1556
        curve25519_mul(nqx, qx, nqz);
1557
        curve25519_sub(nqz, qx, nqz);
1558
        curve25519_scalar_product(zzz, nqz, 121665);
1559
        curve25519_add(zzz, zzz, qx);
1560
        curve25519_mul(nqz, nqz, zzz);
1561

1562
        bit = (e[i/8] >> (i & 7)) & 1;
1563
        curve25519_swap_conditional(nqx, nqpqx, bit ^ lastbit);
1564
        curve25519_swap_conditional(nqz, nqpqz, bit ^ lastbit);
1565
        lastbit = bit;
1566
    }
1567

1568
    /* the final 3 bits are always zero, so we only need to double */
1569
    for (int i = 0; i < 3; i++) {
1570
        curve25519_add(qx, nqx, nqz);
1571
        curve25519_sub(nqz, nqx, nqz);
1572
        curve25519_square(qx, qx);
1573
        curve25519_square(nqz, nqz);
1574
        curve25519_mul(nqx, qx, nqz);
1575
        curve25519_sub(nqz, qx, nqz);
1576
        curve25519_scalar_product(zzz, nqz, 121665);
1577
        curve25519_add(zzz, zzz, qx);
1578
        curve25519_mul(nqz, nqz, zzz);
1579
    }
1580

1581
    curve25519_recip(zmone, nqz);
1582
    curve25519_mul(nqz, nqx, zmone);
1583
    curve25519_contract(sharedKey, nqz);
1584

1585
    return 0;
1586
}
1587

1588
int curve25519_mult(byte publicKey[32], const byte secretKey[32])
1589
{
1590
    using namespace CryptoPP::Donna::X25519;
1591

1592
#if (CRYPTOPP_CURVE25519_SSE2)
1593
    if (HasSSE2())
1594
        return curve25519_mult_SSE2(publicKey, secretKey, basePoint);
1595
    else
1596
#endif
1597

1598
    return curve25519_mult_CXX(publicKey, secretKey, basePoint);
1599
}
1600

1601
int curve25519_mult(byte sharedKey[32], const byte secretKey[32], const byte othersKey[32])
1602
{
1603
#if (CRYPTOPP_CURVE25519_SSE2)
1604
    if (HasSSE2())
1605
        return curve25519_mult_SSE2(sharedKey, secretKey, othersKey);
1606
    else
1607
#endif
1608

1609
    return curve25519_mult_CXX(sharedKey, secretKey, othersKey);
1610
}
1611

1612
NAMESPACE_END  // Donna
1613
NAMESPACE_END  // CryptoPP
1614

1615
//******************************* ed25519 *******************************//
1616

1617
NAMESPACE_BEGIN(CryptoPP)
1618
NAMESPACE_BEGIN(Donna)
1619

1620
int
1621
ed25519_publickey_CXX(byte publicKey[32], const byte secretKey[32])
1622
{
1623
    using namespace CryptoPP::Donna::Ed25519;
1624

1625
    bignum256modm a;
1626
    ALIGN(ALIGN_SPEC) ge25519 A;
1627
    hash_512bits extsk;
1628

1629
    /* A = aB */
1630
    ed25519_extsk(extsk, secretKey);
1631
    expand256_modm(a, extsk, 32);
1632
    ge25519_scalarmult_base_niels(&A, ge25519_niels_base_multiples, a);
1633
    ge25519_pack(publicKey, &A);
1634

1635
    return 0;
1636
}
1637

1638
int
1639
ed25519_publickey(byte publicKey[32], const byte secretKey[32])
1640
{
1641
    return ed25519_publickey_CXX(publicKey, secretKey);
1642
}
1643

1644
int
1645
ed25519_sign_CXX(std::istream& stream, const byte sk[32], const byte pk[32], byte RS[64])
1646
{
1647
    using namespace CryptoPP::Donna::Ed25519;
1648

1649
    bignum256modm r, S, a;
1650
    ALIGN(ALIGN_SPEC) ge25519 R;
1651
    hash_512bits extsk, hashr, hram;
1652

1653
    // Unfortunately we need to read the stream twice. The first time calculates
1654
    // 'r = H(aExt[32..64], m)'. The second time calculates 'S = H(R,A,m)'. There
1655
    // is a data dependency due to hashing 'RS' with 'R = [r]B' that does not
1656
    // allow us to read the stream once.
1657
    std::streampos where = stream.tellg();
1658

1659
    ed25519_extsk(extsk, sk);
1660

1661
    /* r = H(aExt[32..64], m) */
1662
    SHA512 hash;
1663
    hash.Update(extsk + 32, 32);
1664
    UpdateFromStream(hash, stream);
1665
    hash.Final(hashr);
1666
    expand256_modm(r, hashr, 64);
1667

1668
    /* R = rB */
1669
    ge25519_scalarmult_base_niels(&R, ge25519_niels_base_multiples, r);
1670
    ge25519_pack(RS, &R);
1671

1672
    // Reset stream for the second digest
1673
    stream.clear();
1674
    stream.seekg(where);
1675

1676
    /* S = H(R,A,m).. */
1677
    ed25519_hram(hram, RS, pk, stream);
1678
    expand256_modm(S, hram, 64);
1679

1680
    /* S = H(R,A,m)a */
1681
    expand256_modm(a, extsk, 32);
1682
    mul256_modm(S, S, a);
1683

1684
    /* S = (r + H(R,A,m)a) */
1685
    add256_modm(S, S, r);
1686

1687
    /* S = (r + H(R,A,m)a) mod L */
1688
    contract256_modm(RS + 32, S);
1689
    return 0;
1690
}
1691

1692
int
1693
ed25519_sign_CXX(const byte *m, size_t mlen, const byte sk[32], const byte pk[32], byte RS[64])
1694
{
1695
    using namespace CryptoPP::Donna::Ed25519;
1696

1697
    bignum256modm r, S, a;
1698
    ALIGN(ALIGN_SPEC) ge25519 R;
1699
    hash_512bits extsk, hashr, hram;
1700

1701
    ed25519_extsk(extsk, sk);
1702

1703
    /* r = H(aExt[32..64], m) */
1704
    SHA512 hash;
1705
    hash.Update(extsk + 32, 32);
1706
    hash.Update(m, mlen);
1707
    hash.Final(hashr);
1708
    expand256_modm(r, hashr, 64);
1709

1710
    /* R = rB */
1711
    ge25519_scalarmult_base_niels(&R, ge25519_niels_base_multiples, r);
1712
    ge25519_pack(RS, &R);
1713

1714
    /* S = H(R,A,m).. */
1715
    ed25519_hram(hram, RS, pk, m, mlen);
1716
    expand256_modm(S, hram, 64);
1717

1718
    /* S = H(R,A,m)a */
1719
    expand256_modm(a, extsk, 32);
1720
    mul256_modm(S, S, a);
1721

1722
    /* S = (r + H(R,A,m)a) */
1723
    add256_modm(S, S, r);
1724

1725
    /* S = (r + H(R,A,m)a) mod L */
1726
    contract256_modm(RS + 32, S);
1727
    return 0;
1728
}
1729

1730
int
1731
ed25519_sign(std::istream& stream, const byte secretKey[32], const byte publicKey[32],
1732
             byte signature[64])
1733
{
1734
    return ed25519_sign_CXX(stream, secretKey, publicKey, signature);
1735
}
1736

1737
int
1738
ed25519_sign(const byte* message, size_t messageLength, const byte secretKey[32],
1739
             const byte publicKey[32], byte signature[64])
1740
{
1741
    return ed25519_sign_CXX(message, messageLength, secretKey, publicKey, signature);
1742
}
1743

1744
int
1745
ed25519_sign_open_CXX(const byte *m, size_t mlen, const byte pk[32], const byte RS[64]) {
1746

1747
    using namespace CryptoPP::Donna::Ed25519;
1748

1749
    ALIGN(ALIGN_SPEC) ge25519 R, A;
1750
    hash_512bits hash;
1751
    bignum256modm hram, S;
1752
    byte checkR[32];
1753

1754
    if ((RS[63] & 224) || !ge25519_unpack_negative_vartime(&A, pk))
1755
        return -1;
1756

1757
    /* hram = H(R,A,m) */
1758
    ed25519_hram(hash, RS, pk, m, mlen);
1759
    expand256_modm(hram, hash, 64);
1760

1761
    /* S */
1762
    expand256_modm(S, RS + 32, 32);
1763

1764
    /* SB - H(R,A,m)A */
1765
    ge25519_double_scalarmult_vartime(&R, &A, hram, S);
1766
    ge25519_pack(checkR, &R);
1767

1768
    /* check that R = SB - H(R,A,m)A */
1769
    return ed25519_verify(RS, checkR, 32) ? 0 : -1;
1770
}
1771

1772
int
1773
ed25519_sign_open_CXX(std::istream& stream, const byte pk[32], const byte RS[64]) {
1774

1775
    using namespace CryptoPP::Donna::Ed25519;
1776

1777
    ALIGN(ALIGN_SPEC) ge25519 R, A;
1778
    hash_512bits hash;
1779
    bignum256modm hram, S;
1780
    byte checkR[32];
1781

1782
    if ((RS[63] & 224) || !ge25519_unpack_negative_vartime(&A, pk))
1783
        return -1;
1784

1785
    /* hram = H(R,A,m) */
1786
    ed25519_hram(hash, RS, pk, stream);
1787
    expand256_modm(hram, hash, 64);
1788

1789
    /* S */
1790
    expand256_modm(S, RS + 32, 32);
1791

1792
    /* SB - H(R,A,m)A */
1793
    ge25519_double_scalarmult_vartime(&R, &A, hram, S);
1794
    ge25519_pack(checkR, &R);
1795

1796
    /* check that R = SB - H(R,A,m)A */
1797
    return ed25519_verify(RS, checkR, 32) ? 0 : -1;
1798
}
1799

1800
int
1801
ed25519_sign_open(std::istream& stream, const byte publicKey[32], const byte signature[64])
1802
{
1803
    return ed25519_sign_open_CXX(stream, publicKey, signature);
1804
}
1805

1806
int
1807
ed25519_sign_open(const byte *message, size_t messageLength, const byte publicKey[32], const byte signature[64])
1808
{
1809
    return ed25519_sign_open_CXX(message, messageLength, publicKey, signature);
1810
}
1811

1812
NAMESPACE_END  // Donna
1813
NAMESPACE_END  // CryptoPP
1814

1815
#endif  // CRYPTOPP_CURVE25519_64BIT
1816

1817
Product

Resources

Company
