Crypto++  8.8
Free C++ class library of cryptographic schemes
donna_64.cpp
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
FixedSizeSecBlock
Fixed size stack-based SecBlock.
Definition: secblock.h:1246
GetBlock
Access a block of memory.
Definition: misc.h:2975
HashTransformation
Interface for hash functions and data processing part of MACs.
Definition: cryptlib.h:1118
HashTransformation::Update
virtual void Update(const byte *input, size_t length)=0
Updates a hash with additional input.
SHA512
SHA-512 message digest.
Definition: sha.h:142
SecByteBlock
SecBlock<byte> typedef.
Definition: secblock.h:1226
config.h
Library configuration file.
sword64
signed long long sword64
64-bit signed datatype
Definition: config_int.h:109
byte
unsigned char byte
8-bit unsigned datatype
Definition: config_int.h:66
sword32
signed int sword32
32-bit signed datatype
Definition: config_int.h:91
word128
__uint128_t word128
128-bit unsigned datatype
Definition: config_int.h:119
word32
unsigned int word32
32-bit unsigned datatype
Definition: config_int.h:72
word64
unsigned long long word64
64-bit unsigned datatype
Definition: config_int.h:101
cpu.h
Functions for CPU features and intrinsics.
LITTLE_ENDIAN_ORDER
@ LITTLE_ENDIAN_ORDER
byte order is little-endian
Definition: cryptlib.h:150
LittleEndian
EnumToType< ByteOrder, LITTLE_ENDIAN_ORDER > LittleEndian
Provides a constant for LittleEndian.
Definition: cryptlib.h:155
ed25519_sign_open
int ed25519_sign_open(const byte *message, size_t messageLength, const byte publicKey[32], const byte signature[64])
Verifies a signature on a message.
ed25519_sign
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.
ed25519_publickey
int ed25519_publickey(byte publicKey[32], const byte secretKey[32])
Creates a public key from a secret key.
curve25519_mult
int curve25519_mult(byte publicKey[32], const byte secretKey[32])
Generate a public key.
misc.h
Utility functions for the Crypto++ library.
GetWord
T GetWord(bool assumeAligned, ByteOrder order, const byte *block)
Access a block of memory.
Definition: misc.h:2906
PutWord
void PutWord(bool assumeAligned, ByteOrder order, byte *block, T value, const byte *xorBlock=NULL)
Access a block of memory.
Definition: misc.h:2948
CryptoPP
Crypto++ library namespace.
pch.h
Precompiled header file.
secblock.h
Classes and functions for secure memory allocations.
swap
void swap(::SecBlock< T, A > &a, ::SecBlock< T, A > &b)
Swap two SecBlocks.
Definition: secblock.h:1289
sha.h
Classes for SHA-1 and SHA-2 family of message digests.
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