Crypto++  8.2
Free C++ class library of cryptographic schemes
donna_32.cpp
1 // donna_32.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 // Squash MS LNK4221 and libtool warnings
38 extern const char DONNA32_FNAME[] = __FILE__;
39 
40 #if defined(CRYPTOPP_CURVE25519_32BIT)
41 
42 #include "donna_32.h"
43 
44 ANONYMOUS_NAMESPACE_BEGIN
45 
46 using CryptoPP::byte;
47 using CryptoPP::word32;
48 using CryptoPP::GetWord;
49 using CryptoPP::PutWord;
51 
52 inline word32 U8TO32_LE(const byte* p)
53 {
54  return GetWord<word32>(false, LITTLE_ENDIAN_ORDER, p);
55 }
56 
57 inline void U32TO8_LE(byte* p, word32 w)
58 {
59  PutWord(false, LITTLE_ENDIAN_ORDER, p, w);
60 }
61 
62 ANONYMOUS_NAMESPACE_END
63 
64 NAMESPACE_BEGIN(CryptoPP)
65 NAMESPACE_BEGIN(Donna)
66 NAMESPACE_BEGIN(X25519)
67 ANONYMOUS_NAMESPACE_BEGIN
68 
69 using CryptoPP::byte;
70 using CryptoPP::word32;
71 using CryptoPP::sword32;
72 using CryptoPP::word64;
73 using CryptoPP::sword64;
74 
75 using CryptoPP::GetBlock;
77 
78 // Bring in all the symbols from the 32-bit header
79 using namespace CryptoPP::Donna::Arch32;
80 
81 /* out = in */
82 inline void
83 curve25519_copy(bignum25519 out, const bignum25519 in) {
84  out[0] = in[0]; out[1] = in[1];
85  out[2] = in[2]; out[3] = in[3];
86  out[4] = in[4]; out[5] = in[5];
87  out[6] = in[6]; out[7] = in[7];
88  out[8] = in[8]; out[9] = in[9];
89 }
90 
91 /* out = a + b */
92 inline void
93 curve25519_add(bignum25519 out, const bignum25519 a, const bignum25519 b) {
94  out[0] = a[0] + b[0]; out[1] = a[1] + b[1];
95  out[2] = a[2] + b[2]; out[3] = a[3] + b[3];
96  out[4] = a[4] + b[4]; out[5] = a[5] + b[5];
97  out[6] = a[6] + b[6]; out[7] = a[7] + b[7];
98  out[8] = a[8] + b[8]; out[9] = a[9] + b[9];
99 }
100 
101 /* out = a - b */
102 inline void
103 curve25519_sub(bignum25519 out, const bignum25519 a, const bignum25519 b) {
104  word32 c;
105  out[0] = 0x7ffffda + a[0] - b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
106  out[1] = 0x3fffffe + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
107  out[2] = 0x7fffffe + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
108  out[3] = 0x3fffffe + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
109  out[4] = 0x7fffffe + a[4] - b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
110  out[5] = 0x3fffffe + a[5] - b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
111  out[6] = 0x7fffffe + a[6] - b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
112  out[7] = 0x3fffffe + a[7] - b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
113  out[8] = 0x7fffffe + a[8] - b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
114  out[9] = 0x3fffffe + a[9] - b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
115  out[0] += 19 * c;
116 }
117 
118 /* out = in * scalar */
119 inline void
120 curve25519_scalar_product(bignum25519 out, const bignum25519 in, const word32 scalar) {
121  word64 a;
122  word32 c;
123  a = mul32x32_64(in[0], scalar); out[0] = (word32)a & reduce_mask_26; c = (word32)(a >> 26);
124  a = mul32x32_64(in[1], scalar) + c; out[1] = (word32)a & reduce_mask_25; c = (word32)(a >> 25);
125  a = mul32x32_64(in[2], scalar) + c; out[2] = (word32)a & reduce_mask_26; c = (word32)(a >> 26);
126  a = mul32x32_64(in[3], scalar) + c; out[3] = (word32)a & reduce_mask_25; c = (word32)(a >> 25);
127  a = mul32x32_64(in[4], scalar) + c; out[4] = (word32)a & reduce_mask_26; c = (word32)(a >> 26);
128  a = mul32x32_64(in[5], scalar) + c; out[5] = (word32)a & reduce_mask_25; c = (word32)(a >> 25);
129  a = mul32x32_64(in[6], scalar) + c; out[6] = (word32)a & reduce_mask_26; c = (word32)(a >> 26);
130  a = mul32x32_64(in[7], scalar) + c; out[7] = (word32)a & reduce_mask_25; c = (word32)(a >> 25);
131  a = mul32x32_64(in[8], scalar) + c; out[8] = (word32)a & reduce_mask_26; c = (word32)(a >> 26);
132  a = mul32x32_64(in[9], scalar) + c; out[9] = (word32)a & reduce_mask_25; c = (word32)(a >> 25);
133  out[0] += c * 19;
134 }
135 
136 /* out = a * b */
137 inline void
138 curve25519_mul(bignum25519 out, const bignum25519 a, const bignum25519 b) {
139  word32 r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
140  word32 s0,s1,s2,s3,s4,s5,s6,s7,s8,s9;
141  word64 m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
142  word32 p;
143 
144  r0 = b[0]; r1 = b[1]; r2 = b[2]; r3 = b[3]; r4 = b[4];
145  r5 = b[5]; r6 = b[6]; r7 = b[7]; r8 = b[8]; r9 = b[9];
146 
147  s0 = a[0]; s1 = a[1]; s2 = a[2]; s3 = a[3]; s4 = a[4];
148  s5 = a[5]; s6 = a[6]; s7 = a[7]; s8 = a[8]; s9 = a[9];
149 
150  m1 = mul32x32_64(r0, s1) + mul32x32_64(r1, s0);
151  m3 = mul32x32_64(r0, s3) + mul32x32_64(r1, s2) + mul32x32_64(r2, s1) + mul32x32_64(r3, s0);
152  m5 = mul32x32_64(r0, s5) + mul32x32_64(r1, s4) + mul32x32_64(r2, s3) + mul32x32_64(r3, s2) + mul32x32_64(r4, s1) + mul32x32_64(r5, s0);
153  m7 = mul32x32_64(r0, s7) + mul32x32_64(r1, s6) + mul32x32_64(r2, s5) + mul32x32_64(r3, s4) + mul32x32_64(r4, s3) + mul32x32_64(r5, s2) + mul32x32_64(r6, s1) + mul32x32_64(r7, s0);
154  m9 = mul32x32_64(r0, s9) + mul32x32_64(r1, s8) + mul32x32_64(r2, s7) + mul32x32_64(r3, s6) + mul32x32_64(r4, s5) + mul32x32_64(r5, s4) + mul32x32_64(r6, s3) + mul32x32_64(r7, s2) + mul32x32_64(r8, s1) + mul32x32_64(r9, s0);
155 
156  r1 *= 2; r3 *= 2; r5 *= 2; r7 *= 2;
157 
158  m0 = mul32x32_64(r0, s0);
159  m2 = mul32x32_64(r0, s2) + mul32x32_64(r1, s1) + mul32x32_64(r2, s0);
160  m4 = mul32x32_64(r0, s4) + mul32x32_64(r1, s3) + mul32x32_64(r2, s2) + mul32x32_64(r3, s1) + mul32x32_64(r4, s0);
161  m6 = mul32x32_64(r0, s6) + mul32x32_64(r1, s5) + mul32x32_64(r2, s4) + mul32x32_64(r3, s3) + mul32x32_64(r4, s2) + mul32x32_64(r5, s1) + mul32x32_64(r6, s0);
162  m8 = mul32x32_64(r0, s8) + mul32x32_64(r1, s7) + mul32x32_64(r2, s6) + mul32x32_64(r3, s5) + mul32x32_64(r4, s4) + mul32x32_64(r5, s3) + mul32x32_64(r6, s2) + mul32x32_64(r7, s1) + mul32x32_64(r8, s0);
163 
164  r1 *= 19; r2 *= 19;
165  r3 = (r3 / 2) * 19;
166  r4 *= 19;
167  r5 = (r5 / 2) * 19;
168  r6 *= 19;
169  r7 = (r7 / 2) * 19;
170  r8 *= 19; r9 *= 19;
171 
172  m1 += (mul32x32_64(r9, s2) + mul32x32_64(r8, s3) + mul32x32_64(r7, s4) + mul32x32_64(r6, s5) + mul32x32_64(r5, s6) + mul32x32_64(r4, s7) + mul32x32_64(r3, s8) + mul32x32_64(r2, s9));
173  m3 += (mul32x32_64(r9, s4) + mul32x32_64(r8, s5) + mul32x32_64(r7, s6) + mul32x32_64(r6, s7) + mul32x32_64(r5, s8) + mul32x32_64(r4, s9));
174  m5 += (mul32x32_64(r9, s6) + mul32x32_64(r8, s7) + mul32x32_64(r7, s8) + mul32x32_64(r6, s9));
175  m7 += (mul32x32_64(r9, s8) + mul32x32_64(r8, s9));
176 
177  r3 *= 2; r5 *= 2; r7 *= 2; r9 *= 2;
178 
179  m0 += (mul32x32_64(r9, s1) + mul32x32_64(r8, s2) + mul32x32_64(r7, s3) + mul32x32_64(r6, s4) + mul32x32_64(r5, s5) + mul32x32_64(r4, s6) + mul32x32_64(r3, s7) + mul32x32_64(r2, s8) + mul32x32_64(r1, s9));
180  m2 += (mul32x32_64(r9, s3) + mul32x32_64(r8, s4) + mul32x32_64(r7, s5) + mul32x32_64(r6, s6) + mul32x32_64(r5, s7) + mul32x32_64(r4, s8) + mul32x32_64(r3, s9));
181  m4 += (mul32x32_64(r9, s5) + mul32x32_64(r8, s6) + mul32x32_64(r7, s7) + mul32x32_64(r6, s8) + mul32x32_64(r5, s9));
182  m6 += (mul32x32_64(r9, s7) + mul32x32_64(r8, s8) + mul32x32_64(r7, s9));
183  m8 += (mul32x32_64(r9, s9));
184 
185  r0 = (word32)m0 & reduce_mask_26; c = (m0 >> 26);
186  m1 += c; r1 = (word32)m1 & reduce_mask_25; c = (m1 >> 25);
187  m2 += c; r2 = (word32)m2 & reduce_mask_26; c = (m2 >> 26);
188  m3 += c; r3 = (word32)m3 & reduce_mask_25; c = (m3 >> 25);
189  m4 += c; r4 = (word32)m4 & reduce_mask_26; c = (m4 >> 26);
190  m5 += c; r5 = (word32)m5 & reduce_mask_25; c = (m5 >> 25);
191  m6 += c; r6 = (word32)m6 & reduce_mask_26; c = (m6 >> 26);
192  m7 += c; r7 = (word32)m7 & reduce_mask_25; c = (m7 >> 25);
193  m8 += c; r8 = (word32)m8 & reduce_mask_26; c = (m8 >> 26);
194  m9 += c; r9 = (word32)m9 & reduce_mask_25; p = (word32)(m9 >> 25);
195  m0 = r0 + mul32x32_64(p,19); r0 = (word32)m0 & reduce_mask_26; p = (word32)(m0 >> 26);
196  r1 += p;
197 
198  out[0] = r0; out[1] = r1; out[2] = r2; out[3] = r3; out[4] = r4;
199  out[5] = r5; out[6] = r6; out[7] = r7; out[8] = r8; out[9] = r9;
200 }
201 
202 /* out = in * in */
203 inline void
204 curve25519_square(bignum25519 out, const bignum25519 in) {
205  word32 r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
206  word32 d6,d7,d8,d9;
207  word64 m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
208  word32 p;
209 
210  r0 = in[0]; r1 = in[1]; r2 = in[2]; r3 = in[3]; r4 = in[4];
211  r5 = in[5]; r6 = in[6]; r7 = in[7]; r8 = in[8]; r9 = in[9];
212 
213  m0 = mul32x32_64(r0, r0);
214  r0 *= 2;
215  m1 = mul32x32_64(r0, r1);
216  m2 = mul32x32_64(r0, r2) + mul32x32_64(r1, r1 * 2);
217  r1 *= 2;
218  m3 = mul32x32_64(r0, r3) + mul32x32_64(r1, r2 );
219  m4 = mul32x32_64(r0, r4) + mul32x32_64(r1, r3 * 2) + mul32x32_64(r2, r2);
220  r2 *= 2;
221  m5 = mul32x32_64(r0, r5) + mul32x32_64(r1, r4 ) + mul32x32_64(r2, r3);
222  m6 = mul32x32_64(r0, r6) + mul32x32_64(r1, r5 * 2) + mul32x32_64(r2, r4) + mul32x32_64(r3, r3 * 2);
223  r3 *= 2;
224  m7 = mul32x32_64(r0, r7) + mul32x32_64(r1, r6 ) + mul32x32_64(r2, r5) + mul32x32_64(r3, r4 );
225  m8 = mul32x32_64(r0, r8) + mul32x32_64(r1, r7 * 2) + mul32x32_64(r2, r6) + mul32x32_64(r3, r5 * 2) + mul32x32_64(r4, r4 );
226  m9 = mul32x32_64(r0, r9) + mul32x32_64(r1, r8 ) + mul32x32_64(r2, r7) + mul32x32_64(r3, r6 ) + mul32x32_64(r4, r5 * 2);
227 
228  d6 = r6 * 19; d7 = r7 * 2 * 19;
229  d8 = r8 * 19; d9 = r9 * 2 * 19;
230 
231  m0 += (mul32x32_64(d9, r1 ) + mul32x32_64(d8, r2 ) + mul32x32_64(d7, r3 ) + mul32x32_64(d6, r4 * 2) + mul32x32_64(r5, r5 * 2 * 19));
232  m1 += (mul32x32_64(d9, r2 / 2) + mul32x32_64(d8, r3 ) + mul32x32_64(d7, r4 ) + mul32x32_64(d6, r5 * 2));
233  m2 += (mul32x32_64(d9, r3 ) + mul32x32_64(d8, r4 * 2) + mul32x32_64(d7, r5 * 2) + mul32x32_64(d6, r6 ));
234  m3 += (mul32x32_64(d9, r4 ) + mul32x32_64(d8, r5 * 2) + mul32x32_64(d7, r6 ));
235  m4 += (mul32x32_64(d9, r5 * 2) + mul32x32_64(d8, r6 * 2) + mul32x32_64(d7, r7 ));
236  m5 += (mul32x32_64(d9, r6 ) + mul32x32_64(d8, r7 * 2));
237  m6 += (mul32x32_64(d9, r7 * 2) + mul32x32_64(d8, r8 ));
238  m7 += (mul32x32_64(d9, r8 ));
239  m8 += (mul32x32_64(d9, r9 ));
240 
241  r0 = (word32)m0 & reduce_mask_26; c = (m0 >> 26);
242  m1 += c; r1 = (word32)m1 & reduce_mask_25; c = (m1 >> 25);
243  m2 += c; r2 = (word32)m2 & reduce_mask_26; c = (m2 >> 26);
244  m3 += c; r3 = (word32)m3 & reduce_mask_25; c = (m3 >> 25);
245  m4 += c; r4 = (word32)m4 & reduce_mask_26; c = (m4 >> 26);
246  m5 += c; r5 = (word32)m5 & reduce_mask_25; c = (m5 >> 25);
247  m6 += c; r6 = (word32)m6 & reduce_mask_26; c = (m6 >> 26);
248  m7 += c; r7 = (word32)m7 & reduce_mask_25; c = (m7 >> 25);
249  m8 += c; r8 = (word32)m8 & reduce_mask_26; c = (m8 >> 26);
250  m9 += c; r9 = (word32)m9 & reduce_mask_25; p = (word32)(m9 >> 25);
251  m0 = r0 + mul32x32_64(p,19); r0 = (word32)m0 & reduce_mask_26; p = (word32)(m0 >> 26);
252  r1 += p;
253 
254  out[0] = r0; out[1] = r1; out[2] = r2; out[3] = r3; out[4] = r4;
255  out[5] = r5; out[6] = r6; out[7] = r7; out[8] = r8; out[9] = r9;
256 }
257 
258 /* out = in^(2 * count) */
259 void
260 curve25519_square_times(bignum25519 out, const bignum25519 in, int count) {
261  word32 r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
262  word32 d6,d7,d8,d9;
263  word64 m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
264  word32 p;
265 
266  r0 = in[0]; r1 = in[1]; r2 = in[2]; r3 = in[3]; r4 = in[4];
267  r5 = in[5]; r6 = in[6]; r7 = in[7]; r8 = in[8]; r9 = in[9];
268 
269  do {
270  m0 = mul32x32_64(r0, r0);
271  r0 *= 2;
272  m1 = mul32x32_64(r0, r1);
273  m2 = mul32x32_64(r0, r2) + mul32x32_64(r1, r1 * 2);
274  r1 *= 2;
275  m3 = mul32x32_64(r0, r3) + mul32x32_64(r1, r2 );
276  m4 = mul32x32_64(r0, r4) + mul32x32_64(r1, r3 * 2) + mul32x32_64(r2, r2);
277  r2 *= 2;
278  m5 = mul32x32_64(r0, r5) + mul32x32_64(r1, r4 ) + mul32x32_64(r2, r3);
279  m6 = mul32x32_64(r0, r6) + mul32x32_64(r1, r5 * 2) + mul32x32_64(r2, r4) + mul32x32_64(r3, r3 * 2);
280  r3 *= 2;
281  m7 = mul32x32_64(r0, r7) + mul32x32_64(r1, r6 ) + mul32x32_64(r2, r5) + mul32x32_64(r3, r4 );
282  m8 = mul32x32_64(r0, r8) + mul32x32_64(r1, r7 * 2) + mul32x32_64(r2, r6) + mul32x32_64(r3, r5 * 2) + mul32x32_64(r4, r4 );
283  m9 = mul32x32_64(r0, r9) + mul32x32_64(r1, r8 ) + mul32x32_64(r2, r7) + mul32x32_64(r3, r6 ) + mul32x32_64(r4, r5 * 2);
284 
285  d6 = r6 * 19; d7 = r7 * 2 * 19;
286  d8 = r8 * 19; d9 = r9 * 2 * 19;
287 
288  m0 += (mul32x32_64(d9, r1 ) + mul32x32_64(d8, r2 ) + mul32x32_64(d7, r3 ) + mul32x32_64(d6, r4 * 2) + mul32x32_64(r5, r5 * 2 * 19));
289  m1 += (mul32x32_64(d9, r2 / 2) + mul32x32_64(d8, r3 ) + mul32x32_64(d7, r4 ) + mul32x32_64(d6, r5 * 2));
290  m2 += (mul32x32_64(d9, r3 ) + mul32x32_64(d8, r4 * 2) + mul32x32_64(d7, r5 * 2) + mul32x32_64(d6, r6 ));
291  m3 += (mul32x32_64(d9, r4 ) + mul32x32_64(d8, r5 * 2) + mul32x32_64(d7, r6 ));
292  m4 += (mul32x32_64(d9, r5 * 2) + mul32x32_64(d8, r6 * 2) + mul32x32_64(d7, r7 ));
293  m5 += (mul32x32_64(d9, r6 ) + mul32x32_64(d8, r7 * 2));
294  m6 += (mul32x32_64(d9, r7 * 2) + mul32x32_64(d8, r8 ));
295  m7 += (mul32x32_64(d9, r8 ));
296  m8 += (mul32x32_64(d9, r9 ));
297 
298  r0 = (word32)m0 & reduce_mask_26; c = (m0 >> 26);
299  m1 += c; r1 = (word32)m1 & reduce_mask_25; c = (m1 >> 25);
300  m2 += c; r2 = (word32)m2 & reduce_mask_26; c = (m2 >> 26);
301  m3 += c; r3 = (word32)m3 & reduce_mask_25; c = (m3 >> 25);
302  m4 += c; r4 = (word32)m4 & reduce_mask_26; c = (m4 >> 26);
303  m5 += c; r5 = (word32)m5 & reduce_mask_25; c = (m5 >> 25);
304  m6 += c; r6 = (word32)m6 & reduce_mask_26; c = (m6 >> 26);
305  m7 += c; r7 = (word32)m7 & reduce_mask_25; c = (m7 >> 25);
306  m8 += c; r8 = (word32)m8 & reduce_mask_26; c = (m8 >> 26);
307  m9 += c; r9 = (word32)m9 & reduce_mask_25; p = (word32)(m9 >> 25);
308  m0 = r0 + mul32x32_64(p,19); r0 = (word32)m0 & reduce_mask_26; p = (word32)(m0 >> 26);
309  r1 += p;
310  } while (--count);
311 
312  out[0] = r0; out[1] = r1; out[2] = r2; out[3] = r3; out[4] = r4;
313  out[5] = r5; out[6] = r6; out[7] = r7; out[8] = r8; out[9] = r9;
314 }
315 
316 /* Take a little-endian, 32-byte number and expand it into polynomial form */
317 void
318 curve25519_expand(bignum25519 out, const byte in[32]) {
319  word32 x0,x1,x2,x3,x4,x5,x6,x7;
321  block(x0)(x1)(x2)(x3)(x4)(x5)(x6)(x7);
322 
323  out[0] = ( x0 ) & reduce_mask_26;
324  out[1] = ((((word64)x1 << 32) | x0) >> 26) & reduce_mask_25;
325  out[2] = ((((word64)x2 << 32) | x1) >> 19) & reduce_mask_26;
326  out[3] = ((((word64)x3 << 32) | x2) >> 13) & reduce_mask_25;
327  out[4] = (( x3) >> 6) & reduce_mask_26;
328  out[5] = ( x4 ) & reduce_mask_25;
329  out[6] = ((((word64)x5 << 32) | x4) >> 25) & reduce_mask_26;
330  out[7] = ((((word64)x6 << 32) | x5) >> 19) & reduce_mask_25;
331  out[8] = ((((word64)x7 << 32) | x6) >> 12) & reduce_mask_26;
332  out[9] = (( x7) >> 6) & reduce_mask_25; /* ignore the top bit */
333 }
334 
335 /* Take a fully reduced polynomial form number and contract it into a little-endian, 32-byte array */
336 void
337 curve25519_contract(byte out[32], const bignum25519 in) {
338  bignum25519 f;
339  curve25519_copy(f, in);
340 
341  #define carry_pass() \
342  f[1] += f[0] >> 26; f[0] &= reduce_mask_26; \
343  f[2] += f[1] >> 25; f[1] &= reduce_mask_25; \
344  f[3] += f[2] >> 26; f[2] &= reduce_mask_26; \
345  f[4] += f[3] >> 25; f[3] &= reduce_mask_25; \
346  f[5] += f[4] >> 26; f[4] &= reduce_mask_26; \
347  f[6] += f[5] >> 25; f[5] &= reduce_mask_25; \
348  f[7] += f[6] >> 26; f[6] &= reduce_mask_26; \
349  f[8] += f[7] >> 25; f[7] &= reduce_mask_25; \
350  f[9] += f[8] >> 26; f[8] &= reduce_mask_26;
351 
352  #define carry_pass_full() \
353  carry_pass() \
354  f[0] += 19 * (f[9] >> 25); f[9] &= reduce_mask_25;
355 
356  #define carry_pass_final() \
357  carry_pass() \
358  f[9] &= reduce_mask_25;
359 
360  carry_pass_full()
361  carry_pass_full()
362 
363  /* now t is between 0 and 2^255-1, properly carried. */
364  /* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */
365  f[0] += 19;
366  carry_pass_full()
367 
368  /* now between 19 and 2^255-1 in both cases, and offset by 19. */
369  f[0] += (1 << 26) - 19;
370  f[1] += (1 << 25) - 1;
371  f[2] += (1 << 26) - 1;
372  f[3] += (1 << 25) - 1;
373  f[4] += (1 << 26) - 1;
374  f[5] += (1 << 25) - 1;
375  f[6] += (1 << 26) - 1;
376  f[7] += (1 << 25) - 1;
377  f[8] += (1 << 26) - 1;
378  f[9] += (1 << 25) - 1;
379 
380  /* now between 2^255 and 2^256-20, and offset by 2^255. */
381  carry_pass_final()
382 
383  #undef carry_pass
384  #undef carry_full
385  #undef carry_final
386 
387  f[1] <<= 2;
388  f[2] <<= 3;
389  f[3] <<= 5;
390  f[4] <<= 6;
391  f[6] <<= 1;
392  f[7] <<= 3;
393  f[8] <<= 4;
394  f[9] <<= 6;
395 
396  #define F(i, s) \
397  out[s+0] |= (byte)( f[i] & 0xff); \
398  out[s+1] = (byte)((f[i] >> 8) & 0xff); \
399  out[s+2] = (byte)((f[i] >> 16) & 0xff); \
400  out[s+3] = (byte)((f[i] >> 24) & 0xff);
401 
402  out[0] = out[16] = 0;
403  F(0,0); F(1,3);
404  F(2,6); F(3,9);
405  F(4,12); F(5,16);
406  F(6,19); F(7,22);
407  F(8,25); F(9,28);
408  #undef F
409 }
410 
411 inline void
412 curve25519_swap_conditional(bignum25519 x, bignum25519 qpx, word32 iswap) {
413  const word32 swap = (word32)(-(sword32)iswap);
414  word32 x0,x1,x2,x3,x4,x5,x6,x7,x8,x9;
415 
416  x0 = swap & (x[0] ^ qpx[0]); x[0] ^= x0; qpx[0] ^= x0;
417  x1 = swap & (x[1] ^ qpx[1]); x[1] ^= x1; qpx[1] ^= x1;
418  x2 = swap & (x[2] ^ qpx[2]); x[2] ^= x2; qpx[2] ^= x2;
419  x3 = swap & (x[3] ^ qpx[3]); x[3] ^= x3; qpx[3] ^= x3;
420  x4 = swap & (x[4] ^ qpx[4]); x[4] ^= x4; qpx[4] ^= x4;
421  x5 = swap & (x[5] ^ qpx[5]); x[5] ^= x5; qpx[5] ^= x5;
422  x6 = swap & (x[6] ^ qpx[6]); x[6] ^= x6; qpx[6] ^= x6;
423  x7 = swap & (x[7] ^ qpx[7]); x[7] ^= x7; qpx[7] ^= x7;
424  x8 = swap & (x[8] ^ qpx[8]); x[8] ^= x8; qpx[8] ^= x8;
425  x9 = swap & (x[9] ^ qpx[9]); x[9] ^= x9; qpx[9] ^= x9;
426 }
427 
428 /*
429  * In: b = 2^5 - 2^0
430  * Out: b = 2^250 - 2^0
431  */
432 void
433 curve25519_pow_two5mtwo0_two250mtwo0(bignum25519 b) {
434  ALIGN(16) bignum25519 t0,c;
435 
436  /* 2^5 - 2^0 */ /* b */
437  /* 2^10 - 2^5 */ curve25519_square_times(t0, b, 5);
438  /* 2^10 - 2^0 */ curve25519_mul(b, t0, b);
439  /* 2^20 - 2^10 */ curve25519_square_times(t0, b, 10);
440  /* 2^20 - 2^0 */ curve25519_mul(c, t0, b);
441  /* 2^40 - 2^20 */ curve25519_square_times(t0, c, 20);
442  /* 2^40 - 2^0 */ curve25519_mul(t0, t0, c);
443  /* 2^50 - 2^10 */ curve25519_square_times(t0, t0, 10);
444  /* 2^50 - 2^0 */ curve25519_mul(b, t0, b);
445  /* 2^100 - 2^50 */ curve25519_square_times(t0, b, 50);
446  /* 2^100 - 2^0 */ curve25519_mul(c, t0, b);
447  /* 2^200 - 2^100 */ curve25519_square_times(t0, c, 100);
448  /* 2^200 - 2^0 */ curve25519_mul(t0, t0, c);
449  /* 2^250 - 2^50 */ curve25519_square_times(t0, t0, 50);
450  /* 2^250 - 2^0 */ curve25519_mul(b, t0, b);
451 }
452 
453 /*
454  * z^(p - 2) = z(2^255 - 21)
455  */
456 void
457 curve25519_recip(bignum25519 out, const bignum25519 z) {
458  ALIGN(16) bignum25519 a, t0, b;
459 
460  /* 2 */ curve25519_square(a, z); /* a = 2 */
461  /* 8 */ curve25519_square_times(t0, a, 2);
462  /* 9 */ curve25519_mul(b, t0, z); /* b = 9 */
463  /* 11 */ curve25519_mul(a, b, a); /* a = 11 */
464  /* 22 */ curve25519_square(t0, a);
465  /* 2^5 - 2^0 = 31 */ curve25519_mul(b, t0, b);
466  /* 2^250 - 2^0 */ curve25519_pow_two5mtwo0_two250mtwo0(b);
467  /* 2^255 - 2^5 */ curve25519_square_times(b, b, 5);
468  /* 2^255 - 21 */ curve25519_mul(out, b, a);
469 }
470 
471 ANONYMOUS_NAMESPACE_END
472 NAMESPACE_END // X25519
473 NAMESPACE_END // Donna
474 NAMESPACE_END // CryptoPP
475 
476 //******************************* ed25519 *******************************//
477 
478 NAMESPACE_BEGIN(CryptoPP)
479 NAMESPACE_BEGIN(Donna)
480 NAMESPACE_BEGIN(Ed25519)
481 ANONYMOUS_NAMESPACE_BEGIN
482 
483 using CryptoPP::byte;
484 using CryptoPP::word32;
485 using CryptoPP::sword32;
486 using CryptoPP::word64;
487 using CryptoPP::sword64;
488 
489 using CryptoPP::GetBlock;
490 using CryptoPP::LittleEndian;
491 
492 using CryptoPP::SHA512;
493 
494 // Bring in all the symbols from the 32-bit header
495 using namespace CryptoPP::Donna::Arch32;
496 
497 /* out = in */
498 inline void
499 curve25519_copy(bignum25519 out, const bignum25519 in) {
500  out[0] = in[0]; out[1] = in[1];
501  out[2] = in[2]; out[3] = in[3];
502  out[4] = in[4]; out[5] = in[5];
503  out[6] = in[6]; out[7] = in[7];
504  out[8] = in[8]; out[9] = in[9];
505 }
506 
507 /* out = a + b */
508 inline void
509 curve25519_add(bignum25519 out, const bignum25519 a, const bignum25519 b) {
510  out[0] = a[0] + b[0]; out[1] = a[1] + b[1];
511  out[2] = a[2] + b[2]; out[3] = a[3] + b[3];
512  out[4] = a[4] + b[4]; out[5] = a[5] + b[5];
513  out[6] = a[6] + b[6]; out[7] = a[7] + b[7];
514  out[8] = a[8] + b[8]; out[9] = a[9] + b[9];
515 }
516 
517 inline void
518 curve25519_add_after_basic(bignum25519 out, const bignum25519 a, const bignum25519 b) {
519  word32 c;
520  out[0] = a[0] + b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
521  out[1] = a[1] + b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
522  out[2] = a[2] + b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
523  out[3] = a[3] + b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
524  out[4] = a[4] + b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
525  out[5] = a[5] + b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
526  out[6] = a[6] + b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
527  out[7] = a[7] + b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
528  out[8] = a[8] + b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
529  out[9] = a[9] + b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
530  out[0] += 19 * c;
531 }
532 
533 inline void
534 curve25519_add_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) {
535  word32 c;
536  out[0] = a[0] + b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
537  out[1] = a[1] + b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
538  out[2] = a[2] + b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
539  out[3] = a[3] + b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
540  out[4] = a[4] + b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
541  out[5] = a[5] + b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
542  out[6] = a[6] + b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
543  out[7] = a[7] + b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
544  out[8] = a[8] + b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
545  out[9] = a[9] + b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
546  out[0] += 19 * c;
547 }
548 
549 /* out = a - b */
550 inline void
551 curve25519_sub(bignum25519 out, const bignum25519 a, const bignum25519 b) {
552  word32 c;
553  out[0] = twoP0 + a[0] - b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
554  out[1] = twoP13579 + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
555  out[2] = twoP2468 + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
556  out[3] = twoP13579 + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
557  out[4] = twoP2468 + a[4] - b[4] + c;
558  out[5] = twoP13579 + a[5] - b[5] ;
559  out[6] = twoP2468 + a[6] - b[6] ;
560  out[7] = twoP13579 + a[7] - b[7] ;
561  out[8] = twoP2468 + a[8] - b[8] ;
562  out[9] = twoP13579 + a[9] - b[9] ;
563 }
564 
565 /* out = a - b, where a is the result of a basic op (add,sub) */
566 inline void
567 curve25519_sub_after_basic(bignum25519 out, const bignum25519 a, const bignum25519 b) {
568  word32 c;
569  out[0] = fourP0 + a[0] - b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
570  out[1] = fourP13579 + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
571  out[2] = fourP2468 + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
572  out[3] = fourP13579 + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
573  out[4] = fourP2468 + a[4] - b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
574  out[5] = fourP13579 + a[5] - b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
575  out[6] = fourP2468 + a[6] - b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
576  out[7] = fourP13579 + a[7] - b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
577  out[8] = fourP2468 + a[8] - b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
578  out[9] = fourP13579 + a[9] - b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
579  out[0] += 19 * c;
580 }
581 
582 inline void
583 curve25519_sub_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) {
584  word32 c;
585  out[0] = fourP0 + a[0] - b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
586  out[1] = fourP13579 + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
587  out[2] = fourP2468 + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
588  out[3] = fourP13579 + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
589  out[4] = fourP2468 + a[4] - b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
590  out[5] = fourP13579 + a[5] - b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
591  out[6] = fourP2468 + a[6] - b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
592  out[7] = fourP13579 + a[7] - b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
593  out[8] = fourP2468 + a[8] - b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
594  out[9] = fourP13579 + a[9] - b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
595  out[0] += 19 * c;
596 }
597 
598 /* out = -a */
599 inline void
600 curve25519_neg(bignum25519 out, const bignum25519 a) {
601  word32 c;
602  out[0] = twoP0 - a[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
603  out[1] = twoP13579 - a[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
604  out[2] = twoP2468 - a[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
605  out[3] = twoP13579 - a[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
606  out[4] = twoP2468 - a[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
607  out[5] = twoP13579 - a[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
608  out[6] = twoP2468 - a[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
609  out[7] = twoP13579 - a[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
610  out[8] = twoP2468 - a[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
611  out[9] = twoP13579 - a[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
612  out[0] += 19 * c;
613 }
614 
615 /* out = a * b */
616 void
617 curve25519_mul(bignum25519 out, const bignum25519 a, const bignum25519 b) {
618  word32 r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
619  word32 s0,s1,s2,s3,s4,s5,s6,s7,s8,s9;
620  word64 m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
621  word32 p;
622 
623  r0 = b[0]; r1 = b[1];
624  r2 = b[2]; r3 = b[3];
625  r4 = b[4]; r5 = b[5];
626  r6 = b[6]; r7 = b[7];
627  r8 = b[8]; r9 = b[9];
628 
629  s0 = a[0]; s1 = a[1];
630  s2 = a[2]; s3 = a[3];
631  s4 = a[4]; s5 = a[5];
632  s6 = a[6]; s7 = a[7];
633  s8 = a[8]; s9 = a[9];
634 
635  m1 = mul32x32_64(r0, s1) + mul32x32_64(r1, s0);
636  m3 = mul32x32_64(r0, s3) + mul32x32_64(r1, s2) + mul32x32_64(r2, s1) + mul32x32_64(r3, s0);
637  m5 = mul32x32_64(r0, s5) + mul32x32_64(r1, s4) + mul32x32_64(r2, s3) + mul32x32_64(r3, s2) + mul32x32_64(r4, s1) + mul32x32_64(r5, s0);
638  m7 = mul32x32_64(r0, s7) + mul32x32_64(r1, s6) + mul32x32_64(r2, s5) + mul32x32_64(r3, s4) + mul32x32_64(r4, s3) + mul32x32_64(r5, s2) + mul32x32_64(r6, s1) + mul32x32_64(r7, s0);
639  m9 = mul32x32_64(r0, s9) + mul32x32_64(r1, s8) + mul32x32_64(r2, s7) + mul32x32_64(r3, s6) + mul32x32_64(r4, s5) + mul32x32_64(r5, s4) + mul32x32_64(r6, s3) + mul32x32_64(r7, s2) + mul32x32_64(r8, s1) + mul32x32_64(r9, s0);
640 
641  r1 *= 2; r3 *= 2;
642  r5 *= 2; r7 *= 2;
643 
644  m0 = mul32x32_64(r0, s0);
645  m2 = mul32x32_64(r0, s2) + mul32x32_64(r1, s1) + mul32x32_64(r2, s0);
646  m4 = mul32x32_64(r0, s4) + mul32x32_64(r1, s3) + mul32x32_64(r2, s2) + mul32x32_64(r3, s1) + mul32x32_64(r4, s0);
647  m6 = mul32x32_64(r0, s6) + mul32x32_64(r1, s5) + mul32x32_64(r2, s4) + mul32x32_64(r3, s3) + mul32x32_64(r4, s2) + mul32x32_64(r5, s1) + mul32x32_64(r6, s0);
648  m8 = mul32x32_64(r0, s8) + mul32x32_64(r1, s7) + mul32x32_64(r2, s6) + mul32x32_64(r3, s5) + mul32x32_64(r4, s4) + mul32x32_64(r5, s3) + mul32x32_64(r6, s2) + mul32x32_64(r7, s1) + mul32x32_64(r8, s0);
649 
650  r1 *= 19; r2 *= 19;
651  r3 = (r3 / 2) * 19;
652  r4 *= 19;
653  r5 = (r5 / 2) * 19;
654  r6 *= 19;
655  r7 = (r7 / 2) * 19;
656  r8 *= 19; r9 *= 19;
657 
658  m1 += (mul32x32_64(r9, s2) + mul32x32_64(r8, s3) + mul32x32_64(r7, s4) + mul32x32_64(r6, s5) + mul32x32_64(r5, s6) + mul32x32_64(r4, s7) + mul32x32_64(r3, s8) + mul32x32_64(r2, s9));
659  m3 += (mul32x32_64(r9, s4) + mul32x32_64(r8, s5) + mul32x32_64(r7, s6) + mul32x32_64(r6, s7) + mul32x32_64(r5, s8) + mul32x32_64(r4, s9));
660  m5 += (mul32x32_64(r9, s6) + mul32x32_64(r8, s7) + mul32x32_64(r7, s8) + mul32x32_64(r6, s9));
661  m7 += (mul32x32_64(r9, s8) + mul32x32_64(r8, s9));
662 
663  r3 *= 2; r5 *= 2;
664  r7 *= 2; r9 *= 2;
665 
666  m0 += (mul32x32_64(r9, s1) + mul32x32_64(r8, s2) + mul32x32_64(r7, s3) + mul32x32_64(r6, s4) + mul32x32_64(r5, s5) + mul32x32_64(r4, s6) + mul32x32_64(r3, s7) + mul32x32_64(r2, s8) + mul32x32_64(r1, s9));
667  m2 += (mul32x32_64(r9, s3) + mul32x32_64(r8, s4) + mul32x32_64(r7, s5) + mul32x32_64(r6, s6) + mul32x32_64(r5, s7) + mul32x32_64(r4, s8) + mul32x32_64(r3, s9));
668  m4 += (mul32x32_64(r9, s5) + mul32x32_64(r8, s6) + mul32x32_64(r7, s7) + mul32x32_64(r6, s8) + mul32x32_64(r5, s9));
669  m6 += (mul32x32_64(r9, s7) + mul32x32_64(r8, s8) + mul32x32_64(r7, s9));
670  m8 += (mul32x32_64(r9, s9));
671 
672  r0 = (word32)m0 & reduce_mask_26; c = (m0 >> 26);
673  m1 += c; r1 = (word32)m1 & reduce_mask_25; c = (m1 >> 25);
674  m2 += c; r2 = (word32)m2 & reduce_mask_26; c = (m2 >> 26);
675  m3 += c; r3 = (word32)m3 & reduce_mask_25; c = (m3 >> 25);
676  m4 += c; r4 = (word32)m4 & reduce_mask_26; c = (m4 >> 26);
677  m5 += c; r5 = (word32)m5 & reduce_mask_25; c = (m5 >> 25);
678  m6 += c; r6 = (word32)m6 & reduce_mask_26; c = (m6 >> 26);
679  m7 += c; r7 = (word32)m7 & reduce_mask_25; c = (m7 >> 25);
680  m8 += c; r8 = (word32)m8 & reduce_mask_26; c = (m8 >> 26);
681  m9 += c; r9 = (word32)m9 & reduce_mask_25; p = (word32)(m9 >> 25);
682  m0 = r0 + mul32x32_64(p,19); r0 = (word32)m0 & reduce_mask_26; p = (word32)(m0 >> 26);
683  r1 += p;
684 
685  out[0] = r0; out[1] = r1;
686  out[2] = r2; out[3] = r3;
687  out[4] = r4; out[5] = r5;
688  out[6] = r6; out[7] = r7;
689  out[8] = r8; out[9] = r9;
690 }
691 
692 /* out = in*in */
693 void
694 curve25519_square(bignum25519 out, const bignum25519 in) {
695  word32 r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
696  word32 d6,d7,d8,d9;
697  word64 m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
698  word32 p;
699 
700  r0 = in[0]; r1 = in[1];
701  r2 = in[2]; r3 = in[3];
702  r4 = in[4]; r5 = in[5];
703  r6 = in[6]; r7 = in[7];
704  r8 = in[8]; r9 = in[9];
705 
706  m0 = mul32x32_64(r0, r0);
707  r0 *= 2;
708  m1 = mul32x32_64(r0, r1);
709  m2 = mul32x32_64(r0, r2) + mul32x32_64(r1, r1 * 2);
710  r1 *= 2;
711  m3 = mul32x32_64(r0, r3) + mul32x32_64(r1, r2 );
712  m4 = mul32x32_64(r0, r4) + mul32x32_64(r1, r3 * 2) + mul32x32_64(r2, r2);
713  r2 *= 2;
714  m5 = mul32x32_64(r0, r5) + mul32x32_64(r1, r4 ) + mul32x32_64(r2, r3);
715  m6 = mul32x32_64(r0, r6) + mul32x32_64(r1, r5 * 2) + mul32x32_64(r2, r4) + mul32x32_64(r3, r3 * 2);
716  r3 *= 2;
717  m7 = mul32x32_64(r0, r7) + mul32x32_64(r1, r6 ) + mul32x32_64(r2, r5) + mul32x32_64(r3, r4 );
718  m8 = mul32x32_64(r0, r8) + mul32x32_64(r1, r7 * 2) + mul32x32_64(r2, r6) + mul32x32_64(r3, r5 * 2) + mul32x32_64(r4, r4 );
719  m9 = mul32x32_64(r0, r9) + mul32x32_64(r1, r8 ) + mul32x32_64(r2, r7) + mul32x32_64(r3, r6 ) + mul32x32_64(r4, r5 * 2);
720 
721  d6 = r6 * 19;
722  d7 = r7 * 2 * 19;
723  d8 = r8 * 19;
724  d9 = r9 * 2 * 19;
725 
726  m0 += (mul32x32_64(d9, r1 ) + mul32x32_64(d8, r2 ) + mul32x32_64(d7, r3 ) + mul32x32_64(d6, r4 * 2) + mul32x32_64(r5, r5 * 2 * 19));
727  m1 += (mul32x32_64(d9, r2 / 2) + mul32x32_64(d8, r3 ) + mul32x32_64(d7, r4 ) + mul32x32_64(d6, r5 * 2));
728  m2 += (mul32x32_64(d9, r3 ) + mul32x32_64(d8, r4 * 2) + mul32x32_64(d7, r5 * 2) + mul32x32_64(d6, r6 ));
729  m3 += (mul32x32_64(d9, r4 ) + mul32x32_64(d8, r5 * 2) + mul32x32_64(d7, r6 ));
730  m4 += (mul32x32_64(d9, r5 * 2) + mul32x32_64(d8, r6 * 2) + mul32x32_64(d7, r7 ));
731  m5 += (mul32x32_64(d9, r6 ) + mul32x32_64(d8, r7 * 2));
732  m6 += (mul32x32_64(d9, r7 * 2) + mul32x32_64(d8, r8 ));
733  m7 += (mul32x32_64(d9, r8 ));
734  m8 += (mul32x32_64(d9, r9 ));
735 
736  r0 = (word32)m0 & reduce_mask_26; c = (m0 >> 26);
737  m1 += c; r1 = (word32)m1 & reduce_mask_25; c = (m1 >> 25);
738  m2 += c; r2 = (word32)m2 & reduce_mask_26; c = (m2 >> 26);
739  m3 += c; r3 = (word32)m3 & reduce_mask_25; c = (m3 >> 25);
740  m4 += c; r4 = (word32)m4 & reduce_mask_26; c = (m4 >> 26);
741  m5 += c; r5 = (word32)m5 & reduce_mask_25; c = (m5 >> 25);
742  m6 += c; r6 = (word32)m6 & reduce_mask_26; c = (m6 >> 26);
743  m7 += c; r7 = (word32)m7 & reduce_mask_25; c = (m7 >> 25);
744  m8 += c; r8 = (word32)m8 & reduce_mask_26; c = (m8 >> 26);
745  m9 += c; r9 = (word32)m9 & reduce_mask_25; p = (word32)(m9 >> 25);
746  m0 = r0 + mul32x32_64(p,19); r0 = (word32)m0 & reduce_mask_26; p = (word32)(m0 >> 26);
747  r1 += p;
748 
749  out[0] = r0; out[1] = r1;
750  out[2] = r2; out[3] = r3;
751  out[4] = r4; out[5] = r5;
752  out[6] = r6; out[7] = r7;
753  out[8] = r8; out[9] = r9;
754 }
755 
756 /* out = in ^ (2 * count) */
757 void
758 curve25519_square_times(bignum25519 out, const bignum25519 in, int count) {
759  word32 r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
760  word32 d6,d7,d8,d9,p;
761  word64 m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
762 
763  r0 = in[0]; r1 = in[1];
764  r2 = in[2]; r3 = in[3];
765  r4 = in[4]; r5 = in[5];
766  r6 = in[6]; r7 = in[7];
767  r8 = in[8]; r9 = in[9];
768 
769  do {
770  m0 = mul32x32_64(r0, r0);
771  r0 *= 2;
772  m1 = mul32x32_64(r0, r1);
773  m2 = mul32x32_64(r0, r2) + mul32x32_64(r1, r1 * 2);
774  r1 *= 2;
775  m3 = mul32x32_64(r0, r3) + mul32x32_64(r1, r2 );
776  m4 = mul32x32_64(r0, r4) + mul32x32_64(r1, r3 * 2) + mul32x32_64(r2, r2);
777  r2 *= 2;
778  m5 = mul32x32_64(r0, r5) + mul32x32_64(r1, r4 ) + mul32x32_64(r2, r3);
779  m6 = mul32x32_64(r0, r6) + mul32x32_64(r1, r5 * 2) + mul32x32_64(r2, r4) + mul32x32_64(r3, r3 * 2);
780  r3 *= 2;
781  m7 = mul32x32_64(r0, r7) + mul32x32_64(r1, r6 ) + mul32x32_64(r2, r5) + mul32x32_64(r3, r4 );
782  m8 = mul32x32_64(r0, r8) + mul32x32_64(r1, r7 * 2) + mul32x32_64(r2, r6) + mul32x32_64(r3, r5 * 2) + mul32x32_64(r4, r4 );
783  m9 = mul32x32_64(r0, r9) + mul32x32_64(r1, r8 ) + mul32x32_64(r2, r7) + mul32x32_64(r3, r6 ) + mul32x32_64(r4, r5 * 2);
784 
785  d6 = r6 * 19;
786  d7 = r7 * 2 * 19;
787  d8 = r8 * 19;
788  d9 = r9 * 2 * 19;
789 
790  m0 += (mul32x32_64(d9, r1 ) + mul32x32_64(d8, r2 ) + mul32x32_64(d7, r3 ) + mul32x32_64(d6, r4 * 2) + mul32x32_64(r5, r5 * 2 * 19));
791  m1 += (mul32x32_64(d9, r2 / 2) + mul32x32_64(d8, r3 ) + mul32x32_64(d7, r4 ) + mul32x32_64(d6, r5 * 2));
792  m2 += (mul32x32_64(d9, r3 ) + mul32x32_64(d8, r4 * 2) + mul32x32_64(d7, r5 * 2) + mul32x32_64(d6, r6 ));
793  m3 += (mul32x32_64(d9, r4 ) + mul32x32_64(d8, r5 * 2) + mul32x32_64(d7, r6 ));
794  m4 += (mul32x32_64(d9, r5 * 2) + mul32x32_64(d8, r6 * 2) + mul32x32_64(d7, r7 ));
795  m5 += (mul32x32_64(d9, r6 ) + mul32x32_64(d8, r7 * 2));
796  m6 += (mul32x32_64(d9, r7 * 2) + mul32x32_64(d8, r8 ));
797  m7 += (mul32x32_64(d9, r8 ));
798  m8 += (mul32x32_64(d9, r9 ));
799 
800  r0 = (word32)m0 & reduce_mask_26; c = (m0 >> 26);
801  m1 += c; r1 = (word32)m1 & reduce_mask_25; c = (m1 >> 25);
802  m2 += c; r2 = (word32)m2 & reduce_mask_26; c = (m2 >> 26);
803  m3 += c; r3 = (word32)m3 & reduce_mask_25; c = (m3 >> 25);
804  m4 += c; r4 = (word32)m4 & reduce_mask_26; c = (m4 >> 26);
805  m5 += c; r5 = (word32)m5 & reduce_mask_25; c = (m5 >> 25);
806  m6 += c; r6 = (word32)m6 & reduce_mask_26; c = (m6 >> 26);
807  m7 += c; r7 = (word32)m7 & reduce_mask_25; c = (m7 >> 25);
808  m8 += c; r8 = (word32)m8 & reduce_mask_26; c = (m8 >> 26);
809  m9 += c; r9 = (word32)m9 & reduce_mask_25; p = (word32)(m9 >> 25);
810  m0 = r0 + mul32x32_64(p,19); r0 = (word32)m0 & reduce_mask_26; p = (word32)(m0 >> 26);
811  r1 += p;
812  } while (--count);
813 
814  out[0] = r0; out[1] = r1;
815  out[2] = r2; out[3] = r3;
816  out[4] = r4; out[5] = r5;
817  out[6] = r6; out[7] = r7;
818  out[8] = r8; out[9] = r9;
819 }
820 
821 /* Take a little-endian, 32-byte number and expand it into polynomial form */
822 void
823 curve25519_expand(bignum25519 out, const byte in[32]) {
824  word32 x0,x1,x2,x3,x4,x5,x6,x7;
826  block(x0)(x1)(x2)(x3)(x4)(x5)(x6)(x7);
827 
828  out[0] = ( x0 ) & 0x3ffffff;
829  out[1] = ((((word64)x1 << 32) | x0) >> 26) & 0x1ffffff;
830  out[2] = ((((word64)x2 << 32) | x1) >> 19) & 0x3ffffff;
831  out[3] = ((((word64)x3 << 32) | x2) >> 13) & 0x1ffffff;
832  out[4] = (( x3) >> 6) & 0x3ffffff;
833  out[5] = ( x4 ) & 0x1ffffff;
834  out[6] = ((((word64)x5 << 32) | x4) >> 25) & 0x3ffffff;
835  out[7] = ((((word64)x6 << 32) | x5) >> 19) & 0x1ffffff;
836  out[8] = ((((word64)x7 << 32) | x6) >> 12) & 0x3ffffff;
837  out[9] = (( x7) >> 6) & 0x1ffffff;
838 }
839 
840 /* Take a fully reduced polynomial form number and contract it into a
841  * little-endian, 32-byte array
842  */
843 void
844 curve25519_contract(byte out[32], const bignum25519 in) {
845  bignum25519 f;
846  curve25519_copy(f, in);
847 
848  #define carry_pass() \
849  f[1] += f[0] >> 26; f[0] &= reduce_mask_26; \
850  f[2] += f[1] >> 25; f[1] &= reduce_mask_25; \
851  f[3] += f[2] >> 26; f[2] &= reduce_mask_26; \
852  f[4] += f[3] >> 25; f[3] &= reduce_mask_25; \
853  f[5] += f[4] >> 26; f[4] &= reduce_mask_26; \
854  f[6] += f[5] >> 25; f[5] &= reduce_mask_25; \
855  f[7] += f[6] >> 26; f[6] &= reduce_mask_26; \
856  f[8] += f[7] >> 25; f[7] &= reduce_mask_25; \
857  f[9] += f[8] >> 26; f[8] &= reduce_mask_26;
858 
859  #define carry_pass_full() \
860  carry_pass() \
861  f[0] += 19 * (f[9] >> 25); f[9] &= reduce_mask_25;
862 
863  #define carry_pass_final() \
864  carry_pass() \
865  f[9] &= reduce_mask_25;
866 
867  carry_pass_full()
868  carry_pass_full()
869 
870  /* now t is between 0 and 2^255-1, properly carried. */
871  /* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */
872  f[0] += 19;
873  carry_pass_full()
874 
875  /* now between 19 and 2^255-1 in both cases, and offset by 19. */
876  f[0] += (reduce_mask_26 + 1) - 19;
877  f[1] += (reduce_mask_25 + 1) - 1;
878  f[2] += (reduce_mask_26 + 1) - 1;
879  f[3] += (reduce_mask_25 + 1) - 1;
880  f[4] += (reduce_mask_26 + 1) - 1;
881  f[5] += (reduce_mask_25 + 1) - 1;
882  f[6] += (reduce_mask_26 + 1) - 1;
883  f[7] += (reduce_mask_25 + 1) - 1;
884  f[8] += (reduce_mask_26 + 1) - 1;
885  f[9] += (reduce_mask_25 + 1) - 1;
886 
887  /* now between 2^255 and 2^256-20, and offset by 2^255. */
888  carry_pass_final()
889 
890  #undef carry_pass
891  #undef carry_full
892  #undef carry_final
893 
894  f[1] <<= 2; f[2] <<= 3;
895  f[3] <<= 5; f[4] <<= 6;
896  f[6] <<= 1; f[7] <<= 3;
897  f[8] <<= 4; f[9] <<= 6;
898 
899  #define F(i, s) \
900  out[s+0] |= (byte)( f[i] & 0xff); \
901  out[s+1] = (byte)((f[i] >> 8) & 0xff); \
902  out[s+2] = (byte)((f[i] >> 16) & 0xff); \
903  out[s+3] = (byte)((f[i] >> 24) & 0xff);
904 
905  out[0] = out[16] = 0;
906  F(0,0); F(1,3);
907  F(2,6); F(3,9);
908  F(4,12); F(5,16);
909  F(6,19); F(7,22);
910  F(8,25); F(9,28);
911  #undef F
912 }
913 
914 /* out = (flag) ? in : out */
915 inline void
916 curve25519_move_conditional_bytes(byte out[96], const byte in[96], word32 flag) {
917  const word32 nb = flag - 1, b = ~nb;
918  const word32 *inl = (const word32 *)in;
919  word32 *outl = (word32 *)out;
920  outl[0] = (outl[0] & nb) | (inl[0] & b);
921  outl[1] = (outl[1] & nb) | (inl[1] & b);
922  outl[2] = (outl[2] & nb) | (inl[2] & b);
923  outl[3] = (outl[3] & nb) | (inl[3] & b);
924  outl[4] = (outl[4] & nb) | (inl[4] & b);
925  outl[5] = (outl[5] & nb) | (inl[5] & b);
926  outl[6] = (outl[6] & nb) | (inl[6] & b);
927  outl[7] = (outl[7] & nb) | (inl[7] & b);
928  outl[8] = (outl[8] & nb) | (inl[8] & b);
929  outl[9] = (outl[9] & nb) | (inl[9] & b);
930  outl[10] = (outl[10] & nb) | (inl[10] & b);
931  outl[11] = (outl[11] & nb) | (inl[11] & b);
932  outl[12] = (outl[12] & nb) | (inl[12] & b);
933  outl[13] = (outl[13] & nb) | (inl[13] & b);
934  outl[14] = (outl[14] & nb) | (inl[14] & b);
935  outl[15] = (outl[15] & nb) | (inl[15] & b);
936  outl[16] = (outl[16] & nb) | (inl[16] & b);
937  outl[17] = (outl[17] & nb) | (inl[17] & b);
938  outl[18] = (outl[18] & nb) | (inl[18] & b);
939  outl[19] = (outl[19] & nb) | (inl[19] & b);
940  outl[20] = (outl[20] & nb) | (inl[20] & b);
941  outl[21] = (outl[21] & nb) | (inl[21] & b);
942  outl[22] = (outl[22] & nb) | (inl[22] & b);
943  outl[23] = (outl[23] & nb) | (inl[23] & b);
944 }
945 
946 /* if (iswap) swap(a, b) */
947 inline void
948 curve25519_swap_conditional(bignum25519 a, bignum25519 b, word32 iswap) {
949  const word32 swap = (word32)(-(sword32)iswap);
950  word32 x0,x1,x2,x3,x4,x5,x6,x7,x8,x9;
951 
952  x0 = swap & (a[0] ^ b[0]); a[0] ^= x0; b[0] ^= x0;
953  x1 = swap & (a[1] ^ b[1]); a[1] ^= x1; b[1] ^= x1;
954  x2 = swap & (a[2] ^ b[2]); a[2] ^= x2; b[2] ^= x2;
955  x3 = swap & (a[3] ^ b[3]); a[3] ^= x3; b[3] ^= x3;
956  x4 = swap & (a[4] ^ b[4]); a[4] ^= x4; b[4] ^= x4;
957  x5 = swap & (a[5] ^ b[5]); a[5] ^= x5; b[5] ^= x5;
958  x6 = swap & (a[6] ^ b[6]); a[6] ^= x6; b[6] ^= x6;
959  x7 = swap & (a[7] ^ b[7]); a[7] ^= x7; b[7] ^= x7;
960  x8 = swap & (a[8] ^ b[8]); a[8] ^= x8; b[8] ^= x8;
961  x9 = swap & (a[9] ^ b[9]); a[9] ^= x9; b[9] ^= x9;
962 }
963 
964 /*
965  * In: b = 2^5 - 2^0
966  * Out: b = 2^250 - 2^0
967  */
968 void
969 curve25519_pow_two5mtwo0_two250mtwo0(bignum25519 b) {
970  ALIGN(16) bignum25519 t0,c;
971 
972  /* 2^5 - 2^0 */ /* b */
973  /* 2^10 - 2^5 */ curve25519_square_times(t0, b, 5);
974  /* 2^10 - 2^0 */ curve25519_mul(b, t0, b);
975  /* 2^20 - 2^10 */ curve25519_square_times(t0, b, 10);
976  /* 2^20 - 2^0 */ curve25519_mul(c, t0, b);
977  /* 2^40 - 2^20 */ curve25519_square_times(t0, c, 20);
978  /* 2^40 - 2^0 */ curve25519_mul(t0, t0, c);
979  /* 2^50 - 2^10 */ curve25519_square_times(t0, t0, 10);
980  /* 2^50 - 2^0 */ curve25519_mul(b, t0, b);
981  /* 2^100 - 2^50 */ curve25519_square_times(t0, b, 50);
982  /* 2^100 - 2^0 */ curve25519_mul(c, t0, b);
983  /* 2^200 - 2^100 */ curve25519_square_times(t0, c, 100);
984  /* 2^200 - 2^0 */ curve25519_mul(t0, t0, c);
985  /* 2^250 - 2^50 */ curve25519_square_times(t0, t0, 50);
986  /* 2^250 - 2^0 */ curve25519_mul(b, t0, b);
987 }
988 
989 /*
990  * z^(p - 2) = z(2^255 - 21)
991  */
992 void
993 curve25519_recip(bignum25519 out, const bignum25519 z) {
994  ALIGN(16) bignum25519 a,t0,b;
995 
996  /* 2 */ curve25519_square_times(a, z, 1); /* a = 2 */
997  /* 8 */ curve25519_square_times(t0, a, 2);
998  /* 9 */ curve25519_mul(b, t0, z); /* b = 9 */
999  /* 11 */ curve25519_mul(a, b, a); /* a = 11 */
1000  /* 22 */ curve25519_square_times(t0, a, 1);
1001  /* 2^5 - 2^0 = 31 */ curve25519_mul(b, t0, b);
1002  /* 2^250 - 2^0 */ curve25519_pow_two5mtwo0_two250mtwo0(b);
1003  /* 2^255 - 2^5 */ curve25519_square_times(b, b, 5);
1004  /* 2^255 - 21 */ curve25519_mul(out, b, a);
1005 }
1006 
1007 /*
1008  * z^((p-5)/8) = z^(2^252 - 3)
1009  */
1010 void
1011 curve25519_pow_two252m3(bignum25519 two252m3, const bignum25519 z) {
1012  ALIGN(16) bignum25519 b,c,t0;
1013 
1014  /* 2 */ curve25519_square_times(c, z, 1); /* c = 2 */
1015  /* 8 */ curve25519_square_times(t0, c, 2); /* t0 = 8 */
1016  /* 9 */ curve25519_mul(b, t0, z); /* b = 9 */
1017  /* 11 */ curve25519_mul(c, b, c); /* c = 11 */
1018  /* 22 */ curve25519_square_times(t0, c, 1);
1019  /* 2^5 - 2^0 = 31 */ curve25519_mul(b, t0, b);
1020  /* 2^250 - 2^0 */ curve25519_pow_two5mtwo0_two250mtwo0(b);
1021  /* 2^252 - 2^2 */ curve25519_square_times(b, b, 2);
1022  /* 2^252 - 3 */ curve25519_mul(two252m3, b, z);
1023 }
1024 
1025 inline void
1026 ed25519_hash(byte *hash, const byte *in, size_t inlen) {
1027  SHA512().CalculateDigest(hash, in, inlen);
1028 }
1029 
1030 inline void
1031 ed25519_extsk(hash_512bits extsk, const byte sk[32]) {
1032  ed25519_hash(extsk, sk, 32);
1033  extsk[0] &= 248;
1034  extsk[31] &= 127;
1035  extsk[31] |= 64;
1036 }
1037 
1038 void
1039 UpdateFromStream(HashTransformation& hash, std::istream& stream)
1040 {
1041  SecByteBlock block(4096);
1042  while (stream.read((char*)block.begin(), block.size()))
1043  hash.Update(block, block.size());
1044 
1045  std::streamsize rem = stream.gcount();
1046  if (rem)
1047  hash.Update(block, (size_t)rem);
1048 
1049  block.SetMark(0);
1050 }
1051 
1052 void
1053 ed25519_hram(hash_512bits hram, const byte RS[64], const byte pk[32], const byte *m, size_t mlen) {
1054  SHA512 hash;
1055  hash.Update(RS, 32);
1056  hash.Update(pk, 32);
1057  hash.Update(m, mlen);
1058  hash.Final(hram);
1059 }
1060 
1061 void
1062 ed25519_hram(hash_512bits hram, const byte RS[64], const byte pk[32], std::istream& stream) {
1063  SHA512 hash;
1064  hash.Update(RS, 32);
1065  hash.Update(pk, 32);
1066  UpdateFromStream(hash, stream);
1067  hash.Final(hram);
1068 }
1069 
1070 inline bignum256modm_element_t
1071 lt_modm(bignum256modm_element_t a, bignum256modm_element_t b) {
1072  return (a - b) >> 31;
1073 }
1074 
1075 /* see HAC, Alg. 14.42 Step 4 */
1076 void
1077 reduce256_modm(bignum256modm r) {
1078  bignum256modm t;
1079  bignum256modm_element_t b = 0, pb, mask;
1080 
1081  /* t = r - m */
1082  pb = 0;
1083  pb += modm_m[0]; b = lt_modm(r[0], pb); t[0] = (r[0] - pb + (b << 30)); pb = b;
1084  pb += modm_m[1]; b = lt_modm(r[1], pb); t[1] = (r[1] - pb + (b << 30)); pb = b;
1085  pb += modm_m[2]; b = lt_modm(r[2], pb); t[2] = (r[2] - pb + (b << 30)); pb = b;
1086  pb += modm_m[3]; b = lt_modm(r[3], pb); t[3] = (r[3] - pb + (b << 30)); pb = b;
1087  pb += modm_m[4]; b = lt_modm(r[4], pb); t[4] = (r[4] - pb + (b << 30)); pb = b;
1088  pb += modm_m[5]; b = lt_modm(r[5], pb); t[5] = (r[5] - pb + (b << 30)); pb = b;
1089  pb += modm_m[6]; b = lt_modm(r[6], pb); t[6] = (r[6] - pb + (b << 30)); pb = b;
1090  pb += modm_m[7]; b = lt_modm(r[7], pb); t[7] = (r[7] - pb + (b << 30)); pb = b;
1091  pb += modm_m[8]; b = lt_modm(r[8], pb); t[8] = (r[8] - pb + (b << 16));
1092 
1093  /* keep r if r was smaller than m */
1094  mask = b - 1;
1095  r[0] ^= mask & (r[0] ^ t[0]);
1096  r[1] ^= mask & (r[1] ^ t[1]);
1097  r[2] ^= mask & (r[2] ^ t[2]);
1098  r[3] ^= mask & (r[3] ^ t[3]);
1099  r[4] ^= mask & (r[4] ^ t[4]);
1100  r[5] ^= mask & (r[5] ^ t[5]);
1101  r[6] ^= mask & (r[6] ^ t[6]);
1102  r[7] ^= mask & (r[7] ^ t[7]);
1103  r[8] ^= mask & (r[8] ^ t[8]);
1104 }
1105 
1106 /* Barrett reduction, see HAC, Alg. 14.42 */
1107 void
1108 barrett_reduce256_modm(bignum256modm r, const bignum256modm q1, const bignum256modm r1) {
1109  bignum256modm q3, r2;
1110  word64 c;
1111  bignum256modm_element_t f, b, pb;
1112 
1113  /* q1 = x >> 248 = 264 bits = 9 30 bit elements
1114  q2 = mu * q1
1115  q3 = (q2 / 256(32+1)) = q2 / (2^8)^(32+1) = q2 >> 264
1116  */
1117  c = mul32x32_64(modm_mu[0], q1[7]) + mul32x32_64(modm_mu[1], q1[6]) + mul32x32_64(modm_mu[2], q1[5]) + mul32x32_64(modm_mu[3], q1[4]) + mul32x32_64(modm_mu[4], q1[3]) + mul32x32_64(modm_mu[5], q1[2]) + mul32x32_64(modm_mu[6], q1[1]) + mul32x32_64(modm_mu[7], q1[0]);
1118  c >>= 30;
1119  c += mul32x32_64(modm_mu[0], q1[8]) + mul32x32_64(modm_mu[1], q1[7]) + mul32x32_64(modm_mu[2], q1[6]) + mul32x32_64(modm_mu[3], q1[5]) + mul32x32_64(modm_mu[4], q1[4]) + mul32x32_64(modm_mu[5], q1[3]) + mul32x32_64(modm_mu[6], q1[2]) + mul32x32_64(modm_mu[7], q1[1]) + mul32x32_64(modm_mu[8], q1[0]);
1120  f = (bignum256modm_element_t)c; q3[0] = (f >> 24) & 0x3f; c >>= 30;
1121  c += mul32x32_64(modm_mu[1], q1[8]) + mul32x32_64(modm_mu[2], q1[7]) + mul32x32_64(modm_mu[3], q1[6]) + mul32x32_64(modm_mu[4], q1[5]) + mul32x32_64(modm_mu[5], q1[4]) + mul32x32_64(modm_mu[6], q1[3]) + mul32x32_64(modm_mu[7], q1[2]) + mul32x32_64(modm_mu[8], q1[1]);
1122  f = (bignum256modm_element_t)c; q3[0] |= (f << 6) & 0x3fffffff; q3[1] = (f >> 24) & 0x3f; c >>= 30;
1123  c += mul32x32_64(modm_mu[2], q1[8]) + mul32x32_64(modm_mu[3], q1[7]) + mul32x32_64(modm_mu[4], q1[6]) + mul32x32_64(modm_mu[5], q1[5]) + mul32x32_64(modm_mu[6], q1[4]) + mul32x32_64(modm_mu[7], q1[3]) + mul32x32_64(modm_mu[8], q1[2]);
1124  f = (bignum256modm_element_t)c; q3[1] |= (f << 6) & 0x3fffffff; q3[2] = (f >> 24) & 0x3f; c >>= 30;
1125  c += mul32x32_64(modm_mu[3], q1[8]) + mul32x32_64(modm_mu[4], q1[7]) + mul32x32_64(modm_mu[5], q1[6]) + mul32x32_64(modm_mu[6], q1[5]) + mul32x32_64(modm_mu[7], q1[4]) + mul32x32_64(modm_mu[8], q1[3]);
1126  f = (bignum256modm_element_t)c; q3[2] |= (f << 6) & 0x3fffffff; q3[3] = (f >> 24) & 0x3f; c >>= 30;
1127  c += mul32x32_64(modm_mu[4], q1[8]) + mul32x32_64(modm_mu[5], q1[7]) + mul32x32_64(modm_mu[6], q1[6]) + mul32x32_64(modm_mu[7], q1[5]) + mul32x32_64(modm_mu[8], q1[4]);
1128  f = (bignum256modm_element_t)c; q3[3] |= (f << 6) & 0x3fffffff; q3[4] = (f >> 24) & 0x3f; c >>= 30;
1129  c += mul32x32_64(modm_mu[5], q1[8]) + mul32x32_64(modm_mu[6], q1[7]) + mul32x32_64(modm_mu[7], q1[6]) + mul32x32_64(modm_mu[8], q1[5]);
1130  f = (bignum256modm_element_t)c; q3[4] |= (f << 6) & 0x3fffffff; q3[5] = (f >> 24) & 0x3f; c >>= 30;
1131  c += mul32x32_64(modm_mu[6], q1[8]) + mul32x32_64(modm_mu[7], q1[7]) + mul32x32_64(modm_mu[8], q1[6]);
1132  f = (bignum256modm_element_t)c; q3[5] |= (f << 6) & 0x3fffffff; q3[6] = (f >> 24) & 0x3f; c >>= 30;
1133  c += mul32x32_64(modm_mu[7], q1[8]) + mul32x32_64(modm_mu[8], q1[7]);
1134  f = (bignum256modm_element_t)c; q3[6] |= (f << 6) & 0x3fffffff; q3[7] = (f >> 24) & 0x3f; c >>= 30;
1135  c += mul32x32_64(modm_mu[8], q1[8]);
1136  f = (bignum256modm_element_t)c; q3[7] |= (f << 6) & 0x3fffffff; q3[8] = (bignum256modm_element_t)(c >> 24);
1137 
1138  /* r1 = (x mod 256^(32+1)) = x mod (2^8)(31+1) = x & ((1 << 264) - 1)
1139  r2 = (q3 * m) mod (256^(32+1)) = (q3 * m) & ((1 << 264) - 1)
1140  */
1141  c = mul32x32_64(modm_m[0], q3[0]);
1142  r2[0] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
1143  c += mul32x32_64(modm_m[0], q3[1]) + mul32x32_64(modm_m[1], q3[0]);
1144  r2[1] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
1145  c += mul32x32_64(modm_m[0], q3[2]) + mul32x32_64(modm_m[1], q3[1]) + mul32x32_64(modm_m[2], q3[0]);
1146  r2[2] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
1147  c += mul32x32_64(modm_m[0], q3[3]) + mul32x32_64(modm_m[1], q3[2]) + mul32x32_64(modm_m[2], q3[1]) + mul32x32_64(modm_m[3], q3[0]);
1148  r2[3] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
1149  c += mul32x32_64(modm_m[0], q3[4]) + mul32x32_64(modm_m[1], q3[3]) + mul32x32_64(modm_m[2], q3[2]) + mul32x32_64(modm_m[3], q3[1]) + mul32x32_64(modm_m[4], q3[0]);
1150  r2[4] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
1151  c += mul32x32_64(modm_m[0], q3[5]) + mul32x32_64(modm_m[1], q3[4]) + mul32x32_64(modm_m[2], q3[3]) + mul32x32_64(modm_m[3], q3[2]) + mul32x32_64(modm_m[4], q3[1]) + mul32x32_64(modm_m[5], q3[0]);
1152  r2[5] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
1153  c += mul32x32_64(modm_m[0], q3[6]) + mul32x32_64(modm_m[1], q3[5]) + mul32x32_64(modm_m[2], q3[4]) + mul32x32_64(modm_m[3], q3[3]) + mul32x32_64(modm_m[4], q3[2]) + mul32x32_64(modm_m[5], q3[1]) + mul32x32_64(modm_m[6], q3[0]);
1154  r2[6] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
1155  c += mul32x32_64(modm_m[0], q3[7]) + mul32x32_64(modm_m[1], q3[6]) + mul32x32_64(modm_m[2], q3[5]) + mul32x32_64(modm_m[3], q3[4]) + mul32x32_64(modm_m[4], q3[3]) + mul32x32_64(modm_m[5], q3[2]) + mul32x32_64(modm_m[6], q3[1]) + mul32x32_64(modm_m[7], q3[0]);
1156  r2[7] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
1157  c += mul32x32_64(modm_m[0], q3[8]) + mul32x32_64(modm_m[1], q3[7]) + mul32x32_64(modm_m[2], q3[6]) + mul32x32_64(modm_m[3], q3[5]) + mul32x32_64(modm_m[4], q3[4]) + mul32x32_64(modm_m[5], q3[3]) + mul32x32_64(modm_m[6], q3[2]) + mul32x32_64(modm_m[7], q3[1]) + mul32x32_64(modm_m[8], q3[0]);
1158  r2[8] = (bignum256modm_element_t)(c & 0xffffff);
1159 
1160  /* r = r1 - r2
1161  if (r < 0) r += (1 << 264) */
1162  pb = 0;
1163  pb += r2[0]; b = lt_modm(r1[0], pb); r[0] = (r1[0] - pb + (b << 30)); pb = b;
1164  pb += r2[1]; b = lt_modm(r1[1], pb); r[1] = (r1[1] - pb + (b << 30)); pb = b;
1165  pb += r2[2]; b = lt_modm(r1[2], pb); r[2] = (r1[2] - pb + (b << 30)); pb = b;
1166  pb += r2[3]; b = lt_modm(r1[3], pb); r[3] = (r1[3] - pb + (b << 30)); pb = b;
1167  pb += r2[4]; b = lt_modm(r1[4], pb); r[4] = (r1[4] - pb + (b << 30)); pb = b;
1168  pb += r2[5]; b = lt_modm(r1[5], pb); r[5] = (r1[5] - pb + (b << 30)); pb = b;
1169  pb += r2[6]; b = lt_modm(r1[6], pb); r[6] = (r1[6] - pb + (b << 30)); pb = b;
1170  pb += r2[7]; b = lt_modm(r1[7], pb); r[7] = (r1[7] - pb + (b << 30)); pb = b;
1171  pb += r2[8]; b = lt_modm(r1[8], pb); r[8] = (r1[8] - pb + (b << 24));
1172 
1173  reduce256_modm(r);
1174  reduce256_modm(r);
1175 }
1176 
1177 /* addition modulo m */
1178 void
1179 add256_modm(bignum256modm r, const bignum256modm x, const bignum256modm y) {
1180  bignum256modm_element_t c;
1181 
1182  c = x[0] + y[0]; r[0] = c & 0x3fffffff; c >>= 30;
1183  c += x[1] + y[1]; r[1] = c & 0x3fffffff; c >>= 30;
1184  c += x[2] + y[2]; r[2] = c & 0x3fffffff; c >>= 30;
1185  c += x[3] + y[3]; r[3] = c & 0x3fffffff; c >>= 30;
1186  c += x[4] + y[4]; r[4] = c & 0x3fffffff; c >>= 30;
1187  c += x[5] + y[5]; r[5] = c & 0x3fffffff; c >>= 30;
1188  c += x[6] + y[6]; r[6] = c & 0x3fffffff; c >>= 30;
1189  c += x[7] + y[7]; r[7] = c & 0x3fffffff; c >>= 30;
1190  c += x[8] + y[8]; r[8] = c;
1191 
1192  reduce256_modm(r);
1193 }
1194 
1195 /* multiplication modulo m */
1196 void
1197 mul256_modm(bignum256modm r, const bignum256modm x, const bignum256modm y) {
1198  bignum256modm r1, q1;
1199  word64 c;
1200  bignum256modm_element_t f;
1201 
1202  c = mul32x32_64(x[0], y[0]);
1203  f = (bignum256modm_element_t)c; r1[0] = (f & 0x3fffffff); c >>= 30;
1204  c += mul32x32_64(x[0], y[1]) + mul32x32_64(x[1], y[0]);
1205  f = (bignum256modm_element_t)c; r1[1] = (f & 0x3fffffff); c >>= 30;
1206  c += mul32x32_64(x[0], y[2]) + mul32x32_64(x[1], y[1]) + mul32x32_64(x[2], y[0]);
1207  f = (bignum256modm_element_t)c; r1[2] = (f & 0x3fffffff); c >>= 30;
1208  c += mul32x32_64(x[0], y[3]) + mul32x32_64(x[1], y[2]) + mul32x32_64(x[2], y[1]) + mul32x32_64(x[3], y[0]);
1209  f = (bignum256modm_element_t)c; r1[3] = (f & 0x3fffffff); c >>= 30;
1210  c += mul32x32_64(x[0], y[4]) + mul32x32_64(x[1], y[3]) + mul32x32_64(x[2], y[2]) + mul32x32_64(x[3], y[1]) + mul32x32_64(x[4], y[0]);
1211  f = (bignum256modm_element_t)c; r1[4] = (f & 0x3fffffff); c >>= 30;
1212  c += mul32x32_64(x[0], y[5]) + mul32x32_64(x[1], y[4]) + mul32x32_64(x[2], y[3]) + mul32x32_64(x[3], y[2]) + mul32x32_64(x[4], y[1]) + mul32x32_64(x[5], y[0]);
1213  f = (bignum256modm_element_t)c; r1[5] = (f & 0x3fffffff); c >>= 30;
1214  c += mul32x32_64(x[0], y[6]) + mul32x32_64(x[1], y[5]) + mul32x32_64(x[2], y[4]) + mul32x32_64(x[3], y[3]) + mul32x32_64(x[4], y[2]) + mul32x32_64(x[5], y[1]) + mul32x32_64(x[6], y[0]);
1215  f = (bignum256modm_element_t)c; r1[6] = (f & 0x3fffffff); c >>= 30;
1216  c += mul32x32_64(x[0], y[7]) + mul32x32_64(x[1], y[6]) + mul32x32_64(x[2], y[5]) + mul32x32_64(x[3], y[4]) + mul32x32_64(x[4], y[3]) + mul32x32_64(x[5], y[2]) + mul32x32_64(x[6], y[1]) + mul32x32_64(x[7], y[0]);
1217  f = (bignum256modm_element_t)c; r1[7] = (f & 0x3fffffff); c >>= 30;
1218  c += mul32x32_64(x[0], y[8]) + mul32x32_64(x[1], y[7]) + mul32x32_64(x[2], y[6]) + mul32x32_64(x[3], y[5]) + mul32x32_64(x[4], y[4]) + mul32x32_64(x[5], y[3]) + mul32x32_64(x[6], y[2]) + mul32x32_64(x[7], y[1]) + mul32x32_64(x[8], y[0]);
1219  f = (bignum256modm_element_t)c; r1[8] = (f & 0x00ffffff); q1[0] = (f >> 8) & 0x3fffff; c >>= 30;
1220  c += mul32x32_64(x[1], y[8]) + mul32x32_64(x[2], y[7]) + mul32x32_64(x[3], y[6]) + mul32x32_64(x[4], y[5]) + mul32x32_64(x[5], y[4]) + mul32x32_64(x[6], y[3]) + mul32x32_64(x[7], y[2]) + mul32x32_64(x[8], y[1]);
1221  f = (bignum256modm_element_t)c; q1[0] = (q1[0] | (f << 22)) & 0x3fffffff; q1[1] = (f >> 8) & 0x3fffff; c >>= 30;
1222  c += mul32x32_64(x[2], y[8]) + mul32x32_64(x[3], y[7]) + mul32x32_64(x[4], y[6]) + mul32x32_64(x[5], y[5]) + mul32x32_64(x[6], y[4]) + mul32x32_64(x[7], y[3]) + mul32x32_64(x[8], y[2]);
1223  f = (bignum256modm_element_t)c; q1[1] = (q1[1] | (f << 22)) & 0x3fffffff; q1[2] = (f >> 8) & 0x3fffff; c >>= 30;
1224  c += mul32x32_64(x[3], y[8]) + mul32x32_64(x[4], y[7]) + mul32x32_64(x[5], y[6]) + mul32x32_64(x[6], y[5]) + mul32x32_64(x[7], y[4]) + mul32x32_64(x[8], y[3]);
1225  f = (bignum256modm_element_t)c; q1[2] = (q1[2] | (f << 22)) & 0x3fffffff; q1[3] = (f >> 8) & 0x3fffff; c >>= 30;
1226  c += mul32x32_64(x[4], y[8]) + mul32x32_64(x[5], y[7]) + mul32x32_64(x[6], y[6]) + mul32x32_64(x[7], y[5]) + mul32x32_64(x[8], y[4]);
1227  f = (bignum256modm_element_t)c; q1[3] = (q1[3] | (f << 22)) & 0x3fffffff; q1[4] = (f >> 8) & 0x3fffff; c >>= 30;
1228  c += mul32x32_64(x[5], y[8]) + mul32x32_64(x[6], y[7]) + mul32x32_64(x[7], y[6]) + mul32x32_64(x[8], y[5]);
1229  f = (bignum256modm_element_t)c; q1[4] = (q1[4] | (f << 22)) & 0x3fffffff; q1[5] = (f >> 8) & 0x3fffff; c >>= 30;
1230  c += mul32x32_64(x[6], y[8]) + mul32x32_64(x[7], y[7]) + mul32x32_64(x[8], y[6]);
1231  f = (bignum256modm_element_t)c; q1[5] = (q1[5] | (f << 22)) & 0x3fffffff; q1[6] = (f >> 8) & 0x3fffff; c >>= 30;
1232  c += mul32x32_64(x[7], y[8]) + mul32x32_64(x[8], y[7]);
1233  f = (bignum256modm_element_t)c; q1[6] = (q1[6] | (f << 22)) & 0x3fffffff; q1[7] = (f >> 8) & 0x3fffff; c >>= 30;
1234  c += mul32x32_64(x[8], y[8]);
1235  f = (bignum256modm_element_t)c; q1[7] = (q1[7] | (f << 22)) & 0x3fffffff; q1[8] = (f >> 8) & 0x3fffff;
1236 
1237  barrett_reduce256_modm(r, q1, r1);
1238 }
1239 
1240 void
1241 expand256_modm(bignum256modm out, const byte *in, size_t len) {
1242  byte work[64] = {0};
1243  bignum256modm_element_t x[16];
1244  bignum256modm q1;
1245 
1246  memcpy(work, in, len);
1247  x[0] = U8TO32_LE(work + 0);
1248  x[1] = U8TO32_LE(work + 4);
1249  x[2] = U8TO32_LE(work + 8);
1250  x[3] = U8TO32_LE(work + 12);
1251  x[4] = U8TO32_LE(work + 16);
1252  x[5] = U8TO32_LE(work + 20);
1253  x[6] = U8TO32_LE(work + 24);
1254  x[7] = U8TO32_LE(work + 28);
1255  x[8] = U8TO32_LE(work + 32);
1256  x[9] = U8TO32_LE(work + 36);
1257  x[10] = U8TO32_LE(work + 40);
1258  x[11] = U8TO32_LE(work + 44);
1259  x[12] = U8TO32_LE(work + 48);
1260  x[13] = U8TO32_LE(work + 52);
1261  x[14] = U8TO32_LE(work + 56);
1262  x[15] = U8TO32_LE(work + 60);
1263 
1264  /* r1 = (x mod 256^(32+1)) = x mod (2^8)(31+1) = x & ((1 << 264) - 1) */
1265  out[0] = ( x[0]) & 0x3fffffff;
1266  out[1] = ((x[ 0] >> 30) | (x[ 1] << 2)) & 0x3fffffff;
1267  out[2] = ((x[ 1] >> 28) | (x[ 2] << 4)) & 0x3fffffff;
1268  out[3] = ((x[ 2] >> 26) | (x[ 3] << 6)) & 0x3fffffff;
1269  out[4] = ((x[ 3] >> 24) | (x[ 4] << 8)) & 0x3fffffff;
1270  out[5] = ((x[ 4] >> 22) | (x[ 5] << 10)) & 0x3fffffff;
1271  out[6] = ((x[ 5] >> 20) | (x[ 6] << 12)) & 0x3fffffff;
1272  out[7] = ((x[ 6] >> 18) | (x[ 7] << 14)) & 0x3fffffff;
1273  out[8] = ((x[ 7] >> 16) | (x[ 8] << 16)) & 0x00ffffff;
1274 
1275  /* 8*31 = 248 bits, no need to reduce */
1276  if (len < 32)
1277  return;
1278 
1279  /* q1 = x >> 248 = 264 bits = 9 30 bit elements */
1280  q1[0] = ((x[ 7] >> 24) | (x[ 8] << 8)) & 0x3fffffff;
1281  q1[1] = ((x[ 8] >> 22) | (x[ 9] << 10)) & 0x3fffffff;
1282  q1[2] = ((x[ 9] >> 20) | (x[10] << 12)) & 0x3fffffff;
1283  q1[3] = ((x[10] >> 18) | (x[11] << 14)) & 0x3fffffff;
1284  q1[4] = ((x[11] >> 16) | (x[12] << 16)) & 0x3fffffff;
1285  q1[5] = ((x[12] >> 14) | (x[13] << 18)) & 0x3fffffff;
1286  q1[6] = ((x[13] >> 12) | (x[14] << 20)) & 0x3fffffff;
1287  q1[7] = ((x[14] >> 10) | (x[15] << 22)) & 0x3fffffff;
1288  q1[8] = ((x[15] >> 8) );
1289 
1290  barrett_reduce256_modm(out, q1, out);
1291 }
1292 
1293 void
1294 expand_raw256_modm(bignum256modm out, const byte in[32]) {
1295  bignum256modm_element_t x[8];
1296 
1297  x[0] = U8TO32_LE(in + 0);
1298  x[1] = U8TO32_LE(in + 4);
1299  x[2] = U8TO32_LE(in + 8);
1300  x[3] = U8TO32_LE(in + 12);
1301  x[4] = U8TO32_LE(in + 16);
1302  x[5] = U8TO32_LE(in + 20);
1303  x[6] = U8TO32_LE(in + 24);
1304  x[7] = U8TO32_LE(in + 28);
1305 
1306  out[0] = ( x[0]) & 0x3fffffff;
1307  out[1] = ((x[ 0] >> 30) | (x[ 1] << 2)) & 0x3fffffff;
1308  out[2] = ((x[ 1] >> 28) | (x[ 2] << 4)) & 0x3fffffff;
1309  out[3] = ((x[ 2] >> 26) | (x[ 3] << 6)) & 0x3fffffff;
1310  out[4] = ((x[ 3] >> 24) | (x[ 4] << 8)) & 0x3fffffff;
1311  out[5] = ((x[ 4] >> 22) | (x[ 5] << 10)) & 0x3fffffff;
1312  out[6] = ((x[ 5] >> 20) | (x[ 6] << 12)) & 0x3fffffff;
1313  out[7] = ((x[ 6] >> 18) | (x[ 7] << 14)) & 0x3fffffff;
1314  out[8] = ((x[ 7] >> 16) ) & 0x0000ffff;
1315 }
1316 
1317 void
1318 contract256_modm(byte out[32], const bignum256modm in) {
1319  U32TO8_LE(out + 0, (in[0] ) | (in[1] << 30));
1320  U32TO8_LE(out + 4, (in[1] >> 2) | (in[2] << 28));
1321  U32TO8_LE(out + 8, (in[2] >> 4) | (in[3] << 26));
1322  U32TO8_LE(out + 12, (in[3] >> 6) | (in[4] << 24));
1323  U32TO8_LE(out + 16, (in[4] >> 8) | (in[5] << 22));
1324  U32TO8_LE(out + 20, (in[5] >> 10) | (in[6] << 20));
1325  U32TO8_LE(out + 24, (in[6] >> 12) | (in[7] << 18));
1326  U32TO8_LE(out + 28, (in[7] >> 14) | (in[8] << 16));
1327 }
1328 
1329 void
1330 contract256_window4_modm(signed char r[64], const bignum256modm in) {
1331  char carry;
1332  signed char *quads = r;
1333  bignum256modm_element_t i, j, v;
1334 
1335  for (i = 0; i < 8; i += 2) {
1336  v = in[i];
1337  for (j = 0; j < 7; j++) {
1338  *quads++ = (v & 15);
1339  v >>= 4;
1340  }
1341  v |= (in[i+1] << 2);
1342  for (j = 0; j < 8; j++) {
1343  *quads++ = (v & 15);
1344  v >>= 4;
1345  }
1346  }
1347 
1348  v = in[8];
1349  *quads++ = (v & 15); v >>= 4;
1350  *quads++ = (v & 15); v >>= 4;
1351  *quads++ = (v & 15); v >>= 4;
1352  *quads++ = (v & 15); v >>= 4;
1353 
1354  /* making it signed */
1355  carry = 0;
1356  for(i = 0; i < 63; i++) {
1357  r[i] += carry;
1358  r[i+1] += (r[i] >> 4);
1359  r[i] &= 15;
1360  carry = (r[i] >> 3);
1361  r[i] -= (carry << 4);
1362  }
1363  r[63] += carry;
1364 }
1365 
1366 void
1367 contract256_slidingwindow_modm(signed char r[256], const bignum256modm s, int windowsize) {
1368  int i,j,k,b;
1369  int m = (1 << (windowsize - 1)) - 1, soplen = 256;
1370  signed char *bits = r;
1371  bignum256modm_element_t v;
1372 
1373  /* first put the binary expansion into r */
1374  for (i = 0; i < 8; i++) {
1375  v = s[i];
1376  for (j = 0; j < 30; j++, v >>= 1)
1377  *bits++ = (v & 1);
1378  }
1379  v = s[8];
1380  for (j = 0; j < 16; j++, v >>= 1)
1381  *bits++ = (v & 1);
1382 
1383  /* Making it sliding window */
1384  for (j = 0; j < soplen; j++) {
1385  if (!r[j])
1386  continue;
1387 
1388  for (b = 1; (b < (soplen - j)) && (b <= 6); b++) {
1389  if ((r[j] + (r[j + b] << b)) <= m) {
1390  r[j] += r[j + b] << b;
1391  r[j + b] = 0;
1392  } else if ((r[j] - (r[j + b] << b)) >= -m) {
1393  r[j] -= r[j + b] << b;
1394  for (k = j + b; k < soplen; k++) {
1395  if (!r[k]) {
1396  r[k] = 1;
1397  break;
1398  }
1399  r[k] = 0;
1400  }
1401  } else if (r[j + b]) {
1402  break;
1403  }
1404  }
1405  }
1406 }
1407 
1408 inline void
1409 ge25519_p1p1_to_partial(ge25519 *r, const ge25519_p1p1 *p) {
1410  curve25519_mul(r->x, p->x, p->t);
1411  curve25519_mul(r->y, p->y, p->z);
1412  curve25519_mul(r->z, p->z, p->t);
1413 }
1414 
1415 inline void
1416 ge25519_p1p1_to_full(ge25519 *r, const ge25519_p1p1 *p) {
1417  curve25519_mul(r->x, p->x, p->t);
1418  curve25519_mul(r->y, p->y, p->z);
1419  curve25519_mul(r->z, p->z, p->t);
1420  curve25519_mul(r->t, p->x, p->y);
1421 }
1422 
1423 void
1424 ge25519_full_to_pniels(ge25519_pniels *p, const ge25519 *r) {
1425  curve25519_sub(p->ysubx, r->y, r->x);
1426  curve25519_add(p->xaddy, r->y, r->x);
1427  curve25519_copy(p->z, r->z);
1428  curve25519_mul(p->t2d, r->t, ge25519_ec2d);
1429 }
1430 
1431 void
1432 ge25519_add_p1p1(ge25519_p1p1 *r, const ge25519 *p, const ge25519 *q) {
1433  bignum25519 a,b,c,d,t,u;
1434 
1435  curve25519_sub(a, p->y, p->x);
1436  curve25519_add(b, p->y, p->x);
1437  curve25519_sub(t, q->y, q->x);
1438  curve25519_add(u, q->y, q->x);
1439  curve25519_mul(a, a, t);
1440  curve25519_mul(b, b, u);
1441  curve25519_mul(c, p->t, q->t);
1442  curve25519_mul(c, c, ge25519_ec2d);
1443  curve25519_mul(d, p->z, q->z);
1444  curve25519_add(d, d, d);
1445  curve25519_sub(r->x, b, a);
1446  curve25519_add(r->y, b, a);
1447  curve25519_add_after_basic(r->z, d, c);
1448  curve25519_sub_after_basic(r->t, d, c);
1449 }
1450 
1451 void
1452 ge25519_double_p1p1(ge25519_p1p1 *r, const ge25519 *p) {
1453  bignum25519 a,b,c;
1454 
1455  curve25519_square(a, p->x);
1456  curve25519_square(b, p->y);
1457  curve25519_square(c, p->z);
1458  curve25519_add_reduce(c, c, c);
1459  curve25519_add(r->x, p->x, p->y);
1460  curve25519_square(r->x, r->x);
1461  curve25519_add(r->y, b, a);
1462  curve25519_sub(r->z, b, a);
1463  curve25519_sub_after_basic(r->x, r->x, r->y);
1464  curve25519_sub_after_basic(r->t, c, r->z);
1465 }
1466 
1467 void
1468 ge25519_nielsadd2_p1p1(ge25519_p1p1 *r, const ge25519 *p, const ge25519_niels *q, byte signbit) {
1469  const bignum25519 *qb = (const bignum25519 *)q;
1470  bignum25519 *rb = (bignum25519 *)r;
1471  bignum25519 a,b,c;
1472 
1473  curve25519_sub(a, p->y, p->x);
1474  curve25519_add(b, p->y, p->x);
1475  curve25519_mul(a, a, qb[signbit]); /* x for +, y for - */
1476  curve25519_mul(r->x, b, qb[signbit^1]); /* y for +, x for - */
1477  curve25519_add(r->y, r->x, a);
1478  curve25519_sub(r->x, r->x, a);
1479  curve25519_mul(c, p->t, q->t2d);
1480  curve25519_add_reduce(r->t, p->z, p->z);
1481  curve25519_copy(r->z, r->t);
1482  curve25519_add(rb[2+signbit], rb[2+signbit], c); /* z for +, t for - */
1483  curve25519_sub(rb[2+(signbit^1)], rb[2+(signbit^1)], c); /* t for +, z for - */
1484 }
1485 
1486 void
1487 ge25519_pnielsadd_p1p1(ge25519_p1p1 *r, const ge25519 *p, const ge25519_pniels *q, byte signbit) {
1488  const bignum25519 *qb = (const bignum25519 *)q;
1489  bignum25519 *rb = (bignum25519 *)r;
1490  bignum25519 a,b,c;
1491 
1492  curve25519_sub(a, p->y, p->x);
1493  curve25519_add(b, p->y, p->x);
1494  curve25519_mul(a, a, qb[signbit]); /* ysubx for +, xaddy for - */
1495  curve25519_mul(r->x, b, qb[signbit^1]); /* xaddy for +, ysubx for - */
1496  curve25519_add(r->y, r->x, a);
1497  curve25519_sub(r->x, r->x, a);
1498  curve25519_mul(c, p->t, q->t2d);
1499  curve25519_mul(r->t, p->z, q->z);
1500  curve25519_add_reduce(r->t, r->t, r->t);
1501  curve25519_copy(r->z, r->t);
1502  curve25519_add(rb[2+signbit], rb[2+signbit], c); /* z for +, t for - */
1503  curve25519_sub(rb[2+(signbit^1)], rb[2+(signbit^1)], c); /* t for +, z for - */
1504 }
1505 
1506 void
1507 ge25519_double_partial(ge25519 *r, const ge25519 *p) {
1508  ge25519_p1p1 t;
1509  ge25519_double_p1p1(&t, p);
1510  ge25519_p1p1_to_partial(r, &t);
1511 }
1512 
1513 void
1514 ge25519_double(ge25519 *r, const ge25519 *p) {
1515  ge25519_p1p1 t;
1516  ge25519_double_p1p1(&t, p);
1517  ge25519_p1p1_to_full(r, &t);
1518 }
1519 
1520 void
1521 ge25519_add(ge25519 *r, const ge25519 *p, const ge25519 *q) {
1522  ge25519_p1p1 t;
1523  ge25519_add_p1p1(&t, p, q);
1524  ge25519_p1p1_to_full(r, &t);
1525 }
1526 
1527 void
1528 ge25519_nielsadd2(ge25519 *r, const ge25519_niels *q) {
1529  bignum25519 a,b,c,e,f,g,h;
1530 
1531  curve25519_sub(a, r->y, r->x);
1532  curve25519_add(b, r->y, r->x);
1533  curve25519_mul(a, a, q->ysubx);
1534  curve25519_mul(e, b, q->xaddy);
1535  curve25519_add(h, e, a);
1536  curve25519_sub(e, e, a);
1537  curve25519_mul(c, r->t, q->t2d);
1538  curve25519_add(f, r->z, r->z);
1539  curve25519_add_after_basic(g, f, c);
1540  curve25519_sub_after_basic(f, f, c);
1541  curve25519_mul(r->x, e, f);
1542  curve25519_mul(r->y, h, g);
1543  curve25519_mul(r->z, g, f);
1544  curve25519_mul(r->t, e, h);
1545 }
1546 
1547 void
1548 ge25519_pnielsadd(ge25519_pniels *r, const ge25519 *p, const ge25519_pniels *q) {
1549  bignum25519 a,b,c,x,y,z,t;
1550 
1551  curve25519_sub(a, p->y, p->x);
1552  curve25519_add(b, p->y, p->x);
1553  curve25519_mul(a, a, q->ysubx);
1554  curve25519_mul(x, b, q->xaddy);
1555  curve25519_add(y, x, a);
1556  curve25519_sub(x, x, a);
1557  curve25519_mul(c, p->t, q->t2d);
1558  curve25519_mul(t, p->z, q->z);
1559  curve25519_add(t, t, t);
1560  curve25519_add_after_basic(z, t, c);
1561  curve25519_sub_after_basic(t, t, c);
1562  curve25519_mul(r->xaddy, x, t);
1563  curve25519_mul(r->ysubx, y, z);
1564  curve25519_mul(r->z, z, t);
1565  curve25519_mul(r->t2d, x, y);
1566  curve25519_copy(y, r->ysubx);
1567  curve25519_sub(r->ysubx, r->ysubx, r->xaddy);
1568  curve25519_add(r->xaddy, r->xaddy, y);
1569  curve25519_mul(r->t2d, r->t2d, ge25519_ec2d);
1570 }
1571 
1572 void
1573 ge25519_pack(byte r[32], const ge25519 *p) {
1574  bignum25519 tx, ty, zi;
1575  byte parity[32];
1576  curve25519_recip(zi, p->z);
1577  curve25519_mul(tx, p->x, zi);
1578  curve25519_mul(ty, p->y, zi);
1579  curve25519_contract(r, ty);
1580  curve25519_contract(parity, tx);
1581  r[31] ^= ((parity[0] & 1) << 7);
1582 }
1583 
1584 int
1585 ed25519_verify(const byte *x, const byte *y, size_t len) {
1586  size_t differentbits = 0;
1587  while (len--)
1588  differentbits |= (*x++ ^ *y++);
1589  return (int) (1 & ((differentbits - 1) >> 8));
1590 }
1591 
1592 int
1593 ge25519_unpack_negative_vartime(ge25519 *r, const byte p[32]) {
1594  const byte zero[32] = {0};
1595  const bignum25519 one = {1};
1596  byte parity = p[31] >> 7;
1597  byte check[32];
1598  bignum25519 t, root, num, den, d3;
1599 
1600  curve25519_expand(r->y, p);
1601  curve25519_copy(r->z, one);
1602  curve25519_square(num, r->y); /* x = y^2 */
1603  curve25519_mul(den, num, ge25519_ecd); /* den = dy^2 */
1604  curve25519_sub_reduce(num, num, r->z); /* x = y^1 - 1 */
1605  curve25519_add(den, den, r->z); /* den = dy^2 + 1 */
1606 
1607  /* Computation of sqrt(num/den) */
1608  /* 1.: computation of num^((p-5)/8)*den^((7p-35)/8) = (num*den^7)^((p-5)/8) */
1609  curve25519_square(t, den);
1610  curve25519_mul(d3, t, den);
1611  curve25519_square(r->x, d3);
1612  curve25519_mul(r->x, r->x, den);
1613  curve25519_mul(r->x, r->x, num);
1614  curve25519_pow_two252m3(r->x, r->x);
1615 
1616  /* 2. computation of r->x = num * den^3 * (num*den^7)^((p-5)/8) */
1617  curve25519_mul(r->x, r->x, d3);
1618  curve25519_mul(r->x, r->x, num);
1619 
1620  /* 3. Check if either of the roots works: */
1621  curve25519_square(t, r->x);
1622  curve25519_mul(t, t, den);
1623  curve25519_sub_reduce(root, t, num);
1624  curve25519_contract(check, root);
1625  if (!ed25519_verify(check, zero, 32)) {
1626  curve25519_add_reduce(t, t, num);
1627  curve25519_contract(check, t);
1628  if (!ed25519_verify(check, zero, 32))
1629  return 0;
1630  curve25519_mul(r->x, r->x, ge25519_sqrtneg1);
1631  }
1632 
1633  curve25519_contract(check, r->x);
1634  if ((check[0] & 1) == parity) {
1635  curve25519_copy(t, r->x);
1636  curve25519_neg(r->x, t);
1637  }
1638  curve25519_mul(r->t, r->x, r->y);
1639  return 1;
1640 }
1641 
1642 /* computes [s1]p1 + [s2]basepoint */
1643 void
1644 ge25519_double_scalarmult_vartime(ge25519 *r, const ge25519 *p1, const bignum256modm s1, const bignum256modm s2) {
1645  signed char slide1[256], slide2[256];
1646  ge25519_pniels pre1[S1_TABLE_SIZE];
1647  ge25519 d1;
1648  ge25519_p1p1 t;
1649  sword32 i;
1650 
1651  contract256_slidingwindow_modm(slide1, s1, S1_SWINDOWSIZE);
1652  contract256_slidingwindow_modm(slide2, s2, S2_SWINDOWSIZE);
1653 
1654  ge25519_double(&d1, p1);
1655  ge25519_full_to_pniels(pre1, p1);
1656  for (i = 0; i < S1_TABLE_SIZE - 1; i++)
1657  ge25519_pnielsadd(&pre1[i+1], &d1, &pre1[i]);
1658 
1659  /* set neutral */
1660  memset(r, 0, sizeof(ge25519));
1661  r->y[0] = 1;
1662  r->z[0] = 1;
1663 
1664  i = 255;
1665  while ((i >= 0) && !(slide1[i] | slide2[i]))
1666  i--;
1667 
1668  for (; i >= 0; i--) {
1669  ge25519_double_p1p1(&t, r);
1670 
1671  if (slide1[i]) {
1672  ge25519_p1p1_to_full(r, &t);
1673  ge25519_pnielsadd_p1p1(&t, r, &pre1[abs(slide1[i]) / 2], (byte)slide1[i] >> 7);
1674  }
1675 
1676  if (slide2[i]) {
1677  ge25519_p1p1_to_full(r, &t);
1678  ge25519_nielsadd2_p1p1(&t, r, &ge25519_niels_sliding_multiples[abs(slide2[i]) / 2], (byte)slide2[i] >> 7);
1679  }
1680 
1681  ge25519_p1p1_to_partial(r, &t);
1682  }
1683 }
1684 
1685 #if !defined(HAVE_GE25519_SCALARMULT_BASE_CHOOSE_NIELS)
1686 
1687 word32
1688 ge25519_windowb_equal(word32 b, word32 c) {
1689  return ((b ^ c) - 1) >> 31;
1690 }
1691 
1692 void
1693 ge25519_scalarmult_base_choose_niels(ge25519_niels *t, const byte table[256][96], word32 pos, signed char b) {
1694  bignum25519 neg;
1695  word32 sign = (word32)((byte)b >> 7);
1696  word32 mask = ~(sign - 1);
1697  word32 u = (b + mask) ^ mask;
1698  word32 i;
1699 
1700  /* ysubx, xaddy, t2d in packed form. initialize to ysubx = 1, xaddy = 1, t2d = 0 */
1701  byte packed[96] = {0};
1702  packed[0] = 1;
1703  packed[32] = 1;
1704 
1705  for (i = 0; i < 8; i++)
1706  curve25519_move_conditional_bytes(packed, table[(pos * 8) + i], ge25519_windowb_equal(u, i + 1));
1707 
1708  /* expand in to t */
1709  curve25519_expand(t->ysubx, packed + 0);
1710  curve25519_expand(t->xaddy, packed + 32);
1711  curve25519_expand(t->t2d , packed + 64);
1712 
1713  /* adjust for sign */
1714  curve25519_swap_conditional(t->ysubx, t->xaddy, sign);
1715  curve25519_neg(neg, t->t2d);
1716  curve25519_swap_conditional(t->t2d, neg, sign);
1717 }
1718 
1719 #endif /* HAVE_GE25519_SCALARMULT_BASE_CHOOSE_NIELS */
1720 
1721 /* computes [s]basepoint */
1722 void
1723 ge25519_scalarmult_base_niels(ge25519 *r, const byte basepoint_table[256][96], const bignum256modm s) {
1724  signed char b[64];
1725  word32 i;
1726  ge25519_niels t;
1727 
1728  contract256_window4_modm(b, s);
1729 
1730  ge25519_scalarmult_base_choose_niels(&t, basepoint_table, 0, b[1]);
1731  curve25519_sub_reduce(r->x, t.xaddy, t.ysubx);
1732  curve25519_add_reduce(r->y, t.xaddy, t.ysubx);
1733  memset(r->z, 0, sizeof(bignum25519));
1734  curve25519_copy(r->t, t.t2d);
1735  r->z[0] = 2;
1736  for (i = 3; i < 64; i += 2) {
1737  ge25519_scalarmult_base_choose_niels(&t, basepoint_table, i / 2, b[i]);
1738  ge25519_nielsadd2(r, &t);
1739  }
1740  ge25519_double_partial(r, r);
1741  ge25519_double_partial(r, r);
1742  ge25519_double_partial(r, r);
1743  ge25519_double(r, r);
1744  ge25519_scalarmult_base_choose_niels(&t, basepoint_table, 0, b[0]);
1745  curve25519_mul(t.t2d, t.t2d, ge25519_ecd);
1746  ge25519_nielsadd2(r, &t);
1747  for(i = 2; i < 64; i += 2) {
1748  ge25519_scalarmult_base_choose_niels(&t, basepoint_table, i / 2, b[i]);
1749  ge25519_nielsadd2(r, &t);
1750  }
1751 }
1752 
1753 ANONYMOUS_NAMESPACE_END
1754 NAMESPACE_END // Ed25519
1755 NAMESPACE_END // Donna
1756 NAMESPACE_END // CryptoPP
1757 
1758 //***************************** curve25519 *****************************//
1759 
1760 NAMESPACE_BEGIN(CryptoPP)
1761 NAMESPACE_BEGIN(Donna)
1762 
1763 int curve25519_mult_CXX(byte sharedKey[32], const byte secretKey[32], const byte othersKey[32])
1764 {
1765  using namespace CryptoPP::Donna::X25519;
1766 
1768  for (size_t i = 0; i < 32; ++i)
1769  e[i] = secretKey[i];
1770  e[0] &= 0xf8; e[31] &= 0x7f; e[31] |= 0x40;
1771 
1772  bignum25519 nqpqx = {1}, nqpqz = {0}, nqz = {1}, nqx;
1773  bignum25519 q, qx, qpqx, qqx, zzz, zmone;
1774  size_t bit, lastbit;
1775 
1776  curve25519_expand(q, othersKey);
1777  curve25519_copy(nqx, q);
1778 
1779  /* bit 255 is always 0, and bit 254 is always 1, so skip bit 255 and
1780  start pre-swapped on bit 254 */
1781  lastbit = 1;
1782 
1783  /* we are doing bits 254..3 in the loop, but are swapping in bits 253..2 */
1784  for (int i = 253; i >= 2; i--) {
1785  curve25519_add(qx, nqx, nqz);
1786  curve25519_sub(nqz, nqx, nqz);
1787  curve25519_add(qpqx, nqpqx, nqpqz);
1788  curve25519_sub(nqpqz, nqpqx, nqpqz);
1789  curve25519_mul(nqpqx, qpqx, nqz);
1790  curve25519_mul(nqpqz, qx, nqpqz);
1791  curve25519_add(qqx, nqpqx, nqpqz);
1792  curve25519_sub(nqpqz, nqpqx, nqpqz);
1793  curve25519_square(nqpqz, nqpqz);
1794  curve25519_square(nqpqx, qqx);
1795  curve25519_mul(nqpqz, nqpqz, q);
1796  curve25519_square(qx, qx);
1797  curve25519_square(nqz, nqz);
1798  curve25519_mul(nqx, qx, nqz);
1799  curve25519_sub(nqz, qx, nqz);
1800  curve25519_scalar_product(zzz, nqz, 121665);
1801  curve25519_add(zzz, zzz, qx);
1802  curve25519_mul(nqz, nqz, zzz);
1803 
1804  bit = (e[i/8] >> (i & 7)) & 1;
1805  curve25519_swap_conditional(nqx, nqpqx, bit ^ lastbit);
1806  curve25519_swap_conditional(nqz, nqpqz, bit ^ lastbit);
1807  lastbit = bit;
1808  }
1809 
1810  /* the final 3 bits are always zero, so we only need to double */
1811  for (int i = 0; i < 3; i++) {
1812  curve25519_add(qx, nqx, nqz);
1813  curve25519_sub(nqz, nqx, nqz);
1814  curve25519_square(qx, qx);
1815  curve25519_square(nqz, nqz);
1816  curve25519_mul(nqx, qx, nqz);
1817  curve25519_sub(nqz, qx, nqz);
1818  curve25519_scalar_product(zzz, nqz, 121665);
1819  curve25519_add(zzz, zzz, qx);
1820  curve25519_mul(nqz, nqz, zzz);
1821  }
1822 
1823  curve25519_recip(zmone, nqz);
1824  curve25519_mul(nqz, nqx, zmone);
1825  curve25519_contract(sharedKey, nqz);
1826 
1827  return 0;
1828 }
1829 
1830 int curve25519_mult(byte publicKey[32], const byte secretKey[32])
1831 {
1832  using namespace CryptoPP::Donna::X25519;
1833 
1834 #if (CRYPTOPP_CURVE25519_SSE2)
1835  if (HasSSE2())
1836  return curve25519_mult_SSE2(publicKey, secretKey, basePoint);
1837  else
1838 #endif
1839 
1840  return curve25519_mult_CXX(publicKey, secretKey, basePoint);
1841 }
1842 
1843 int curve25519_mult(byte sharedKey[32], const byte secretKey[32], const byte othersKey[32])
1844 {
1845 #if (CRYPTOPP_CURVE25519_SSE2)
1846  if (HasSSE2())
1847  return curve25519_mult_SSE2(sharedKey, secretKey, othersKey);
1848  else
1849 #endif
1850 
1851  return curve25519_mult_CXX(sharedKey, secretKey, othersKey);
1852 }
1853 
1854 NAMESPACE_END // Donna
1855 NAMESPACE_END // CryptoPP
1856 
1857 //******************************* ed25519 *******************************//
1858 
1859 NAMESPACE_BEGIN(CryptoPP)
1860 NAMESPACE_BEGIN(Donna)
1861 
1862 int
1863 ed25519_publickey_CXX(byte publicKey[32], const byte secretKey[32])
1864 {
1865  using namespace CryptoPP::Donna::Ed25519;
1866 
1867  bignum256modm a;
1868  ALIGN(16) ge25519 A;
1869  hash_512bits extsk;
1870 
1871  /* A = aB */
1872  ed25519_extsk(extsk, secretKey);
1873  expand256_modm(a, extsk, 32);
1874  ge25519_scalarmult_base_niels(&A, ge25519_niels_base_multiples, a);
1875  ge25519_pack(publicKey, &A);
1876 
1877  return 0;
1878 }
1879 
1880 int
1881 ed25519_publickey(byte publicKey[32], const byte secretKey[32])
1882 {
1883  return ed25519_publickey_CXX(publicKey, secretKey);
1884 }
1885 
1886 int
1887 ed25519_sign_CXX(std::istream& stream, const byte sk[32], const byte pk[32], byte RS[64])
1888 {
1889  using namespace CryptoPP::Donna::Ed25519;
1890 
1891  bignum256modm r, S, a;
1892  ALIGN(16) ge25519 R;
1893  hash_512bits extsk, hashr, hram;
1894 
1895  // Unfortunately we need to read the stream twice. The fisrt time calculates
1896  // 'r = H(aExt[32..64], m)'. The second time calculates 'S = H(R,A,m)'. There
1897  // is a data dependency due to hashing 'RS' with 'R = [r]B' that does not
1898  // allow us to read the stream once.
1899  std::streampos where = stream.tellg();
1900 
1901  ed25519_extsk(extsk, sk);
1902 
1903  /* r = H(aExt[32..64], m) */
1904  SHA512 hash;
1905  hash.Update(extsk + 32, 32);
1906  UpdateFromStream(hash, stream);
1907  hash.Final(hashr);
1908  expand256_modm(r, hashr, 64);
1909 
1910  /* R = rB */
1911  ge25519_scalarmult_base_niels(&R, ge25519_niels_base_multiples, r);
1912  ge25519_pack(RS, &R);
1913 
1914  // Reset stream for the second digest
1915  stream.clear();
1916  stream.seekg(where);
1917 
1918  /* S = H(R,A,m).. */
1919  ed25519_hram(hram, RS, pk, stream);
1920  expand256_modm(S, hram, 64);
1921 
1922  /* S = H(R,A,m)a */
1923  expand256_modm(a, extsk, 32);
1924  mul256_modm(S, S, a);
1925 
1926  /* S = (r + H(R,A,m)a) */
1927  add256_modm(S, S, r);
1928 
1929  /* S = (r + H(R,A,m)a) mod L */
1930  contract256_modm(RS + 32, S);
1931 
1932  return 0;
1933 }
1934 
1935 int
1936 ed25519_sign_CXX(const byte *m, size_t mlen, const byte sk[32], const byte pk[32], byte RS[64])
1937 {
1938  using namespace CryptoPP::Donna::Ed25519;
1939 
1940  bignum256modm r, S, a;
1941  ALIGN(16) ge25519 R;
1942  hash_512bits extsk, hashr, hram;
1943 
1944  ed25519_extsk(extsk, sk);
1945 
1946  /* r = H(aExt[32..64], m) */
1947  SHA512 hash;
1948  hash.Update(extsk + 32, 32);
1949  hash.Update(m, mlen);
1950  hash.Final(hashr);
1951  expand256_modm(r, hashr, 64);
1952 
1953  /* R = rB */
1954  ge25519_scalarmult_base_niels(&R, ge25519_niels_base_multiples, r);
1955  ge25519_pack(RS, &R);
1956 
1957  /* S = H(R,A,m).. */
1958  ed25519_hram(hram, RS, pk, m, mlen);
1959  expand256_modm(S, hram, 64);
1960 
1961  /* S = H(R,A,m)a */
1962  expand256_modm(a, extsk, 32);
1963  mul256_modm(S, S, a);
1964 
1965  /* S = (r + H(R,A,m)a) */
1966  add256_modm(S, S, r);
1967 
1968  /* S = (r + H(R,A,m)a) mod L */
1969  contract256_modm(RS + 32, S);
1970 
1971  return 0;
1972 }
1973 
1974 int
1975 ed25519_sign(std::istream& stream, const byte secretKey[32], const byte publicKey[32],
1976  byte signature[64])
1977 {
1978  return ed25519_sign_CXX(stream, secretKey, publicKey, signature);
1979 }
1980 
1981 int
1982 ed25519_sign(const byte* message, size_t messageLength, const byte secretKey[32],
1983  const byte publicKey[32], byte signature[64])
1984 {
1985  return ed25519_sign_CXX(message, messageLength, secretKey, publicKey, signature);
1986 }
1987 
1988 int
1989 ed25519_sign_open_CXX(std::istream& stream, const byte pk[32], const byte RS[64]) {
1990 
1991  using namespace CryptoPP::Donna::Ed25519;
1992 
1993  ALIGN(16) ge25519 R, A;
1994  hash_512bits hash;
1995  bignum256modm hram, S;
1996  byte checkR[32];
1997 
1998  if ((RS[63] & 224) || !ge25519_unpack_negative_vartime(&A, pk))
1999  return -1;
2000 
2001  /* hram = H(R,A,m) */
2002  ed25519_hram(hash, RS, pk, stream);
2003  expand256_modm(hram, hash, 64);
2004 
2005  /* S */
2006  expand256_modm(S, RS + 32, 32);
2007 
2008  /* SB - H(R,A,m)A */
2009  ge25519_double_scalarmult_vartime(&R, &A, hram, S);
2010  ge25519_pack(checkR, &R);
2011 
2012  /* check that R = SB - H(R,A,m)A */
2013  return ed25519_verify(RS, checkR, 32) ? 0 : -1;
2014 }
2015 
2016 int
2017 ed25519_sign_open_CXX(const byte *m, size_t mlen, const byte pk[32], const byte RS[64]) {
2018 
2019  using namespace CryptoPP::Donna::Ed25519;
2020 
2021  ALIGN(16) ge25519 R, A;
2022  hash_512bits hash;
2023  bignum256modm hram, S;
2024  byte checkR[32];
2025 
2026  if ((RS[63] & 224) || !ge25519_unpack_negative_vartime(&A, pk))
2027  return -1;
2028 
2029  /* hram = H(R,A,m) */
2030  ed25519_hram(hash, RS, pk, m, mlen);
2031  expand256_modm(hram, hash, 64);
2032 
2033  /* S */
2034  expand256_modm(S, RS + 32, 32);
2035 
2036  /* SB - H(R,A,m)A */
2037  ge25519_double_scalarmult_vartime(&R, &A, hram, S);
2038  ge25519_pack(checkR, &R);
2039 
2040  /* check that R = SB - H(R,A,m)A */
2041  return ed25519_verify(RS, checkR, 32) ? 0 : -1;
2042 }
2043 
2044 int
2045 ed25519_sign_open(const byte *message, size_t messageLength, const byte publicKey[32], const byte signature[64])
2046 {
2047  return ed25519_sign_open_CXX(message, messageLength, publicKey, signature);
2048 }
2049 
2050 int
2051 ed25519_sign_open(std::istream& stream, const byte publicKey[32], const byte signature[64])
2052 {
2053  return ed25519_sign_open_CXX(stream, publicKey, signature);
2054 }
2055 
2056 NAMESPACE_END // Donna
2057 NAMESPACE_END // CryptoPP
2058 
2059 #endif // CRYPTOPP_CURVE25519_32BIT
Utility functions for the Crypto++ library.
void PutWord(bool assumeAligned, ByteOrder order, byte *block, T value, const byte *xorBlock=NULL)
Access a block of memory.
Definition: misc.h:2428
Converts an enumeration to a type suitable for use as a template parameter.
Definition: cryptlib.h:135
EnumToType< ByteOrder, LITTLE_ENDIAN_ORDER > LittleEndian
Provides a constant for LittleEndian.
Definition: cryptlib.h:150
Library configuration file.
void Update(const byte *input, size_t length)
Updates a hash with additional input.
Definition: iterhash.cpp:13
STL namespace.
SecBlock<byte> typedef.
Definition: secblock.h:1058
byte order is little-endian
Definition: cryptlib.h:145
Classes and functions for secure memory allocations.
T GetWord(bool assumeAligned, ByteOrder order, const byte *block)
Access a block of memory.
Definition: misc.h:2386
int ed25519_sign(const byte *message, size_t messageLength, const byte secretKey[32], const byte publicKey[32], byte signature[64])
Creates a signature on a message.
int curve25519_mult(byte publicKey[32], const byte secretKey[32])
Generate a public key.
SHA-512 message digest.
Definition: sha.h:141
Precompiled header file.
int ed25519_sign_open(const byte *message, size_t messageLength, const byte publicKey[32], const byte signature[64])
Verifies a signature on a message.
Fixed size stack-based SecBlock.
Definition: secblock.h:1077
Functions for CPU features and intrinsics.
Classes for SHA-1 and SHA-2 family of message digests.
virtual void CalculateDigest(byte *digest, const byte *input, size_t length)
Updates the hash with additional input and computes the hash of the current message.
Definition: cryptlib.h:1160
bool HasSSE2()
Determines SSE2 availability.
Definition: cpu.h:116
Interface for hash functions and data processing part of MACs.
Definition: cryptlib.h:1084
Access a block of memory.
Definition: misc.h:2454
Crypto++ library namespace.
int ed25519_publickey(byte publicKey[32], const byte secretKey[32])
Creates a public key from a secret key.
virtual void Final(byte *digest)
Computes the hash of the current message.
Definition: cryptlib.h:1114
virtual void Update(const byte *input, size_t length)=0
Updates a hash with additional input.