Crypto++  8.8
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 #if CRYPTOPP_MSC_VERSION
38 # pragma warning(disable: 4244)
39 #endif
40 
41 // Squash MS LNK4221 and libtool warnings
42 extern const char DONNA32_FNAME[] = __FILE__;
43 
44 ANONYMOUS_NAMESPACE_BEGIN
45 
46 // Can't use GetAlignmentOf<word32>() 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 4
52 #endif
53 
54 ANONYMOUS_NAMESPACE_END
55 
56 #if defined(CRYPTOPP_CURVE25519_32BIT)
57 
58 #include "donna_32.h"
59 
60 ANONYMOUS_NAMESPACE_BEGIN
61 
62 using CryptoPP::byte;
63 using CryptoPP::word32;
64 using CryptoPP::GetWord;
65 using CryptoPP::PutWord;
66 using CryptoPP::LITTLE_ENDIAN_ORDER;
67 
68 inline word32 U8TO32_LE(const byte* p)
69 {
70  return GetWord<word32>(false, LITTLE_ENDIAN_ORDER, p);
71 }
72 
73 inline void U32TO8_LE(byte* p, word32 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 32-bit header
95 using namespace CryptoPP::Donna::Arch32;
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]; out[5] = in[5];
103  out[6] = in[6]; out[7] = in[7];
104  out[8] = in[8]; out[9] = in[9];
105 }
106 
107 /* out = a + b */
108 inline void
109 curve25519_add(bignum25519 out, const bignum25519 a, const bignum25519 b) {
110  out[0] = a[0] + b[0]; out[1] = a[1] + b[1];
111  out[2] = a[2] + b[2]; out[3] = a[3] + b[3];
112  out[4] = a[4] + b[4]; out[5] = a[5] + b[5];
113  out[6] = a[6] + b[6]; out[7] = a[7] + b[7];
114  out[8] = a[8] + b[8]; out[9] = a[9] + b[9];
115 }
116 
117 /* out = a - b */
118 inline void
119 curve25519_sub(bignum25519 out, const bignum25519 a, const bignum25519 b) {
120  word32 c;
121  out[0] = 0x7ffffda + a[0] - b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
122  out[1] = 0x3fffffe + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
123  out[2] = 0x7fffffe + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
124  out[3] = 0x3fffffe + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
125  out[4] = 0x7fffffe + a[4] - b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
126  out[5] = 0x3fffffe + a[5] - b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
127  out[6] = 0x7fffffe + a[6] - b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
128  out[7] = 0x3fffffe + a[7] - b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
129  out[8] = 0x7fffffe + a[8] - b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
130  out[9] = 0x3fffffe + a[9] - b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
131  out[0] += 19 * c;
132 }
133 
134 /* out = in * scalar */
135 inline void
136 curve25519_scalar_product(bignum25519 out, const bignum25519 in, const word32 scalar) {
137  word64 a;
138  word32 c;
139  a = mul32x32_64(in[0], scalar); out[0] = (word32)a & reduce_mask_26; c = (word32)(a >> 26);
140  a = mul32x32_64(in[1], scalar) + c; out[1] = (word32)a & reduce_mask_25; c = (word32)(a >> 25);
141  a = mul32x32_64(in[2], scalar) + c; out[2] = (word32)a & reduce_mask_26; c = (word32)(a >> 26);
142  a = mul32x32_64(in[3], scalar) + c; out[3] = (word32)a & reduce_mask_25; c = (word32)(a >> 25);
143  a = mul32x32_64(in[4], scalar) + c; out[4] = (word32)a & reduce_mask_26; c = (word32)(a >> 26);
144  a = mul32x32_64(in[5], scalar) + c; out[5] = (word32)a & reduce_mask_25; c = (word32)(a >> 25);
145  a = mul32x32_64(in[6], scalar) + c; out[6] = (word32)a & reduce_mask_26; c = (word32)(a >> 26);
146  a = mul32x32_64(in[7], scalar) + c; out[7] = (word32)a & reduce_mask_25; c = (word32)(a >> 25);
147  a = mul32x32_64(in[8], scalar) + c; out[8] = (word32)a & reduce_mask_26; c = (word32)(a >> 26);
148  a = mul32x32_64(in[9], scalar) + c; out[9] = (word32)a & reduce_mask_25; c = (word32)(a >> 25);
149  out[0] += c * 19;
150 }
151 
152 /* out = a * b */
153 inline void
154 curve25519_mul(bignum25519 out, const bignum25519 a, const bignum25519 b) {
155  word32 r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
156  word32 s0,s1,s2,s3,s4,s5,s6,s7,s8,s9;
157  word64 m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
158  word32 p;
159 
160  r0 = b[0]; r1 = b[1]; r2 = b[2]; r3 = b[3]; r4 = b[4];
161  r5 = b[5]; r6 = b[6]; r7 = b[7]; r8 = b[8]; r9 = b[9];
162 
163  s0 = a[0]; s1 = a[1]; s2 = a[2]; s3 = a[3]; s4 = a[4];
164  s5 = a[5]; s6 = a[6]; s7 = a[7]; s8 = a[8]; s9 = a[9];
165 
166  m1 = mul32x32_64(r0, s1) + mul32x32_64(r1, s0);
167  m3 = mul32x32_64(r0, s3) + mul32x32_64(r1, s2) + mul32x32_64(r2, s1) + mul32x32_64(r3, s0);
168  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);
169  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);
170  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);
171 
172  r1 *= 2; r3 *= 2; r5 *= 2; r7 *= 2;
173 
174  m0 = mul32x32_64(r0, s0);
175  m2 = mul32x32_64(r0, s2) + mul32x32_64(r1, s1) + mul32x32_64(r2, s0);
176  m4 = mul32x32_64(r0, s4) + mul32x32_64(r1, s3) + mul32x32_64(r2, s2) + mul32x32_64(r3, s1) + mul32x32_64(r4, s0);
177  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);
178  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);
179 
180  r1 *= 19; r2 *= 19;
181  r3 = (r3 / 2) * 19;
182  r4 *= 19;
183  r5 = (r5 / 2) * 19;
184  r6 *= 19;
185  r7 = (r7 / 2) * 19;
186  r8 *= 19; r9 *= 19;
187 
188  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));
189  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));
190  m5 += (mul32x32_64(r9, s6) + mul32x32_64(r8, s7) + mul32x32_64(r7, s8) + mul32x32_64(r6, s9));
191  m7 += (mul32x32_64(r9, s8) + mul32x32_64(r8, s9));
192 
193  r3 *= 2; r5 *= 2; r7 *= 2; r9 *= 2;
194 
195  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));
196  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));
197  m4 += (mul32x32_64(r9, s5) + mul32x32_64(r8, s6) + mul32x32_64(r7, s7) + mul32x32_64(r6, s8) + mul32x32_64(r5, s9));
198  m6 += (mul32x32_64(r9, s7) + mul32x32_64(r8, s8) + mul32x32_64(r7, s9));
199  m8 += (mul32x32_64(r9, s9));
200 
201  r0 = (word32)m0 & reduce_mask_26; c = (m0 >> 26);
202  m1 += c; r1 = (word32)m1 & reduce_mask_25; c = (m1 >> 25);
203  m2 += c; r2 = (word32)m2 & reduce_mask_26; c = (m2 >> 26);
204  m3 += c; r3 = (word32)m3 & reduce_mask_25; c = (m3 >> 25);
205  m4 += c; r4 = (word32)m4 & reduce_mask_26; c = (m4 >> 26);
206  m5 += c; r5 = (word32)m5 & reduce_mask_25; c = (m5 >> 25);
207  m6 += c; r6 = (word32)m6 & reduce_mask_26; c = (m6 >> 26);
208  m7 += c; r7 = (word32)m7 & reduce_mask_25; c = (m7 >> 25);
209  m8 += c; r8 = (word32)m8 & reduce_mask_26; c = (m8 >> 26);
210  m9 += c; r9 = (word32)m9 & reduce_mask_25; p = (word32)(m9 >> 25);
211  m0 = r0 + mul32x32_64(p,19); r0 = (word32)m0 & reduce_mask_26; p = (word32)(m0 >> 26);
212  r1 += p;
213 
214  out[0] = r0; out[1] = r1; out[2] = r2; out[3] = r3; out[4] = r4;
215  out[5] = r5; out[6] = r6; out[7] = r7; out[8] = r8; out[9] = r9;
216 }
217 
218 /* out = in * in */
219 inline void
220 curve25519_square(bignum25519 out, const bignum25519 in) {
221  word32 r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
222  word32 d6,d7,d8,d9;
223  word64 m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
224  word32 p;
225 
226  r0 = in[0]; r1 = in[1]; r2 = in[2]; r3 = in[3]; r4 = in[4];
227  r5 = in[5]; r6 = in[6]; r7 = in[7]; r8 = in[8]; r9 = in[9];
228 
229  m0 = mul32x32_64(r0, r0);
230  r0 *= 2;
231  m1 = mul32x32_64(r0, r1);
232  m2 = mul32x32_64(r0, r2) + mul32x32_64(r1, r1 * 2);
233  r1 *= 2;
234  m3 = mul32x32_64(r0, r3) + mul32x32_64(r1, r2 );
235  m4 = mul32x32_64(r0, r4) + mul32x32_64(r1, r3 * 2) + mul32x32_64(r2, r2);
236  r2 *= 2;
237  m5 = mul32x32_64(r0, r5) + mul32x32_64(r1, r4 ) + mul32x32_64(r2, r3);
238  m6 = mul32x32_64(r0, r6) + mul32x32_64(r1, r5 * 2) + mul32x32_64(r2, r4) + mul32x32_64(r3, r3 * 2);
239  r3 *= 2;
240  m7 = mul32x32_64(r0, r7) + mul32x32_64(r1, r6 ) + mul32x32_64(r2, r5) + mul32x32_64(r3, r4 );
241  m8 = mul32x32_64(r0, r8) + mul32x32_64(r1, r7 * 2) + mul32x32_64(r2, r6) + mul32x32_64(r3, r5 * 2) + mul32x32_64(r4, r4 );
242  m9 = mul32x32_64(r0, r9) + mul32x32_64(r1, r8 ) + mul32x32_64(r2, r7) + mul32x32_64(r3, r6 ) + mul32x32_64(r4, r5 * 2);
243 
244  d6 = r6 * 19; d7 = r7 * 2 * 19;
245  d8 = r8 * 19; d9 = r9 * 2 * 19;
246 
247  m0 += (mul32x32_64(d9, r1 ) + mul32x32_64(d8, r2 ) + mul32x32_64(d7, r3 ) + mul32x32_64(d6, r4 * 2) + mul32x32_64(r5, r5 * 2 * 19));
248  m1 += (mul32x32_64(d9, r2 / 2) + mul32x32_64(d8, r3 ) + mul32x32_64(d7, r4 ) + mul32x32_64(d6, r5 * 2));
249  m2 += (mul32x32_64(d9, r3 ) + mul32x32_64(d8, r4 * 2) + mul32x32_64(d7, r5 * 2) + mul32x32_64(d6, r6 ));
250  m3 += (mul32x32_64(d9, r4 ) + mul32x32_64(d8, r5 * 2) + mul32x32_64(d7, r6 ));
251  m4 += (mul32x32_64(d9, r5 * 2) + mul32x32_64(d8, r6 * 2) + mul32x32_64(d7, r7 ));
252  m5 += (mul32x32_64(d9, r6 ) + mul32x32_64(d8, r7 * 2));
253  m6 += (mul32x32_64(d9, r7 * 2) + mul32x32_64(d8, r8 ));
254  m7 += (mul32x32_64(d9, r8 ));
255  m8 += (mul32x32_64(d9, r9 ));
256 
257  r0 = (word32)m0 & reduce_mask_26; c = (m0 >> 26);
258  m1 += c; r1 = (word32)m1 & reduce_mask_25; c = (m1 >> 25);
259  m2 += c; r2 = (word32)m2 & reduce_mask_26; c = (m2 >> 26);
260  m3 += c; r3 = (word32)m3 & reduce_mask_25; c = (m3 >> 25);
261  m4 += c; r4 = (word32)m4 & reduce_mask_26; c = (m4 >> 26);
262  m5 += c; r5 = (word32)m5 & reduce_mask_25; c = (m5 >> 25);
263  m6 += c; r6 = (word32)m6 & reduce_mask_26; c = (m6 >> 26);
264  m7 += c; r7 = (word32)m7 & reduce_mask_25; c = (m7 >> 25);
265  m8 += c; r8 = (word32)m8 & reduce_mask_26; c = (m8 >> 26);
266  m9 += c; r9 = (word32)m9 & reduce_mask_25; p = (word32)(m9 >> 25);
267  m0 = r0 + mul32x32_64(p,19); r0 = (word32)m0 & reduce_mask_26; p = (word32)(m0 >> 26);
268  r1 += p;
269 
270  out[0] = r0; out[1] = r1; out[2] = r2; out[3] = r3; out[4] = r4;
271  out[5] = r5; out[6] = r6; out[7] = r7; out[8] = r8; out[9] = r9;
272 }
273 
274 /* out = in^(2 * count) */
275 void
276 curve25519_square_times(bignum25519 out, const bignum25519 in, int count) {
277  word32 r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
278  word32 d6,d7,d8,d9;
279  word64 m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
280  word32 p;
281 
282  r0 = in[0]; r1 = in[1]; r2 = in[2]; r3 = in[3]; r4 = in[4];
283  r5 = in[5]; r6 = in[6]; r7 = in[7]; r8 = in[8]; r9 = in[9];
284 
285  do {
286  m0 = mul32x32_64(r0, r0);
287  r0 *= 2;
288  m1 = mul32x32_64(r0, r1);
289  m2 = mul32x32_64(r0, r2) + mul32x32_64(r1, r1 * 2);
290  r1 *= 2;
291  m3 = mul32x32_64(r0, r3) + mul32x32_64(r1, r2 );
292  m4 = mul32x32_64(r0, r4) + mul32x32_64(r1, r3 * 2) + mul32x32_64(r2, r2);
293  r2 *= 2;
294  m5 = mul32x32_64(r0, r5) + mul32x32_64(r1, r4 ) + mul32x32_64(r2, r3);
295  m6 = mul32x32_64(r0, r6) + mul32x32_64(r1, r5 * 2) + mul32x32_64(r2, r4) + mul32x32_64(r3, r3 * 2);
296  r3 *= 2;
297  m7 = mul32x32_64(r0, r7) + mul32x32_64(r1, r6 ) + mul32x32_64(r2, r5) + mul32x32_64(r3, r4 );
298  m8 = mul32x32_64(r0, r8) + mul32x32_64(r1, r7 * 2) + mul32x32_64(r2, r6) + mul32x32_64(r3, r5 * 2) + mul32x32_64(r4, r4 );
299  m9 = mul32x32_64(r0, r9) + mul32x32_64(r1, r8 ) + mul32x32_64(r2, r7) + mul32x32_64(r3, r6 ) + mul32x32_64(r4, r5 * 2);
300 
301  d6 = r6 * 19; d7 = r7 * 2 * 19;
302  d8 = r8 * 19; d9 = r9 * 2 * 19;
303 
304  m0 += (mul32x32_64(d9, r1 ) + mul32x32_64(d8, r2 ) + mul32x32_64(d7, r3 ) + mul32x32_64(d6, r4 * 2) + mul32x32_64(r5, r5 * 2 * 19));
305  m1 += (mul32x32_64(d9, r2 / 2) + mul32x32_64(d8, r3 ) + mul32x32_64(d7, r4 ) + mul32x32_64(d6, r5 * 2));
306  m2 += (mul32x32_64(d9, r3 ) + mul32x32_64(d8, r4 * 2) + mul32x32_64(d7, r5 * 2) + mul32x32_64(d6, r6 ));
307  m3 += (mul32x32_64(d9, r4 ) + mul32x32_64(d8, r5 * 2) + mul32x32_64(d7, r6 ));
308  m4 += (mul32x32_64(d9, r5 * 2) + mul32x32_64(d8, r6 * 2) + mul32x32_64(d7, r7 ));
309  m5 += (mul32x32_64(d9, r6 ) + mul32x32_64(d8, r7 * 2));
310  m6 += (mul32x32_64(d9, r7 * 2) + mul32x32_64(d8, r8 ));
311  m7 += (mul32x32_64(d9, r8 ));
312  m8 += (mul32x32_64(d9, r9 ));
313 
314  r0 = (word32)m0 & reduce_mask_26; c = (m0 >> 26);
315  m1 += c; r1 = (word32)m1 & reduce_mask_25; c = (m1 >> 25);
316  m2 += c; r2 = (word32)m2 & reduce_mask_26; c = (m2 >> 26);
317  m3 += c; r3 = (word32)m3 & reduce_mask_25; c = (m3 >> 25);
318  m4 += c; r4 = (word32)m4 & reduce_mask_26; c = (m4 >> 26);
319  m5 += c; r5 = (word32)m5 & reduce_mask_25; c = (m5 >> 25);
320  m6 += c; r6 = (word32)m6 & reduce_mask_26; c = (m6 >> 26);
321  m7 += c; r7 = (word32)m7 & reduce_mask_25; c = (m7 >> 25);
322  m8 += c; r8 = (word32)m8 & reduce_mask_26; c = (m8 >> 26);
323  m9 += c; r9 = (word32)m9 & reduce_mask_25; p = (word32)(m9 >> 25);
324  m0 = r0 + mul32x32_64(p,19); r0 = (word32)m0 & reduce_mask_26; p = (word32)(m0 >> 26);
325  r1 += p;
326  } while (--count);
327 
328  out[0] = r0; out[1] = r1; out[2] = r2; out[3] = r3; out[4] = r4;
329  out[5] = r5; out[6] = r6; out[7] = r7; out[8] = r8; out[9] = r9;
330 }
331 
332 /* Take a little-endian, 32-byte number and expand it into polynomial form */
333 void
334 curve25519_expand(bignum25519 out, const byte in[32]) {
335  word32 x0,x1,x2,x3,x4,x5,x6,x7;
336  GetBlock<word32, LittleEndian> block(in);
337  block(x0)(x1)(x2)(x3)(x4)(x5)(x6)(x7);
338 
339  out[0] = ( x0 ) & reduce_mask_26;
340  out[1] = ((((word64)x1 << 32) | x0) >> 26) & reduce_mask_25;
341  out[2] = ((((word64)x2 << 32) | x1) >> 19) & reduce_mask_26;
342  out[3] = ((((word64)x3 << 32) | x2) >> 13) & reduce_mask_25;
343  out[4] = (( x3) >> 6) & reduce_mask_26;
344  out[5] = ( x4 ) & reduce_mask_25;
345  out[6] = ((((word64)x5 << 32) | x4) >> 25) & reduce_mask_26;
346  out[7] = ((((word64)x6 << 32) | x5) >> 19) & reduce_mask_25;
347  out[8] = ((((word64)x7 << 32) | x6) >> 12) & reduce_mask_26;
348  out[9] = (( x7) >> 6) & reduce_mask_25; /* ignore the top bit */
349 }
350 
351 /* Take a fully reduced polynomial form number and contract it into a little-endian, 32-byte array */
352 void
353 curve25519_contract(byte out[32], const bignum25519 in) {
354  bignum25519 f;
355  curve25519_copy(f, in);
356 
357  #define carry_pass() \
358  f[1] += f[0] >> 26; f[0] &= reduce_mask_26; \
359  f[2] += f[1] >> 25; f[1] &= reduce_mask_25; \
360  f[3] += f[2] >> 26; f[2] &= reduce_mask_26; \
361  f[4] += f[3] >> 25; f[3] &= reduce_mask_25; \
362  f[5] += f[4] >> 26; f[4] &= reduce_mask_26; \
363  f[6] += f[5] >> 25; f[5] &= reduce_mask_25; \
364  f[7] += f[6] >> 26; f[6] &= reduce_mask_26; \
365  f[8] += f[7] >> 25; f[7] &= reduce_mask_25; \
366  f[9] += f[8] >> 26; f[8] &= reduce_mask_26;
367 
368  #define carry_pass_full() \
369  carry_pass() \
370  f[0] += 19 * (f[9] >> 25); f[9] &= reduce_mask_25;
371 
372  #define carry_pass_final() \
373  carry_pass() \
374  f[9] &= reduce_mask_25;
375 
376  carry_pass_full()
377  carry_pass_full()
378 
379  /* now t is between 0 and 2^255-1, properly carried. */
380  /* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */
381  f[0] += 19;
382  carry_pass_full()
383 
384  /* now between 19 and 2^255-1 in both cases, and offset by 19. */
385  f[0] += (1 << 26) - 19;
386  f[1] += (1 << 25) - 1;
387  f[2] += (1 << 26) - 1;
388  f[3] += (1 << 25) - 1;
389  f[4] += (1 << 26) - 1;
390  f[5] += (1 << 25) - 1;
391  f[6] += (1 << 26) - 1;
392  f[7] += (1 << 25) - 1;
393  f[8] += (1 << 26) - 1;
394  f[9] += (1 << 25) - 1;
395 
396  /* now between 2^255 and 2^256-20, and offset by 2^255. */
397  carry_pass_final()
398 
399  #undef carry_pass
400  #undef carry_full
401  #undef carry_final
402 
403  f[1] <<= 2;
404  f[2] <<= 3;
405  f[3] <<= 5;
406  f[4] <<= 6;
407  f[6] <<= 1;
408  f[7] <<= 3;
409  f[8] <<= 4;
410  f[9] <<= 6;
411 
412  #define F(i, s) \
413  out[s+0] |= (byte)( f[i] & 0xff); \
414  out[s+1] = (byte)((f[i] >> 8) & 0xff); \
415  out[s+2] = (byte)((f[i] >> 16) & 0xff); \
416  out[s+3] = (byte)((f[i] >> 24) & 0xff);
417 
418  out[0] = out[16] = 0;
419  F(0,0); F(1,3);
420  F(2,6); F(3,9);
421  F(4,12); F(5,16);
422  F(6,19); F(7,22);
423  F(8,25); F(9,28);
424  #undef F
425 }
426 
427 inline void
428 curve25519_swap_conditional(bignum25519 x, bignum25519 qpx, word32 iswap) {
429  const word32 swap = (word32)(-(sword32)iswap);
430  word32 x0,x1,x2,x3,x4,x5,x6,x7,x8,x9;
431 
432  x0 = swap & (x[0] ^ qpx[0]); x[0] ^= x0; qpx[0] ^= x0;
433  x1 = swap & (x[1] ^ qpx[1]); x[1] ^= x1; qpx[1] ^= x1;
434  x2 = swap & (x[2] ^ qpx[2]); x[2] ^= x2; qpx[2] ^= x2;
435  x3 = swap & (x[3] ^ qpx[3]); x[3] ^= x3; qpx[3] ^= x3;
436  x4 = swap & (x[4] ^ qpx[4]); x[4] ^= x4; qpx[4] ^= x4;
437  x5 = swap & (x[5] ^ qpx[5]); x[5] ^= x5; qpx[5] ^= x5;
438  x6 = swap & (x[6] ^ qpx[6]); x[6] ^= x6; qpx[6] ^= x6;
439  x7 = swap & (x[7] ^ qpx[7]); x[7] ^= x7; qpx[7] ^= x7;
440  x8 = swap & (x[8] ^ qpx[8]); x[8] ^= x8; qpx[8] ^= x8;
441  x9 = swap & (x[9] ^ qpx[9]); x[9] ^= x9; qpx[9] ^= x9;
442 }
443 
444 /*
445  * In: b = 2^5 - 2^0
446  * Out: b = 2^250 - 2^0
447  */
448 void
449 curve25519_pow_two5mtwo0_two250mtwo0(bignum25519 b) {
450  ALIGN(ALIGN_SPEC) bignum25519 t0,c;
451 
452  /* 2^5 - 2^0 */ /* b */
453  /* 2^10 - 2^5 */ curve25519_square_times(t0, b, 5);
454  /* 2^10 - 2^0 */ curve25519_mul(b, t0, b);
455  /* 2^20 - 2^10 */ curve25519_square_times(t0, b, 10);
456  /* 2^20 - 2^0 */ curve25519_mul(c, t0, b);
457  /* 2^40 - 2^20 */ curve25519_square_times(t0, c, 20);
458  /* 2^40 - 2^0 */ curve25519_mul(t0, t0, c);
459  /* 2^50 - 2^10 */ curve25519_square_times(t0, t0, 10);
460  /* 2^50 - 2^0 */ curve25519_mul(b, t0, b);
461  /* 2^100 - 2^50 */ curve25519_square_times(t0, b, 50);
462  /* 2^100 - 2^0 */ curve25519_mul(c, t0, b);
463  /* 2^200 - 2^100 */ curve25519_square_times(t0, c, 100);
464  /* 2^200 - 2^0 */ curve25519_mul(t0, t0, c);
465  /* 2^250 - 2^50 */ curve25519_square_times(t0, t0, 50);
466  /* 2^250 - 2^0 */ curve25519_mul(b, t0, b);
467 }
468 
469 /*
470  * z^(p - 2) = z(2^255 - 21)
471  */
472 void
473 curve25519_recip(bignum25519 out, const bignum25519 z) {
474  ALIGN(ALIGN_SPEC) bignum25519 a, t0, b;
475 
476  /* 2 */ curve25519_square(a, z); /* a = 2 */
477  /* 8 */ curve25519_square_times(t0, a, 2);
478  /* 9 */ curve25519_mul(b, t0, z); /* b = 9 */
479  /* 11 */ curve25519_mul(a, b, a); /* a = 11 */
480  /* 22 */ curve25519_square(t0, a);
481  /* 2^5 - 2^0 = 31 */ curve25519_mul(b, t0, b);
482  /* 2^250 - 2^0 */ curve25519_pow_two5mtwo0_two250mtwo0(b);
483  /* 2^255 - 2^5 */ curve25519_square_times(b, b, 5);
484  /* 2^255 - 21 */ curve25519_mul(out, b, a);
485 }
486 
487 ANONYMOUS_NAMESPACE_END
488 NAMESPACE_END // X25519
489 NAMESPACE_END // Donna
490 NAMESPACE_END // CryptoPP
491 
492 //******************************* ed25519 *******************************//
493 
494 NAMESPACE_BEGIN(CryptoPP)
495 NAMESPACE_BEGIN(Donna)
496 NAMESPACE_BEGIN(Ed25519)
497 ANONYMOUS_NAMESPACE_BEGIN
498 
499 using CryptoPP::byte;
500 using CryptoPP::word32;
501 using CryptoPP::sword32;
502 using CryptoPP::word64;
503 using CryptoPP::sword64;
504 
505 using CryptoPP::GetBlock;
506 using CryptoPP::LittleEndian;
507 
508 using CryptoPP::SHA512;
509 
510 // Bring in all the symbols from the 32-bit header
511 using namespace CryptoPP::Donna::Arch32;
512 
513 /* out = in */
514 inline void
515 curve25519_copy(bignum25519 out, const bignum25519 in) {
516  out[0] = in[0]; out[1] = in[1];
517  out[2] = in[2]; out[3] = in[3];
518  out[4] = in[4]; out[5] = in[5];
519  out[6] = in[6]; out[7] = in[7];
520  out[8] = in[8]; out[9] = in[9];
521 }
522 
523 /* out = a + b */
524 inline void
525 curve25519_add(bignum25519 out, const bignum25519 a, const bignum25519 b) {
526  out[0] = a[0] + b[0]; out[1] = a[1] + b[1];
527  out[2] = a[2] + b[2]; out[3] = a[3] + b[3];
528  out[4] = a[4] + b[4]; out[5] = a[5] + b[5];
529  out[6] = a[6] + b[6]; out[7] = a[7] + b[7];
530  out[8] = a[8] + b[8]; out[9] = a[9] + b[9];
531 }
532 
533 inline void
534 curve25519_add_after_basic(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 inline void
550 curve25519_add_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) {
551  word32 c;
552  out[0] = a[0] + b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
553  out[1] = a[1] + b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
554  out[2] = a[2] + b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
555  out[3] = a[3] + b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
556  out[4] = a[4] + b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
557  out[5] = a[5] + b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
558  out[6] = a[6] + b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
559  out[7] = a[7] + b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
560  out[8] = a[8] + b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
561  out[9] = a[9] + b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
562  out[0] += 19 * c;
563 }
564 
565 /* out = a - b */
566 inline void
567 curve25519_sub(bignum25519 out, const bignum25519 a, const bignum25519 b) {
568  word32 c;
569  out[0] = twoP0 + a[0] - b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
570  out[1] = twoP13579 + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
571  out[2] = twoP2468 + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
572  out[3] = twoP13579 + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
573  out[4] = twoP2468 + a[4] - b[4] + c;
574  out[5] = twoP13579 + a[5] - b[5] ;
575  out[6] = twoP2468 + a[6] - b[6] ;
576  out[7] = twoP13579 + a[7] - b[7] ;
577  out[8] = twoP2468 + a[8] - b[8] ;
578  out[9] = twoP13579 + a[9] - b[9] ;
579 }
580 
581 /* out = a - b, where a is the result of a basic op (add,sub) */
582 inline void
583 curve25519_sub_after_basic(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 inline void
599 curve25519_sub_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) {
600  word32 c;
601  out[0] = fourP0 + a[0] - b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
602  out[1] = fourP13579 + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
603  out[2] = fourP2468 + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
604  out[3] = fourP13579 + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
605  out[4] = fourP2468 + a[4] - b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
606  out[5] = fourP13579 + a[5] - b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
607  out[6] = fourP2468 + a[6] - b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
608  out[7] = fourP13579 + a[7] - b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
609  out[8] = fourP2468 + a[8] - b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
610  out[9] = fourP13579 + a[9] - b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
611  out[0] += 19 * c;
612 }
613 
614 /* out = -a */
615 inline void
616 curve25519_neg(bignum25519 out, const bignum25519 a) {
617  word32 c;
618  out[0] = twoP0 - a[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
619  out[1] = twoP13579 - a[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
620  out[2] = twoP2468 - a[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
621  out[3] = twoP13579 - a[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
622  out[4] = twoP2468 - a[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
623  out[5] = twoP13579 - a[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
624  out[6] = twoP2468 - a[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
625  out[7] = twoP13579 - a[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
626  out[8] = twoP2468 - a[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
627  out[9] = twoP13579 - a[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
628  out[0] += 19 * c;
629 }
630 
631 /* out = a * b */
632 void
633 curve25519_mul(bignum25519 out, const bignum25519 a, const bignum25519 b) {
634  word32 r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
635  word32 s0,s1,s2,s3,s4,s5,s6,s7,s8,s9;
636  word64 m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
637  word32 p;
638 
639  r0 = b[0]; r1 = b[1];
640  r2 = b[2]; r3 = b[3];
641  r4 = b[4]; r5 = b[5];
642  r6 = b[6]; r7 = b[7];
643  r8 = b[8]; r9 = b[9];
644 
645  s0 = a[0]; s1 = a[1];
646  s2 = a[2]; s3 = a[3];
647  s4 = a[4]; s5 = a[5];
648  s6 = a[6]; s7 = a[7];
649  s8 = a[8]; s9 = a[9];
650 
651  m1 = mul32x32_64(r0, s1) + mul32x32_64(r1, s0);
652  m3 = mul32x32_64(r0, s3) + mul32x32_64(r1, s2) + mul32x32_64(r2, s1) + mul32x32_64(r3, s0);
653  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);
654  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);
655  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);
656 
657  r1 *= 2; r3 *= 2;
658  r5 *= 2; r7 *= 2;
659 
660  m0 = mul32x32_64(r0, s0);
661  m2 = mul32x32_64(r0, s2) + mul32x32_64(r1, s1) + mul32x32_64(r2, s0);
662  m4 = mul32x32_64(r0, s4) + mul32x32_64(r1, s3) + mul32x32_64(r2, s2) + mul32x32_64(r3, s1) + mul32x32_64(r4, s0);
663  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);
664  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);
665 
666  r1 *= 19; r2 *= 19;
667  r3 = (r3 / 2) * 19;
668  r4 *= 19;
669  r5 = (r5 / 2) * 19;
670  r6 *= 19;
671  r7 = (r7 / 2) * 19;
672  r8 *= 19; r9 *= 19;
673 
674  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));
675  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));
676  m5 += (mul32x32_64(r9, s6) + mul32x32_64(r8, s7) + mul32x32_64(r7, s8) + mul32x32_64(r6, s9));
677  m7 += (mul32x32_64(r9, s8) + mul32x32_64(r8, s9));
678 
679  r3 *= 2; r5 *= 2;
680  r7 *= 2; r9 *= 2;
681 
682  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));
683  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));
684  m4 += (mul32x32_64(r9, s5) + mul32x32_64(r8, s6) + mul32x32_64(r7, s7) + mul32x32_64(r6, s8) + mul32x32_64(r5, s9));
685  m6 += (mul32x32_64(r9, s7) + mul32x32_64(r8, s8) + mul32x32_64(r7, s9));
686  m8 += (mul32x32_64(r9, s9));
687 
688  r0 = (word32)m0 & reduce_mask_26; c = (m0 >> 26);
689  m1 += c; r1 = (word32)m1 & reduce_mask_25; c = (m1 >> 25);
690  m2 += c; r2 = (word32)m2 & reduce_mask_26; c = (m2 >> 26);
691  m3 += c; r3 = (word32)m3 & reduce_mask_25; c = (m3 >> 25);
692  m4 += c; r4 = (word32)m4 & reduce_mask_26; c = (m4 >> 26);
693  m5 += c; r5 = (word32)m5 & reduce_mask_25; c = (m5 >> 25);
694  m6 += c; r6 = (word32)m6 & reduce_mask_26; c = (m6 >> 26);
695  m7 += c; r7 = (word32)m7 & reduce_mask_25; c = (m7 >> 25);
696  m8 += c; r8 = (word32)m8 & reduce_mask_26; c = (m8 >> 26);
697  m9 += c; r9 = (word32)m9 & reduce_mask_25; p = (word32)(m9 >> 25);
698  m0 = r0 + mul32x32_64(p,19); r0 = (word32)m0 & reduce_mask_26; p = (word32)(m0 >> 26);
699  r1 += p;
700 
701  out[0] = r0; out[1] = r1;
702  out[2] = r2; out[3] = r3;
703  out[4] = r4; out[5] = r5;
704  out[6] = r6; out[7] = r7;
705  out[8] = r8; out[9] = r9;
706 }
707 
708 /* out = in*in */
709 void
710 curve25519_square(bignum25519 out, const bignum25519 in) {
711  word32 r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
712  word32 d6,d7,d8,d9;
713  word64 m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
714  word32 p;
715 
716  r0 = in[0]; r1 = in[1];
717  r2 = in[2]; r3 = in[3];
718  r4 = in[4]; r5 = in[5];
719  r6 = in[6]; r7 = in[7];
720  r8 = in[8]; r9 = in[9];
721 
722  m0 = mul32x32_64(r0, r0);
723  r0 *= 2;
724  m1 = mul32x32_64(r0, r1);
725  m2 = mul32x32_64(r0, r2) + mul32x32_64(r1, r1 * 2);
726  r1 *= 2;
727  m3 = mul32x32_64(r0, r3) + mul32x32_64(r1, r2 );
728  m4 = mul32x32_64(r0, r4) + mul32x32_64(r1, r3 * 2) + mul32x32_64(r2, r2);
729  r2 *= 2;
730  m5 = mul32x32_64(r0, r5) + mul32x32_64(r1, r4 ) + mul32x32_64(r2, r3);
731  m6 = mul32x32_64(r0, r6) + mul32x32_64(r1, r5 * 2) + mul32x32_64(r2, r4) + mul32x32_64(r3, r3 * 2);
732  r3 *= 2;
733  m7 = mul32x32_64(r0, r7) + mul32x32_64(r1, r6 ) + mul32x32_64(r2, r5) + mul32x32_64(r3, r4 );
734  m8 = mul32x32_64(r0, r8) + mul32x32_64(r1, r7 * 2) + mul32x32_64(r2, r6) + mul32x32_64(r3, r5 * 2) + mul32x32_64(r4, r4 );
735  m9 = mul32x32_64(r0, r9) + mul32x32_64(r1, r8 ) + mul32x32_64(r2, r7) + mul32x32_64(r3, r6 ) + mul32x32_64(r4, r5 * 2);
736 
737  d6 = r6 * 19;
738  d7 = r7 * 2 * 19;
739  d8 = r8 * 19;
740  d9 = r9 * 2 * 19;
741 
742  m0 += (mul32x32_64(d9, r1 ) + mul32x32_64(d8, r2 ) + mul32x32_64(d7, r3 ) + mul32x32_64(d6, r4 * 2) + mul32x32_64(r5, r5 * 2 * 19));
743  m1 += (mul32x32_64(d9, r2 / 2) + mul32x32_64(d8, r3 ) + mul32x32_64(d7, r4 ) + mul32x32_64(d6, r5 * 2));
744  m2 += (mul32x32_64(d9, r3 ) + mul32x32_64(d8, r4 * 2) + mul32x32_64(d7, r5 * 2) + mul32x32_64(d6, r6 ));
745  m3 += (mul32x32_64(d9, r4 ) + mul32x32_64(d8, r5 * 2) + mul32x32_64(d7, r6 ));
746  m4 += (mul32x32_64(d9, r5 * 2) + mul32x32_64(d8, r6 * 2) + mul32x32_64(d7, r7 ));
747  m5 += (mul32x32_64(d9, r6 ) + mul32x32_64(d8, r7 * 2));
748  m6 += (mul32x32_64(d9, r7 * 2) + mul32x32_64(d8, r8 ));
749  m7 += (mul32x32_64(d9, r8 ));
750  m8 += (mul32x32_64(d9, r9 ));
751 
752  r0 = (word32)m0 & reduce_mask_26; c = (m0 >> 26);
753  m1 += c; r1 = (word32)m1 & reduce_mask_25; c = (m1 >> 25);
754  m2 += c; r2 = (word32)m2 & reduce_mask_26; c = (m2 >> 26);
755  m3 += c; r3 = (word32)m3 & reduce_mask_25; c = (m3 >> 25);
756  m4 += c; r4 = (word32)m4 & reduce_mask_26; c = (m4 >> 26);
757  m5 += c; r5 = (word32)m5 & reduce_mask_25; c = (m5 >> 25);
758  m6 += c; r6 = (word32)m6 & reduce_mask_26; c = (m6 >> 26);
759  m7 += c; r7 = (word32)m7 & reduce_mask_25; c = (m7 >> 25);
760  m8 += c; r8 = (word32)m8 & reduce_mask_26; c = (m8 >> 26);
761  m9 += c; r9 = (word32)m9 & reduce_mask_25; p = (word32)(m9 >> 25);
762  m0 = r0 + mul32x32_64(p,19); r0 = (word32)m0 & reduce_mask_26; p = (word32)(m0 >> 26);
763  r1 += p;
764 
765  out[0] = r0; out[1] = r1;
766  out[2] = r2; out[3] = r3;
767  out[4] = r4; out[5] = r5;
768  out[6] = r6; out[7] = r7;
769  out[8] = r8; out[9] = r9;
770 }
771 
772 /* out = in ^ (2 * count) */
773 void
774 curve25519_square_times(bignum25519 out, const bignum25519 in, int count) {
775  word32 r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
776  word32 d6,d7,d8,d9,p;
777  word64 m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
778 
779  r0 = in[0]; r1 = in[1];
780  r2 = in[2]; r3 = in[3];
781  r4 = in[4]; r5 = in[5];
782  r6 = in[6]; r7 = in[7];
783  r8 = in[8]; r9 = in[9];
784 
785  do {
786  m0 = mul32x32_64(r0, r0);
787  r0 *= 2;
788  m1 = mul32x32_64(r0, r1);
789  m2 = mul32x32_64(r0, r2) + mul32x32_64(r1, r1 * 2);
790  r1 *= 2;
791  m3 = mul32x32_64(r0, r3) + mul32x32_64(r1, r2 );
792  m4 = mul32x32_64(r0, r4) + mul32x32_64(r1, r3 * 2) + mul32x32_64(r2, r2);
793  r2 *= 2;
794  m5 = mul32x32_64(r0, r5) + mul32x32_64(r1, r4 ) + mul32x32_64(r2, r3);
795  m6 = mul32x32_64(r0, r6) + mul32x32_64(r1, r5 * 2) + mul32x32_64(r2, r4) + mul32x32_64(r3, r3 * 2);
796  r3 *= 2;
797  m7 = mul32x32_64(r0, r7) + mul32x32_64(r1, r6 ) + mul32x32_64(r2, r5) + mul32x32_64(r3, r4 );
798  m8 = mul32x32_64(r0, r8) + mul32x32_64(r1, r7 * 2) + mul32x32_64(r2, r6) + mul32x32_64(r3, r5 * 2) + mul32x32_64(r4, r4 );
799  m9 = mul32x32_64(r0, r9) + mul32x32_64(r1, r8 ) + mul32x32_64(r2, r7) + mul32x32_64(r3, r6 ) + mul32x32_64(r4, r5 * 2);
800 
801  d6 = r6 * 19;
802  d7 = r7 * 2 * 19;
803  d8 = r8 * 19;
804  d9 = r9 * 2 * 19;
805 
806  m0 += (mul32x32_64(d9, r1 ) + mul32x32_64(d8, r2 ) + mul32x32_64(d7, r3 ) + mul32x32_64(d6, r4 * 2) + mul32x32_64(r5, r5 * 2 * 19));
807  m1 += (mul32x32_64(d9, r2 / 2) + mul32x32_64(d8, r3 ) + mul32x32_64(d7, r4 ) + mul32x32_64(d6, r5 * 2));
808  m2 += (mul32x32_64(d9, r3 ) + mul32x32_64(d8, r4 * 2) + mul32x32_64(d7, r5 * 2) + mul32x32_64(d6, r6 ));
809  m3 += (mul32x32_64(d9, r4 ) + mul32x32_64(d8, r5 * 2) + mul32x32_64(d7, r6 ));
810  m4 += (mul32x32_64(d9, r5 * 2) + mul32x32_64(d8, r6 * 2) + mul32x32_64(d7, r7 ));
811  m5 += (mul32x32_64(d9, r6 ) + mul32x32_64(d8, r7 * 2));
812  m6 += (mul32x32_64(d9, r7 * 2) + mul32x32_64(d8, r8 ));
813  m7 += (mul32x32_64(d9, r8 ));
814  m8 += (mul32x32_64(d9, r9 ));
815 
816  r0 = (word32)m0 & reduce_mask_26; c = (m0 >> 26);
817  m1 += c; r1 = (word32)m1 & reduce_mask_25; c = (m1 >> 25);
818  m2 += c; r2 = (word32)m2 & reduce_mask_26; c = (m2 >> 26);
819  m3 += c; r3 = (word32)m3 & reduce_mask_25; c = (m3 >> 25);
820  m4 += c; r4 = (word32)m4 & reduce_mask_26; c = (m4 >> 26);
821  m5 += c; r5 = (word32)m5 & reduce_mask_25; c = (m5 >> 25);
822  m6 += c; r6 = (word32)m6 & reduce_mask_26; c = (m6 >> 26);
823  m7 += c; r7 = (word32)m7 & reduce_mask_25; c = (m7 >> 25);
824  m8 += c; r8 = (word32)m8 & reduce_mask_26; c = (m8 >> 26);
825  m9 += c; r9 = (word32)m9 & reduce_mask_25; p = (word32)(m9 >> 25);
826  m0 = r0 + mul32x32_64(p,19); r0 = (word32)m0 & reduce_mask_26; p = (word32)(m0 >> 26);
827  r1 += p;
828  } while (--count);
829 
830  out[0] = r0; out[1] = r1;
831  out[2] = r2; out[3] = r3;
832  out[4] = r4; out[5] = r5;
833  out[6] = r6; out[7] = r7;
834  out[8] = r8; out[9] = r9;
835 }
836 
837 /* Take a little-endian, 32-byte number and expand it into polynomial form */
838 void
839 curve25519_expand(bignum25519 out, const byte in[32]) {
840  word32 x0,x1,x2,x3,x4,x5,x6,x7;
841  GetBlock<word32, LittleEndian> block(in);
842  block(x0)(x1)(x2)(x3)(x4)(x5)(x6)(x7);
843 
844  out[0] = ( x0 ) & 0x3ffffff;
845  out[1] = ((((word64)x1 << 32) | x0) >> 26) & 0x1ffffff;
846  out[2] = ((((word64)x2 << 32) | x1) >> 19) & 0x3ffffff;
847  out[3] = ((((word64)x3 << 32) | x2) >> 13) & 0x1ffffff;
848  out[4] = (( x3) >> 6) & 0x3ffffff;
849  out[5] = ( x4 ) & 0x1ffffff;
850  out[6] = ((((word64)x5 << 32) | x4) >> 25) & 0x3ffffff;
851  out[7] = ((((word64)x6 << 32) | x5) >> 19) & 0x1ffffff;
852  out[8] = ((((word64)x7 << 32) | x6) >> 12) & 0x3ffffff;
853  out[9] = (( x7) >> 6) & 0x1ffffff;
854 }
855 
856 /* Take a fully reduced polynomial form number and contract it into a
857  * little-endian, 32-byte array
858  */
859 void
860 curve25519_contract(byte out[32], const bignum25519 in) {
861  bignum25519 f;
862  curve25519_copy(f, in);
863 
864  #define carry_pass() \
865  f[1] += f[0] >> 26; f[0] &= reduce_mask_26; \
866  f[2] += f[1] >> 25; f[1] &= reduce_mask_25; \
867  f[3] += f[2] >> 26; f[2] &= reduce_mask_26; \
868  f[4] += f[3] >> 25; f[3] &= reduce_mask_25; \
869  f[5] += f[4] >> 26; f[4] &= reduce_mask_26; \
870  f[6] += f[5] >> 25; f[5] &= reduce_mask_25; \
871  f[7] += f[6] >> 26; f[6] &= reduce_mask_26; \
872  f[8] += f[7] >> 25; f[7] &= reduce_mask_25; \
873  f[9] += f[8] >> 26; f[8] &= reduce_mask_26;
874 
875  #define carry_pass_full() \
876  carry_pass() \
877  f[0] += 19 * (f[9] >> 25); f[9] &= reduce_mask_25;
878 
879  #define carry_pass_final() \
880  carry_pass() \
881  f[9] &= reduce_mask_25;
882 
883  carry_pass_full()
884  carry_pass_full()
885 
886  /* now t is between 0 and 2^255-1, properly carried. */
887  /* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */
888  f[0] += 19;
889  carry_pass_full()
890 
891  /* now between 19 and 2^255-1 in both cases, and offset by 19. */
892  f[0] += (reduce_mask_26 + 1) - 19;
893  f[1] += (reduce_mask_25 + 1) - 1;
894  f[2] += (reduce_mask_26 + 1) - 1;
895  f[3] += (reduce_mask_25 + 1) - 1;
896  f[4] += (reduce_mask_26 + 1) - 1;
897  f[5] += (reduce_mask_25 + 1) - 1;
898  f[6] += (reduce_mask_26 + 1) - 1;
899  f[7] += (reduce_mask_25 + 1) - 1;
900  f[8] += (reduce_mask_26 + 1) - 1;
901  f[9] += (reduce_mask_25 + 1) - 1;
902 
903  /* now between 2^255 and 2^256-20, and offset by 2^255. */
904  carry_pass_final()
905 
906  #undef carry_pass
907  #undef carry_full
908  #undef carry_final
909 
910  f[1] <<= 2; f[2] <<= 3;
911  f[3] <<= 5; f[4] <<= 6;
912  f[6] <<= 1; f[7] <<= 3;
913  f[8] <<= 4; f[9] <<= 6;
914 
915  #define F(i, s) \
916  out[s+0] |= (byte)( f[i] & 0xff); \
917  out[s+1] = (byte)((f[i] >> 8) & 0xff); \
918  out[s+2] = (byte)((f[i] >> 16) & 0xff); \
919  out[s+3] = (byte)((f[i] >> 24) & 0xff);
920 
921  out[0] = out[16] = 0;
922  F(0,0); F(1,3);
923  F(2,6); F(3,9);
924  F(4,12); F(5,16);
925  F(6,19); F(7,22);
926  F(8,25); F(9,28);
927  #undef F
928 }
929 
930 /* out = (flag) ? in : out */
931 inline void
932 curve25519_move_conditional_bytes(byte out[96], const byte in[96], word32 flag)
933 {
934  // TODO: enable this code path once we can test and benchmark it.
935  // It is about 48 insns shorter, it avoids punning which may be UB,
936  // and it is guaranteed constant time.
937 #if defined(__GNUC__) && defined(__i686__) && 0
938  const word32 iter = 96/sizeof(word32);
939  word32* outl = reinterpret_cast<word32*>(out);
940  const word32* inl = reinterpret_cast<const word32*>(in);
941  word32 idx=0, val;
942 
943  __asm__ __volatile__ (
944  ".att_syntax ;\n"
945  "cmpl $0, %[flag] ;\n" // compare, set ZERO flag
946  "movl %[iter], %%ecx ;\n" // load iteration count
947  "1: ;\n"
948  " movl (%[idx],%[out]), %[val] ;\n" // val = out[idx]
949  " cmovnzl (%[idx],%[in]), %[val] ;\n" // copy in[idx] to val if NZ
950  " movl %[val], (%[idx],%[out]) ;\n" // out[idx] = val
951  " leal 4(%[idx]), %[idx] ;\n" // increment index
952  " loopnz 1b ;\n" // does not affect flags
953  : [out] "+S" (outl), [in] "+D" (inl),
954  [idx] "+b" (idx), [val] "=r" (val)
955  : [flag] "g" (flag), [iter] "I" (iter)
956  : "ecx", "memory", "cc"
957  );
958 #else
959  const word32 nb = flag - 1, b = ~nb;
960  const word32 *inl = (const word32 *)in;
961  word32 *outl = (word32 *)out;
962  outl[0] = (outl[0] & nb) | (inl[0] & b);
963  outl[1] = (outl[1] & nb) | (inl[1] & b);
964  outl[2] = (outl[2] & nb) | (inl[2] & b);
965  outl[3] = (outl[3] & nb) | (inl[3] & b);
966  outl[4] = (outl[4] & nb) | (inl[4] & b);
967  outl[5] = (outl[5] & nb) | (inl[5] & b);
968  outl[6] = (outl[6] & nb) | (inl[6] & b);
969  outl[7] = (outl[7] & nb) | (inl[7] & b);
970  outl[8] = (outl[8] & nb) | (inl[8] & b);
971  outl[9] = (outl[9] & nb) | (inl[9] & b);
972  outl[10] = (outl[10] & nb) | (inl[10] & b);
973  outl[11] = (outl[11] & nb) | (inl[11] & b);
974  outl[12] = (outl[12] & nb) | (inl[12] & b);
975  outl[13] = (outl[13] & nb) | (inl[13] & b);
976  outl[14] = (outl[14] & nb) | (inl[14] & b);
977  outl[15] = (outl[15] & nb) | (inl[15] & b);
978  outl[16] = (outl[16] & nb) | (inl[16] & b);
979  outl[17] = (outl[17] & nb) | (inl[17] & b);
980  outl[18] = (outl[18] & nb) | (inl[18] & b);
981  outl[19] = (outl[19] & nb) | (inl[19] & b);
982  outl[20] = (outl[20] & nb) | (inl[20] & b);
983  outl[21] = (outl[21] & nb) | (inl[21] & b);
984  outl[22] = (outl[22] & nb) | (inl[22] & b);
985  outl[23] = (outl[23] & nb) | (inl[23] & b);
986 #endif
987 }
988 
989 /* if (iswap) swap(a, b) */
990 inline void
991 curve25519_swap_conditional(bignum25519 a, bignum25519 b, word32 iswap) {
992  const word32 swap = (word32)(-(sword32)iswap);
993  word32 x0,x1,x2,x3,x4,x5,x6,x7,x8,x9;
994 
995  x0 = swap & (a[0] ^ b[0]); a[0] ^= x0; b[0] ^= x0;
996  x1 = swap & (a[1] ^ b[1]); a[1] ^= x1; b[1] ^= x1;
997  x2 = swap & (a[2] ^ b[2]); a[2] ^= x2; b[2] ^= x2;
998  x3 = swap & (a[3] ^ b[3]); a[3] ^= x3; b[3] ^= x3;
999  x4 = swap & (a[4] ^ b[4]); a[4] ^= x4; b[4] ^= x4;
1000  x5 = swap & (a[5] ^ b[5]); a[5] ^= x5; b[5] ^= x5;
1001  x6 = swap & (a[6] ^ b[6]); a[6] ^= x6; b[6] ^= x6;
1002  x7 = swap & (a[7] ^ b[7]); a[7] ^= x7; b[7] ^= x7;
1003  x8 = swap & (a[8] ^ b[8]); a[8] ^= x8; b[8] ^= x8;
1004  x9 = swap & (a[9] ^ b[9]); a[9] ^= x9; b[9] ^= x9;
1005 }
1006 
1007 /*
1008  * In: b = 2^5 - 2^0
1009  * Out: b = 2^250 - 2^0
1010  */
1011 void
1012 curve25519_pow_two5mtwo0_two250mtwo0(bignum25519 b) {
1013  ALIGN(ALIGN_SPEC) bignum25519 t0,c;
1014 
1015  /* 2^5 - 2^0 */ /* b */
1016  /* 2^10 - 2^5 */ curve25519_square_times(t0, b, 5);
1017  /* 2^10 - 2^0 */ curve25519_mul(b, t0, b);
1018  /* 2^20 - 2^10 */ curve25519_square_times(t0, b, 10);
1019  /* 2^20 - 2^0 */ curve25519_mul(c, t0, b);
1020  /* 2^40 - 2^20 */ curve25519_square_times(t0, c, 20);
1021  /* 2^40 - 2^0 */ curve25519_mul(t0, t0, c);
1022  /* 2^50 - 2^10 */ curve25519_square_times(t0, t0, 10);
1023  /* 2^50 - 2^0 */ curve25519_mul(b, t0, b);
1024  /* 2^100 - 2^50 */ curve25519_square_times(t0, b, 50);
1025  /* 2^100 - 2^0 */ curve25519_mul(c, t0, b);
1026  /* 2^200 - 2^100 */ curve25519_square_times(t0, c, 100);
1027  /* 2^200 - 2^0 */ curve25519_mul(t0, t0, c);
1028  /* 2^250 - 2^50 */ curve25519_square_times(t0, t0, 50);
1029  /* 2^250 - 2^0 */ curve25519_mul(b, t0, b);
1030 }
1031 
1032 /*
1033  * z^(p - 2) = z(2^255 - 21)
1034  */
1035 void
1036 curve25519_recip(bignum25519 out, const bignum25519 z) {
1037  ALIGN(ALIGN_SPEC) bignum25519 a,t0,b;
1038 
1039  /* 2 */ curve25519_square_times(a, z, 1); /* a = 2 */
1040  /* 8 */ curve25519_square_times(t0, a, 2);
1041  /* 9 */ curve25519_mul(b, t0, z); /* b = 9 */
1042  /* 11 */ curve25519_mul(a, b, a); /* a = 11 */
1043  /* 22 */ curve25519_square_times(t0, a, 1);
1044  /* 2^5 - 2^0 = 31 */ curve25519_mul(b, t0, b);
1045  /* 2^250 - 2^0 */ curve25519_pow_two5mtwo0_two250mtwo0(b);
1046  /* 2^255 - 2^5 */ curve25519_square_times(b, b, 5);
1047  /* 2^255 - 21 */ curve25519_mul(out, b, a);
1048 }
1049 
1050 /*
1051  * z^((p-5)/8) = z^(2^252 - 3)
1052  */
1053 void
1054 curve25519_pow_two252m3(bignum25519 two252m3, const bignum25519 z) {
1055  ALIGN(ALIGN_SPEC) bignum25519 b,c,t0;
1056 
1057  /* 2 */ curve25519_square_times(c, z, 1); /* c = 2 */
1058  /* 8 */ curve25519_square_times(t0, c, 2); /* t0 = 8 */
1059  /* 9 */ curve25519_mul(b, t0, z); /* b = 9 */
1060  /* 11 */ curve25519_mul(c, b, c); /* c = 11 */
1061  /* 22 */ curve25519_square_times(t0, c, 1);
1062  /* 2^5 - 2^0 = 31 */ curve25519_mul(b, t0, b);
1063  /* 2^250 - 2^0 */ curve25519_pow_two5mtwo0_two250mtwo0(b);
1064  /* 2^252 - 2^2 */ curve25519_square_times(b, b, 2);
1065  /* 2^252 - 3 */ curve25519_mul(two252m3, b, z);
1066 }
1067 
1068 inline void
1069 ed25519_hash(byte *hash, const byte *in, size_t inlen) {
1070  SHA512().CalculateDigest(hash, in, inlen);
1071 }
1072 
1073 inline void
1074 ed25519_extsk(hash_512bits extsk, const byte sk[32]) {
1075  ed25519_hash(extsk, sk, 32);
1076  extsk[0] &= 248;
1077  extsk[31] &= 127;
1078  extsk[31] |= 64;
1079 }
1080 
1081 void
1082 UpdateFromStream(HashTransformation& hash, std::istream& stream)
1083 {
1084  SecByteBlock block(4096);
1085  while (stream.read((char*)block.begin(), block.size()))
1086  hash.Update(block, block.size());
1087 
1088  std::streamsize rem = stream.gcount();
1089  if (rem)
1090  hash.Update(block, (size_t)rem);
1091 
1092  block.SetMark(0);
1093 }
1094 
1095 void
1096 ed25519_hram(hash_512bits hram, const byte RS[64], const byte pk[32], const byte *m, size_t mlen) {
1097  SHA512 hash;
1098  hash.Update(RS, 32);
1099  hash.Update(pk, 32);
1100  hash.Update(m, mlen);
1101  hash.Final(hram);
1102 }
1103 
1104 void
1105 ed25519_hram(hash_512bits hram, const byte RS[64], const byte pk[32], std::istream& stream) {
1106  SHA512 hash;
1107  hash.Update(RS, 32);
1108  hash.Update(pk, 32);
1109  UpdateFromStream(hash, stream);
1110  hash.Final(hram);
1111 }
1112 
1113 inline bignum256modm_element_t
1114 lt_modm(bignum256modm_element_t a, bignum256modm_element_t b) {
1115  return (a - b) >> 31;
1116 }
1117 
1118 /* see HAC, Alg. 14.42 Step 4 */
1119 void
1120 reduce256_modm(bignum256modm r) {
1121  bignum256modm t;
1122  bignum256modm_element_t b = 0, pb, mask;
1123 
1124  /* t = r - m */
1125  pb = 0;
1126  pb += modm_m[0]; b = lt_modm(r[0], pb); t[0] = (r[0] - pb + (b << 30)); pb = b;
1127  pb += modm_m[1]; b = lt_modm(r[1], pb); t[1] = (r[1] - pb + (b << 30)); pb = b;
1128  pb += modm_m[2]; b = lt_modm(r[2], pb); t[2] = (r[2] - pb + (b << 30)); pb = b;
1129  pb += modm_m[3]; b = lt_modm(r[3], pb); t[3] = (r[3] - pb + (b << 30)); pb = b;
1130  pb += modm_m[4]; b = lt_modm(r[4], pb); t[4] = (r[4] - pb + (b << 30)); pb = b;
1131  pb += modm_m[5]; b = lt_modm(r[5], pb); t[5] = (r[5] - pb + (b << 30)); pb = b;
1132  pb += modm_m[6]; b = lt_modm(r[6], pb); t[6] = (r[6] - pb + (b << 30)); pb = b;
1133  pb += modm_m[7]; b = lt_modm(r[7], pb); t[7] = (r[7] - pb + (b << 30)); pb = b;
1134  pb += modm_m[8]; b = lt_modm(r[8], pb); t[8] = (r[8] - pb + (b << 16));
1135 
1136  /* keep r if r was smaller than m */
1137  mask = b - 1;
1138  r[0] ^= mask & (r[0] ^ t[0]);
1139  r[1] ^= mask & (r[1] ^ t[1]);
1140  r[2] ^= mask & (r[2] ^ t[2]);
1141  r[3] ^= mask & (r[3] ^ t[3]);
1142  r[4] ^= mask & (r[4] ^ t[4]);
1143  r[5] ^= mask & (r[5] ^ t[5]);
1144  r[6] ^= mask & (r[6] ^ t[6]);
1145  r[7] ^= mask & (r[7] ^ t[7]);
1146  r[8] ^= mask & (r[8] ^ t[8]);
1147 }
1148 
1149 /* Barrett reduction, see HAC, Alg. 14.42 */
1150 void
1151 barrett_reduce256_modm(bignum256modm r, const bignum256modm q1, const bignum256modm r1) {
1152  bignum256modm q3, r2;
1153  word64 c;
1154  bignum256modm_element_t f, b, pb;
1155 
1156  /* q1 = x >> 248 = 264 bits = 9 30 bit elements
1157  q2 = mu * q1
1158  q3 = (q2 / 256(32+1)) = q2 / (2^8)^(32+1) = q2 >> 264
1159  */
1160  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]);
1161  c >>= 30;
1162  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]);
1163  f = (bignum256modm_element_t)c; q3[0] = (f >> 24) & 0x3f; c >>= 30;
1164  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]);
1165  f = (bignum256modm_element_t)c; q3[0] |= (f << 6) & 0x3fffffff; q3[1] = (f >> 24) & 0x3f; c >>= 30;
1166  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]);
1167  f = (bignum256modm_element_t)c; q3[1] |= (f << 6) & 0x3fffffff; q3[2] = (f >> 24) & 0x3f; c >>= 30;
1168  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]);
1169  f = (bignum256modm_element_t)c; q3[2] |= (f << 6) & 0x3fffffff; q3[3] = (f >> 24) & 0x3f; c >>= 30;
1170  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]);
1171  f = (bignum256modm_element_t)c; q3[3] |= (f << 6) & 0x3fffffff; q3[4] = (f >> 24) & 0x3f; c >>= 30;
1172  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]);
1173  f = (bignum256modm_element_t)c; q3[4] |= (f << 6) & 0x3fffffff; q3[5] = (f >> 24) & 0x3f; c >>= 30;
1174  c += mul32x32_64(modm_mu[6], q1[8]) + mul32x32_64(modm_mu[7], q1[7]) + mul32x32_64(modm_mu[8], q1[6]);
1175  f = (bignum256modm_element_t)c; q3[5] |= (f << 6) & 0x3fffffff; q3[6] = (f >> 24) & 0x3f; c >>= 30;
1176  c += mul32x32_64(modm_mu[7], q1[8]) + mul32x32_64(modm_mu[8], q1[7]);
1177  f = (bignum256modm_element_t)c; q3[6] |= (f << 6) & 0x3fffffff; q3[7] = (f >> 24) & 0x3f; c >>= 30;
1178  c += mul32x32_64(modm_mu[8], q1[8]);
1179  f = (bignum256modm_element_t)c; q3[7] |= (f << 6) & 0x3fffffff; q3[8] = (bignum256modm_element_t)(c >> 24);
1180 
1181  /* r1 = (x mod 256^(32+1)) = x mod (2^8)(31+1) = x & ((1 << 264) - 1)
1182  r2 = (q3 * m) mod (256^(32+1)) = (q3 * m) & ((1 << 264) - 1)
1183  */
1184  c = mul32x32_64(modm_m[0], q3[0]);
1185  r2[0] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
1186  c += mul32x32_64(modm_m[0], q3[1]) + mul32x32_64(modm_m[1], q3[0]);
1187  r2[1] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
1188  c += mul32x32_64(modm_m[0], q3[2]) + mul32x32_64(modm_m[1], q3[1]) + mul32x32_64(modm_m[2], q3[0]);
1189  r2[2] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
1190  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]);
1191  r2[3] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
1192  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]);
1193  r2[4] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
1194  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]);
1195  r2[5] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
1196  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]);
1197  r2[6] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
1198  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]);
1199  r2[7] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
1200  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]);
1201  r2[8] = (bignum256modm_element_t)(c & 0xffffff);
1202 
1203  /* r = r1 - r2
1204  if (r < 0) r += (1 << 264) */
1205  pb = 0;
1206  pb += r2[0]; b = lt_modm(r1[0], pb); r[0] = (r1[0] - pb + (b << 30)); pb = b;
1207  pb += r2[1]; b = lt_modm(r1[1], pb); r[1] = (r1[1] - pb + (b << 30)); pb = b;
1208  pb += r2[2]; b = lt_modm(r1[2], pb); r[2] = (r1[2] - pb + (b << 30)); pb = b;
1209  pb += r2[3]; b = lt_modm(r1[3], pb); r[3] = (r1[3] - pb + (b << 30)); pb = b;
1210  pb += r2[4]; b = lt_modm(r1[4], pb); r[4] = (r1[4] - pb + (b << 30)); pb = b;
1211  pb += r2[5]; b = lt_modm(r1[5], pb); r[5] = (r1[5] - pb + (b << 30)); pb = b;
1212  pb += r2[6]; b = lt_modm(r1[6], pb); r[6] = (r1[6] - pb + (b << 30)); pb = b;
1213  pb += r2[7]; b = lt_modm(r1[7], pb); r[7] = (r1[7] - pb + (b << 30)); pb = b;
1214  pb += r2[8]; b = lt_modm(r1[8], pb); r[8] = (r1[8] - pb + (b << 24));
1215 
1216  reduce256_modm(r);
1217  reduce256_modm(r);
1218 }
1219 
1220 /* addition modulo m */
1221 void
1222 add256_modm(bignum256modm r, const bignum256modm x, const bignum256modm y) {
1223  bignum256modm_element_t c;
1224 
1225  c = x[0] + y[0]; r[0] = c & 0x3fffffff; c >>= 30;
1226  c += x[1] + y[1]; r[1] = c & 0x3fffffff; c >>= 30;
1227  c += x[2] + y[2]; r[2] = c & 0x3fffffff; c >>= 30;
1228  c += x[3] + y[3]; r[3] = c & 0x3fffffff; c >>= 30;
1229  c += x[4] + y[4]; r[4] = c & 0x3fffffff; c >>= 30;
1230  c += x[5] + y[5]; r[5] = c & 0x3fffffff; c >>= 30;
1231  c += x[6] + y[6]; r[6] = c & 0x3fffffff; c >>= 30;
1232  c += x[7] + y[7]; r[7] = c & 0x3fffffff; c >>= 30;
1233  c += x[8] + y[8]; r[8] = c;
1234 
1235  reduce256_modm(r);
1236 }
1237 
1238 /* multiplication modulo m */
1239 void
1240 mul256_modm(bignum256modm r, const bignum256modm x, const bignum256modm y) {
1241  bignum256modm r1, q1;
1242  word64 c;
1243  bignum256modm_element_t f;
1244 
1245  c = mul32x32_64(x[0], y[0]);
1246  f = (bignum256modm_element_t)c; r1[0] = (f & 0x3fffffff); c >>= 30;
1247  c += mul32x32_64(x[0], y[1]) + mul32x32_64(x[1], y[0]);
1248  f = (bignum256modm_element_t)c; r1[1] = (f & 0x3fffffff); c >>= 30;
1249  c += mul32x32_64(x[0], y[2]) + mul32x32_64(x[1], y[1]) + mul32x32_64(x[2], y[0]);
1250  f = (bignum256modm_element_t)c; r1[2] = (f & 0x3fffffff); c >>= 30;
1251  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]);
1252  f = (bignum256modm_element_t)c; r1[3] = (f & 0x3fffffff); c >>= 30;
1253  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]);
1254  f = (bignum256modm_element_t)c; r1[4] = (f & 0x3fffffff); c >>= 30;
1255  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]);
1256  f = (bignum256modm_element_t)c; r1[5] = (f & 0x3fffffff); c >>= 30;
1257  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]);
1258  f = (bignum256modm_element_t)c; r1[6] = (f & 0x3fffffff); c >>= 30;
1259  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]);
1260  f = (bignum256modm_element_t)c; r1[7] = (f & 0x3fffffff); c >>= 30;
1261  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]);
1262  f = (bignum256modm_element_t)c; r1[8] = (f & 0x00ffffff); q1[0] = (f >> 8) & 0x3fffff; c >>= 30;
1263  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]);
1264  f = (bignum256modm_element_t)c; q1[0] = (q1[0] | (f << 22)) & 0x3fffffff; q1[1] = (f >> 8) & 0x3fffff; c >>= 30;
1265  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]);
1266  f = (bignum256modm_element_t)c; q1[1] = (q1[1] | (f << 22)) & 0x3fffffff; q1[2] = (f >> 8) & 0x3fffff; c >>= 30;
1267  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]);
1268  f = (bignum256modm_element_t)c; q1[2] = (q1[2] | (f << 22)) & 0x3fffffff; q1[3] = (f >> 8) & 0x3fffff; c >>= 30;
1269  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]);
1270  f = (bignum256modm_element_t)c; q1[3] = (q1[3] | (f << 22)) & 0x3fffffff; q1[4] = (f >> 8) & 0x3fffff; c >>= 30;
1271  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]);
1272  f = (bignum256modm_element_t)c; q1[4] = (q1[4] | (f << 22)) & 0x3fffffff; q1[5] = (f >> 8) & 0x3fffff; c >>= 30;
1273  c += mul32x32_64(x[6], y[8]) + mul32x32_64(x[7], y[7]) + mul32x32_64(x[8], y[6]);
1274  f = (bignum256modm_element_t)c; q1[5] = (q1[5] | (f << 22)) & 0x3fffffff; q1[6] = (f >> 8) & 0x3fffff; c >>= 30;
1275  c += mul32x32_64(x[7], y[8]) + mul32x32_64(x[8], y[7]);
1276  f = (bignum256modm_element_t)c; q1[6] = (q1[6] | (f << 22)) & 0x3fffffff; q1[7] = (f >> 8) & 0x3fffff; c >>= 30;
1277  c += mul32x32_64(x[8], y[8]);
1278  f = (bignum256modm_element_t)c; q1[7] = (q1[7] | (f << 22)) & 0x3fffffff; q1[8] = (f >> 8) & 0x3fffff;
1279 
1280  barrett_reduce256_modm(r, q1, r1);
1281 }
1282 
1283 void
1284 expand256_modm(bignum256modm out, const byte *in, size_t len) {
1285  byte work[64] = {0};
1286  bignum256modm_element_t x[16];
1287  bignum256modm q1;
1288 
1289  std::memcpy(work, in, len);
1290  x[0] = U8TO32_LE(work + 0);
1291  x[1] = U8TO32_LE(work + 4);
1292  x[2] = U8TO32_LE(work + 8);
1293  x[3] = U8TO32_LE(work + 12);
1294  x[4] = U8TO32_LE(work + 16);
1295  x[5] = U8TO32_LE(work + 20);
1296  x[6] = U8TO32_LE(work + 24);
1297  x[7] = U8TO32_LE(work + 28);
1298  x[8] = U8TO32_LE(work + 32);
1299  x[9] = U8TO32_LE(work + 36);
1300  x[10] = U8TO32_LE(work + 40);
1301  x[11] = U8TO32_LE(work + 44);
1302  x[12] = U8TO32_LE(work + 48);
1303  x[13] = U8TO32_LE(work + 52);
1304  x[14] = U8TO32_LE(work + 56);
1305  x[15] = U8TO32_LE(work + 60);
1306 
1307  /* r1 = (x mod 256^(32+1)) = x mod (2^8)(31+1) = x & ((1 << 264) - 1) */
1308  out[0] = ( x[0]) & 0x3fffffff;
1309  out[1] = ((x[ 0] >> 30) | (x[ 1] << 2)) & 0x3fffffff;
1310  out[2] = ((x[ 1] >> 28) | (x[ 2] << 4)) & 0x3fffffff;
1311  out[3] = ((x[ 2] >> 26) | (x[ 3] << 6)) & 0x3fffffff;
1312  out[4] = ((x[ 3] >> 24) | (x[ 4] << 8)) & 0x3fffffff;
1313  out[5] = ((x[ 4] >> 22) | (x[ 5] << 10)) & 0x3fffffff;
1314  out[6] = ((x[ 5] >> 20) | (x[ 6] << 12)) & 0x3fffffff;
1315  out[7] = ((x[ 6] >> 18) | (x[ 7] << 14)) & 0x3fffffff;
1316  out[8] = ((x[ 7] >> 16) | (x[ 8] << 16)) & 0x00ffffff;
1317 
1318  /* 8*31 = 248 bits, no need to reduce */
1319  if (len < 32)
1320  return;
1321 
1322  /* q1 = x >> 248 = 264 bits = 9 30 bit elements */
1323  q1[0] = ((x[ 7] >> 24) | (x[ 8] << 8)) & 0x3fffffff;
1324  q1[1] = ((x[ 8] >> 22) | (x[ 9] << 10)) & 0x3fffffff;
1325  q1[2] = ((x[ 9] >> 20) | (x[10] << 12)) & 0x3fffffff;
1326  q1[3] = ((x[10] >> 18) | (x[11] << 14)) & 0x3fffffff;
1327  q1[4] = ((x[11] >> 16) | (x[12] << 16)) & 0x3fffffff;
1328  q1[5] = ((x[12] >> 14) | (x[13] << 18)) & 0x3fffffff;
1329  q1[6] = ((x[13] >> 12) | (x[14] << 20)) & 0x3fffffff;
1330  q1[7] = ((x[14] >> 10) | (x[15] << 22)) & 0x3fffffff;
1331  q1[8] = ((x[15] >> 8) );
1332 
1333  barrett_reduce256_modm(out, q1, out);
1334 }
1335 
1336 void
1337 expand_raw256_modm(bignum256modm out, const byte in[32]) {
1338  bignum256modm_element_t x[8];
1339 
1340  x[0] = U8TO32_LE(in + 0);
1341  x[1] = U8TO32_LE(in + 4);
1342  x[2] = U8TO32_LE(in + 8);
1343  x[3] = U8TO32_LE(in + 12);
1344  x[4] = U8TO32_LE(in + 16);
1345  x[5] = U8TO32_LE(in + 20);
1346  x[6] = U8TO32_LE(in + 24);
1347  x[7] = U8TO32_LE(in + 28);
1348 
1349  out[0] = ( x[0]) & 0x3fffffff;
1350  out[1] = ((x[ 0] >> 30) | (x[ 1] << 2)) & 0x3fffffff;
1351  out[2] = ((x[ 1] >> 28) | (x[ 2] << 4)) & 0x3fffffff;
1352  out[3] = ((x[ 2] >> 26) | (x[ 3] << 6)) & 0x3fffffff;
1353  out[4] = ((x[ 3] >> 24) | (x[ 4] << 8)) & 0x3fffffff;
1354  out[5] = ((x[ 4] >> 22) | (x[ 5] << 10)) & 0x3fffffff;
1355  out[6] = ((x[ 5] >> 20) | (x[ 6] << 12)) & 0x3fffffff;
1356  out[7] = ((x[ 6] >> 18) | (x[ 7] << 14)) & 0x3fffffff;
1357  out[8] = ((x[ 7] >> 16) ) & 0x0000ffff;
1358 }
1359 
1360 void
1361 contract256_modm(byte out[32], const bignum256modm in) {
1362  U32TO8_LE(out + 0, (in[0] ) | (in[1] << 30));
1363  U32TO8_LE(out + 4, (in[1] >> 2) | (in[2] << 28));
1364  U32TO8_LE(out + 8, (in[2] >> 4) | (in[3] << 26));
1365  U32TO8_LE(out + 12, (in[3] >> 6) | (in[4] << 24));
1366  U32TO8_LE(out + 16, (in[4] >> 8) | (in[5] << 22));
1367  U32TO8_LE(out + 20, (in[5] >> 10) | (in[6] << 20));
1368  U32TO8_LE(out + 24, (in[6] >> 12) | (in[7] << 18));
1369  U32TO8_LE(out + 28, (in[7] >> 14) | (in[8] << 16));
1370 }
1371 
1372 void
1373 contract256_window4_modm(signed char r[64], const bignum256modm in) {
1374  char carry;
1375  signed char *quads = r;
1376  bignum256modm_element_t i, j, v;
1377 
1378  for (i = 0; i < 8; i += 2) {
1379  v = in[i];
1380  for (j = 0; j < 7; j++) {
1381  *quads++ = (v & 15);
1382  v >>= 4;
1383  }
1384  v |= (in[i+1] << 2);
1385  for (j = 0; j < 8; j++) {
1386  *quads++ = (v & 15);
1387  v >>= 4;
1388  }
1389  }
1390 
1391  v = in[8];
1392  *quads++ = (v & 15); v >>= 4;
1393  *quads++ = (v & 15); v >>= 4;
1394  *quads++ = (v & 15); v >>= 4;
1395  *quads++ = (v & 15); v >>= 4;
1396 
1397  /* making it signed */
1398  carry = 0;
1399  for(i = 0; i < 63; i++) {
1400  r[i] += carry;
1401  r[i+1] += (r[i] >> 4);
1402  r[i] &= 15;
1403  carry = (r[i] >> 3);
1404  r[i] -= (carry << 4);
1405  }
1406  r[63] += carry;
1407 }
1408 
1409 void
1410 contract256_slidingwindow_modm(signed char r[256], const bignum256modm s, int windowsize) {
1411  int i,j,k,b;
1412  int m = (1 << (windowsize - 1)) - 1, soplen = 256;
1413  signed char *bits = r;
1414  bignum256modm_element_t v;
1415 
1416  /* first put the binary expansion into r */
1417  for (i = 0; i < 8; i++) {
1418  v = s[i];
1419  for (j = 0; j < 30; j++, v >>= 1)
1420  *bits++ = (v & 1);
1421  }
1422  v = s[8];
1423  for (j = 0; j < 16; j++, v >>= 1)
1424  *bits++ = (v & 1);
1425 
1426  /* Making it sliding window */
1427  for (j = 0; j < soplen; j++) {
1428  if (!r[j])
1429  continue;
1430 
1431  for (b = 1; (b < (soplen - j)) && (b <= 6); b++) {
1432  if ((r[j] + (r[j + b] << b)) <= m) {
1433  r[j] += r[j + b] << b;
1434  r[j + b] = 0;
1435  } else if ((r[j] - (r[j + b] << b)) >= -m) {
1436  r[j] -= r[j + b] << b;
1437  for (k = j + b; k < soplen; k++) {
1438  if (!r[k]) {
1439  r[k] = 1;
1440  break;
1441  }
1442  r[k] = 0;
1443  }
1444  } else if (r[j + b]) {
1445  break;
1446  }
1447  }
1448  }
1449 }
1450 
1451 inline void
1452 ge25519_p1p1_to_partial(ge25519 *r, const ge25519_p1p1 *p) {
1453  curve25519_mul(r->x, p->x, p->t);
1454  curve25519_mul(r->y, p->y, p->z);
1455  curve25519_mul(r->z, p->z, p->t);
1456 }
1457 
1458 inline void
1459 ge25519_p1p1_to_full(ge25519 *r, const ge25519_p1p1 *p) {
1460  curve25519_mul(r->x, p->x, p->t);
1461  curve25519_mul(r->y, p->y, p->z);
1462  curve25519_mul(r->z, p->z, p->t);
1463  curve25519_mul(r->t, p->x, p->y);
1464 }
1465 
1466 void
1467 ge25519_full_to_pniels(ge25519_pniels *p, const ge25519 *r) {
1468  curve25519_sub(p->ysubx, r->y, r->x);
1469  curve25519_add(p->xaddy, r->y, r->x);
1470  curve25519_copy(p->z, r->z);
1471  curve25519_mul(p->t2d, r->t, ge25519_ec2d);
1472 }
1473 
1474 void
1475 ge25519_add_p1p1(ge25519_p1p1 *r, const ge25519 *p, const ge25519 *q) {
1476  bignum25519 a,b,c,d,t,u;
1477 
1478  curve25519_sub(a, p->y, p->x);
1479  curve25519_add(b, p->y, p->x);
1480  curve25519_sub(t, q->y, q->x);
1481  curve25519_add(u, q->y, q->x);
1482  curve25519_mul(a, a, t);
1483  curve25519_mul(b, b, u);
1484  curve25519_mul(c, p->t, q->t);
1485  curve25519_mul(c, c, ge25519_ec2d);
1486  curve25519_mul(d, p->z, q->z);
1487  curve25519_add(d, d, d);
1488  curve25519_sub(r->x, b, a);
1489  curve25519_add(r->y, b, a);
1490  curve25519_add_after_basic(r->z, d, c);
1491  curve25519_sub_after_basic(r->t, d, c);
1492 }
1493 
1494 void
1495 ge25519_double_p1p1(ge25519_p1p1 *r, const ge25519 *p) {
1496  bignum25519 a,b,c;
1497 
1498  curve25519_square(a, p->x);
1499  curve25519_square(b, p->y);
1500  curve25519_square(c, p->z);
1501  curve25519_add_reduce(c, c, c);
1502  curve25519_add(r->x, p->x, p->y);
1503  curve25519_square(r->x, r->x);
1504  curve25519_add(r->y, b, a);
1505  curve25519_sub(r->z, b, a);
1506  curve25519_sub_after_basic(r->x, r->x, r->y);
1507  curve25519_sub_after_basic(r->t, c, r->z);
1508 }
1509 
1510 void
1511 ge25519_nielsadd2_p1p1(ge25519_p1p1 *r, const ge25519 *p, const ge25519_niels *q, byte signbit) {
1512  const bignum25519 *qb = (const bignum25519 *)q;
1513  bignum25519 *rb = (bignum25519 *)r;
1514  bignum25519 a,b,c;
1515 
1516  curve25519_sub(a, p->y, p->x);
1517  curve25519_add(b, p->y, p->x);
1518  curve25519_mul(a, a, qb[signbit]); /* x for +, y for - */
1519  curve25519_mul(r->x, b, qb[signbit^1]); /* y for +, x for - */
1520  curve25519_add(r->y, r->x, a);
1521  curve25519_sub(r->x, r->x, a);
1522  curve25519_mul(c, p->t, q->t2d);
1523  curve25519_add_reduce(r->t, p->z, p->z);
1524  curve25519_copy(r->z, r->t);
1525  curve25519_add(rb[2+signbit], rb[2+signbit], c); /* z for +, t for - */
1526  curve25519_sub(rb[2+(signbit^1)], rb[2+(signbit^1)], c); /* t for +, z for - */
1527 }
1528 
1529 void
1530 ge25519_pnielsadd_p1p1(ge25519_p1p1 *r, const ge25519 *p, const ge25519_pniels *q, byte signbit) {
1531  const bignum25519 *qb = (const bignum25519 *)q;
1532  bignum25519 *rb = (bignum25519 *)r;
1533  bignum25519 a,b,c;
1534 
1535  curve25519_sub(a, p->y, p->x);
1536  curve25519_add(b, p->y, p->x);
1537  curve25519_mul(a, a, qb[signbit]); /* ysubx for +, xaddy for - */
1538  curve25519_mul(r->x, b, qb[signbit^1]); /* xaddy for +, ysubx for - */
1539  curve25519_add(r->y, r->x, a);
1540  curve25519_sub(r->x, r->x, a);
1541  curve25519_mul(c, p->t, q->t2d);
1542  curve25519_mul(r->t, p->z, q->z);
1543  curve25519_add_reduce(r->t, r->t, r->t);
1544  curve25519_copy(r->z, r->t);
1545  curve25519_add(rb[2+signbit], rb[2+signbit], c); /* z for +, t for - */
1546  curve25519_sub(rb[2+(signbit^1)], rb[2+(signbit^1)], c); /* t for +, z for - */
1547 }
1548 
1549 void
1550 ge25519_double_partial(ge25519 *r, const ge25519 *p) {
1551  ge25519_p1p1 t;
1552  ge25519_double_p1p1(&t, p);
1553  ge25519_p1p1_to_partial(r, &t);
1554 }
1555 
1556 void
1557 ge25519_double(ge25519 *r, const ge25519 *p) {
1558  ge25519_p1p1 t;
1559  ge25519_double_p1p1(&t, p);
1560  ge25519_p1p1_to_full(r, &t);
1561 }
1562 
1563 void
1564 ge25519_add(ge25519 *r, const ge25519 *p, const ge25519 *q) {
1565  ge25519_p1p1 t;
1566  ge25519_add_p1p1(&t, p, q);
1567  ge25519_p1p1_to_full(r, &t);
1568 }
1569 
1570 void
1571 ge25519_nielsadd2(ge25519 *r, const ge25519_niels *q) {
1572  bignum25519 a,b,c,e,f,g,h;
1573 
1574  curve25519_sub(a, r->y, r->x);
1575  curve25519_add(b, r->y, r->x);
1576  curve25519_mul(a, a, q->ysubx);
1577  curve25519_mul(e, b, q->xaddy);
1578  curve25519_add(h, e, a);
1579  curve25519_sub(e, e, a);
1580  curve25519_mul(c, r->t, q->t2d);
1581  curve25519_add(f, r->z, r->z);
1582  curve25519_add_after_basic(g, f, c);
1583  curve25519_sub_after_basic(f, f, c);
1584  curve25519_mul(r->x, e, f);
1585  curve25519_mul(r->y, h, g);
1586  curve25519_mul(r->z, g, f);
1587  curve25519_mul(r->t, e, h);
1588 }
1589 
1590 void
1591 ge25519_pnielsadd(ge25519_pniels *r, const ge25519 *p, const ge25519_pniels *q) {
1592  bignum25519 a,b,c,x,y,z,t;
1593 
1594  curve25519_sub(a, p->y, p->x);
1595  curve25519_add(b, p->y, p->x);
1596  curve25519_mul(a, a, q->ysubx);
1597  curve25519_mul(x, b, q->xaddy);
1598  curve25519_add(y, x, a);
1599  curve25519_sub(x, x, a);
1600  curve25519_mul(c, p->t, q->t2d);
1601  curve25519_mul(t, p->z, q->z);
1602  curve25519_add(t, t, t);
1603  curve25519_add_after_basic(z, t, c);
1604  curve25519_sub_after_basic(t, t, c);
1605  curve25519_mul(r->xaddy, x, t);
1606  curve25519_mul(r->ysubx, y, z);
1607  curve25519_mul(r->z, z, t);
1608  curve25519_mul(r->t2d, x, y);
1609  curve25519_copy(y, r->ysubx);
1610  curve25519_sub(r->ysubx, r->ysubx, r->xaddy);
1611  curve25519_add(r->xaddy, r->xaddy, y);
1612  curve25519_mul(r->t2d, r->t2d, ge25519_ec2d);
1613 }
1614 
1615 void
1616 ge25519_pack(byte r[32], const ge25519 *p) {
1617  bignum25519 tx, ty, zi;
1618  byte parity[32];
1619  curve25519_recip(zi, p->z);
1620  curve25519_mul(tx, p->x, zi);
1621  curve25519_mul(ty, p->y, zi);
1622  curve25519_contract(r, ty);
1623  curve25519_contract(parity, tx);
1624  r[31] ^= ((parity[0] & 1) << 7);
1625 }
1626 
1627 int
1628 ed25519_verify(const byte *x, const byte *y, size_t len) {
1629  size_t differentbits = 0;
1630  while (len--)
1631  differentbits |= (*x++ ^ *y++);
1632  return (int) (1 & ((differentbits - 1) >> 8));
1633 }
1634 
1635 int
1636 ge25519_unpack_negative_vartime(ge25519 *r, const byte p[32]) {
1637  const byte zero[32] = {0};
1638  const bignum25519 one = {1};
1639  byte parity = p[31] >> 7;
1640  byte check[32];
1641  bignum25519 t, root, num, den, d3;
1642 
1643  curve25519_expand(r->y, p);
1644  curve25519_copy(r->z, one);
1645  curve25519_square(num, r->y); /* x = y^2 */
1646  curve25519_mul(den, num, ge25519_ecd); /* den = dy^2 */
1647  curve25519_sub_reduce(num, num, r->z); /* x = y^1 - 1 */
1648  curve25519_add(den, den, r->z); /* den = dy^2 + 1 */
1649 
1650  /* Computation of sqrt(num/den) */
1651  /* 1.: computation of num^((p-5)/8)*den^((7p-35)/8) = (num*den^7)^((p-5)/8) */
1652  curve25519_square(t, den);
1653  curve25519_mul(d3, t, den);
1654  curve25519_square(r->x, d3);
1655  curve25519_mul(r->x, r->x, den);
1656  curve25519_mul(r->x, r->x, num);
1657  curve25519_pow_two252m3(r->x, r->x);
1658 
1659  /* 2. computation of r->x = num * den^3 * (num*den^7)^((p-5)/8) */
1660  curve25519_mul(r->x, r->x, d3);
1661  curve25519_mul(r->x, r->x, num);
1662 
1663  /* 3. Check if either of the roots works: */
1664  curve25519_square(t, r->x);
1665  curve25519_mul(t, t, den);
1666  curve25519_sub_reduce(root, t, num);
1667  curve25519_contract(check, root);
1668  if (!ed25519_verify(check, zero, 32)) {
1669  curve25519_add_reduce(t, t, num);
1670  curve25519_contract(check, t);
1671  if (!ed25519_verify(check, zero, 32))
1672  return 0;
1673  curve25519_mul(r->x, r->x, ge25519_sqrtneg1);
1674  }
1675 
1676  curve25519_contract(check, r->x);
1677  if ((check[0] & 1) == parity) {
1678  curve25519_copy(t, r->x);
1679  curve25519_neg(r->x, t);
1680  }
1681  curve25519_mul(r->t, r->x, r->y);
1682  return 1;
1683 }
1684 
1685 /* computes [s1]p1 + [s2]basepoint */
1686 void
1687 ge25519_double_scalarmult_vartime(ge25519 *r, const ge25519 *p1, const bignum256modm s1, const bignum256modm s2) {
1688  signed char slide1[256], slide2[256];
1689  ge25519_pniels pre1[S1_TABLE_SIZE];
1690  ge25519 d1;
1691  ge25519_p1p1 t;
1692  sword32 i;
1693 
1694  contract256_slidingwindow_modm(slide1, s1, S1_SWINDOWSIZE);
1695  contract256_slidingwindow_modm(slide2, s2, S2_SWINDOWSIZE);
1696 
1697  ge25519_double(&d1, p1);
1698  ge25519_full_to_pniels(pre1, p1);
1699  for (i = 0; i < S1_TABLE_SIZE - 1; i++)
1700  ge25519_pnielsadd(&pre1[i+1], &d1, &pre1[i]);
1701 
1702  /* set neutral */
1703  std::memset(r, 0, sizeof(ge25519));
1704  r->y[0] = 1;
1705  r->z[0] = 1;
1706 
1707  i = 255;
1708  while ((i >= 0) && !(slide1[i] | slide2[i]))
1709  i--;
1710 
1711  for (; i >= 0; i--) {
1712  ge25519_double_p1p1(&t, r);
1713 
1714  if (slide1[i]) {
1715  ge25519_p1p1_to_full(r, &t);
1716  ge25519_pnielsadd_p1p1(&t, r, &pre1[abs(slide1[i]) / 2], (byte)slide1[i] >> 7);
1717  }
1718 
1719  if (slide2[i]) {
1720  ge25519_p1p1_to_full(r, &t);
1721  ge25519_nielsadd2_p1p1(&t, r, &ge25519_niels_sliding_multiples[abs(slide2[i]) / 2], (byte)slide2[i] >> 7);
1722  }
1723 
1724  ge25519_p1p1_to_partial(r, &t);
1725  }
1726 }
1727 
1728 #if !defined(HAVE_GE25519_SCALARMULT_BASE_CHOOSE_NIELS)
1729 
1730 word32
1731 ge25519_windowb_equal(word32 b, word32 c) {
1732  return ((b ^ c) - 1) >> 31;
1733 }
1734 
1735 void
1736 ge25519_scalarmult_base_choose_niels(ge25519_niels *t, const byte table[256][96], word32 pos, signed char b) {
1737  bignum25519 neg;
1738  word32 sign = (word32)((byte)b >> 7);
1739  word32 mask = ~(sign - 1);
1740  word32 u = (b + mask) ^ mask;
1741  word32 i;
1742 
1743  /* ysubx, xaddy, t2d in packed form. initialize to ysubx = 1, xaddy = 1, t2d = 0 */
1744  byte packed[96] = {0};
1745  packed[0] = 1;
1746  packed[32] = 1;
1747 
1748  for (i = 0; i < 8; i++)
1749  curve25519_move_conditional_bytes(packed, table[(pos * 8) + i], ge25519_windowb_equal(u, i + 1));
1750 
1751  /* expand in to t */
1752  curve25519_expand(t->ysubx, packed + 0);
1753  curve25519_expand(t->xaddy, packed + 32);
1754  curve25519_expand(t->t2d , packed + 64);
1755 
1756  /* adjust for sign */
1757  curve25519_swap_conditional(t->ysubx, t->xaddy, sign);
1758  curve25519_neg(neg, t->t2d);
1759  curve25519_swap_conditional(t->t2d, neg, sign);
1760 }
1761 
1762 #endif /* HAVE_GE25519_SCALARMULT_BASE_CHOOSE_NIELS */
1763 
1764 /* computes [s]basepoint */
1765 void
1766 ge25519_scalarmult_base_niels(ge25519 *r, const byte basepoint_table[256][96], const bignum256modm s) {
1767  signed char b[64];
1768  word32 i;
1769  ge25519_niels t;
1770 
1771  contract256_window4_modm(b, s);
1772 
1773  ge25519_scalarmult_base_choose_niels(&t, basepoint_table, 0, b[1]);
1774  curve25519_sub_reduce(r->x, t.xaddy, t.ysubx);
1775  curve25519_add_reduce(r->y, t.xaddy, t.ysubx);
1776  std::memset(r->z, 0, sizeof(bignum25519));
1777  curve25519_copy(r->t, t.t2d);
1778  r->z[0] = 2;
1779  for (i = 3; i < 64; i += 2) {
1780  ge25519_scalarmult_base_choose_niels(&t, basepoint_table, i / 2, b[i]);
1781  ge25519_nielsadd2(r, &t);
1782  }
1783  ge25519_double_partial(r, r);
1784  ge25519_double_partial(r, r);
1785  ge25519_double_partial(r, r);
1786  ge25519_double(r, r);
1787  ge25519_scalarmult_base_choose_niels(&t, basepoint_table, 0, b[0]);
1788  curve25519_mul(t.t2d, t.t2d, ge25519_ecd);
1789  ge25519_nielsadd2(r, &t);
1790  for(i = 2; i < 64; i += 2) {
1791  ge25519_scalarmult_base_choose_niels(&t, basepoint_table, i / 2, b[i]);
1792  ge25519_nielsadd2(r, &t);
1793  }
1794 }
1795 
1796 ANONYMOUS_NAMESPACE_END
1797 NAMESPACE_END // Ed25519
1798 NAMESPACE_END // Donna
1799 NAMESPACE_END // CryptoPP
1800 
1801 //***************************** curve25519 *****************************//
1802 
1803 NAMESPACE_BEGIN(CryptoPP)
1804 NAMESPACE_BEGIN(Donna)
1805 
1806 int curve25519_mult_CXX(byte sharedKey[32], const byte secretKey[32], const byte othersKey[32])
1807 {
1808  using namespace CryptoPP::Donna::X25519;
1809 
1810  FixedSizeSecBlock<byte, 32> e;
1811  for (size_t i = 0; i < 32; ++i)
1812  e[i] = secretKey[i];
1813  e[0] &= 0xf8; e[31] &= 0x7f; e[31] |= 0x40;
1814 
1815  bignum25519 nqpqx = {1}, nqpqz = {0}, nqz = {1}, nqx;
1816  bignum25519 q, qx, qpqx, qqx, zzz, zmone;
1817  size_t bit, lastbit;
1818 
1819  curve25519_expand(q, othersKey);
1820  curve25519_copy(nqx, q);
1821 
1822  /* bit 255 is always 0, and bit 254 is always 1, so skip bit 255 and
1823  start pre-swapped on bit 254 */
1824  lastbit = 1;
1825 
1826  /* we are doing bits 254..3 in the loop, but are swapping in bits 253..2 */
1827  for (int i = 253; i >= 2; i--) {
1828  curve25519_add(qx, nqx, nqz);
1829  curve25519_sub(nqz, nqx, nqz);
1830  curve25519_add(qpqx, nqpqx, nqpqz);
1831  curve25519_sub(nqpqz, nqpqx, nqpqz);
1832  curve25519_mul(nqpqx, qpqx, nqz);
1833  curve25519_mul(nqpqz, qx, nqpqz);
1834  curve25519_add(qqx, nqpqx, nqpqz);
1835  curve25519_sub(nqpqz, nqpqx, nqpqz);
1836  curve25519_square(nqpqz, nqpqz);
1837  curve25519_square(nqpqx, qqx);
1838  curve25519_mul(nqpqz, nqpqz, q);
1839  curve25519_square(qx, qx);
1840  curve25519_square(nqz, nqz);
1841  curve25519_mul(nqx, qx, nqz);
1842  curve25519_sub(nqz, qx, nqz);
1843  curve25519_scalar_product(zzz, nqz, 121665);
1844  curve25519_add(zzz, zzz, qx);
1845  curve25519_mul(nqz, nqz, zzz);
1846 
1847  bit = (e[i/8] >> (i & 7)) & 1;
1848  curve25519_swap_conditional(nqx, nqpqx, (word32)(bit ^ lastbit));
1849  curve25519_swap_conditional(nqz, nqpqz, (word32)(bit ^ lastbit));
1850  lastbit = bit;
1851  }
1852 
1853  /* the final 3 bits are always zero, so we only need to double */
1854  for (int i = 0; i < 3; i++) {
1855  curve25519_add(qx, nqx, nqz);
1856  curve25519_sub(nqz, nqx, nqz);
1857  curve25519_square(qx, qx);
1858  curve25519_square(nqz, nqz);
1859  curve25519_mul(nqx, qx, nqz);
1860  curve25519_sub(nqz, qx, nqz);
1861  curve25519_scalar_product(zzz, nqz, 121665);
1862  curve25519_add(zzz, zzz, qx);
1863  curve25519_mul(nqz, nqz, zzz);
1864  }
1865 
1866  curve25519_recip(zmone, nqz);
1867  curve25519_mul(nqz, nqx, zmone);
1868  curve25519_contract(sharedKey, nqz);
1869 
1870  return 0;
1871 }
1872 
1873 int curve25519_mult(byte publicKey[32], const byte secretKey[32])
1874 {
1875  using namespace CryptoPP::Donna::X25519;
1876 
1877 #if (CRYPTOPP_CURVE25519_SSE2)
1878  if (HasSSE2())
1879  return curve25519_mult_SSE2(publicKey, secretKey, basePoint);
1880  else
1881 #endif
1882 
1883  return curve25519_mult_CXX(publicKey, secretKey, basePoint);
1884 }
1885 
1886 int curve25519_mult(byte sharedKey[32], const byte secretKey[32], const byte othersKey[32])
1887 {
1888 #if (CRYPTOPP_CURVE25519_SSE2)
1889  if (HasSSE2())
1890  return curve25519_mult_SSE2(sharedKey, secretKey, othersKey);
1891  else
1892 #endif
1893 
1894  return curve25519_mult_CXX(sharedKey, secretKey, othersKey);
1895 }
1896 
1897 NAMESPACE_END // Donna
1898 NAMESPACE_END // CryptoPP
1899 
1900 //******************************* ed25519 *******************************//
1901 
1902 NAMESPACE_BEGIN(CryptoPP)
1903 NAMESPACE_BEGIN(Donna)
1904 
1905 int
1906 ed25519_publickey_CXX(byte publicKey[32], const byte secretKey[32])
1907 {
1908  using namespace CryptoPP::Donna::Ed25519;
1909 
1910  bignum256modm a;
1911  ALIGN(ALIGN_SPEC) ge25519 A;
1912  hash_512bits extsk;
1913 
1914  /* A = aB */
1915  ed25519_extsk(extsk, secretKey);
1916  expand256_modm(a, extsk, 32);
1917  ge25519_scalarmult_base_niels(&A, ge25519_niels_base_multiples, a);
1918  ge25519_pack(publicKey, &A);
1919 
1920  return 0;
1921 }
1922 
1923 int
1924 ed25519_publickey(byte publicKey[32], const byte secretKey[32])
1925 {
1926  return ed25519_publickey_CXX(publicKey, secretKey);
1927 }
1928 
1929 int
1930 ed25519_sign_CXX(std::istream& stream, const byte sk[32], const byte pk[32], byte RS[64])
1931 {
1932  using namespace CryptoPP::Donna::Ed25519;
1933 
1934  bignum256modm r, S, a;
1935  ALIGN(ALIGN_SPEC) ge25519 R;
1936  hash_512bits extsk, hashr, hram;
1937 
1938  // Unfortunately we need to read the stream twice. The first time calculates
1939  // 'r = H(aExt[32..64], m)'. The second time calculates 'S = H(R,A,m)'. There
1940  // is a data dependency due to hashing 'RS' with 'R = [r]B' that does not
1941  // allow us to read the stream once.
1942  std::streampos where = stream.tellg();
1943 
1944  ed25519_extsk(extsk, sk);
1945 
1946  /* r = H(aExt[32..64], m) */
1947  SHA512 hash;
1948  hash.Update(extsk + 32, 32);
1949  UpdateFromStream(hash, stream);
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  // Reset stream for the second digest
1958  stream.clear();
1959  stream.seekg(where);
1960 
1961  /* S = H(R,A,m).. */
1962  ed25519_hram(hram, RS, pk, stream);
1963  expand256_modm(S, hram, 64);
1964 
1965  /* S = H(R,A,m)a */
1966  expand256_modm(a, extsk, 32);
1967  mul256_modm(S, S, a);
1968 
1969  /* S = (r + H(R,A,m)a) */
1970  add256_modm(S, S, r);
1971 
1972  /* S = (r + H(R,A,m)a) mod L */
1973  contract256_modm(RS + 32, S);
1974 
1975  return 0;
1976 }
1977 
1978 int
1979 ed25519_sign_CXX(const byte *m, size_t mlen, const byte sk[32], const byte pk[32], byte RS[64])
1980 {
1981  using namespace CryptoPP::Donna::Ed25519;
1982 
1983  bignum256modm r, S, a;
1984  ALIGN(ALIGN_SPEC) ge25519 R;
1985  hash_512bits extsk, hashr, hram;
1986 
1987  ed25519_extsk(extsk, sk);
1988 
1989  /* r = H(aExt[32..64], m) */
1990  SHA512 hash;
1991  hash.Update(extsk + 32, 32);
1992  hash.Update(m, mlen);
1993  hash.Final(hashr);
1994  expand256_modm(r, hashr, 64);
1995 
1996  /* R = rB */
1997  ge25519_scalarmult_base_niels(&R, ge25519_niels_base_multiples, r);
1998  ge25519_pack(RS, &R);
1999 
2000  /* S = H(R,A,m).. */
2001  ed25519_hram(hram, RS, pk, m, mlen);
2002  expand256_modm(S, hram, 64);
2003 
2004  /* S = H(R,A,m)a */
2005  expand256_modm(a, extsk, 32);
2006  mul256_modm(S, S, a);
2007 
2008  /* S = (r + H(R,A,m)a) */
2009  add256_modm(S, S, r);
2010 
2011  /* S = (r + H(R,A,m)a) mod L */
2012  contract256_modm(RS + 32, S);
2013 
2014  return 0;
2015 }
2016 
2017 int
2018 ed25519_sign(std::istream& stream, const byte secretKey[32], const byte publicKey[32],
2019  byte signature[64])
2020 {
2021  return ed25519_sign_CXX(stream, secretKey, publicKey, signature);
2022 }
2023 
2024 int
2025 ed25519_sign(const byte* message, size_t messageLength, const byte secretKey[32],
2026  const byte publicKey[32], byte signature[64])
2027 {
2028  return ed25519_sign_CXX(message, messageLength, secretKey, publicKey, signature);
2029 }
2030 
2031 int
2032 ed25519_sign_open_CXX(std::istream& stream, const byte pk[32], const byte RS[64]) {
2033 
2034  using namespace CryptoPP::Donna::Ed25519;
2035 
2036  ALIGN(ALIGN_SPEC) ge25519 R, A;
2037  hash_512bits hash;
2038  bignum256modm hram, S;
2039  byte checkR[32];
2040 
2041  if ((RS[63] & 224) || !ge25519_unpack_negative_vartime(&A, pk))
2042  return -1;
2043 
2044  /* hram = H(R,A,m) */
2045  ed25519_hram(hash, RS, pk, stream);
2046  expand256_modm(hram, hash, 64);
2047 
2048  /* S */
2049  expand256_modm(S, RS + 32, 32);
2050 
2051  /* SB - H(R,A,m)A */
2052  ge25519_double_scalarmult_vartime(&R, &A, hram, S);
2053  ge25519_pack(checkR, &R);
2054 
2055  /* check that R = SB - H(R,A,m)A */
2056  return ed25519_verify(RS, checkR, 32) ? 0 : -1;
2057 }
2058 
2059 int
2060 ed25519_sign_open_CXX(const byte *m, size_t mlen, const byte pk[32], const byte RS[64]) {
2061 
2062  using namespace CryptoPP::Donna::Ed25519;
2063 
2064  ALIGN(ALIGN_SPEC) ge25519 R, A;
2065  hash_512bits hash;
2066  bignum256modm hram, S;
2067  byte checkR[32];
2068 
2069  if ((RS[63] & 224) || !ge25519_unpack_negative_vartime(&A, pk))
2070  return -1;
2071 
2072  /* hram = H(R,A,m) */
2073  ed25519_hram(hash, RS, pk, m, mlen);
2074  expand256_modm(hram, hash, 64);
2075 
2076  /* S */
2077  expand256_modm(S, RS + 32, 32);
2078 
2079  /* SB - H(R,A,m)A */
2080  ge25519_double_scalarmult_vartime(&R, &A, hram, S);
2081  ge25519_pack(checkR, &R);
2082 
2083  /* check that R = SB - H(R,A,m)A */
2084  return ed25519_verify(RS, checkR, 32) ? 0 : -1;
2085 }
2086 
2087 int
2088 ed25519_sign_open(const byte *message, size_t messageLength, const byte publicKey[32], const byte signature[64])
2089 {
2090  return ed25519_sign_open_CXX(message, messageLength, publicKey, signature);
2091 }
2092 
2093 int
2094 ed25519_sign_open(std::istream& stream, const byte publicKey[32], const byte signature[64])
2095 {
2096  return ed25519_sign_open_CXX(stream, publicKey, signature);
2097 }
2098 
2099 NAMESPACE_END // Donna
2100 NAMESPACE_END // CryptoPP
2101 
2102 #endif // CRYPTOPP_CURVE25519_32BIT
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
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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