31 extern const char DONNA32_FNAME[] = __FILE__;
33 #if defined(CRYPTOPP_CURVE25519_32BIT) 37 ANONYMOUS_NAMESPACE_BEGIN
40 using CryptoPP::word32;
45 inline word32 U8TO32_LE(
const byte* p)
50 inline void U32TO8_LE(byte* p, word32 w)
55 ANONYMOUS_NAMESPACE_END
58 NAMESPACE_BEGIN(Donna)
59 NAMESPACE_BEGIN(X25519)
60 ANONYMOUS_NAMESPACE_BEGIN
63 using CryptoPP::word32;
64 using CryptoPP::sword32;
65 using CryptoPP::word64;
66 using CryptoPP::sword64;
68 using CryptoPP::GetBlock;
72 using namespace CryptoPP::Donna::Arch32;
76 curve25519_copy(bignum25519 out,
const bignum25519 in) {
77 out[0] = in[0]; out[1] = in[1];
78 out[2] = in[2]; out[3] = in[3];
79 out[4] = in[4]; out[5] = in[5];
80 out[6] = in[6]; out[7] = in[7];
81 out[8] = in[8]; out[9] = in[9];
86 curve25519_add(bignum25519 out,
const bignum25519 a,
const bignum25519 b) {
87 out[0] = a[0] + b[0]; out[1] = a[1] + b[1];
88 out[2] = a[2] + b[2]; out[3] = a[3] + b[3];
89 out[4] = a[4] + b[4]; out[5] = a[5] + b[5];
90 out[6] = a[6] + b[6]; out[7] = a[7] + b[7];
91 out[8] = a[8] + b[8]; out[9] = a[9] + b[9];
96 curve25519_sub(bignum25519 out,
const bignum25519 a,
const bignum25519 b) {
98 out[0] = 0x7ffffda + a[0] - b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
99 out[1] = 0x3fffffe + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
100 out[2] = 0x7fffffe + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
101 out[3] = 0x3fffffe + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
102 out[4] = 0x7fffffe + a[4] - b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
103 out[5] = 0x3fffffe + a[5] - b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
104 out[6] = 0x7fffffe + a[6] - b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
105 out[7] = 0x3fffffe + a[7] - b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
106 out[8] = 0x7fffffe + a[8] - b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
107 out[9] = 0x3fffffe + a[9] - b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
113 curve25519_scalar_product(bignum25519 out,
const bignum25519 in,
const word32 scalar) {
116 a = mul32x32_64(in[0], scalar); out[0] = (word32)a & reduce_mask_26; c = (word32)(a >> 26);
117 a = mul32x32_64(in[1], scalar) + c; out[1] = (word32)a & reduce_mask_25; c = (word32)(a >> 25);
118 a = mul32x32_64(in[2], scalar) + c; out[2] = (word32)a & reduce_mask_26; c = (word32)(a >> 26);
119 a = mul32x32_64(in[3], scalar) + c; out[3] = (word32)a & reduce_mask_25; c = (word32)(a >> 25);
120 a = mul32x32_64(in[4], scalar) + c; out[4] = (word32)a & reduce_mask_26; c = (word32)(a >> 26);
121 a = mul32x32_64(in[5], scalar) + c; out[5] = (word32)a & reduce_mask_25; c = (word32)(a >> 25);
122 a = mul32x32_64(in[6], scalar) + c; out[6] = (word32)a & reduce_mask_26; c = (word32)(a >> 26);
123 a = mul32x32_64(in[7], scalar) + c; out[7] = (word32)a & reduce_mask_25; c = (word32)(a >> 25);
124 a = mul32x32_64(in[8], scalar) + c; out[8] = (word32)a & reduce_mask_26; c = (word32)(a >> 26);
125 a = mul32x32_64(in[9], scalar) + c; out[9] = (word32)a & reduce_mask_25; c = (word32)(a >> 25);
131 curve25519_mul(bignum25519 out,
const bignum25519 a,
const bignum25519 b) {
132 word32 r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
133 word32 s0,s1,s2,s3,s4,s5,s6,s7,s8,s9;
134 word64 m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
137 r0 = b[0]; r1 = b[1]; r2 = b[2]; r3 = b[3]; r4 = b[4];
138 r5 = b[5]; r6 = b[6]; r7 = b[7]; r8 = b[8]; r9 = b[9];
140 s0 = a[0]; s1 = a[1]; s2 = a[2]; s3 = a[3]; s4 = a[4];
141 s5 = a[5]; s6 = a[6]; s7 = a[7]; s8 = a[8]; s9 = a[9];
143 m1 = mul32x32_64(r0, s1) + mul32x32_64(r1, s0);
144 m3 = mul32x32_64(r0, s3) + mul32x32_64(r1, s2) + mul32x32_64(r2, s1) + mul32x32_64(r3, s0);
145 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);
146 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);
147 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);
149 r1 *= 2; r3 *= 2; r5 *= 2; r7 *= 2;
151 m0 = mul32x32_64(r0, s0);
152 m2 = mul32x32_64(r0, s2) + mul32x32_64(r1, s1) + mul32x32_64(r2, s0);
153 m4 = mul32x32_64(r0, s4) + mul32x32_64(r1, s3) + mul32x32_64(r2, s2) + mul32x32_64(r3, s1) + mul32x32_64(r4, s0);
154 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);
155 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);
165 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));
166 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));
167 m5 += (mul32x32_64(r9, s6) + mul32x32_64(r8, s7) + mul32x32_64(r7, s8) + mul32x32_64(r6, s9));
168 m7 += (mul32x32_64(r9, s8) + mul32x32_64(r8, s9));
170 r3 *= 2; r5 *= 2; r7 *= 2; r9 *= 2;
172 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));
173 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));
174 m4 += (mul32x32_64(r9, s5) + mul32x32_64(r8, s6) + mul32x32_64(r7, s7) + mul32x32_64(r6, s8) + mul32x32_64(r5, s9));
175 m6 += (mul32x32_64(r9, s7) + mul32x32_64(r8, s8) + mul32x32_64(r7, s9));
176 m8 += (mul32x32_64(r9, s9));
178 r0 = (word32)m0 & reduce_mask_26; c = (m0 >> 26);
179 m1 += c; r1 = (word32)m1 & reduce_mask_25; c = (m1 >> 25);
180 m2 += c; r2 = (word32)m2 & reduce_mask_26; c = (m2 >> 26);
181 m3 += c; r3 = (word32)m3 & reduce_mask_25; c = (m3 >> 25);
182 m4 += c; r4 = (word32)m4 & reduce_mask_26; c = (m4 >> 26);
183 m5 += c; r5 = (word32)m5 & reduce_mask_25; c = (m5 >> 25);
184 m6 += c; r6 = (word32)m6 & reduce_mask_26; c = (m6 >> 26);
185 m7 += c; r7 = (word32)m7 & reduce_mask_25; c = (m7 >> 25);
186 m8 += c; r8 = (word32)m8 & reduce_mask_26; c = (m8 >> 26);
187 m9 += c; r9 = (word32)m9 & reduce_mask_25; p = (word32)(m9 >> 25);
188 m0 = r0 + mul32x32_64(p,19); r0 = (word32)m0 & reduce_mask_26; p = (word32)(m0 >> 26);
191 out[0] = r0; out[1] = r1; out[2] = r2; out[3] = r3; out[4] = r4;
192 out[5] = r5; out[6] = r6; out[7] = r7; out[8] = r8; out[9] = r9;
197 curve25519_square(bignum25519 out,
const bignum25519 in) {
198 word32 r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
200 word64 m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
203 r0 = in[0]; r1 = in[1]; r2 = in[2]; r3 = in[3]; r4 = in[4];
204 r5 = in[5]; r6 = in[6]; r7 = in[7]; r8 = in[8]; r9 = in[9];
206 m0 = mul32x32_64(r0, r0);
208 m1 = mul32x32_64(r0, r1);
209 m2 = mul32x32_64(r0, r2) + mul32x32_64(r1, r1 * 2);
211 m3 = mul32x32_64(r0, r3) + mul32x32_64(r1, r2 );
212 m4 = mul32x32_64(r0, r4) + mul32x32_64(r1, r3 * 2) + mul32x32_64(r2, r2);
214 m5 = mul32x32_64(r0, r5) + mul32x32_64(r1, r4 ) + mul32x32_64(r2, r3);
215 m6 = mul32x32_64(r0, r6) + mul32x32_64(r1, r5 * 2) + mul32x32_64(r2, r4) + mul32x32_64(r3, r3 * 2);
217 m7 = mul32x32_64(r0, r7) + mul32x32_64(r1, r6 ) + mul32x32_64(r2, r5) + mul32x32_64(r3, r4 );
218 m8 = mul32x32_64(r0, r8) + mul32x32_64(r1, r7 * 2) + mul32x32_64(r2, r6) + mul32x32_64(r3, r5 * 2) + mul32x32_64(r4, r4 );
219 m9 = mul32x32_64(r0, r9) + mul32x32_64(r1, r8 ) + mul32x32_64(r2, r7) + mul32x32_64(r3, r6 ) + mul32x32_64(r4, r5 * 2);
221 d6 = r6 * 19; d7 = r7 * 2 * 19;
222 d8 = r8 * 19; d9 = r9 * 2 * 19;
224 m0 += (mul32x32_64(d9, r1 ) + mul32x32_64(d8, r2 ) + mul32x32_64(d7, r3 ) + mul32x32_64(d6, r4 * 2) + mul32x32_64(r5, r5 * 2 * 19));
225 m1 += (mul32x32_64(d9, r2 / 2) + mul32x32_64(d8, r3 ) + mul32x32_64(d7, r4 ) + mul32x32_64(d6, r5 * 2));
226 m2 += (mul32x32_64(d9, r3 ) + mul32x32_64(d8, r4 * 2) + mul32x32_64(d7, r5 * 2) + mul32x32_64(d6, r6 ));
227 m3 += (mul32x32_64(d9, r4 ) + mul32x32_64(d8, r5 * 2) + mul32x32_64(d7, r6 ));
228 m4 += (mul32x32_64(d9, r5 * 2) + mul32x32_64(d8, r6 * 2) + mul32x32_64(d7, r7 ));
229 m5 += (mul32x32_64(d9, r6 ) + mul32x32_64(d8, r7 * 2));
230 m6 += (mul32x32_64(d9, r7 * 2) + mul32x32_64(d8, r8 ));
231 m7 += (mul32x32_64(d9, r8 ));
232 m8 += (mul32x32_64(d9, r9 ));
234 r0 = (word32)m0 & reduce_mask_26; c = (m0 >> 26);
235 m1 += c; r1 = (word32)m1 & reduce_mask_25; c = (m1 >> 25);
236 m2 += c; r2 = (word32)m2 & reduce_mask_26; c = (m2 >> 26);
237 m3 += c; r3 = (word32)m3 & reduce_mask_25; c = (m3 >> 25);
238 m4 += c; r4 = (word32)m4 & reduce_mask_26; c = (m4 >> 26);
239 m5 += c; r5 = (word32)m5 & reduce_mask_25; c = (m5 >> 25);
240 m6 += c; r6 = (word32)m6 & reduce_mask_26; c = (m6 >> 26);
241 m7 += c; r7 = (word32)m7 & reduce_mask_25; c = (m7 >> 25);
242 m8 += c; r8 = (word32)m8 & reduce_mask_26; c = (m8 >> 26);
243 m9 += c; r9 = (word32)m9 & reduce_mask_25; p = (word32)(m9 >> 25);
244 m0 = r0 + mul32x32_64(p,19); r0 = (word32)m0 & reduce_mask_26; p = (word32)(m0 >> 26);
247 out[0] = r0; out[1] = r1; out[2] = r2; out[3] = r3; out[4] = r4;
248 out[5] = r5; out[6] = r6; out[7] = r7; out[8] = r8; out[9] = r9;
253 curve25519_square_times(bignum25519 out,
const bignum25519 in,
int count) {
254 word32 r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
256 word64 m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
259 r0 = in[0]; r1 = in[1]; r2 = in[2]; r3 = in[3]; r4 = in[4];
260 r5 = in[5]; r6 = in[6]; r7 = in[7]; r8 = in[8]; r9 = in[9];
263 m0 = mul32x32_64(r0, r0);
265 m1 = mul32x32_64(r0, r1);
266 m2 = mul32x32_64(r0, r2) + mul32x32_64(r1, r1 * 2);
268 m3 = mul32x32_64(r0, r3) + mul32x32_64(r1, r2 );
269 m4 = mul32x32_64(r0, r4) + mul32x32_64(r1, r3 * 2) + mul32x32_64(r2, r2);
271 m5 = mul32x32_64(r0, r5) + mul32x32_64(r1, r4 ) + mul32x32_64(r2, r3);
272 m6 = mul32x32_64(r0, r6) + mul32x32_64(r1, r5 * 2) + mul32x32_64(r2, r4) + mul32x32_64(r3, r3 * 2);
274 m7 = mul32x32_64(r0, r7) + mul32x32_64(r1, r6 ) + mul32x32_64(r2, r5) + mul32x32_64(r3, r4 );
275 m8 = mul32x32_64(r0, r8) + mul32x32_64(r1, r7 * 2) + mul32x32_64(r2, r6) + mul32x32_64(r3, r5 * 2) + mul32x32_64(r4, r4 );
276 m9 = mul32x32_64(r0, r9) + mul32x32_64(r1, r8 ) + mul32x32_64(r2, r7) + mul32x32_64(r3, r6 ) + mul32x32_64(r4, r5 * 2);
278 d6 = r6 * 19; d7 = r7 * 2 * 19;
279 d8 = r8 * 19; d9 = r9 * 2 * 19;
281 m0 += (mul32x32_64(d9, r1 ) + mul32x32_64(d8, r2 ) + mul32x32_64(d7, r3 ) + mul32x32_64(d6, r4 * 2) + mul32x32_64(r5, r5 * 2 * 19));
282 m1 += (mul32x32_64(d9, r2 / 2) + mul32x32_64(d8, r3 ) + mul32x32_64(d7, r4 ) + mul32x32_64(d6, r5 * 2));
283 m2 += (mul32x32_64(d9, r3 ) + mul32x32_64(d8, r4 * 2) + mul32x32_64(d7, r5 * 2) + mul32x32_64(d6, r6 ));
284 m3 += (mul32x32_64(d9, r4 ) + mul32x32_64(d8, r5 * 2) + mul32x32_64(d7, r6 ));
285 m4 += (mul32x32_64(d9, r5 * 2) + mul32x32_64(d8, r6 * 2) + mul32x32_64(d7, r7 ));
286 m5 += (mul32x32_64(d9, r6 ) + mul32x32_64(d8, r7 * 2));
287 m6 += (mul32x32_64(d9, r7 * 2) + mul32x32_64(d8, r8 ));
288 m7 += (mul32x32_64(d9, r8 ));
289 m8 += (mul32x32_64(d9, r9 ));
291 r0 = (word32)m0 & reduce_mask_26; c = (m0 >> 26);
292 m1 += c; r1 = (word32)m1 & reduce_mask_25; c = (m1 >> 25);
293 m2 += c; r2 = (word32)m2 & reduce_mask_26; c = (m2 >> 26);
294 m3 += c; r3 = (word32)m3 & reduce_mask_25; c = (m3 >> 25);
295 m4 += c; r4 = (word32)m4 & reduce_mask_26; c = (m4 >> 26);
296 m5 += c; r5 = (word32)m5 & reduce_mask_25; c = (m5 >> 25);
297 m6 += c; r6 = (word32)m6 & reduce_mask_26; c = (m6 >> 26);
298 m7 += c; r7 = (word32)m7 & reduce_mask_25; c = (m7 >> 25);
299 m8 += c; r8 = (word32)m8 & reduce_mask_26; c = (m8 >> 26);
300 m9 += c; r9 = (word32)m9 & reduce_mask_25; p = (word32)(m9 >> 25);
301 m0 = r0 + mul32x32_64(p,19); r0 = (word32)m0 & reduce_mask_26; p = (word32)(m0 >> 26);
305 out[0] = r0; out[1] = r1; out[2] = r2; out[3] = r3; out[4] = r4;
306 out[5] = r5; out[6] = r6; out[7] = r7; out[8] = r8; out[9] = r9;
311 curve25519_expand(bignum25519 out,
const byte in[32]) {
312 word32 x0,x1,x2,x3,x4,x5,x6,x7;
314 block(x0)(x1)(x2)(x3)(x4)(x5)(x6)(x7);
316 out[0] = ( x0 ) & reduce_mask_26;
317 out[1] = ((((word64)x1 << 32) | x0) >> 26) & reduce_mask_25;
318 out[2] = ((((word64)x2 << 32) | x1) >> 19) & reduce_mask_26;
319 out[3] = ((((word64)x3 << 32) | x2) >> 13) & reduce_mask_25;
320 out[4] = (( x3) >> 6) & reduce_mask_26;
321 out[5] = ( x4 ) & reduce_mask_25;
322 out[6] = ((((word64)x5 << 32) | x4) >> 25) & reduce_mask_26;
323 out[7] = ((((word64)x6 << 32) | x5) >> 19) & reduce_mask_25;
324 out[8] = ((((word64)x7 << 32) | x6) >> 12) & reduce_mask_26;
325 out[9] = (( x7) >> 6) & reduce_mask_25;
330 curve25519_contract(byte out[32],
const bignum25519 in) {
332 curve25519_copy(f, in);
334 #define carry_pass() \ 335 f[1] += f[0] >> 26; f[0] &= reduce_mask_26; \ 336 f[2] += f[1] >> 25; f[1] &= reduce_mask_25; \ 337 f[3] += f[2] >> 26; f[2] &= reduce_mask_26; \ 338 f[4] += f[3] >> 25; f[3] &= reduce_mask_25; \ 339 f[5] += f[4] >> 26; f[4] &= reduce_mask_26; \ 340 f[6] += f[5] >> 25; f[5] &= reduce_mask_25; \ 341 f[7] += f[6] >> 26; f[6] &= reduce_mask_26; \ 342 f[8] += f[7] >> 25; f[7] &= reduce_mask_25; \ 343 f[9] += f[8] >> 26; f[8] &= reduce_mask_26; 345 #define carry_pass_full() \ 347 f[0] += 19 * (f[9] >> 25); f[9] &= reduce_mask_25; 349 #define carry_pass_final() \ 351 f[9] &= reduce_mask_25; 362 f[0] += (1 << 26) - 19;
363 f[1] += (1 << 25) - 1;
364 f[2] += (1 << 26) - 1;
365 f[3] += (1 << 25) - 1;
366 f[4] += (1 << 26) - 1;
367 f[5] += (1 << 25) - 1;
368 f[6] += (1 << 26) - 1;
369 f[7] += (1 << 25) - 1;
370 f[8] += (1 << 26) - 1;
371 f[9] += (1 << 25) - 1;
390 out[s+0] |= (byte)( f[i] & 0xff); \ 391 out[s+1] = (byte)((f[i] >> 8) & 0xff); \ 392 out[s+2] = (byte)((f[i] >> 16) & 0xff); \ 393 out[s+3] = (byte)((f[i] >> 24) & 0xff); 395 out[0] = out[16] = 0;
405 curve25519_swap_conditional(bignum25519 x, bignum25519 qpx, word32 iswap) {
406 const word32 swap = (word32)(-(sword32)iswap);
407 word32 x0,x1,x2,x3,x4,x5,x6,x7,x8,x9;
409 x0 = swap & (x[0] ^ qpx[0]); x[0] ^= x0; qpx[0] ^= x0;
410 x1 = swap & (x[1] ^ qpx[1]); x[1] ^= x1; qpx[1] ^= x1;
411 x2 = swap & (x[2] ^ qpx[2]); x[2] ^= x2; qpx[2] ^= x2;
412 x3 = swap & (x[3] ^ qpx[3]); x[3] ^= x3; qpx[3] ^= x3;
413 x4 = swap & (x[4] ^ qpx[4]); x[4] ^= x4; qpx[4] ^= x4;
414 x5 = swap & (x[5] ^ qpx[5]); x[5] ^= x5; qpx[5] ^= x5;
415 x6 = swap & (x[6] ^ qpx[6]); x[6] ^= x6; qpx[6] ^= x6;
416 x7 = swap & (x[7] ^ qpx[7]); x[7] ^= x7; qpx[7] ^= x7;
417 x8 = swap & (x[8] ^ qpx[8]); x[8] ^= x8; qpx[8] ^= x8;
418 x9 = swap & (x[9] ^ qpx[9]); x[9] ^= x9; qpx[9] ^= x9;
426 curve25519_pow_two5mtwo0_two250mtwo0(bignum25519 b) {
427 ALIGN(16) bignum25519 t0,c;
430 curve25519_square_times(t0, b, 5);
431 curve25519_mul(b, t0, b);
432 curve25519_square_times(t0, b, 10);
433 curve25519_mul(c, t0, b);
434 curve25519_square_times(t0, c, 20);
435 curve25519_mul(t0, t0, c);
436 curve25519_square_times(t0, t0, 10);
437 curve25519_mul(b, t0, b);
438 curve25519_square_times(t0, b, 50);
439 curve25519_mul(c, t0, b);
440 curve25519_square_times(t0, c, 100);
441 curve25519_mul(t0, t0, c);
442 curve25519_square_times(t0, t0, 50);
443 curve25519_mul(b, t0, b);
450 curve25519_recip(bignum25519 out, const bignum25519 z) {
451 ALIGN(16) bignum25519 a, t0, b;
453 curve25519_square(a, z);
454 curve25519_square_times(t0, a, 2);
455 curve25519_mul(b, t0, z);
456 curve25519_mul(a, b, a);
457 curve25519_square(t0, a);
458 curve25519_mul(b, t0, b);
459 curve25519_pow_two5mtwo0_two250mtwo0(b);
460 curve25519_square_times(b, b, 5);
461 curve25519_mul(out, b, a);
464 ANONYMOUS_NAMESPACE_END
472 NAMESPACE_BEGIN(Donna)
473 NAMESPACE_BEGIN(Ed25519)
474 ANONYMOUS_NAMESPACE_BEGIN
488 using namespace
CryptoPP::Donna::Arch32;
492 curve25519_copy(bignum25519 out, const bignum25519 in) {
493 out[0] = in[0]; out[1] = in[1];
494 out[2] = in[2]; out[3] = in[3];
495 out[4] = in[4]; out[5] = in[5];
496 out[6] = in[6]; out[7] = in[7];
497 out[8] = in[8]; out[9] = in[9];
502 curve25519_add(bignum25519 out,
const bignum25519 a,
const bignum25519 b) {
503 out[0] = a[0] + b[0]; out[1] = a[1] + b[1];
504 out[2] = a[2] + b[2]; out[3] = a[3] + b[3];
505 out[4] = a[4] + b[4]; out[5] = a[5] + b[5];
506 out[6] = a[6] + b[6]; out[7] = a[7] + b[7];
507 out[8] = a[8] + b[8]; out[9] = a[9] + b[9];
511 curve25519_add_after_basic(bignum25519 out,
const bignum25519 a,
const bignum25519 b) {
513 out[0] = a[0] + b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
514 out[1] = a[1] + b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
515 out[2] = a[2] + b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
516 out[3] = a[3] + b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
517 out[4] = a[4] + b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
518 out[5] = a[5] + b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
519 out[6] = a[6] + b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
520 out[7] = a[7] + b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
521 out[8] = a[8] + b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
522 out[9] = a[9] + b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
527 curve25519_add_reduce(bignum25519 out,
const bignum25519 a,
const bignum25519 b) {
529 out[0] = a[0] + b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
530 out[1] = a[1] + b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
531 out[2] = a[2] + b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
532 out[3] = a[3] + b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
533 out[4] = a[4] + b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
534 out[5] = a[5] + b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
535 out[6] = a[6] + b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
536 out[7] = a[7] + b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
537 out[8] = a[8] + b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
538 out[9] = a[9] + b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
544 curve25519_sub(bignum25519 out,
const bignum25519 a,
const bignum25519 b) {
546 out[0] = twoP0 + a[0] - b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
547 out[1] = twoP13579 + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
548 out[2] = twoP2468 + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
549 out[3] = twoP13579 + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
550 out[4] = twoP2468 + a[4] - b[4] + c;
551 out[5] = twoP13579 + a[5] - b[5] ;
552 out[6] = twoP2468 + a[6] - b[6] ;
553 out[7] = twoP13579 + a[7] - b[7] ;
554 out[8] = twoP2468 + a[8] - b[8] ;
555 out[9] = twoP13579 + a[9] - b[9] ;
560 curve25519_sub_after_basic(bignum25519 out,
const bignum25519 a,
const bignum25519 b) {
562 out[0] = fourP0 + a[0] - b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
563 out[1] = fourP13579 + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
564 out[2] = fourP2468 + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
565 out[3] = fourP13579 + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
566 out[4] = fourP2468 + a[4] - b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
567 out[5] = fourP13579 + a[5] - b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
568 out[6] = fourP2468 + a[6] - b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
569 out[7] = fourP13579 + a[7] - b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
570 out[8] = fourP2468 + a[8] - b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
571 out[9] = fourP13579 + a[9] - b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
576 curve25519_sub_reduce(bignum25519 out,
const bignum25519 a,
const bignum25519 b) {
578 out[0] = fourP0 + a[0] - b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
579 out[1] = fourP13579 + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
580 out[2] = fourP2468 + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
581 out[3] = fourP13579 + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
582 out[4] = fourP2468 + a[4] - b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
583 out[5] = fourP13579 + a[5] - b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
584 out[6] = fourP2468 + a[6] - b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
585 out[7] = fourP13579 + a[7] - b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
586 out[8] = fourP2468 + a[8] - b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
587 out[9] = fourP13579 + a[9] - b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
593 curve25519_neg(bignum25519 out,
const bignum25519 a) {
595 out[0] = twoP0 - a[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
596 out[1] = twoP13579 - a[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
597 out[2] = twoP2468 - a[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
598 out[3] = twoP13579 - a[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
599 out[4] = twoP2468 - a[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
600 out[5] = twoP13579 - a[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
601 out[6] = twoP2468 - a[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
602 out[7] = twoP13579 - a[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
603 out[8] = twoP2468 - a[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
604 out[9] = twoP13579 - a[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
610 curve25519_mul(bignum25519 out,
const bignum25519 a,
const bignum25519 b) {
611 word32 r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
612 word32 s0,s1,s2,s3,s4,s5,s6,s7,s8,s9;
613 word64 m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
616 r0 = b[0]; r1 = b[1];
617 r2 = b[2]; r3 = b[3];
618 r4 = b[4]; r5 = b[5];
619 r6 = b[6]; r7 = b[7];
620 r8 = b[8]; r9 = b[9];
622 s0 = a[0]; s1 = a[1];
623 s2 = a[2]; s3 = a[3];
624 s4 = a[4]; s5 = a[5];
625 s6 = a[6]; s7 = a[7];
626 s8 = a[8]; s9 = a[9];
628 m1 = mul32x32_64(r0, s1) + mul32x32_64(r1, s0);
629 m3 = mul32x32_64(r0, s3) + mul32x32_64(r1, s2) + mul32x32_64(r2, s1) + mul32x32_64(r3, s0);
630 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);
631 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);
632 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);
637 m0 = mul32x32_64(r0, s0);
638 m2 = mul32x32_64(r0, s2) + mul32x32_64(r1, s1) + mul32x32_64(r2, s0);
639 m4 = mul32x32_64(r0, s4) + mul32x32_64(r1, s3) + mul32x32_64(r2, s2) + mul32x32_64(r3, s1) + mul32x32_64(r4, s0);
640 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);
641 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);
651 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));
652 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));
653 m5 += (mul32x32_64(r9, s6) + mul32x32_64(r8, s7) + mul32x32_64(r7, s8) + mul32x32_64(r6, s9));
654 m7 += (mul32x32_64(r9, s8) + mul32x32_64(r8, s9));
659 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));
660 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));
661 m4 += (mul32x32_64(r9, s5) + mul32x32_64(r8, s6) + mul32x32_64(r7, s7) + mul32x32_64(r6, s8) + mul32x32_64(r5, s9));
662 m6 += (mul32x32_64(r9, s7) + mul32x32_64(r8, s8) + mul32x32_64(r7, s9));
663 m8 += (mul32x32_64(r9, s9));
665 r0 = (word32)m0 & reduce_mask_26; c = (m0 >> 26);
666 m1 += c; r1 = (word32)m1 & reduce_mask_25; c = (m1 >> 25);
667 m2 += c; r2 = (word32)m2 & reduce_mask_26; c = (m2 >> 26);
668 m3 += c; r3 = (word32)m3 & reduce_mask_25; c = (m3 >> 25);
669 m4 += c; r4 = (word32)m4 & reduce_mask_26; c = (m4 >> 26);
670 m5 += c; r5 = (word32)m5 & reduce_mask_25; c = (m5 >> 25);
671 m6 += c; r6 = (word32)m6 & reduce_mask_26; c = (m6 >> 26);
672 m7 += c; r7 = (word32)m7 & reduce_mask_25; c = (m7 >> 25);
673 m8 += c; r8 = (word32)m8 & reduce_mask_26; c = (m8 >> 26);
674 m9 += c; r9 = (word32)m9 & reduce_mask_25; p = (word32)(m9 >> 25);
675 m0 = r0 + mul32x32_64(p,19); r0 = (word32)m0 & reduce_mask_26; p = (word32)(m0 >> 26);
678 out[0] = r0; out[1] = r1;
679 out[2] = r2; out[3] = r3;
680 out[4] = r4; out[5] = r5;
681 out[6] = r6; out[7] = r7;
682 out[8] = r8; out[9] = r9;
687 curve25519_square(bignum25519 out,
const bignum25519 in) {
688 word32 r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
690 word64 m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
693 r0 = in[0]; r1 = in[1];
694 r2 = in[2]; r3 = in[3];
695 r4 = in[4]; r5 = in[5];
696 r6 = in[6]; r7 = in[7];
697 r8 = in[8]; r9 = in[9];
699 m0 = mul32x32_64(r0, r0);
701 m1 = mul32x32_64(r0, r1);
702 m2 = mul32x32_64(r0, r2) + mul32x32_64(r1, r1 * 2);
704 m3 = mul32x32_64(r0, r3) + mul32x32_64(r1, r2 );
705 m4 = mul32x32_64(r0, r4) + mul32x32_64(r1, r3 * 2) + mul32x32_64(r2, r2);
707 m5 = mul32x32_64(r0, r5) + mul32x32_64(r1, r4 ) + mul32x32_64(r2, r3);
708 m6 = mul32x32_64(r0, r6) + mul32x32_64(r1, r5 * 2) + mul32x32_64(r2, r4) + mul32x32_64(r3, r3 * 2);
710 m7 = mul32x32_64(r0, r7) + mul32x32_64(r1, r6 ) + mul32x32_64(r2, r5) + mul32x32_64(r3, r4 );
711 m8 = mul32x32_64(r0, r8) + mul32x32_64(r1, r7 * 2) + mul32x32_64(r2, r6) + mul32x32_64(r3, r5 * 2) + mul32x32_64(r4, r4 );
712 m9 = mul32x32_64(r0, r9) + mul32x32_64(r1, r8 ) + mul32x32_64(r2, r7) + mul32x32_64(r3, r6 ) + mul32x32_64(r4, r5 * 2);
719 m0 += (mul32x32_64(d9, r1 ) + mul32x32_64(d8, r2 ) + mul32x32_64(d7, r3 ) + mul32x32_64(d6, r4 * 2) + mul32x32_64(r5, r5 * 2 * 19));
720 m1 += (mul32x32_64(d9, r2 / 2) + mul32x32_64(d8, r3 ) + mul32x32_64(d7, r4 ) + mul32x32_64(d6, r5 * 2));
721 m2 += (mul32x32_64(d9, r3 ) + mul32x32_64(d8, r4 * 2) + mul32x32_64(d7, r5 * 2) + mul32x32_64(d6, r6 ));
722 m3 += (mul32x32_64(d9, r4 ) + mul32x32_64(d8, r5 * 2) + mul32x32_64(d7, r6 ));
723 m4 += (mul32x32_64(d9, r5 * 2) + mul32x32_64(d8, r6 * 2) + mul32x32_64(d7, r7 ));
724 m5 += (mul32x32_64(d9, r6 ) + mul32x32_64(d8, r7 * 2));
725 m6 += (mul32x32_64(d9, r7 * 2) + mul32x32_64(d8, r8 ));
726 m7 += (mul32x32_64(d9, r8 ));
727 m8 += (mul32x32_64(d9, r9 ));
729 r0 = (word32)m0 & reduce_mask_26; c = (m0 >> 26);
730 m1 += c; r1 = (word32)m1 & reduce_mask_25; c = (m1 >> 25);
731 m2 += c; r2 = (word32)m2 & reduce_mask_26; c = (m2 >> 26);
732 m3 += c; r3 = (word32)m3 & reduce_mask_25; c = (m3 >> 25);
733 m4 += c; r4 = (word32)m4 & reduce_mask_26; c = (m4 >> 26);
734 m5 += c; r5 = (word32)m5 & reduce_mask_25; c = (m5 >> 25);
735 m6 += c; r6 = (word32)m6 & reduce_mask_26; c = (m6 >> 26);
736 m7 += c; r7 = (word32)m7 & reduce_mask_25; c = (m7 >> 25);
737 m8 += c; r8 = (word32)m8 & reduce_mask_26; c = (m8 >> 26);
738 m9 += c; r9 = (word32)m9 & reduce_mask_25; p = (word32)(m9 >> 25);
739 m0 = r0 + mul32x32_64(p,19); r0 = (word32)m0 & reduce_mask_26; p = (word32)(m0 >> 26);
742 out[0] = r0; out[1] = r1;
743 out[2] = r2; out[3] = r3;
744 out[4] = r4; out[5] = r5;
745 out[6] = r6; out[7] = r7;
746 out[8] = r8; out[9] = r9;
751 curve25519_square_times(bignum25519 out,
const bignum25519 in,
int count) {
752 word32 r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
753 word32 d6,d7,d8,d9,p;
754 word64 m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
756 r0 = in[0]; r1 = in[1];
757 r2 = in[2]; r3 = in[3];
758 r4 = in[4]; r5 = in[5];
759 r6 = in[6]; r7 = in[7];
760 r8 = in[8]; r9 = in[9];
763 m0 = mul32x32_64(r0, r0);
765 m1 = mul32x32_64(r0, r1);
766 m2 = mul32x32_64(r0, r2) + mul32x32_64(r1, r1 * 2);
768 m3 = mul32x32_64(r0, r3) + mul32x32_64(r1, r2 );
769 m4 = mul32x32_64(r0, r4) + mul32x32_64(r1, r3 * 2) + mul32x32_64(r2, r2);
771 m5 = mul32x32_64(r0, r5) + mul32x32_64(r1, r4 ) + mul32x32_64(r2, r3);
772 m6 = mul32x32_64(r0, r6) + mul32x32_64(r1, r5 * 2) + mul32x32_64(r2, r4) + mul32x32_64(r3, r3 * 2);
774 m7 = mul32x32_64(r0, r7) + mul32x32_64(r1, r6 ) + mul32x32_64(r2, r5) + mul32x32_64(r3, r4 );
775 m8 = mul32x32_64(r0, r8) + mul32x32_64(r1, r7 * 2) + mul32x32_64(r2, r6) + mul32x32_64(r3, r5 * 2) + mul32x32_64(r4, r4 );
776 m9 = mul32x32_64(r0, r9) + mul32x32_64(r1, r8 ) + mul32x32_64(r2, r7) + mul32x32_64(r3, r6 ) + mul32x32_64(r4, r5 * 2);
783 m0 += (mul32x32_64(d9, r1 ) + mul32x32_64(d8, r2 ) + mul32x32_64(d7, r3 ) + mul32x32_64(d6, r4 * 2) + mul32x32_64(r5, r5 * 2 * 19));
784 m1 += (mul32x32_64(d9, r2 / 2) + mul32x32_64(d8, r3 ) + mul32x32_64(d7, r4 ) + mul32x32_64(d6, r5 * 2));
785 m2 += (mul32x32_64(d9, r3 ) + mul32x32_64(d8, r4 * 2) + mul32x32_64(d7, r5 * 2) + mul32x32_64(d6, r6 ));
786 m3 += (mul32x32_64(d9, r4 ) + mul32x32_64(d8, r5 * 2) + mul32x32_64(d7, r6 ));
787 m4 += (mul32x32_64(d9, r5 * 2) + mul32x32_64(d8, r6 * 2) + mul32x32_64(d7, r7 ));
788 m5 += (mul32x32_64(d9, r6 ) + mul32x32_64(d8, r7 * 2));
789 m6 += (mul32x32_64(d9, r7 * 2) + mul32x32_64(d8, r8 ));
790 m7 += (mul32x32_64(d9, r8 ));
791 m8 += (mul32x32_64(d9, r9 ));
793 r0 = (word32)m0 & reduce_mask_26; c = (m0 >> 26);
794 m1 += c; r1 = (word32)m1 & reduce_mask_25; c = (m1 >> 25);
795 m2 += c; r2 = (word32)m2 & reduce_mask_26; c = (m2 >> 26);
796 m3 += c; r3 = (word32)m3 & reduce_mask_25; c = (m3 >> 25);
797 m4 += c; r4 = (word32)m4 & reduce_mask_26; c = (m4 >> 26);
798 m5 += c; r5 = (word32)m5 & reduce_mask_25; c = (m5 >> 25);
799 m6 += c; r6 = (word32)m6 & reduce_mask_26; c = (m6 >> 26);
800 m7 += c; r7 = (word32)m7 & reduce_mask_25; c = (m7 >> 25);
801 m8 += c; r8 = (word32)m8 & reduce_mask_26; c = (m8 >> 26);
802 m9 += c; r9 = (word32)m9 & reduce_mask_25; p = (word32)(m9 >> 25);
803 m0 = r0 + mul32x32_64(p,19); r0 = (word32)m0 & reduce_mask_26; p = (word32)(m0 >> 26);
807 out[0] = r0; out[1] = r1;
808 out[2] = r2; out[3] = r3;
809 out[4] = r4; out[5] = r5;
810 out[6] = r6; out[7] = r7;
811 out[8] = r8; out[9] = r9;
816 curve25519_expand(bignum25519 out,
const byte in[32]) {
817 word32 x0,x1,x2,x3,x4,x5,x6,x7;
819 block(x0)(x1)(x2)(x3)(x4)(x5)(x6)(x7);
821 out[0] = ( x0 ) & 0x3ffffff;
822 out[1] = ((((word64)x1 << 32) | x0) >> 26) & 0x1ffffff;
823 out[2] = ((((word64)x2 << 32) | x1) >> 19) & 0x3ffffff;
824 out[3] = ((((word64)x3 << 32) | x2) >> 13) & 0x1ffffff;
825 out[4] = (( x3) >> 6) & 0x3ffffff;
826 out[5] = ( x4 ) & 0x1ffffff;
827 out[6] = ((((word64)x5 << 32) | x4) >> 25) & 0x3ffffff;
828 out[7] = ((((word64)x6 << 32) | x5) >> 19) & 0x1ffffff;
829 out[8] = ((((word64)x7 << 32) | x6) >> 12) & 0x3ffffff;
830 out[9] = (( x7) >> 6) & 0x1ffffff;
837 curve25519_contract(byte out[32],
const bignum25519 in) {
839 curve25519_copy(f, in);
841 #define carry_pass() \ 842 f[1] += f[0] >> 26; f[0] &= reduce_mask_26; \ 843 f[2] += f[1] >> 25; f[1] &= reduce_mask_25; \ 844 f[3] += f[2] >> 26; f[2] &= reduce_mask_26; \ 845 f[4] += f[3] >> 25; f[3] &= reduce_mask_25; \ 846 f[5] += f[4] >> 26; f[4] &= reduce_mask_26; \ 847 f[6] += f[5] >> 25; f[5] &= reduce_mask_25; \ 848 f[7] += f[6] >> 26; f[6] &= reduce_mask_26; \ 849 f[8] += f[7] >> 25; f[7] &= reduce_mask_25; \ 850 f[9] += f[8] >> 26; f[8] &= reduce_mask_26; 852 #define carry_pass_full() \ 854 f[0] += 19 * (f[9] >> 25); f[9] &= reduce_mask_25; 856 #define carry_pass_final() \ 858 f[9] &= reduce_mask_25; 869 f[0] += (reduce_mask_26 + 1) - 19;
870 f[1] += (reduce_mask_25 + 1) - 1;
871 f[2] += (reduce_mask_26 + 1) - 1;
872 f[3] += (reduce_mask_25 + 1) - 1;
873 f[4] += (reduce_mask_26 + 1) - 1;
874 f[5] += (reduce_mask_25 + 1) - 1;
875 f[6] += (reduce_mask_26 + 1) - 1;
876 f[7] += (reduce_mask_25 + 1) - 1;
877 f[8] += (reduce_mask_26 + 1) - 1;
878 f[9] += (reduce_mask_25 + 1) - 1;
887 f[1] <<= 2; f[2] <<= 3;
888 f[3] <<= 5; f[4] <<= 6;
889 f[6] <<= 1; f[7] <<= 3;
890 f[8] <<= 4; f[9] <<= 6;
893 out[s+0] |= (byte)( f[i] & 0xff); \ 894 out[s+1] = (byte)((f[i] >> 8) & 0xff); \ 895 out[s+2] = (byte)((f[i] >> 16) & 0xff); \ 896 out[s+3] = (byte)((f[i] >> 24) & 0xff); 898 out[0] = out[16] = 0;
909 curve25519_move_conditional_bytes(byte out[96],
const byte in[96], word32 flag) {
910 const word32 nb = flag - 1, b = ~nb;
911 const word32 *inl = (
const word32 *)in;
912 word32 *outl = (word32 *)out;
913 outl[0] = (outl[0] & nb) | (inl[0] & b);
914 outl[1] = (outl[1] & nb) | (inl[1] & b);
915 outl[2] = (outl[2] & nb) | (inl[2] & b);
916 outl[3] = (outl[3] & nb) | (inl[3] & b);
917 outl[4] = (outl[4] & nb) | (inl[4] & b);
918 outl[5] = (outl[5] & nb) | (inl[5] & b);
919 outl[6] = (outl[6] & nb) | (inl[6] & b);
920 outl[7] = (outl[7] & nb) | (inl[7] & b);
921 outl[8] = (outl[8] & nb) | (inl[8] & b);
922 outl[9] = (outl[9] & nb) | (inl[9] & b);
923 outl[10] = (outl[10] & nb) | (inl[10] & b);
924 outl[11] = (outl[11] & nb) | (inl[11] & b);
925 outl[12] = (outl[12] & nb) | (inl[12] & b);
926 outl[13] = (outl[13] & nb) | (inl[13] & b);
927 outl[14] = (outl[14] & nb) | (inl[14] & b);
928 outl[15] = (outl[15] & nb) | (inl[15] & b);
929 outl[16] = (outl[16] & nb) | (inl[16] & b);
930 outl[17] = (outl[17] & nb) | (inl[17] & b);
931 outl[18] = (outl[18] & nb) | (inl[18] & b);
932 outl[19] = (outl[19] & nb) | (inl[19] & b);
933 outl[20] = (outl[20] & nb) | (inl[20] & b);
934 outl[21] = (outl[21] & nb) | (inl[21] & b);
935 outl[22] = (outl[22] & nb) | (inl[22] & b);
936 outl[23] = (outl[23] & nb) | (inl[23] & b);
941 curve25519_swap_conditional(bignum25519 a, bignum25519 b, word32 iswap) {
942 const word32 swap = (word32)(-(sword32)iswap);
943 word32 x0,x1,x2,x3,x4,x5,x6,x7,x8,x9;
945 x0 = swap & (a[0] ^ b[0]); a[0] ^= x0; b[0] ^= x0;
946 x1 = swap & (a[1] ^ b[1]); a[1] ^= x1; b[1] ^= x1;
947 x2 = swap & (a[2] ^ b[2]); a[2] ^= x2; b[2] ^= x2;
948 x3 = swap & (a[3] ^ b[3]); a[3] ^= x3; b[3] ^= x3;
949 x4 = swap & (a[4] ^ b[4]); a[4] ^= x4; b[4] ^= x4;
950 x5 = swap & (a[5] ^ b[5]); a[5] ^= x5; b[5] ^= x5;
951 x6 = swap & (a[6] ^ b[6]); a[6] ^= x6; b[6] ^= x6;
952 x7 = swap & (a[7] ^ b[7]); a[7] ^= x7; b[7] ^= x7;
953 x8 = swap & (a[8] ^ b[8]); a[8] ^= x8; b[8] ^= x8;
954 x9 = swap & (a[9] ^ b[9]); a[9] ^= x9; b[9] ^= x9;
962 curve25519_pow_two5mtwo0_two250mtwo0(bignum25519 b) {
963 ALIGN(16) bignum25519 t0,c;
966 curve25519_square_times(t0, b, 5);
967 curve25519_mul(b, t0, b);
968 curve25519_square_times(t0, b, 10);
969 curve25519_mul(c, t0, b);
970 curve25519_square_times(t0, c, 20);
971 curve25519_mul(t0, t0, c);
972 curve25519_square_times(t0, t0, 10);
973 curve25519_mul(b, t0, b);
974 curve25519_square_times(t0, b, 50);
975 curve25519_mul(c, t0, b);
976 curve25519_square_times(t0, c, 100);
977 curve25519_mul(t0, t0, c);
978 curve25519_square_times(t0, t0, 50);
979 curve25519_mul(b, t0, b);
986 curve25519_recip(bignum25519 out, const bignum25519 z) {
987 ALIGN(16) bignum25519 a,t0,b;
989 curve25519_square_times(a, z, 1);
990 curve25519_square_times(t0, a, 2);
991 curve25519_mul(b, t0, z);
992 curve25519_mul(a, b, a);
993 curve25519_square_times(t0, a, 1);
994 curve25519_mul(b, t0, b);
995 curve25519_pow_two5mtwo0_two250mtwo0(b);
996 curve25519_square_times(b, b, 5);
997 curve25519_mul(out, b, a);
1004 curve25519_pow_two252m3(bignum25519 two252m3, const bignum25519 z) {
1005 ALIGN(16) bignum25519 b,c,t0;
1007 curve25519_square_times(c, z, 1);
1008 curve25519_square_times(t0, c, 2);
1009 curve25519_mul(b, t0, z);
1010 curve25519_mul(c, b, c);
1011 curve25519_square_times(t0, c, 1);
1012 curve25519_mul(b, t0, b);
1013 curve25519_pow_two5mtwo0_two250mtwo0(b);
1014 curve25519_square_times(b, b, 2);
1015 curve25519_mul(two252m3, b, z);
1019 ed25519_hash(byte *hash, const byte *in,
size_t inlen) {
1024 ed25519_extsk(hash_512bits extsk,
const byte sk[32]) {
1025 ed25519_hash(extsk, sk, 32);
1032 ed25519_hram(hash_512bits hram,
const byte RS[64],
const byte pk[32],
const unsigned char *m,
size_t mlen) {
1040 inline bignum256modm_element_t
1041 lt_modm(bignum256modm_element_t a, bignum256modm_element_t b) {
1042 return (a - b) >> 31;
1047 reduce256_modm(bignum256modm r) {
1049 bignum256modm_element_t b = 0, pb, mask;
1053 pb += modm_m[0]; b = lt_modm(r[0], pb); t[0] = (r[0] - pb + (b << 30)); pb = b;
1054 pb += modm_m[1]; b = lt_modm(r[1], pb); t[1] = (r[1] - pb + (b << 30)); pb = b;
1055 pb += modm_m[2]; b = lt_modm(r[2], pb); t[2] = (r[2] - pb + (b << 30)); pb = b;
1056 pb += modm_m[3]; b = lt_modm(r[3], pb); t[3] = (r[3] - pb + (b << 30)); pb = b;
1057 pb += modm_m[4]; b = lt_modm(r[4], pb); t[4] = (r[4] - pb + (b << 30)); pb = b;
1058 pb += modm_m[5]; b = lt_modm(r[5], pb); t[5] = (r[5] - pb + (b << 30)); pb = b;
1059 pb += modm_m[6]; b = lt_modm(r[6], pb); t[6] = (r[6] - pb + (b << 30)); pb = b;
1060 pb += modm_m[7]; b = lt_modm(r[7], pb); t[7] = (r[7] - pb + (b << 30)); pb = b;
1061 pb += modm_m[8]; b = lt_modm(r[8], pb); t[8] = (r[8] - pb + (b << 16));
1065 r[0] ^= mask & (r[0] ^ t[0]);
1066 r[1] ^= mask & (r[1] ^ t[1]);
1067 r[2] ^= mask & (r[2] ^ t[2]);
1068 r[3] ^= mask & (r[3] ^ t[3]);
1069 r[4] ^= mask & (r[4] ^ t[4]);
1070 r[5] ^= mask & (r[5] ^ t[5]);
1071 r[6] ^= mask & (r[6] ^ t[6]);
1072 r[7] ^= mask & (r[7] ^ t[7]);
1073 r[8] ^= mask & (r[8] ^ t[8]);
1078 barrett_reduce256_modm(bignum256modm r,
const bignum256modm q1,
const bignum256modm r1) {
1079 bignum256modm q3, r2;
1081 bignum256modm_element_t f, b, pb;
1087 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]);
1089 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]);
1090 f = (bignum256modm_element_t)c; q3[0] = (f >> 24) & 0x3f; c >>= 30;
1091 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]);
1092 f = (bignum256modm_element_t)c; q3[0] |= (f << 6) & 0x3fffffff; q3[1] = (f >> 24) & 0x3f; c >>= 30;
1093 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]);
1094 f = (bignum256modm_element_t)c; q3[1] |= (f << 6) & 0x3fffffff; q3[2] = (f >> 24) & 0x3f; c >>= 30;
1095 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]);
1096 f = (bignum256modm_element_t)c; q3[2] |= (f << 6) & 0x3fffffff; q3[3] = (f >> 24) & 0x3f; c >>= 30;
1097 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]);
1098 f = (bignum256modm_element_t)c; q3[3] |= (f << 6) & 0x3fffffff; q3[4] = (f >> 24) & 0x3f; c >>= 30;
1099 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]);
1100 f = (bignum256modm_element_t)c; q3[4] |= (f << 6) & 0x3fffffff; q3[5] = (f >> 24) & 0x3f; c >>= 30;
1101 c += mul32x32_64(modm_mu[6], q1[8]) + mul32x32_64(modm_mu[7], q1[7]) + mul32x32_64(modm_mu[8], q1[6]);
1102 f = (bignum256modm_element_t)c; q3[5] |= (f << 6) & 0x3fffffff; q3[6] = (f >> 24) & 0x3f; c >>= 30;
1103 c += mul32x32_64(modm_mu[7], q1[8]) + mul32x32_64(modm_mu[8], q1[7]);
1104 f = (bignum256modm_element_t)c; q3[6] |= (f << 6) & 0x3fffffff; q3[7] = (f >> 24) & 0x3f; c >>= 30;
1105 c += mul32x32_64(modm_mu[8], q1[8]);
1106 f = (bignum256modm_element_t)c; q3[7] |= (f << 6) & 0x3fffffff; q3[8] = (bignum256modm_element_t)(c >> 24);
1111 c = mul32x32_64(modm_m[0], q3[0]);
1112 r2[0] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
1113 c += mul32x32_64(modm_m[0], q3[1]) + mul32x32_64(modm_m[1], q3[0]);
1114 r2[1] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
1115 c += mul32x32_64(modm_m[0], q3[2]) + mul32x32_64(modm_m[1], q3[1]) + mul32x32_64(modm_m[2], q3[0]);
1116 r2[2] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
1117 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]);
1118 r2[3] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
1119 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]);
1120 r2[4] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
1121 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]);
1122 r2[5] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
1123 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]);
1124 r2[6] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
1125 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]);
1126 r2[7] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
1127 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]);
1128 r2[8] = (bignum256modm_element_t)(c & 0xffffff);
1133 pb += r2[0]; b = lt_modm(r1[0], pb); r[0] = (r1[0] - pb + (b << 30)); pb = b;
1134 pb += r2[1]; b = lt_modm(r1[1], pb); r[1] = (r1[1] - pb + (b << 30)); pb = b;
1135 pb += r2[2]; b = lt_modm(r1[2], pb); r[2] = (r1[2] - pb + (b << 30)); pb = b;
1136 pb += r2[3]; b = lt_modm(r1[3], pb); r[3] = (r1[3] - pb + (b << 30)); pb = b;
1137 pb += r2[4]; b = lt_modm(r1[4], pb); r[4] = (r1[4] - pb + (b << 30)); pb = b;
1138 pb += r2[5]; b = lt_modm(r1[5], pb); r[5] = (r1[5] - pb + (b << 30)); pb = b;
1139 pb += r2[6]; b = lt_modm(r1[6], pb); r[6] = (r1[6] - pb + (b << 30)); pb = b;
1140 pb += r2[7]; b = lt_modm(r1[7], pb); r[7] = (r1[7] - pb + (b << 30)); pb = b;
1141 pb += r2[8]; b = lt_modm(r1[8], pb); r[8] = (r1[8] - pb + (b << 24));
1149 add256_modm(bignum256modm r,
const bignum256modm x,
const bignum256modm y) {
1150 bignum256modm_element_t c;
1152 c = x[0] + y[0]; r[0] = c & 0x3fffffff; c >>= 30;
1153 c += x[1] + y[1]; r[1] = c & 0x3fffffff; c >>= 30;
1154 c += x[2] + y[2]; r[2] = c & 0x3fffffff; c >>= 30;
1155 c += x[3] + y[3]; r[3] = c & 0x3fffffff; c >>= 30;
1156 c += x[4] + y[4]; r[4] = c & 0x3fffffff; c >>= 30;
1157 c += x[5] + y[5]; r[5] = c & 0x3fffffff; c >>= 30;
1158 c += x[6] + y[6]; r[6] = c & 0x3fffffff; c >>= 30;
1159 c += x[7] + y[7]; r[7] = c & 0x3fffffff; c >>= 30;
1160 c += x[8] + y[8]; r[8] = c;
1167 mul256_modm(bignum256modm r,
const bignum256modm x,
const bignum256modm y) {
1168 bignum256modm r1, q1;
1170 bignum256modm_element_t f;
1172 c = mul32x32_64(x[0], y[0]);
1173 f = (bignum256modm_element_t)c; r1[0] = (f & 0x3fffffff); c >>= 30;
1174 c += mul32x32_64(x[0], y[1]) + mul32x32_64(x[1], y[0]);
1175 f = (bignum256modm_element_t)c; r1[1] = (f & 0x3fffffff); c >>= 30;
1176 c += mul32x32_64(x[0], y[2]) + mul32x32_64(x[1], y[1]) + mul32x32_64(x[2], y[0]);
1177 f = (bignum256modm_element_t)c; r1[2] = (f & 0x3fffffff); c >>= 30;
1178 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]);
1179 f = (bignum256modm_element_t)c; r1[3] = (f & 0x3fffffff); c >>= 30;
1180 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]);
1181 f = (bignum256modm_element_t)c; r1[4] = (f & 0x3fffffff); c >>= 30;
1182 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]);
1183 f = (bignum256modm_element_t)c; r1[5] = (f & 0x3fffffff); c >>= 30;
1184 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]);
1185 f = (bignum256modm_element_t)c; r1[6] = (f & 0x3fffffff); c >>= 30;
1186 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]);
1187 f = (bignum256modm_element_t)c; r1[7] = (f & 0x3fffffff); c >>= 30;
1188 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]);
1189 f = (bignum256modm_element_t)c; r1[8] = (f & 0x00ffffff); q1[0] = (f >> 8) & 0x3fffff; c >>= 30;
1190 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]);
1191 f = (bignum256modm_element_t)c; q1[0] = (q1[0] | (f << 22)) & 0x3fffffff; q1[1] = (f >> 8) & 0x3fffff; c >>= 30;
1192 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]);
1193 f = (bignum256modm_element_t)c; q1[1] = (q1[1] | (f << 22)) & 0x3fffffff; q1[2] = (f >> 8) & 0x3fffff; c >>= 30;
1194 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]);
1195 f = (bignum256modm_element_t)c; q1[2] = (q1[2] | (f << 22)) & 0x3fffffff; q1[3] = (f >> 8) & 0x3fffff; c >>= 30;
1196 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]);
1197 f = (bignum256modm_element_t)c; q1[3] = (q1[3] | (f << 22)) & 0x3fffffff; q1[4] = (f >> 8) & 0x3fffff; c >>= 30;
1198 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]);
1199 f = (bignum256modm_element_t)c; q1[4] = (q1[4] | (f << 22)) & 0x3fffffff; q1[5] = (f >> 8) & 0x3fffff; c >>= 30;
1200 c += mul32x32_64(x[6], y[8]) + mul32x32_64(x[7], y[7]) + mul32x32_64(x[8], y[6]);
1201 f = (bignum256modm_element_t)c; q1[5] = (q1[5] | (f << 22)) & 0x3fffffff; q1[6] = (f >> 8) & 0x3fffff; c >>= 30;
1202 c += mul32x32_64(x[7], y[8]) + mul32x32_64(x[8], y[7]);
1203 f = (bignum256modm_element_t)c; q1[6] = (q1[6] | (f << 22)) & 0x3fffffff; q1[7] = (f >> 8) & 0x3fffff; c >>= 30;
1204 c += mul32x32_64(x[8], y[8]);
1205 f = (bignum256modm_element_t)c; q1[7] = (q1[7] | (f << 22)) & 0x3fffffff; q1[8] = (f >> 8) & 0x3fffff;
1207 barrett_reduce256_modm(r, q1, r1);
1211 expand256_modm(bignum256modm out,
const byte *in,
size_t len) {
1212 byte work[64] = {0};
1213 bignum256modm_element_t x[16];
1216 memcpy(work, in, len);
1217 x[0] = U8TO32_LE(work + 0);
1218 x[1] = U8TO32_LE(work + 4);
1219 x[2] = U8TO32_LE(work + 8);
1220 x[3] = U8TO32_LE(work + 12);
1221 x[4] = U8TO32_LE(work + 16);
1222 x[5] = U8TO32_LE(work + 20);
1223 x[6] = U8TO32_LE(work + 24);
1224 x[7] = U8TO32_LE(work + 28);
1225 x[8] = U8TO32_LE(work + 32);
1226 x[9] = U8TO32_LE(work + 36);
1227 x[10] = U8TO32_LE(work + 40);
1228 x[11] = U8TO32_LE(work + 44);
1229 x[12] = U8TO32_LE(work + 48);
1230 x[13] = U8TO32_LE(work + 52);
1231 x[14] = U8TO32_LE(work + 56);
1232 x[15] = U8TO32_LE(work + 60);
1235 out[0] = ( x[0]) & 0x3fffffff;
1236 out[1] = ((x[ 0] >> 30) | (x[ 1] << 2)) & 0x3fffffff;
1237 out[2] = ((x[ 1] >> 28) | (x[ 2] << 4)) & 0x3fffffff;
1238 out[3] = ((x[ 2] >> 26) | (x[ 3] << 6)) & 0x3fffffff;
1239 out[4] = ((x[ 3] >> 24) | (x[ 4] << 8)) & 0x3fffffff;
1240 out[5] = ((x[ 4] >> 22) | (x[ 5] << 10)) & 0x3fffffff;
1241 out[6] = ((x[ 5] >> 20) | (x[ 6] << 12)) & 0x3fffffff;
1242 out[7] = ((x[ 6] >> 18) | (x[ 7] << 14)) & 0x3fffffff;
1243 out[8] = ((x[ 7] >> 16) | (x[ 8] << 16)) & 0x00ffffff;
1250 q1[0] = ((x[ 7] >> 24) | (x[ 8] << 8)) & 0x3fffffff;
1251 q1[1] = ((x[ 8] >> 22) | (x[ 9] << 10)) & 0x3fffffff;
1252 q1[2] = ((x[ 9] >> 20) | (x[10] << 12)) & 0x3fffffff;
1253 q1[3] = ((x[10] >> 18) | (x[11] << 14)) & 0x3fffffff;
1254 q1[4] = ((x[11] >> 16) | (x[12] << 16)) & 0x3fffffff;
1255 q1[5] = ((x[12] >> 14) | (x[13] << 18)) & 0x3fffffff;
1256 q1[6] = ((x[13] >> 12) | (x[14] << 20)) & 0x3fffffff;
1257 q1[7] = ((x[14] >> 10) | (x[15] << 22)) & 0x3fffffff;
1258 q1[8] = ((x[15] >> 8) );
1260 barrett_reduce256_modm(out, q1, out);
1264 expand_raw256_modm(bignum256modm out,
const byte in[32]) {
1265 bignum256modm_element_t x[8];
1267 x[0] = U8TO32_LE(in + 0);
1268 x[1] = U8TO32_LE(in + 4);
1269 x[2] = U8TO32_LE(in + 8);
1270 x[3] = U8TO32_LE(in + 12);
1271 x[4] = U8TO32_LE(in + 16);
1272 x[5] = U8TO32_LE(in + 20);
1273 x[6] = U8TO32_LE(in + 24);
1274 x[7] = U8TO32_LE(in + 28);
1276 out[0] = ( x[0]) & 0x3fffffff;
1277 out[1] = ((x[ 0] >> 30) | (x[ 1] << 2)) & 0x3fffffff;
1278 out[2] = ((x[ 1] >> 28) | (x[ 2] << 4)) & 0x3fffffff;
1279 out[3] = ((x[ 2] >> 26) | (x[ 3] << 6)) & 0x3fffffff;
1280 out[4] = ((x[ 3] >> 24) | (x[ 4] << 8)) & 0x3fffffff;
1281 out[5] = ((x[ 4] >> 22) | (x[ 5] << 10)) & 0x3fffffff;
1282 out[6] = ((x[ 5] >> 20) | (x[ 6] << 12)) & 0x3fffffff;
1283 out[7] = ((x[ 6] >> 18) | (x[ 7] << 14)) & 0x3fffffff;
1284 out[8] = ((x[ 7] >> 16) ) & 0x0000ffff;
1288 contract256_modm(byte out[32],
const bignum256modm in) {
1289 U32TO8_LE(out + 0, (in[0] ) | (in[1] << 30));
1290 U32TO8_LE(out + 4, (in[1] >> 2) | (in[2] << 28));
1291 U32TO8_LE(out + 8, (in[2] >> 4) | (in[3] << 26));
1292 U32TO8_LE(out + 12, (in[3] >> 6) | (in[4] << 24));
1293 U32TO8_LE(out + 16, (in[4] >> 8) | (in[5] << 22));
1294 U32TO8_LE(out + 20, (in[5] >> 10) | (in[6] << 20));
1295 U32TO8_LE(out + 24, (in[6] >> 12) | (in[7] << 18));
1296 U32TO8_LE(out + 28, (in[7] >> 14) | (in[8] << 16));
1300 contract256_window4_modm(
signed char r[64],
const bignum256modm in) {
1302 signed char *quads = r;
1303 bignum256modm_element_t i, j, v;
1305 for (i = 0; i < 8; i += 2) {
1307 for (j = 0; j < 7; j++) {
1308 *quads++ = (v & 15);
1311 v |= (in[i+1] << 2);
1312 for (j = 0; j < 8; j++) {
1313 *quads++ = (v & 15);
1319 *quads++ = (v & 15); v >>= 4;
1320 *quads++ = (v & 15); v >>= 4;
1321 *quads++ = (v & 15); v >>= 4;
1322 *quads++ = (v & 15); v >>= 4;
1326 for(i = 0; i < 63; i++) {
1328 r[i+1] += (r[i] >> 4);
1330 carry = (r[i] >> 3);
1331 r[i] -= (carry << 4);
1337 contract256_slidingwindow_modm(
signed char r[256],
const bignum256modm s,
int windowsize) {
1339 int m = (1 << (windowsize - 1)) - 1, soplen = 256;
1340 signed char *bits = r;
1341 bignum256modm_element_t v;
1344 for (i = 0; i < 8; i++) {
1346 for (j = 0; j < 30; j++, v >>= 1)
1350 for (j = 0; j < 16; j++, v >>= 1)
1354 for (j = 0; j < soplen; j++) {
1358 for (b = 1; (b < (soplen - j)) && (b <= 6); b++) {
1359 if ((r[j] + (r[j + b] << b)) <= m) {
1360 r[j] += r[j + b] << b;
1362 }
else if ((r[j] - (r[j + b] << b)) >= -m) {
1363 r[j] -= r[j + b] << b;
1364 for (k = j + b; k < soplen; k++) {
1371 }
else if (r[j + b]) {
1379 ge25519_p1p1_to_partial(ge25519 *r,
const ge25519_p1p1 *p) {
1380 curve25519_mul(r->x, p->x, p->t);
1381 curve25519_mul(r->y, p->y, p->z);
1382 curve25519_mul(r->z, p->z, p->t);
1386 ge25519_p1p1_to_full(ge25519 *r,
const ge25519_p1p1 *p) {
1387 curve25519_mul(r->x, p->x, p->t);
1388 curve25519_mul(r->y, p->y, p->z);
1389 curve25519_mul(r->z, p->z, p->t);
1390 curve25519_mul(r->t, p->x, p->y);
1394 ge25519_full_to_pniels(ge25519_pniels *p,
const ge25519 *r) {
1395 curve25519_sub(p->ysubx, r->y, r->x);
1396 curve25519_add(p->xaddy, r->y, r->x);
1397 curve25519_copy(p->z, r->z);
1398 curve25519_mul(p->t2d, r->t, ge25519_ec2d);
1402 ge25519_add_p1p1(ge25519_p1p1 *r,
const ge25519 *p,
const ge25519 *q) {
1403 bignum25519 a,b,c,d,t,u;
1405 curve25519_sub(a, p->y, p->x);
1406 curve25519_add(b, p->y, p->x);
1407 curve25519_sub(t, q->y, q->x);
1408 curve25519_add(u, q->y, q->x);
1409 curve25519_mul(a, a, t);
1410 curve25519_mul(b, b, u);
1411 curve25519_mul(c, p->t, q->t);
1412 curve25519_mul(c, c, ge25519_ec2d);
1413 curve25519_mul(d, p->z, q->z);
1414 curve25519_add(d, d, d);
1415 curve25519_sub(r->x, b, a);
1416 curve25519_add(r->y, b, a);
1417 curve25519_add_after_basic(r->z, d, c);
1418 curve25519_sub_after_basic(r->t, d, c);
1422 ge25519_double_p1p1(ge25519_p1p1 *r,
const ge25519 *p) {
1425 curve25519_square(a, p->x);
1426 curve25519_square(b, p->y);
1427 curve25519_square(c, p->z);
1428 curve25519_add_reduce(c, c, c);
1429 curve25519_add(r->x, p->x, p->y);
1430 curve25519_square(r->x, r->x);
1431 curve25519_add(r->y, b, a);
1432 curve25519_sub(r->z, b, a);
1433 curve25519_sub_after_basic(r->x, r->x, r->y);
1434 curve25519_sub_after_basic(r->t, c, r->z);
1438 ge25519_nielsadd2_p1p1(ge25519_p1p1 *r,
const ge25519 *p,
const ge25519_niels *q, byte signbit) {
1439 const bignum25519 *qb = (
const bignum25519 *)q;
1440 bignum25519 *rb = (bignum25519 *)r;
1443 curve25519_sub(a, p->y, p->x);
1444 curve25519_add(b, p->y, p->x);
1445 curve25519_mul(a, a, qb[signbit]);
1446 curve25519_mul(r->x, b, qb[signbit^1]);
1447 curve25519_add(r->y, r->x, a);
1448 curve25519_sub(r->x, r->x, a);
1449 curve25519_mul(c, p->t, q->t2d);
1450 curve25519_add_reduce(r->t, p->z, p->z);
1451 curve25519_copy(r->z, r->t);
1452 curve25519_add(rb[2+signbit], rb[2+signbit], c);
1453 curve25519_sub(rb[2+(signbit^1)], rb[2+(signbit^1)], c);
1457 ge25519_pnielsadd_p1p1(ge25519_p1p1 *r,
const ge25519 *p,
const ge25519_pniels *q, byte signbit) {
1458 const bignum25519 *qb = (
const bignum25519 *)q;
1459 bignum25519 *rb = (bignum25519 *)r;
1462 curve25519_sub(a, p->y, p->x);
1463 curve25519_add(b, p->y, p->x);
1464 curve25519_mul(a, a, qb[signbit]);
1465 curve25519_mul(r->x, b, qb[signbit^1]);
1466 curve25519_add(r->y, r->x, a);
1467 curve25519_sub(r->x, r->x, a);
1468 curve25519_mul(c, p->t, q->t2d);
1469 curve25519_mul(r->t, p->z, q->z);
1470 curve25519_add_reduce(r->t, r->t, r->t);
1471 curve25519_copy(r->z, r->t);
1472 curve25519_add(rb[2+signbit], rb[2+signbit], c);
1473 curve25519_sub(rb[2+(signbit^1)], rb[2+(signbit^1)], c);
1477 ge25519_double_partial(ge25519 *r,
const ge25519 *p) {
1479 ge25519_double_p1p1(&t, p);
1480 ge25519_p1p1_to_partial(r, &t);
1484 ge25519_double(ge25519 *r,
const ge25519 *p) {
1486 ge25519_double_p1p1(&t, p);
1487 ge25519_p1p1_to_full(r, &t);
1491 ge25519_add(ge25519 *r,
const ge25519 *p,
const ge25519 *q) {
1493 ge25519_add_p1p1(&t, p, q);
1494 ge25519_p1p1_to_full(r, &t);
1498 ge25519_nielsadd2(ge25519 *r,
const ge25519_niels *q) {
1499 bignum25519 a,b,c,e,f,g,h;
1501 curve25519_sub(a, r->y, r->x);
1502 curve25519_add(b, r->y, r->x);
1503 curve25519_mul(a, a, q->ysubx);
1504 curve25519_mul(e, b, q->xaddy);
1505 curve25519_add(h, e, a);
1506 curve25519_sub(e, e, a);
1507 curve25519_mul(c, r->t, q->t2d);
1508 curve25519_add(f, r->z, r->z);
1509 curve25519_add_after_basic(g, f, c);
1510 curve25519_sub_after_basic(f, f, c);
1511 curve25519_mul(r->x, e, f);
1512 curve25519_mul(r->y, h, g);
1513 curve25519_mul(r->z, g, f);
1514 curve25519_mul(r->t, e, h);
1518 ge25519_pnielsadd(ge25519_pniels *r,
const ge25519 *p,
const ge25519_pniels *q) {
1519 bignum25519 a,b,c,x,y,z,t;
1521 curve25519_sub(a, p->y, p->x);
1522 curve25519_add(b, p->y, p->x);
1523 curve25519_mul(a, a, q->ysubx);
1524 curve25519_mul(x, b, q->xaddy);
1525 curve25519_add(y, x, a);
1526 curve25519_sub(x, x, a);
1527 curve25519_mul(c, p->t, q->t2d);
1528 curve25519_mul(t, p->z, q->z);
1529 curve25519_add(t, t, t);
1530 curve25519_add_after_basic(z, t, c);
1531 curve25519_sub_after_basic(t, t, c);
1532 curve25519_mul(r->xaddy, x, t);
1533 curve25519_mul(r->ysubx, y, z);
1534 curve25519_mul(r->z, z, t);
1535 curve25519_mul(r->t2d, x, y);
1536 curve25519_copy(y, r->ysubx);
1537 curve25519_sub(r->ysubx, r->ysubx, r->xaddy);
1538 curve25519_add(r->xaddy, r->xaddy, y);
1539 curve25519_mul(r->t2d, r->t2d, ge25519_ec2d);
1543 ge25519_pack(byte r[32],
const ge25519 *p) {
1544 bignum25519 tx, ty, zi;
1546 curve25519_recip(zi, p->z);
1547 curve25519_mul(tx, p->x, zi);
1548 curve25519_mul(ty, p->y, zi);
1549 curve25519_contract(r, ty);
1550 curve25519_contract(parity, tx);
1551 r[31] ^= ((parity[0] & 1) << 7);
1555 ed25519_verify(
const unsigned char *x,
const unsigned char *y,
size_t len) {
1556 size_t differentbits = 0;
1558 differentbits |= (*x++ ^ *y++);
1559 return (
int) (1 & ((differentbits - 1) >> 8));
1563 ge25519_unpack_negative_vartime(ge25519 *r,
const byte p[32]) {
1564 const byte zero[32] = {0};
1565 const bignum25519 one = {1};
1566 byte parity = p[31] >> 7;
1568 bignum25519 t, root, num, den, d3;
1570 curve25519_expand(r->y, p);
1571 curve25519_copy(r->z, one);
1572 curve25519_square(num, r->y);
1573 curve25519_mul(den, num, ge25519_ecd);
1574 curve25519_sub_reduce(num, num, r->z);
1575 curve25519_add(den, den, r->z);
1579 curve25519_square(t, den);
1580 curve25519_mul(d3, t, den);
1581 curve25519_square(r->x, d3);
1582 curve25519_mul(r->x, r->x, den);
1583 curve25519_mul(r->x, r->x, num);
1584 curve25519_pow_two252m3(r->x, r->x);
1587 curve25519_mul(r->x, r->x, d3);
1588 curve25519_mul(r->x, r->x, num);
1591 curve25519_square(t, r->x);
1592 curve25519_mul(t, t, den);
1593 curve25519_sub_reduce(root, t, num);
1594 curve25519_contract(check, root);
1595 if (!ed25519_verify(check, zero, 32)) {
1596 curve25519_add_reduce(t, t, num);
1597 curve25519_contract(check, t);
1598 if (!ed25519_verify(check, zero, 32))
1600 curve25519_mul(r->x, r->x, ge25519_sqrtneg1);
1603 curve25519_contract(check, r->x);
1604 if ((check[0] & 1) == parity) {
1605 curve25519_copy(t, r->x);
1606 curve25519_neg(r->x, t);
1608 curve25519_mul(r->t, r->x, r->y);
1614 ge25519_double_scalarmult_vartime(ge25519 *r,
const ge25519 *p1,
const bignum256modm s1,
const bignum256modm s2) {
1615 signed char slide1[256], slide2[256];
1616 ge25519_pniels pre1[S1_TABLE_SIZE];
1621 contract256_slidingwindow_modm(slide1, s1, S1_SWINDOWSIZE);
1622 contract256_slidingwindow_modm(slide2, s2, S2_SWINDOWSIZE);
1624 ge25519_double(&d1, p1);
1625 ge25519_full_to_pniels(pre1, p1);
1626 for (i = 0; i < S1_TABLE_SIZE - 1; i++)
1627 ge25519_pnielsadd(&pre1[i+1], &d1, &pre1[i]);
1630 memset(r, 0,
sizeof(ge25519));
1635 while ((i >= 0) && !(slide1[i] | slide2[i]))
1638 for (; i >= 0; i--) {
1639 ge25519_double_p1p1(&t, r);
1642 ge25519_p1p1_to_full(r, &t);
1643 ge25519_pnielsadd_p1p1(&t, r, &pre1[abs(slide1[i]) / 2], (byte)slide1[i] >> 7);
1647 ge25519_p1p1_to_full(r, &t);
1648 ge25519_nielsadd2_p1p1(&t, r, &ge25519_niels_sliding_multiples[abs(slide2[i]) / 2], (byte)slide2[i] >> 7);
1651 ge25519_p1p1_to_partial(r, &t);
1655 #if !defined(HAVE_GE25519_SCALARMULT_BASE_CHOOSE_NIELS) 1658 ge25519_windowb_equal(word32 b, word32 c) {
1659 return ((b ^ c) - 1) >> 31;
1663 ge25519_scalarmult_base_choose_niels(ge25519_niels *t,
const byte table[256][96], word32 pos,
signed char b) {
1665 word32 sign = (word32)((byte)b >> 7);
1666 word32 mask = ~(sign - 1);
1667 word32 u = (b + mask) ^ mask;
1671 byte packed[96] = {0};
1675 for (i = 0; i < 8; i++)
1676 curve25519_move_conditional_bytes(packed, table[(pos * 8) + i], ge25519_windowb_equal(u, i + 1));
1679 curve25519_expand(t->ysubx, packed + 0);
1680 curve25519_expand(t->xaddy, packed + 32);
1681 curve25519_expand(t->t2d , packed + 64);
1684 curve25519_swap_conditional(t->ysubx, t->xaddy, sign);
1685 curve25519_neg(neg, t->t2d);
1686 curve25519_swap_conditional(t->t2d, neg, sign);
1693 ge25519_scalarmult_base_niels(ge25519 *r,
const byte basepoint_table[256][96],
const bignum256modm s) {
1698 contract256_window4_modm(b, s);
1700 ge25519_scalarmult_base_choose_niels(&t, basepoint_table, 0, b[1]);
1701 curve25519_sub_reduce(r->x, t.xaddy, t.ysubx);
1702 curve25519_add_reduce(r->y, t.xaddy, t.ysubx);
1703 memset(r->z, 0,
sizeof(bignum25519));
1704 curve25519_copy(r->t, t.t2d);
1706 for (i = 3; i < 64; i += 2) {
1707 ge25519_scalarmult_base_choose_niels(&t, basepoint_table, i / 2, b[i]);
1708 ge25519_nielsadd2(r, &t);
1710 ge25519_double_partial(r, r);
1711 ge25519_double_partial(r, r);
1712 ge25519_double_partial(r, r);
1713 ge25519_double(r, r);
1714 ge25519_scalarmult_base_choose_niels(&t, basepoint_table, 0, b[0]);
1715 curve25519_mul(t.t2d, t.t2d, ge25519_ecd);
1716 ge25519_nielsadd2(r, &t);
1717 for(i = 2; i < 64; i += 2) {
1718 ge25519_scalarmult_base_choose_niels(&t, basepoint_table, i / 2, b[i]);
1719 ge25519_nielsadd2(r, &t);
1723 ANONYMOUS_NAMESPACE_END
1731 NAMESPACE_BEGIN(Donna)
1733 int curve25519_mult_CXX(byte sharedKey[32],
const byte secretKey[32],
const byte othersKey[32])
1735 using namespace CryptoPP::Donna::X25519;
1738 for (
size_t i = 0;i < 32;++i)
1739 e[i] = secretKey[i];
1740 e[0] &= 0xf8; e[31] &= 0x7f; e[31] |= 0x40;
1742 bignum25519 nqpqx = {1}, nqpqz = {0}, nqz = {1}, nqx;
1743 bignum25519 q, qx, qpqx, qqx, zzz, zmone;
1744 size_t bit, lastbit;
1746 curve25519_expand(q, othersKey);
1747 curve25519_copy(nqx, q);
1754 for (
int i = 253; i >= 2; i--) {
1755 curve25519_add(qx, nqx, nqz);
1756 curve25519_sub(nqz, nqx, nqz);
1757 curve25519_add(qpqx, nqpqx, nqpqz);
1758 curve25519_sub(nqpqz, nqpqx, nqpqz);
1759 curve25519_mul(nqpqx, qpqx, nqz);
1760 curve25519_mul(nqpqz, qx, nqpqz);
1761 curve25519_add(qqx, nqpqx, nqpqz);
1762 curve25519_sub(nqpqz, nqpqx, nqpqz);
1763 curve25519_square(nqpqz, nqpqz);
1764 curve25519_square(nqpqx, qqx);
1765 curve25519_mul(nqpqz, nqpqz, q);
1766 curve25519_square(qx, qx);
1767 curve25519_square(nqz, nqz);
1768 curve25519_mul(nqx, qx, nqz);
1769 curve25519_sub(nqz, qx, nqz);
1770 curve25519_scalar_product(zzz, nqz, 121665);
1771 curve25519_add(zzz, zzz, qx);
1772 curve25519_mul(nqz, nqz, zzz);
1774 bit = (e[i/8] >> (i & 7)) & 1;
1775 curve25519_swap_conditional(nqx, nqpqx, bit ^ lastbit);
1776 curve25519_swap_conditional(nqz, nqpqz, bit ^ lastbit);
1781 for (
int i = 0; i < 3; i++) {
1782 curve25519_add(qx, nqx, nqz);
1783 curve25519_sub(nqz, nqx, nqz);
1784 curve25519_square(qx, qx);
1785 curve25519_square(nqz, nqz);
1786 curve25519_mul(nqx, qx, nqz);
1787 curve25519_sub(nqz, qx, nqz);
1788 curve25519_scalar_product(zzz, nqz, 121665);
1789 curve25519_add(zzz, zzz, qx);
1790 curve25519_mul(nqz, nqz, zzz);
1793 curve25519_recip(zmone, nqz);
1794 curve25519_mul(nqz, nqx, zmone);
1795 curve25519_contract(sharedKey, nqz);
1802 using namespace CryptoPP::Donna::X25519;
1804 #if (CRYPTOPP_CURVE25519_SSE2) 1806 return curve25519_mult_SSE2(publicKey, secretKey, basePoint);
1810 return curve25519_mult_CXX(publicKey, secretKey, basePoint);
1813 int curve25519_mult(byte sharedKey[32],
const byte secretKey[32],
const byte othersKey[32])
1815 #if (CRYPTOPP_CURVE25519_SSE2) 1817 return curve25519_mult_SSE2(sharedKey, secretKey, othersKey);
1821 return curve25519_mult_CXX(sharedKey, secretKey, othersKey);
1830 NAMESPACE_BEGIN(Donna)
1833 ed25519_publickey_CXX(byte publicKey[32],
const byte secretKey[32])
1835 using namespace CryptoPP::Donna::Ed25519;
1838 ALIGN(16) ge25519 A;
1842 ed25519_extsk(extsk, secretKey);
1843 expand256_modm(a, extsk, 32);
1844 ge25519_scalarmult_base_niels(&A, ge25519_niels_base_multiples, a);
1845 ge25519_pack(publicKey, &A);
1853 return ed25519_publickey_CXX(publicKey, secretKey);
1857 ed25519_sign_CXX(
const byte *m,
size_t mlen,
const byte sk[32],
const byte pk[32], byte RS[64])
1859 using namespace CryptoPP::Donna::Ed25519;
1861 bignum256modm r, S, a;
1862 ALIGN(16) ge25519 R;
1863 hash_512bits extsk, hashr, hram;
1865 ed25519_extsk(extsk, sk);
1869 hash.Update(extsk + 32, 32);
1870 hash.Update(m, mlen);
1872 expand256_modm(r, hashr, 64);
1875 ge25519_scalarmult_base_niels(&R, ge25519_niels_base_multiples, r);
1876 ge25519_pack(RS, &R);
1879 ed25519_hram(hram, RS, pk, m, mlen);
1880 expand256_modm(S, hram, 64);
1883 expand256_modm(a, extsk, 32);
1884 mul256_modm(S, S, a);
1887 add256_modm(S, S, r);
1890 contract256_modm(RS + 32, S);
1896 ed25519_sign(const byte* message,
size_t messageLength, const byte secretKey[32],
1897 const byte publicKey[32], byte signature[64])
1899 return ed25519_sign_CXX(message, messageLength, secretKey, publicKey, signature);
1903 ed25519_sign_open_CXX(
const byte *m,
size_t mlen,
const byte pk[32],
const byte RS[64]) {
1905 using namespace CryptoPP::Donna::Ed25519;
1907 ALIGN(16) ge25519 R, A;
1909 bignum256modm hram, S;
1910 unsigned char checkR[32];
1912 if ((RS[63] & 224) || !ge25519_unpack_negative_vartime(&A, pk))
1916 ed25519_hram(hash, RS, pk, m, mlen);
1917 expand256_modm(hram, hash, 64);
1920 expand256_modm(S, RS + 32, 32);
1923 ge25519_double_scalarmult_vartime(&R, &A, hram, S);
1924 ge25519_pack(checkR, &R);
1927 return ed25519_verify(RS, checkR, 32) ? 0 : -1;
1931 ed25519_sign_open(const byte *message,
size_t messageLength, const byte publicKey[32], const byte signature[64])
1933 return ed25519_sign_open_CXX(message, messageLength, publicKey, signature);
1939 #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.
Converts an enumeration to a type suitable for use as a template parameter.
EnumToType< ByteOrder, LITTLE_ENDIAN_ORDER > LittleEndian
Provides a constant for LittleEndian.
Library configuration file.
void Update(const byte *input, size_t length)
Updates a hash with additional input.
byte order is little-endian
Classes and functions for secure memory allocations.
T GetWord(bool assumeAligned, ByteOrder order, const byte *block)
Access a block of memory.
int ed25519_sign(const byte *message, size_t messageLength, const byte secretKey[32], const byte publicKey[32], byte signature[64])
Creates a signature on a message.
int curve25519_mult(byte publicKey[32], const byte secretKey[32])
Generate a public key.
int ed25519_sign_open(const byte *message, size_t messageLength, const byte publicKey[32], const byte signature[64])
Verifies a signature on a message.
Fixed size stack-based SecBlock.
Functions for CPU features and intrinsics.
Classes for SHA-1 and SHA-2 family of message digests.
bool HasSSE2()
Determines SSE2 availability.
Access a block of memory.
Crypto++ library namespace.
int ed25519_publickey(byte publicKey[32], const byte secretKey[32])
Creates a public key from a secret key.