Electroneum
Loading...
Searching...
No Matches
curve25519-donna-64bit.h
Go to the documentation of this file.
1/*
2 Public domain by Adam Langley <agl@imperialviolet.org> &
3 Andrew M. <liquidsun@gmail.com>
4 See: https://github.com/floodyberry/curve25519-donna
5
6 64bit integer curve25519 implementation
7*/
8
9typedef uint64_t bignum25519[5];
10
11static const uint64_t reduce_mask_40 = ((uint64_t)1 << 40) - 1;
12static const uint64_t reduce_mask_51 = ((uint64_t)1 << 51) - 1;
13static const uint64_t reduce_mask_56 = ((uint64_t)1 << 56) - 1;
14
15/* out = in */
16DONNA_INLINE static void
17curve25519_copy(bignum25519 out, const bignum25519 in) {
18 out[0] = in[0];
19 out[1] = in[1];
20 out[2] = in[2];
21 out[3] = in[3];
22 out[4] = in[4];
23}
24
25/* out = a + b */
26DONNA_INLINE static void
27curve25519_add(bignum25519 out, const bignum25519 a, const bignum25519 b) {
28 out[0] = a[0] + b[0];
29 out[1] = a[1] + b[1];
30 out[2] = a[2] + b[2];
31 out[3] = a[3] + b[3];
32 out[4] = a[4] + b[4];
33}
34
35/* out = a + b, where a and/or b are the result of a basic op (add,sub) */
36DONNA_INLINE static void
37curve25519_add_after_basic(bignum25519 out, const bignum25519 a, const bignum25519 b) {
38 out[0] = a[0] + b[0];
39 out[1] = a[1] + b[1];
40 out[2] = a[2] + b[2];
41 out[3] = a[3] + b[3];
42 out[4] = a[4] + b[4];
43}
44
45DONNA_INLINE static void
46curve25519_add_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) {
47 uint64_t c;
48 out[0] = a[0] + b[0] ; c = (out[0] >> 51); out[0] &= reduce_mask_51;
49 out[1] = a[1] + b[1] + c; c = (out[1] >> 51); out[1] &= reduce_mask_51;
50 out[2] = a[2] + b[2] + c; c = (out[2] >> 51); out[2] &= reduce_mask_51;
51 out[3] = a[3] + b[3] + c; c = (out[3] >> 51); out[3] &= reduce_mask_51;
52 out[4] = a[4] + b[4] + c; c = (out[4] >> 51); out[4] &= reduce_mask_51;
53 out[0] += c * 19;
54}
55
56/* multiples of p */
57static const uint64_t twoP0 = 0x0fffffffffffda;
58static const uint64_t twoP1234 = 0x0ffffffffffffe;
59static const uint64_t fourP0 = 0x1fffffffffffb4;
60static const uint64_t fourP1234 = 0x1ffffffffffffc;
61
62/* out = a - b */
63DONNA_INLINE static void
64curve25519_sub(bignum25519 out, const bignum25519 a, const bignum25519 b) {
65 out[0] = a[0] + twoP0 - b[0];
66 out[1] = a[1] + twoP1234 - b[1];
67 out[2] = a[2] + twoP1234 - b[2];
68 out[3] = a[3] + twoP1234 - b[3];
69 out[4] = a[4] + twoP1234 - b[4];
70}
71
72/* out = a - b, where a and/or b are the result of a basic op (add,sub) */
73DONNA_INLINE static void
74curve25519_sub_after_basic(bignum25519 out, const bignum25519 a, const bignum25519 b) {
75 out[0] = a[0] + fourP0 - b[0];
76 out[1] = a[1] + fourP1234 - b[1];
77 out[2] = a[2] + fourP1234 - b[2];
78 out[3] = a[3] + fourP1234 - b[3];
79 out[4] = a[4] + fourP1234 - b[4];
80}
81
82DONNA_INLINE static void
83curve25519_sub_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) {
84 uint64_t c;
85 out[0] = a[0] + fourP0 - b[0] ; c = (out[0] >> 51); out[0] &= reduce_mask_51;
86 out[1] = a[1] + fourP1234 - b[1] + c; c = (out[1] >> 51); out[1] &= reduce_mask_51;
87 out[2] = a[2] + fourP1234 - b[2] + c; c = (out[2] >> 51); out[2] &= reduce_mask_51;
88 out[3] = a[3] + fourP1234 - b[3] + c; c = (out[3] >> 51); out[3] &= reduce_mask_51;
89 out[4] = a[4] + fourP1234 - b[4] + c; c = (out[4] >> 51); out[4] &= reduce_mask_51;
90 out[0] += c * 19;
91}
92
93/* out = -a */
94DONNA_INLINE static void
95curve25519_neg(bignum25519 out, const bignum25519 a) {
96 uint64_t c;
97 out[0] = twoP0 - a[0] ; c = (out[0] >> 51); out[0] &= reduce_mask_51;
98 out[1] = twoP1234 - a[1] + c; c = (out[1] >> 51); out[1] &= reduce_mask_51;
99 out[2] = twoP1234 - a[2] + c; c = (out[2] >> 51); out[2] &= reduce_mask_51;
100 out[3] = twoP1234 - a[3] + c; c = (out[3] >> 51); out[3] &= reduce_mask_51;
101 out[4] = twoP1234 - a[4] + c; c = (out[4] >> 51); out[4] &= reduce_mask_51;
102 out[0] += c * 19;
103}
104
105/* out = a * b */
106DONNA_INLINE static void
107curve25519_mul(bignum25519 out, const bignum25519 in2, const bignum25519 in) {
108#if !defined(HAVE_NATIVE_UINT128)
109 uint128_t mul;
110#endif
111 uint128_t t[5];
112 uint64_t r0,r1,r2,r3,r4,s0,s1,s2,s3,s4,c;
113
114 r0 = in[0];
115 r1 = in[1];
116 r2 = in[2];
117 r3 = in[3];
118 r4 = in[4];
119
120 s0 = in2[0];
121 s1 = in2[1];
122 s2 = in2[2];
123 s3 = in2[3];
124 s4 = in2[4];
125
126#if defined(HAVE_NATIVE_UINT128)
127 t[0] = ((uint128_t) r0) * s0;
128 t[1] = ((uint128_t) r0) * s1 + ((uint128_t) r1) * s0;
129 t[2] = ((uint128_t) r0) * s2 + ((uint128_t) r2) * s0 + ((uint128_t) r1) * s1;
130 t[3] = ((uint128_t) r0) * s3 + ((uint128_t) r3) * s0 + ((uint128_t) r1) * s2 + ((uint128_t) r2) * s1;
131 t[4] = ((uint128_t) r0) * s4 + ((uint128_t) r4) * s0 + ((uint128_t) r3) * s1 + ((uint128_t) r1) * s3 + ((uint128_t) r2) * s2;
132#else
133 mul64x64_128(t[0], r0, s0)
134 mul64x64_128(t[1], r0, s1) mul64x64_128(mul, r1, s0) add128(t[1], mul)
135 mul64x64_128(t[2], r0, s2) mul64x64_128(mul, r2, s0) add128(t[2], mul) mul64x64_128(mul, r1, s1) add128(t[2], mul)
136 mul64x64_128(t[3], r0, s3) mul64x64_128(mul, r3, s0) add128(t[3], mul) mul64x64_128(mul, r1, s2) add128(t[3], mul) mul64x64_128(mul, r2, s1) add128(t[3], mul)
137 mul64x64_128(t[4], r0, s4) mul64x64_128(mul, r4, s0) add128(t[4], mul) mul64x64_128(mul, r3, s1) add128(t[4], mul) mul64x64_128(mul, r1, s3) add128(t[4], mul) mul64x64_128(mul, r2, s2) add128(t[4], mul)
138#endif
139
140 r1 *= 19;
141 r2 *= 19;
142 r3 *= 19;
143 r4 *= 19;
144
145#if defined(HAVE_NATIVE_UINT128)
146 t[0] += ((uint128_t) r4) * s1 + ((uint128_t) r1) * s4 + ((uint128_t) r2) * s3 + ((uint128_t) r3) * s2;
147 t[1] += ((uint128_t) r4) * s2 + ((uint128_t) r2) * s4 + ((uint128_t) r3) * s3;
148 t[2] += ((uint128_t) r4) * s3 + ((uint128_t) r3) * s4;
149 t[3] += ((uint128_t) r4) * s4;
150#else
151 mul64x64_128(mul, r4, s1) add128(t[0], mul) mul64x64_128(mul, r1, s4) add128(t[0], mul) mul64x64_128(mul, r2, s3) add128(t[0], mul) mul64x64_128(mul, r3, s2) add128(t[0], mul)
152 mul64x64_128(mul, r4, s2) add128(t[1], mul) mul64x64_128(mul, r2, s4) add128(t[1], mul) mul64x64_128(mul, r3, s3) add128(t[1], mul)
153 mul64x64_128(mul, r4, s3) add128(t[2], mul) mul64x64_128(mul, r3, s4) add128(t[2], mul)
154 mul64x64_128(mul, r4, s4) add128(t[3], mul)
155#endif
156
157
158 r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51);
159 add128_64(t[1], c) r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51);
160 add128_64(t[2], c) r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51);
161 add128_64(t[3], c) r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51);
162 add128_64(t[4], c) r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51);
163 r0 += c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51;
164 r1 += c;
165
166 out[0] = r0;
167 out[1] = r1;
168 out[2] = r2;
169 out[3] = r3;
170 out[4] = r4;
171}
172
173DONNA_NOINLINE static void
174curve25519_mul_noinline(bignum25519 out, const bignum25519 in2, const bignum25519 in) {
175 curve25519_mul(out, in2, in);
176}
177
178/* out = in^(2 * count) */
179DONNA_NOINLINE static void
180curve25519_square_times(bignum25519 out, const bignum25519 in, uint64_t count) {
181#if !defined(HAVE_NATIVE_UINT128)
182 uint128_t mul;
183#endif
184 uint128_t t[5];
185 uint64_t r0,r1,r2,r3,r4,c;
186 uint64_t d0,d1,d2,d4,d419;
187
188 r0 = in[0];
189 r1 = in[1];
190 r2 = in[2];
191 r3 = in[3];
192 r4 = in[4];
193
194 do {
195 d0 = r0 * 2;
196 d1 = r1 * 2;
197 d2 = r2 * 2 * 19;
198 d419 = r4 * 19;
199 d4 = d419 * 2;
200
201#if defined(HAVE_NATIVE_UINT128)
202 t[0] = ((uint128_t) r0) * r0 + ((uint128_t) d4) * r1 + (((uint128_t) d2) * (r3 ));
203 t[1] = ((uint128_t) d0) * r1 + ((uint128_t) d4) * r2 + (((uint128_t) r3) * (r3 * 19));
204 t[2] = ((uint128_t) d0) * r2 + ((uint128_t) r1) * r1 + (((uint128_t) d4) * (r3 ));
205 t[3] = ((uint128_t) d0) * r3 + ((uint128_t) d1) * r2 + (((uint128_t) r4) * (d419 ));
206 t[4] = ((uint128_t) d0) * r4 + ((uint128_t) d1) * r3 + (((uint128_t) r2) * (r2 ));
207#else
208 mul64x64_128(t[0], r0, r0) mul64x64_128(mul, d4, r1) add128(t[0], mul) mul64x64_128(mul, d2, r3) add128(t[0], mul)
209 mul64x64_128(t[1], d0, r1) mul64x64_128(mul, d4, r2) add128(t[1], mul) mul64x64_128(mul, r3, r3 * 19) add128(t[1], mul)
210 mul64x64_128(t[2], d0, r2) mul64x64_128(mul, r1, r1) add128(t[2], mul) mul64x64_128(mul, d4, r3) add128(t[2], mul)
211 mul64x64_128(t[3], d0, r3) mul64x64_128(mul, d1, r2) add128(t[3], mul) mul64x64_128(mul, r4, d419) add128(t[3], mul)
212 mul64x64_128(t[4], d0, r4) mul64x64_128(mul, d1, r3) add128(t[4], mul) mul64x64_128(mul, r2, r2) add128(t[4], mul)
213#endif
214
215 r0 = lo128(t[0]) & reduce_mask_51;
216 r1 = lo128(t[1]) & reduce_mask_51; shl128(c, t[0], 13); r1 += c;
217 r2 = lo128(t[2]) & reduce_mask_51; shl128(c, t[1], 13); r2 += c;
218 r3 = lo128(t[3]) & reduce_mask_51; shl128(c, t[2], 13); r3 += c;
219 r4 = lo128(t[4]) & reduce_mask_51; shl128(c, t[3], 13); r4 += c;
220 shl128(c, t[4], 13); r0 += c * 19;
221 c = r0 >> 51; r0 &= reduce_mask_51;
222 r1 += c ; c = r1 >> 51; r1 &= reduce_mask_51;
223 r2 += c ; c = r2 >> 51; r2 &= reduce_mask_51;
224 r3 += c ; c = r3 >> 51; r3 &= reduce_mask_51;
225 r4 += c ; c = r4 >> 51; r4 &= reduce_mask_51;
226 r0 += c * 19;
227 } while(--count);
228
229 out[0] = r0;
230 out[1] = r1;
231 out[2] = r2;
232 out[3] = r3;
233 out[4] = r4;
234}
235
236DONNA_INLINE static void
237curve25519_square(bignum25519 out, const bignum25519 in) {
238#if !defined(HAVE_NATIVE_UINT128)
239 uint128_t mul;
240#endif
241 uint128_t t[5];
242 uint64_t r0,r1,r2,r3,r4,c;
243 uint64_t d0,d1,d2,d4,d419;
244
245 r0 = in[0];
246 r1 = in[1];
247 r2 = in[2];
248 r3 = in[3];
249 r4 = in[4];
250
251 d0 = r0 * 2;
252 d1 = r1 * 2;
253 d2 = r2 * 2 * 19;
254 d419 = r4 * 19;
255 d4 = d419 * 2;
256
257#if defined(HAVE_NATIVE_UINT128)
258 t[0] = ((uint128_t) r0) * r0 + ((uint128_t) d4) * r1 + (((uint128_t) d2) * (r3 ));
259 t[1] = ((uint128_t) d0) * r1 + ((uint128_t) d4) * r2 + (((uint128_t) r3) * (r3 * 19));
260 t[2] = ((uint128_t) d0) * r2 + ((uint128_t) r1) * r1 + (((uint128_t) d4) * (r3 ));
261 t[3] = ((uint128_t) d0) * r3 + ((uint128_t) d1) * r2 + (((uint128_t) r4) * (d419 ));
262 t[4] = ((uint128_t) d0) * r4 + ((uint128_t) d1) * r3 + (((uint128_t) r2) * (r2 ));
263#else
264 mul64x64_128(t[0], r0, r0) mul64x64_128(mul, d4, r1) add128(t[0], mul) mul64x64_128(mul, d2, r3) add128(t[0], mul)
265 mul64x64_128(t[1], d0, r1) mul64x64_128(mul, d4, r2) add128(t[1], mul) mul64x64_128(mul, r3, r3 * 19) add128(t[1], mul)
266 mul64x64_128(t[2], d0, r2) mul64x64_128(mul, r1, r1) add128(t[2], mul) mul64x64_128(mul, d4, r3) add128(t[2], mul)
267 mul64x64_128(t[3], d0, r3) mul64x64_128(mul, d1, r2) add128(t[3], mul) mul64x64_128(mul, r4, d419) add128(t[3], mul)
268 mul64x64_128(t[4], d0, r4) mul64x64_128(mul, d1, r3) add128(t[4], mul) mul64x64_128(mul, r2, r2) add128(t[4], mul)
269#endif
270
271 r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51);
272 add128_64(t[1], c) r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51);
273 add128_64(t[2], c) r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51);
274 add128_64(t[3], c) r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51);
275 add128_64(t[4], c) r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51);
276 r0 += c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51;
277 r1 += c;
278
279 out[0] = r0;
280 out[1] = r1;
281 out[2] = r2;
282 out[3] = r3;
283 out[4] = r4;
284}
285
286/* Take a little-endian, 32-byte number and expand it into polynomial form */
287DONNA_INLINE static void
288curve25519_expand(bignum25519 out, const unsigned char *in) {
289 static const union { uint8_t b[2]; uint16_t s; } endian_check = {{1,0}};
290 uint64_t x0,x1,x2,x3;
291
292 if (endian_check.s == 1) {
293 x0 = *(uint64_t *)(in + 0);
294 x1 = *(uint64_t *)(in + 8);
295 x2 = *(uint64_t *)(in + 16);
296 x3 = *(uint64_t *)(in + 24);
297 } else {
298 #define F(s) \
299 ((((uint64_t)in[s + 0]) ) | \
300 (((uint64_t)in[s + 1]) << 8) | \
301 (((uint64_t)in[s + 2]) << 16) | \
302 (((uint64_t)in[s + 3]) << 24) | \
303 (((uint64_t)in[s + 4]) << 32) | \
304 (((uint64_t)in[s + 5]) << 40) | \
305 (((uint64_t)in[s + 6]) << 48) | \
306 (((uint64_t)in[s + 7]) << 56))
307
308 x0 = F(0);
309 x1 = F(8);
310 x2 = F(16);
311 x3 = F(24);
312 }
313
314 out[0] = x0 & reduce_mask_51; x0 = (x0 >> 51) | (x1 << 13);
315 out[1] = x0 & reduce_mask_51; x1 = (x1 >> 38) | (x2 << 26);
316 out[2] = x1 & reduce_mask_51; x2 = (x2 >> 25) | (x3 << 39);
317 out[3] = x2 & reduce_mask_51; x3 = (x3 >> 12);
318 out[4] = x3 & reduce_mask_51;
319}
320
321/* Take a fully reduced polynomial form number and contract it into a
322 * little-endian, 32-byte array
323 */
324DONNA_INLINE static void
325curve25519_contract(unsigned char *out, const bignum25519 input) {
326 uint64_t t[5];
327 uint64_t f, i;
328
329 t[0] = input[0];
330 t[1] = input[1];
331 t[2] = input[2];
332 t[3] = input[3];
333 t[4] = input[4];
334
335 #define curve25519_contract_carry() \
336 t[1] += t[0] >> 51; t[0] &= reduce_mask_51; \
337 t[2] += t[1] >> 51; t[1] &= reduce_mask_51; \
338 t[3] += t[2] >> 51; t[2] &= reduce_mask_51; \
339 t[4] += t[3] >> 51; t[3] &= reduce_mask_51;
340
341 #define curve25519_contract_carry_full() curve25519_contract_carry() \
342 t[0] += 19 * (t[4] >> 51); t[4] &= reduce_mask_51;
343
344 #define curve25519_contract_carry_final() curve25519_contract_carry() \
345 t[4] &= reduce_mask_51;
346
347 curve25519_contract_carry_full()
348 curve25519_contract_carry_full()
349
350 /* now t is between 0 and 2^255-1, properly carried. */
351 /* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */
352 t[0] += 19;
353 curve25519_contract_carry_full()
354
355 /* now between 19 and 2^255-1 in both cases, and offset by 19. */
356 t[0] += (reduce_mask_51 + 1) - 19;
357 t[1] += (reduce_mask_51 + 1) - 1;
358 t[2] += (reduce_mask_51 + 1) - 1;
359 t[3] += (reduce_mask_51 + 1) - 1;
360 t[4] += (reduce_mask_51 + 1) - 1;
361
362 /* now between 2^255 and 2^256-20, and offset by 2^255. */
363 curve25519_contract_carry_final()
364
365 #define write51full(n,shift) \
366 f = ((t[n] >> shift) | (t[n+1] << (51 - shift))); \
367 for (i = 0; i < 8; i++, f >>= 8) *out++ = (unsigned char)f;
368 #define write51(n) write51full(n,13*n)
369 write51(0)
370 write51(1)
371 write51(2)
372 write51(3)
373}
374
375#if !defined(ED25519_GCC_64BIT_CHOOSE)
376
377/* out = (flag) ? in : out */
378DONNA_INLINE static void
379curve25519_move_conditional_bytes(uint8_t out[96], const uint8_t in[96], uint64_t flag) {
380 const uint64_t nb = flag - 1, b = ~nb;
381 const uint64_t *inq = (const uint64_t *)in;
382 uint64_t *outq = (uint64_t *)out;
383 outq[0] = (outq[0] & nb) | (inq[0] & b);
384 outq[1] = (outq[1] & nb) | (inq[1] & b);
385 outq[2] = (outq[2] & nb) | (inq[2] & b);
386 outq[3] = (outq[3] & nb) | (inq[3] & b);
387 outq[4] = (outq[4] & nb) | (inq[4] & b);
388 outq[5] = (outq[5] & nb) | (inq[5] & b);
389 outq[6] = (outq[6] & nb) | (inq[6] & b);
390 outq[7] = (outq[7] & nb) | (inq[7] & b);
391 outq[8] = (outq[8] & nb) | (inq[8] & b);
392 outq[9] = (outq[9] & nb) | (inq[9] & b);
393 outq[10] = (outq[10] & nb) | (inq[10] & b);
394 outq[11] = (outq[11] & nb) | (inq[11] & b);
395}
396
397/* if (iswap) swap(a, b) */
398DONNA_INLINE static void
399curve25519_swap_conditional(bignum25519 a, bignum25519 b, uint64_t iswap) {
400 const uint64_t swap = (uint64_t)(-(int64_t)iswap);
401 uint64_t x0,x1,x2,x3,x4;
402
403 x0 = swap & (a[0] ^ b[0]); a[0] ^= x0; b[0] ^= x0;
404 x1 = swap & (a[1] ^ b[1]); a[1] ^= x1; b[1] ^= x1;
405 x2 = swap & (a[2] ^ b[2]); a[2] ^= x2; b[2] ^= x2;
406 x3 = swap & (a[3] ^ b[3]); a[3] ^= x3; b[3] ^= x3;
407 x4 = swap & (a[4] ^ b[4]); a[4] ^= x4; b[4] ^= x4;
408}
409
410#endif /* ED25519_GCC_64BIT_CHOOSE */
411
412#define ED25519_64BIT_TABLES
413
bignum25519
uint32_t bignum25519[10]
Definition curve25519-donna-32bit.h:8
curve25519_mul_noinline
#define curve25519_mul_noinline
Definition curve25519-donna-32bit.h:152
F
#define F(s)
curve25519_contract_carry_final
#define curve25519_contract_carry_final()
write51
#define write51(n)
curve25519_contract_carry_full
#define curve25519_contract_carry_full()
curve25519_add_after_basic
#define curve25519_add_after_basic
Definition curve25519-donna-sse2.h:99
curve25519_square
#define curve25519_square(r, n)
Definition curve25519-donna-sse2.h:431
DONNA_NOINLINE
#define DONNA_NOINLINE
Definition ed25519-donna-portable.h:22
DONNA_INLINE
#define DONNA_INLINE
Definition ed25519-donna-portable.h:21
a
const GenericPointer< typename T::ValueType > T2 T::AllocatorType & a
Definition pointer.h:1124
uint16_t
unsigned short uint16_t
Definition stdint.h:125
int64_t
signed __int64 int64_t
Definition stdint.h:135
uint8_t
unsigned char uint8_t
Definition stdint.h:124
uint64_t
unsigned __int64 uint64_t
Definition stdint.h:136