31 typedef uint64_t limb;
32 typedef limb felem[5];
35 typedef unsigned uint128_t __attribute__((mode(TI)));
38 #define force_inline __attribute__((always_inline))
41 static inline void force_inline
42 fsum(limb *output,
const limb *in) {
56 static inline void force_inline
57 fdifference_backwards(felem out,
const felem in) {
59 static const limb two54m152 = (((limb)1) << 54) - 152;
60 static const limb two54m8 = (((limb)1) << 54) - 8;
62 out[0] = in[0] + two54m152 - out[0];
63 out[1] = in[1] + two54m8 - out[1];
64 out[2] = in[2] + two54m8 - out[2];
65 out[3] = in[3] + two54m8 - out[3];
66 out[4] = in[4] + two54m8 - out[4];
70 static inline void force_inline
71 fscalar_product(felem output,
const felem in,
const limb scalar) {
74 a = ((uint128_t) in[0]) * scalar;
75 output[0] = ((limb)a) & 0x7ffffffffffff;
77 a = ((uint128_t) in[1]) * scalar + ((limb) (a >> 51));
78 output[1] = ((limb)a) & 0x7ffffffffffff;
80 a = ((uint128_t) in[2]) * scalar + ((limb) (a >> 51));
81 output[2] = ((limb)a) & 0x7ffffffffffff;
83 a = ((uint128_t) in[3]) * scalar + ((limb) (a >> 51));
84 output[3] = ((limb)a) & 0x7ffffffffffff;
86 a = ((uint128_t) in[4]) * scalar + ((limb) (a >> 51));
87 output[4] = ((limb)a) & 0x7ffffffffffff;
89 output[0] += (a >> 51) * 19;
100 static inline void force_inline
101 fmul(felem output,
const felem in2,
const felem in) {
103 limb r0,r1,r2,r3,r4,s0,s1,s2,s3,s4,c;
117 t[0] = ((uint128_t) r0) * s0;
118 t[1] = ((uint128_t) r0) * s1 + ((uint128_t) r1) * s0;
119 t[2] = ((uint128_t) r0) * s2 + ((uint128_t) r2) * s0 + ((uint128_t) r1) * s1;
120 t[3] = ((uint128_t) r0) * s3 + ((uint128_t) r3) * s0 + ((uint128_t) r1) * s2 + ((uint128_t) r2) * s1;
121 t[4] = ((uint128_t) r0) * s4 + ((uint128_t) r4) * s0 + ((uint128_t) r3) * s1 + ((uint128_t) r1) * s3 + ((uint128_t) r2) * s2;
128 t[0] += ((uint128_t) r4) * s1 + ((uint128_t) r1) * s4 + ((uint128_t) r2) * s3 + ((uint128_t) r3) * s2;
129 t[1] += ((uint128_t) r4) * s2 + ((uint128_t) r2) * s4 + ((uint128_t) r3) * s3;
130 t[2] += ((uint128_t) r4) * s3 + ((uint128_t) r3) * s4;
131 t[3] += ((uint128_t) r4) * s4;
133 r0 = (limb)t[0] & 0x7ffffffffffff; c = (limb)(t[0] >> 51);
134 t[1] += c; r1 = (limb)t[1] & 0x7ffffffffffff; c = (limb)(t[1] >> 51);
135 t[2] += c; r2 = (limb)t[2] & 0x7ffffffffffff; c = (limb)(t[2] >> 51);
136 t[3] += c; r3 = (limb)t[3] & 0x7ffffffffffff; c = (limb)(t[3] >> 51);
137 t[4] += c; r4 = (limb)t[4] & 0x7ffffffffffff; c = (limb)(t[4] >> 51);
138 r0 += c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffff;
139 r1 += c; c = r1 >> 51; r1 = r1 & 0x7ffffffffffff;
149 static inline void force_inline
150 fsquare_times(felem output,
const felem in, limb count) {
152 limb r0,r1,r2,r3,r4,c;
153 limb d0,d1,d2,d4,d419;
168 t[0] = ((uint128_t) r0) * r0 + ((uint128_t) d4) * r1 + (((uint128_t) d2) * (r3 ));
169 t[1] = ((uint128_t) d0) * r1 + ((uint128_t) d4) * r2 + (((uint128_t) r3) * (r3 * 19));
170 t[2] = ((uint128_t) d0) * r2 + ((uint128_t) r1) * r1 + (((uint128_t) d4) * (r3 ));
171 t[3] = ((uint128_t) d0) * r3 + ((uint128_t) d1) * r2 + (((uint128_t) r4) * (d419 ));
172 t[4] = ((uint128_t) d0) * r4 + ((uint128_t) d1) * r3 + (((uint128_t) r2) * (r2 ));
174 r0 = (limb)t[0] & 0x7ffffffffffff; c = (limb)(t[0] >> 51);
175 t[1] += c; r1 = (limb)t[1] & 0x7ffffffffffff; c = (limb)(t[1] >> 51);
176 t[2] += c; r2 = (limb)t[2] & 0x7ffffffffffff; c = (limb)(t[2] >> 51);
177 t[3] += c; r3 = (limb)t[3] & 0x7ffffffffffff; c = (limb)(t[3] >> 51);
178 t[4] += c; r4 = (limb)t[4] & 0x7ffffffffffff; c = (limb)(t[4] >> 51);
179 r0 += c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffff;
180 r1 += c; c = r1 >> 51; r1 = r1 & 0x7ffffffffffff;
193 load_limb(
const u8 *in) {
196 (((limb)in[1]) << 8) |
197 (((limb)in[2]) << 16) |
198 (((limb)in[3]) << 24) |
199 (((limb)in[4]) << 32) |
200 (((limb)in[5]) << 40) |
201 (((limb)in[6]) << 48) |
202 (((limb)in[7]) << 56);
206 store_limb(u8 *out, limb in) {
208 out[1] = (in >> 8) & 0xff;
209 out[2] = (in >> 16) & 0xff;
210 out[3] = (in >> 24) & 0xff;
211 out[4] = (in >> 32) & 0xff;
212 out[5] = (in >> 40) & 0xff;
213 out[6] = (in >> 48) & 0xff;
214 out[7] = (in >> 56) & 0xff;
219 fexpand(limb *output,
const u8 *in) {
220 output[0] = load_limb(in) & 0x7ffffffffffff;
221 output[1] = (load_limb(in+6) >> 3) & 0x7ffffffffffff;
222 output[2] = (load_limb(in+12) >> 6) & 0x7ffffffffffff;
223 output[3] = (load_limb(in+19) >> 1) & 0x7ffffffffffff;
224 output[4] = (load_limb(in+24) >> 12) & 0x7ffffffffffff;
231 fcontract(u8 *output,
const felem input) {
240 t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffff;
241 t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffff;
242 t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffff;
243 t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffff;
244 t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffff;
246 t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffff;
247 t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffff;
248 t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffff;
249 t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffff;
250 t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffff;
257 t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffff;
258 t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffff;
259 t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffff;
260 t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffff;
261 t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffff;
265 t[0] += 0x8000000000000 - 19;
266 t[1] += 0x8000000000000 - 1;
267 t[2] += 0x8000000000000 - 1;
268 t[3] += 0x8000000000000 - 1;
269 t[4] += 0x8000000000000 - 1;
273 t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffff;
274 t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffff;
275 t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffff;
276 t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffff;
277 t[4] &= 0x7ffffffffffff;
279 store_limb(output, t[0] | (t[1] << 51));
280 store_limb(output+8, (t[1] >> 13) | (t[2] << 38));
281 store_limb(output+16, (t[2] >> 26) | (t[3] << 25));
282 store_limb(output+24, (t[3] >> 39) | (t[4] << 12));
295 fmonty(limb *x2, limb *z2,
298 limb *xprime, limb *zprime,
300 limb origx[5], origxprime[5], zzz[5], xx[5], zz[5], xxprime[5],
301 zzprime[5], zzzprime[5];
303 memcpy(origx, x, 5 *
sizeof(limb));
305 fdifference_backwards(z, origx);
307 memcpy(origxprime, xprime,
sizeof(limb) * 5);
308 fsum(xprime, zprime);
309 fdifference_backwards(zprime, origxprime);
310 fmul(xxprime, xprime, z);
311 fmul(zzprime, x, zprime);
312 memcpy(origxprime, xxprime,
sizeof(limb) * 5);
313 fsum(xxprime, zzprime);
314 fdifference_backwards(zzprime, origxprime);
315 fsquare_times(x3, xxprime, 1);
316 fsquare_times(zzzprime, zzprime, 1);
317 fmul(z3, zzzprime, qmqp);
319 fsquare_times(xx, x, 1);
320 fsquare_times(zz, z, 1);
322 fdifference_backwards(zz, xx);
323 fscalar_product(zzz, zz, 121665);
336 swap_conditional(limb a[5], limb b[5], limb iswap) {
338 const limb swap = -iswap;
340 for (i = 0; i < 5; ++i) {
341 const limb x = swap & (a[i] ^ b[i]);
354 cmult(limb *resultx, limb *resultz,
const u8 *n,
const limb *q) {
355 limb a[5] = {0}, b[5] = {1}, c[5] = {1}, d[5] = {0};
356 limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t;
357 limb e[5] = {0}, f[5] = {1}, g[5] = {0}, h[5] = {1};
358 limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h;
362 memcpy(nqpqx, q,
sizeof(limb) * 5);
364 for (i = 0; i < 32; ++i) {
366 for (j = 0; j < 8; ++j) {
367 const limb bit =
byte >> 7;
369 swap_conditional(nqx, nqpqx, bit);
370 swap_conditional(nqz, nqpqz, bit);
376 swap_conditional(nqx2, nqpqx2, bit);
377 swap_conditional(nqz2, nqpqz2, bit);
396 memcpy(resultx, nqx,
sizeof(limb) * 5);
397 memcpy(resultz, nqz,
sizeof(limb) * 5);
405 crecip(felem out,
const felem z) {
408 fsquare_times(a, z, 1);
409 fsquare_times(t0, a, 2);
412 fsquare_times(t0, a, 1);
414 fsquare_times(t0, b, 5);
416 fsquare_times(t0, b, 10);
418 fsquare_times(t0, c, 20);
420 fsquare_times(t0, t0, 10);
422 fsquare_times(t0, b, 50);
424 fsquare_times(t0, c, 100);
426 fsquare_times(t0, t0, 50);
428 fsquare_times(t0, t0, 5);
432 int curve25519_donna(u8 *,
const u8 *,
const u8 *);
435 curve25519_donna(u8 *mypublic,
const u8 *secret,
const u8 *basepoint) {
436 limb bp[5], x[5], z[5], zmone[5];
440 for (i = 0;i < 32;++i) e[i] = secret[i];
445 fexpand(bp, basepoint);
449 fcontract(mypublic, z);
Integer definitions used throughout Tor.