1 /*
2 conversions
3 */
4
5 DONNA_INLINE static void
ge25519_p1p1_to_partial(ge25519 * r,const ge25519_p1p1 * p)6 ge25519_p1p1_to_partial(ge25519 *r, const ge25519_p1p1 *p) {
7 curve25519_mul(r->x, p->x, p->t);
8 curve25519_mul(r->y, p->y, p->z);
9 curve25519_mul(r->z, p->z, p->t);
10 }
11
12 DONNA_INLINE static void
ge25519_p1p1_to_full(ge25519 * r,const ge25519_p1p1 * p)13 ge25519_p1p1_to_full(ge25519 *r, const ge25519_p1p1 *p) {
14 curve25519_mul(r->x, p->x, p->t);
15 curve25519_mul(r->y, p->y, p->z);
16 curve25519_mul(r->z, p->z, p->t);
17 curve25519_mul(r->t, p->x, p->y);
18 }
19
20 static void
ge25519_full_to_pniels(ge25519_pniels * p,const ge25519 * r)21 ge25519_full_to_pniels(ge25519_pniels *p, const ge25519 *r) {
22 curve25519_sub(p->ysubx, r->y, r->x);
23 curve25519_add(p->xaddy, r->y, r->x);
24 curve25519_copy(p->z, r->z);
25 curve25519_mul(p->t2d, r->t, ge25519_ec2d);
26 }
27
28 /*
29 adding & doubling
30 */
31
32 static void
ge25519_add_p1p1(ge25519_p1p1 * r,const ge25519 * p,const ge25519 * q)33 ge25519_add_p1p1(ge25519_p1p1 *r, const ge25519 *p, const ge25519 *q) {
34 bignum25519 a,b,c,d,t,u;
35
36 curve25519_sub(a, p->y, p->x);
37 curve25519_add(b, p->y, p->x);
38 curve25519_sub(t, q->y, q->x);
39 curve25519_add(u, q->y, q->x);
40 curve25519_mul(a, a, t);
41 curve25519_mul(b, b, u);
42 curve25519_mul(c, p->t, q->t);
43 curve25519_mul(c, c, ge25519_ec2d);
44 curve25519_mul(d, p->z, q->z);
45 curve25519_add(d, d, d);
46 curve25519_sub(r->x, b, a);
47 curve25519_add(r->y, b, a);
48 curve25519_add_after_basic(r->z, d, c);
49 curve25519_sub_after_basic(r->t, d, c);
50 }
51
52
53 static void
ge25519_double_p1p1(ge25519_p1p1 * r,const ge25519 * p)54 ge25519_double_p1p1(ge25519_p1p1 *r, const ge25519 *p) {
55 bignum25519 a,b,c;
56
57 curve25519_square(a, p->x);
58 curve25519_square(b, p->y);
59 curve25519_square(c, p->z);
60 curve25519_add_reduce(c, c, c);
61 curve25519_add(r->x, p->x, p->y);
62 curve25519_square(r->x, r->x);
63 curve25519_add(r->y, b, a);
64 curve25519_sub(r->z, b, a);
65 curve25519_sub_after_basic(r->x, r->x, r->y);
66 curve25519_sub_after_basic(r->t, c, r->z);
67 }
68
69 static void
ge25519_nielsadd2_p1p1(ge25519_p1p1 * r,const ge25519 * p,const ge25519_niels * q,unsigned char signbit)70 ge25519_nielsadd2_p1p1(ge25519_p1p1 *r, const ge25519 *p, const ge25519_niels *q, unsigned char signbit) {
71 const bignum25519 *qb = (const bignum25519 *)q;
72 bignum25519 *rb = (bignum25519 *)r;
73 bignum25519 a,b,c;
74
75 curve25519_sub(a, p->y, p->x);
76 curve25519_add(b, p->y, p->x);
77 curve25519_mul(a, a, qb[signbit]); /* x for +, y for - */
78 curve25519_mul(r->x, b, qb[signbit^1]); /* y for +, x for - */
79 curve25519_add(r->y, r->x, a);
80 curve25519_sub(r->x, r->x, a);
81 curve25519_mul(c, p->t, q->t2d);
82 curve25519_add_reduce(r->t, p->z, p->z);
83 curve25519_copy(r->z, r->t);
84 curve25519_add(rb[2+signbit], rb[2+signbit], c); /* z for +, t for - */
85 curve25519_sub(rb[2+(signbit^1)], rb[2+(signbit^1)], c); /* t for +, z for - */
86 }
87
88 static void
ge25519_pnielsadd_p1p1(ge25519_p1p1 * r,const ge25519 * p,const ge25519_pniels * q,unsigned char signbit)89 ge25519_pnielsadd_p1p1(ge25519_p1p1 *r, const ge25519 *p, const ge25519_pniels *q, unsigned char signbit) {
90 const bignum25519 *qb = (const bignum25519 *)q;
91 bignum25519 *rb = (bignum25519 *)r;
92 bignum25519 a,b,c;
93
94 curve25519_sub(a, p->y, p->x);
95 curve25519_add(b, p->y, p->x);
96 curve25519_mul(a, a, qb[signbit]); /* ysubx for +, xaddy for - */
97 curve25519_mul(r->x, b, qb[signbit^1]); /* xaddy for +, ysubx for - */
98 curve25519_add(r->y, r->x, a);
99 curve25519_sub(r->x, r->x, a);
100 curve25519_mul(c, p->t, q->t2d);
101 curve25519_mul(r->t, p->z, q->z);
102 curve25519_add_reduce(r->t, r->t, r->t);
103 curve25519_copy(r->z, r->t);
104 curve25519_add(rb[2+signbit], rb[2+signbit], c); /* z for +, t for - */
105 curve25519_sub(rb[2+(signbit^1)], rb[2+(signbit^1)], c); /* t for +, z for - */
106 }
107
108 static void
ge25519_double_partial(ge25519 * r,const ge25519 * p)109 ge25519_double_partial(ge25519 *r, const ge25519 *p) {
110 ge25519_p1p1 t;
111 ge25519_double_p1p1(&t, p);
112 ge25519_p1p1_to_partial(r, &t);
113 }
114
115 static void
ge25519_double(ge25519 * r,const ge25519 * p)116 ge25519_double(ge25519 *r, const ge25519 *p) {
117 ge25519_p1p1 t;
118 ge25519_double_p1p1(&t, p);
119 ge25519_p1p1_to_full(r, &t);
120 }
121
122 static void
ge25519_add(ge25519 * r,const ge25519 * p,const ge25519 * q)123 ge25519_add(ge25519 *r, const ge25519 *p, const ge25519 *q) {
124 ge25519_p1p1 t;
125 ge25519_add_p1p1(&t, p, q);
126 ge25519_p1p1_to_full(r, &t);
127 }
128
129 static void
ge25519_nielsadd2(ge25519 * r,const ge25519_niels * q)130 ge25519_nielsadd2(ge25519 *r, const ge25519_niels *q) {
131 bignum25519 a,b,c,e,f,g,h;
132
133 curve25519_sub(a, r->y, r->x);
134 curve25519_add(b, r->y, r->x);
135 curve25519_mul(a, a, q->ysubx);
136 curve25519_mul(e, b, q->xaddy);
137 curve25519_add(h, e, a);
138 curve25519_sub(e, e, a);
139 curve25519_mul(c, r->t, q->t2d);
140 curve25519_add(f, r->z, r->z);
141 curve25519_add_after_basic(g, f, c);
142 curve25519_sub_after_basic(f, f, c);
143 curve25519_mul(r->x, e, f);
144 curve25519_mul(r->y, h, g);
145 curve25519_mul(r->z, g, f);
146 curve25519_mul(r->t, e, h);
147 }
148
149 static void
ge25519_pnielsadd(ge25519_pniels * r,const ge25519 * p,const ge25519_pniels * q)150 ge25519_pnielsadd(ge25519_pniels *r, const ge25519 *p, const ge25519_pniels *q) {
151 bignum25519 a,b,c,x,y,z,t;
152
153 curve25519_sub(a, p->y, p->x);
154 curve25519_add(b, p->y, p->x);
155 curve25519_mul(a, a, q->ysubx);
156 curve25519_mul(x, b, q->xaddy);
157 curve25519_add(y, x, a);
158 curve25519_sub(x, x, a);
159 curve25519_mul(c, p->t, q->t2d);
160 curve25519_mul(t, p->z, q->z);
161 curve25519_add(t, t, t);
162 curve25519_add_after_basic(z, t, c);
163 curve25519_sub_after_basic(t, t, c);
164 curve25519_mul(r->xaddy, x, t);
165 curve25519_mul(r->ysubx, y, z);
166 curve25519_mul(r->z, z, t);
167 curve25519_mul(r->t2d, x, y);
168 curve25519_copy(y, r->ysubx);
169 curve25519_sub(r->ysubx, r->ysubx, r->xaddy);
170 curve25519_add(r->xaddy, r->xaddy, y);
171 curve25519_mul(r->t2d, r->t2d, ge25519_ec2d);
172 }
173
174
175 /*
176 pack & unpack
177 */
178
179 static void
ge25519_pack(unsigned char r[32],const ge25519 * p)180 ge25519_pack(unsigned char r[32], const ge25519 *p) {
181 bignum25519 tx, ty, zi;
182 unsigned char parity[32];
183 curve25519_recip(zi, p->z);
184 curve25519_mul(tx, p->x, zi);
185 curve25519_mul(ty, p->y, zi);
186 curve25519_contract(r, ty);
187 curve25519_contract(parity, tx);
188 r[31] ^= ((parity[0] & 1) << 7);
189 }
190
191 static int
ge25519_unpack_negative_vartime(ge25519 * r,const unsigned char p[32])192 ge25519_unpack_negative_vartime(ge25519 *r, const unsigned char p[32]) {
193 static const unsigned char zero[32] = {0};
194 static const bignum25519 one = {1};
195 unsigned char parity = p[31] >> 7;
196 unsigned char check[32];
197 bignum25519 t, root, num, den, d3;
198
199 curve25519_expand(r->y, p);
200 curve25519_copy(r->z, one);
201 curve25519_square(num, r->y); /* x = y^2 */
202 curve25519_mul(den, num, ge25519_ecd); /* den = dy^2 */
203 curve25519_sub_reduce(num, num, r->z); /* x = y^1 - 1 */
204 curve25519_add(den, den, r->z); /* den = dy^2 + 1 */
205
206 /* Computation of sqrt(num/den) */
207 /* 1.: computation of num^((p-5)/8)*den^((7p-35)/8) = (num*den^7)^((p-5)/8) */
208 curve25519_square(t, den);
209 curve25519_mul(d3, t, den);
210 curve25519_square(r->x, d3);
211 curve25519_mul(r->x, r->x, den);
212 curve25519_mul(r->x, r->x, num);
213 curve25519_pow_two252m3(r->x, r->x);
214
215 /* 2. computation of r->x = num * den^3 * (num*den^7)^((p-5)/8) */
216 curve25519_mul(r->x, r->x, d3);
217 curve25519_mul(r->x, r->x, num);
218
219 /* 3. Check if either of the roots works: */
220 curve25519_square(t, r->x);
221 curve25519_mul(t, t, den);
222 curve25519_sub_reduce(root, t, num);
223 curve25519_contract(check, root);
224 if (!ed25519_verify(check, zero, 32)) {
225 curve25519_add_reduce(t, t, num);
226 curve25519_contract(check, t);
227 if (!ed25519_verify(check, zero, 32))
228 return 0;
229 curve25519_mul(r->x, r->x, ge25519_sqrtneg1);
230 }
231
232 curve25519_contract(check, r->x);
233 if ((check[0] & 1) == parity) {
234 curve25519_copy(t, r->x);
235 curve25519_neg(r->x, t);
236 }
237 curve25519_mul(r->t, r->x, r->y);
238 return 1;
239 }
240
241
242 /*
243 scalarmults
244 */
245
246 #define S1_SWINDOWSIZE 5
247 #define S1_TABLE_SIZE (1<<(S1_SWINDOWSIZE-2))
248 #define S2_SWINDOWSIZE 7
249 #define S2_TABLE_SIZE (1<<(S2_SWINDOWSIZE-2))
250
251 /* computes [s1]p1 + [s2]basepoint */
252 static void
ge25519_double_scalarmult_vartime(ge25519 * r,const ge25519 * p1,const bignum256modm s1,const bignum256modm s2)253 ge25519_double_scalarmult_vartime(ge25519 *r, const ge25519 *p1, const bignum256modm s1, const bignum256modm s2) {
254 signed char slide1[256], slide2[256];
255 ge25519_pniels pre1[S1_TABLE_SIZE];
256 ge25519 d1;
257 ge25519_p1p1 t;
258 int32_t i;
259
260 contract256_slidingwindow_modm(slide1, s1, S1_SWINDOWSIZE);
261 contract256_slidingwindow_modm(slide2, s2, S2_SWINDOWSIZE);
262
263 ge25519_double(&d1, p1);
264 ge25519_full_to_pniels(pre1, p1);
265 for (i = 0; i < S1_TABLE_SIZE - 1; i++)
266 ge25519_pnielsadd(&pre1[i+1], &d1, &pre1[i]);
267
268 /* set neutral */
269 memset(r, 0, sizeof(ge25519));
270 r->y[0] = 1;
271 r->z[0] = 1;
272
273 i = 255;
274 while ((i >= 0) && !(slide1[i] | slide2[i]))
275 i--;
276
277 for (; i >= 0; i--) {
278 ge25519_double_p1p1(&t, r);
279
280 if (slide1[i]) {
281 ge25519_p1p1_to_full(r, &t);
282 ge25519_pnielsadd_p1p1(&t, r, &pre1[abs(slide1[i]) / 2], (unsigned char)slide1[i] >> 7);
283 }
284
285 if (slide2[i]) {
286 ge25519_p1p1_to_full(r, &t);
287 ge25519_nielsadd2_p1p1(&t, r, &ge25519_niels_sliding_multiples[abs(slide2[i]) / 2], (unsigned char)slide2[i] >> 7);
288 }
289
290 // diverges from the original source code and resolves bug explained
291 // in <https://github.com/floodyberry/ed25519-donna/issues/31>
292 if (i == 0) {
293 ge25519_p1p1_to_full(r, &t);
294 } else {
295 ge25519_p1p1_to_partial(r, &t);
296 }
297 }
298 }
299
300
301
302 #if !defined(HAVE_GE25519_SCALARMULT_BASE_CHOOSE_NIELS)
303
304 static uint32_t
ge25519_windowb_equal(uint32_t b,uint32_t c)305 ge25519_windowb_equal(uint32_t b, uint32_t c) {
306 return ((b ^ c) - 1) >> 31;
307 }
308
309 static void
ge25519_scalarmult_base_choose_niels(ge25519_niels * t,const uint8_t table[256][96],uint32_t pos,signed char b)310 ge25519_scalarmult_base_choose_niels(ge25519_niels *t, const uint8_t table[256][96], uint32_t pos, signed char b) {
311 bignum25519 neg;
312 uint32_t sign = (uint32_t)((unsigned char)b >> 7);
313 uint32_t mask = ~(sign - 1);
314 uint32_t u = (b + mask) ^ mask;
315 uint32_t i;
316
317 /* ysubx, xaddy, t2d in packed form. initialize to ysubx = 1, xaddy = 1, t2d = 0 */
318 uint8_t packed[96] = {0};
319 packed[0] = 1;
320 packed[32] = 1;
321
322 for (i = 0; i < 8; i++)
323 curve25519_move_conditional_bytes(packed, table[(pos * 8) + i], ge25519_windowb_equal(u, i + 1));
324
325 /* expand in to t */
326 curve25519_expand(t->ysubx, packed + 0);
327 curve25519_expand(t->xaddy, packed + 32);
328 curve25519_expand(t->t2d , packed + 64);
329
330 /* adjust for sign */
331 curve25519_swap_conditional(t->ysubx, t->xaddy, sign);
332 curve25519_neg(neg, t->t2d);
333 curve25519_swap_conditional(t->t2d, neg, sign);
334 }
335
336 #endif /* HAVE_GE25519_SCALARMULT_BASE_CHOOSE_NIELS */
337
338
339 /* computes [s]basepoint */
340 static void
ge25519_scalarmult_base_niels(ge25519 * r,const uint8_t basepoint_table[256][96],const bignum256modm s)341 ge25519_scalarmult_base_niels(ge25519 *r, const uint8_t basepoint_table[256][96], const bignum256modm s) {
342 signed char b[64];
343 uint32_t i;
344 ge25519_niels t;
345
346 contract256_window4_modm(b, s);
347
348 ge25519_scalarmult_base_choose_niels(&t, basepoint_table, 0, b[1]);
349 curve25519_sub_reduce(r->x, t.xaddy, t.ysubx);
350 curve25519_add_reduce(r->y, t.xaddy, t.ysubx);
351 memset(r->z, 0, sizeof(bignum25519));
352 curve25519_copy(r->t, t.t2d);
353 r->z[0] = 2;
354 for (i = 3; i < 64; i += 2) {
355 ge25519_scalarmult_base_choose_niels(&t, basepoint_table, i / 2, b[i]);
356 ge25519_nielsadd2(r, &t);
357 }
358 ge25519_double_partial(r, r);
359 ge25519_double_partial(r, r);
360 ge25519_double_partial(r, r);
361 ge25519_double(r, r);
362 ge25519_scalarmult_base_choose_niels(&t, basepoint_table, 0, b[0]);
363 curve25519_mul(t.t2d, t.t2d, ge25519_ecd);
364 ge25519_nielsadd2(r, &t);
365 for(i = 2; i < 64; i += 2) {
366 ge25519_scalarmult_base_choose_niels(&t, basepoint_table, i / 2, b[i]);
367 ge25519_nielsadd2(r, &t);
368 }
369 }
370
371