1 /*
2 * Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
3 *
4 * Permission is hereby granted, free of charge, to any person obtaining
5 * a copy of this software and associated documentation files (the
6 * "Software"), to deal in the Software without restriction, including
7 * without limitation the rights to use, copy, modify, merge, publish,
8 * distribute, sublicense, and/or sell copies of the Software, and to
9 * permit persons to whom the Software is furnished to do so, subject to
10 * the following conditions:
11 *
12 * The above copyright notice and this permission notice shall be
13 * included in all copies or substantial portions of the Software.
14 *
15 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
16 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
17 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
18 * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
19 * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
20 * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
21 * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
22 * SOFTWARE.
23 */
24
25 #include "inner.h"
26
27 /*
28 * Parameters for the field:
29 * - field modulus p = 2^255-19
30 * - R^2 mod p (R = 2^(15k) for the smallest k such that R >= p)
31 */
32
33 static const uint16_t C255_P[] = {
34 0x0110,
35 0x7FED, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF,
36 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF,
37 0x7FFF
38 };
39
40 #define P0I 0x4A1B
41
42 static const uint16_t C255_R2[] = {
43 0x0110,
44 0x0169, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
45 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
46 0x0000
47 };
48
49 /* obsolete
50 #include <stdio.h>
51 #include <stdlib.h>
52 static void
53 print_int_mont(const char *name, const uint16_t *x)
54 {
55 uint16_t y[18];
56 unsigned char tmp[32];
57 size_t u;
58
59 printf("%s = ", name);
60 memcpy(y, x, sizeof y);
61 br_i15_from_monty(y, C255_P, P0I);
62 br_i15_encode(tmp, sizeof tmp, y);
63 for (u = 0; u < sizeof tmp; u ++) {
64 printf("%02X", tmp[u]);
65 }
66 printf("\n");
67 }
68 */
69
70 static const uint16_t C255_A24[] = {
71 0x0110,
72 0x45D3, 0x0046, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
73 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
74 0x0000
75 };
76
77 static const unsigned char GEN[] = {
78 0x09, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
79 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
80 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
81 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
82 };
83
84 static const unsigned char ORDER[] = {
85 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
86 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
87 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
88 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF
89 };
90
91 static const unsigned char *
api_generator(int curve,size_t * len)92 api_generator(int curve, size_t *len)
93 {
94 (void)curve;
95 *len = 32;
96 return GEN;
97 }
98
99 static const unsigned char *
api_order(int curve,size_t * len)100 api_order(int curve, size_t *len)
101 {
102 (void)curve;
103 *len = 32;
104 return ORDER;
105 }
106
107 static size_t
api_xoff(int curve,size_t * len)108 api_xoff(int curve, size_t *len)
109 {
110 (void)curve;
111 *len = 32;
112 return 0;
113 }
114
115 static void
cswap(uint16_t * a,uint16_t * b,uint32_t ctl)116 cswap(uint16_t *a, uint16_t *b, uint32_t ctl)
117 {
118 int i;
119
120 ctl = -ctl;
121 for (i = 0; i < 18; i ++) {
122 uint32_t aw, bw, tw;
123
124 aw = a[i];
125 bw = b[i];
126 tw = ctl & (aw ^ bw);
127 a[i] = aw ^ tw;
128 b[i] = bw ^ tw;
129 }
130 }
131
132 static void
c255_add(uint16_t * d,const uint16_t * a,const uint16_t * b)133 c255_add(uint16_t *d, const uint16_t *a, const uint16_t *b)
134 {
135 uint32_t ctl;
136 uint16_t t[18];
137
138 memcpy(t, a, sizeof t);
139 ctl = br_i15_add(t, b, 1);
140 ctl |= NOT(br_i15_sub(t, C255_P, 0));
141 br_i15_sub(t, C255_P, ctl);
142 memcpy(d, t, sizeof t);
143 }
144
145 static void
c255_sub(uint16_t * d,const uint16_t * a,const uint16_t * b)146 c255_sub(uint16_t *d, const uint16_t *a, const uint16_t *b)
147 {
148 uint16_t t[18];
149
150 memcpy(t, a, sizeof t);
151 br_i15_add(t, C255_P, br_i15_sub(t, b, 1));
152 memcpy(d, t, sizeof t);
153 }
154
155 static void
c255_mul(uint16_t * d,const uint16_t * a,const uint16_t * b)156 c255_mul(uint16_t *d, const uint16_t *a, const uint16_t *b)
157 {
158 uint16_t t[18];
159
160 br_i15_montymul(t, a, b, C255_P, P0I);
161 memcpy(d, t, sizeof t);
162 }
163
164 static void
byteswap(unsigned char * G)165 byteswap(unsigned char *G)
166 {
167 int i;
168
169 for (i = 0; i < 16; i ++) {
170 unsigned char t;
171
172 t = G[i];
173 G[i] = G[31 - i];
174 G[31 - i] = t;
175 }
176 }
177
178 static uint32_t
api_mul(unsigned char * G,size_t Glen,const unsigned char * kb,size_t kblen,int curve)179 api_mul(unsigned char *G, size_t Glen,
180 const unsigned char *kb, size_t kblen, int curve)
181 {
182 #define ILEN (18 * sizeof(uint16_t))
183
184 /*
185 * The a[] and b[] arrays have an extra word to allow for
186 * decoding without using br_i15_decode_reduce().
187 */
188 uint16_t x1[18], x2[18], x3[18], z2[18], z3[18];
189 uint16_t a[19], aa[18], b[19], bb[18];
190 uint16_t c[18], d[18], e[18], da[18], cb[18];
191 unsigned char k[32];
192 uint32_t swap;
193 int i;
194
195 (void)curve;
196
197 /*
198 * Points are encoded over exactly 32 bytes. Multipliers must fit
199 * in 32 bytes as well.
200 * RFC 7748 mandates that the high bit of the last point byte must
201 * be ignored/cleared.
202 */
203 if (Glen != 32 || kblen > 32) {
204 return 0;
205 }
206 G[31] &= 0x7F;
207
208 /*
209 * Byteswap the point encoding, because it uses little-endian, and
210 * the generic decoding routine uses big-endian.
211 */
212 byteswap(G);
213
214 /*
215 * Decode the point ('u' coordinate). This should be reduced
216 * modulo p, but we prefer to avoid the dependency on
217 * br_i15_decode_reduce(). Instead, we use br_i15_decode_mod()
218 * with a synthetic modulus of value 2^255 (this must work
219 * since G was truncated to 255 bits), then use a conditional
220 * subtraction. We use br_i15_decode_mod() and not
221 * br_i15_decode(), because the ec_prime_i15 implementation uses
222 * the former but not the latter.
223 * br_i15_decode_reduce(a, G, 32, C255_P);
224 */
225 br_i15_zero(b, 0x111);
226 b[18] = 1;
227 br_i15_decode_mod(a, G, 32, b);
228 a[0] = 0x110;
229 br_i15_sub(a, C255_P, NOT(br_i15_sub(a, C255_P, 0)));
230
231 /*
232 * Initialise variables x1, x2, z2, x3 and z3. We set all of them
233 * into Montgomery representation.
234 */
235 br_i15_montymul(x1, a, C255_R2, C255_P, P0I);
236 memcpy(x3, x1, ILEN);
237 br_i15_zero(z2, C255_P[0]);
238 memcpy(x2, z2, ILEN);
239 x2[1] = 19;
240 memcpy(z3, x2, ILEN);
241
242 memset(k, 0, (sizeof k) - kblen);
243 memcpy(k + (sizeof k) - kblen, kb, kblen);
244 k[31] &= 0xF8;
245 k[0] &= 0x7F;
246 k[0] |= 0x40;
247
248 /* obsolete
249 print_int_mont("x1", x1);
250 */
251
252 swap = 0;
253 for (i = 254; i >= 0; i --) {
254 uint32_t kt;
255
256 kt = (k[31 - (i >> 3)] >> (i & 7)) & 1;
257 swap ^= kt;
258 cswap(x2, x3, swap);
259 cswap(z2, z3, swap);
260 swap = kt;
261
262 /* obsolete
263 print_int_mont("x2", x2);
264 print_int_mont("z2", z2);
265 print_int_mont("x3", x3);
266 print_int_mont("z3", z3);
267 */
268
269 c255_add(a, x2, z2);
270 c255_mul(aa, a, a);
271 c255_sub(b, x2, z2);
272 c255_mul(bb, b, b);
273 c255_sub(e, aa, bb);
274 c255_add(c, x3, z3);
275 c255_sub(d, x3, z3);
276 c255_mul(da, d, a);
277 c255_mul(cb, c, b);
278
279 /* obsolete
280 print_int_mont("a ", a);
281 print_int_mont("aa", aa);
282 print_int_mont("b ", b);
283 print_int_mont("bb", bb);
284 print_int_mont("e ", e);
285 print_int_mont("c ", c);
286 print_int_mont("d ", d);
287 print_int_mont("da", da);
288 print_int_mont("cb", cb);
289 */
290
291 c255_add(x3, da, cb);
292 c255_mul(x3, x3, x3);
293 c255_sub(z3, da, cb);
294 c255_mul(z3, z3, z3);
295 c255_mul(z3, z3, x1);
296 c255_mul(x2, aa, bb);
297 c255_mul(z2, C255_A24, e);
298 c255_add(z2, z2, aa);
299 c255_mul(z2, e, z2);
300
301 /* obsolete
302 print_int_mont("x2", x2);
303 print_int_mont("z2", z2);
304 print_int_mont("x3", x3);
305 print_int_mont("z3", z3);
306 */
307 }
308 cswap(x2, x3, swap);
309 cswap(z2, z3, swap);
310
311 /*
312 * Inverse z2 with a modular exponentiation. This is a simple
313 * square-and-multiply algorithm; we mutualise most non-squarings
314 * since the exponent contains almost only ones.
315 */
316 memcpy(a, z2, ILEN);
317 for (i = 0; i < 15; i ++) {
318 c255_mul(a, a, a);
319 c255_mul(a, a, z2);
320 }
321 memcpy(b, a, ILEN);
322 for (i = 0; i < 14; i ++) {
323 int j;
324
325 for (j = 0; j < 16; j ++) {
326 c255_mul(b, b, b);
327 }
328 c255_mul(b, b, a);
329 }
330 for (i = 14; i >= 0; i --) {
331 c255_mul(b, b, b);
332 if ((0xFFEB >> i) & 1) {
333 c255_mul(b, z2, b);
334 }
335 }
336 c255_mul(b, x2, b);
337
338 /*
339 * To avoid a dependency on br_i15_from_monty(), we use a
340 * Montgomery multiplication with 1.
341 * memcpy(x2, b, ILEN);
342 * br_i15_from_monty(x2, C255_P, P0I);
343 */
344 br_i15_zero(a, C255_P[0]);
345 a[1] = 1;
346 br_i15_montymul(x2, a, b, C255_P, P0I);
347
348 br_i15_encode(G, 32, x2);
349 byteswap(G);
350 return 1;
351
352 #undef ILEN
353 }
354
355 static size_t
api_mulgen(unsigned char * R,const unsigned char * x,size_t xlen,int curve)356 api_mulgen(unsigned char *R,
357 const unsigned char *x, size_t xlen, int curve)
358 {
359 const unsigned char *G;
360 size_t Glen;
361
362 G = api_generator(curve, &Glen);
363 memcpy(R, G, Glen);
364 api_mul(R, Glen, x, xlen, curve);
365 return Glen;
366 }
367
368 static uint32_t
api_muladd(unsigned char * A,const unsigned char * B,size_t len,const unsigned char * x,size_t xlen,const unsigned char * y,size_t ylen,int curve)369 api_muladd(unsigned char *A, const unsigned char *B, size_t len,
370 const unsigned char *x, size_t xlen,
371 const unsigned char *y, size_t ylen, int curve)
372 {
373 /*
374 * We don't implement this method, since it is used for ECDSA
375 * only, and there is no ECDSA over Curve25519 (which instead
376 * uses EdDSA).
377 */
378 (void)A;
379 (void)B;
380 (void)len;
381 (void)x;
382 (void)xlen;
383 (void)y;
384 (void)ylen;
385 (void)curve;
386 return 0;
387 }
388
389 /* see bearssl_ec.h */
390 const br_ec_impl br_ec_c25519_i15 = {
391 (uint32_t)0x20000000,
392 &api_generator,
393 &api_order,
394 &api_xoff,
395 &api_mul,
396 &api_mulgen,
397 &api_muladd
398 };
399