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^(31k) for the smallest k such that R >= p)
31 */
32
33 static const uint32_t C255_P[] = {
34 0x00000107,
35 0x7FFFFFED, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF,
36 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x0000007F
37 };
38
39 #define P0I 0x286BCA1B
40
41 static const uint32_t C255_R2[] = {
42 0x00000107,
43 0x00000000, 0x02D20000, 0x00000000, 0x00000000, 0x00000000,
44 0x00000000, 0x00000000, 0x00000000, 0x00000000
45 };
46
47 static const uint32_t C255_A24[] = {
48 0x00000107,
49 0x53000000, 0x0000468B, 0x00000000, 0x00000000, 0x00000000,
50 0x00000000, 0x00000000, 0x00000000, 0x00000000
51 };
52
53 /* obsolete
54 #include <stdio.h>
55 #include <stdlib.h>
56 static void
57 print_int_mont(const char *name, const uint32_t *x)
58 {
59 uint32_t y[10];
60 unsigned char tmp[32];
61 size_t u;
62
63 printf("%s = ", name);
64 memcpy(y, x, sizeof y);
65 br_i31_from_monty(y, C255_P, P0I);
66 br_i31_encode(tmp, sizeof tmp, y);
67 for (u = 0; u < sizeof tmp; u ++) {
68 printf("%02X", tmp[u]);
69 }
70 printf("\n");
71 }
72 */
73
74 static const unsigned char GEN[] = {
75 0x09, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
76 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
77 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
78 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
79 };
80
81 static const unsigned char ORDER[] = {
82 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
83 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
84 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
85 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF
86 };
87
88 static const unsigned char *
api_generator(int curve,size_t * len)89 api_generator(int curve, size_t *len)
90 {
91 (void)curve;
92 *len = 32;
93 return GEN;
94 }
95
96 static const unsigned char *
api_order(int curve,size_t * len)97 api_order(int curve, size_t *len)
98 {
99 (void)curve;
100 *len = 32;
101 return ORDER;
102 }
103
104 static size_t
api_xoff(int curve,size_t * len)105 api_xoff(int curve, size_t *len)
106 {
107 (void)curve;
108 *len = 32;
109 return 0;
110 }
111
112 static void
cswap(uint32_t * a,uint32_t * b,uint32_t ctl)113 cswap(uint32_t *a, uint32_t *b, uint32_t ctl)
114 {
115 int i;
116
117 ctl = -ctl;
118 for (i = 0; i < 10; i ++) {
119 uint32_t aw, bw, tw;
120
121 aw = a[i];
122 bw = b[i];
123 tw = ctl & (aw ^ bw);
124 a[i] = aw ^ tw;
125 b[i] = bw ^ tw;
126 }
127 }
128
129 static void
c255_add(uint32_t * d,const uint32_t * a,const uint32_t * b)130 c255_add(uint32_t *d, const uint32_t *a, const uint32_t *b)
131 {
132 uint32_t ctl;
133 uint32_t t[10];
134
135 memcpy(t, a, sizeof t);
136 ctl = br_i31_add(t, b, 1);
137 ctl |= NOT(br_i31_sub(t, C255_P, 0));
138 br_i31_sub(t, C255_P, ctl);
139 memcpy(d, t, sizeof t);
140 }
141
142 static void
c255_sub(uint32_t * d,const uint32_t * a,const uint32_t * b)143 c255_sub(uint32_t *d, const uint32_t *a, const uint32_t *b)
144 {
145 uint32_t t[10];
146
147 memcpy(t, a, sizeof t);
148 br_i31_add(t, C255_P, br_i31_sub(t, b, 1));
149 memcpy(d, t, sizeof t);
150 }
151
152 static void
c255_mul(uint32_t * d,const uint32_t * a,const uint32_t * b)153 c255_mul(uint32_t *d, const uint32_t *a, const uint32_t *b)
154 {
155 uint32_t t[10];
156
157 br_i31_montymul(t, a, b, C255_P, P0I);
158 memcpy(d, t, sizeof t);
159 }
160
161 static void
byteswap(unsigned char * G)162 byteswap(unsigned char *G)
163 {
164 int i;
165
166 for (i = 0; i < 16; i ++) {
167 unsigned char t;
168
169 t = G[i];
170 G[i] = G[31 - i];
171 G[31 - i] = t;
172 }
173 }
174
175 static uint32_t
api_mul(unsigned char * G,size_t Glen,const unsigned char * kb,size_t kblen,int curve)176 api_mul(unsigned char *G, size_t Glen,
177 const unsigned char *kb, size_t kblen, int curve)
178 {
179 uint32_t x1[10], x2[10], x3[10], z2[10], z3[10];
180 uint32_t a[10], aa[10], b[10], bb[10];
181 uint32_t c[10], d[10], e[10], da[10], cb[10];
182 unsigned char k[32];
183 uint32_t swap;
184 int i;
185
186 (void)curve;
187
188 /*
189 * Points are encoded over exactly 32 bytes. Multipliers must fit
190 * in 32 bytes as well.
191 * RFC 7748 mandates that the high bit of the last point byte must
192 * be ignored/cleared.
193 */
194 if (Glen != 32 || kblen > 32) {
195 return 0;
196 }
197 G[31] &= 0x7F;
198
199 /*
200 * Byteswap the point encoding, because it uses little-endian, and
201 * the generic decoding routine uses big-endian.
202 */
203 byteswap(G);
204
205 /*
206 * Decode the point ('u' coordinate). This should be reduced
207 * modulo p, but we prefer to avoid the dependency on
208 * br_i31_decode_reduce(). Instead, we use br_i31_decode_mod()
209 * with a synthetic modulus of value 2^255 (this must work
210 * since G was truncated to 255 bits), then use a conditional
211 * subtraction. We use br_i31_decode_mod() and not
212 * br_i31_decode(), because the ec_prime_i31 implementation uses
213 * the former but not the latter.
214 * br_i31_decode_reduce(a, G, 32, C255_P);
215 */
216 br_i31_zero(b, 0x108);
217 b[9] = 0x0080;
218 br_i31_decode_mod(a, G, 32, b);
219 a[0] = 0x107;
220 br_i31_sub(a, C255_P, NOT(br_i31_sub(a, C255_P, 0)));
221
222 /*
223 * Initialise variables x1, x2, z2, x3 and z3. We set all of them
224 * into Montgomery representation.
225 */
226 br_i31_montymul(x1, a, C255_R2, C255_P, P0I);
227 memcpy(x3, x1, sizeof x1);
228 br_i31_zero(z2, C255_P[0]);
229 memcpy(x2, z2, sizeof z2);
230 x2[1] = 0x13000000;
231 memcpy(z3, x2, sizeof x2);
232
233 /*
234 * kb[] is in big-endian notation, but possibly shorter than k[].
235 */
236 memset(k, 0, (sizeof k) - kblen);
237 memcpy(k + (sizeof k) - kblen, kb, kblen);
238 k[31] &= 0xF8;
239 k[0] &= 0x7F;
240 k[0] |= 0x40;
241
242 /* obsolete
243 print_int_mont("x1", x1);
244 */
245
246 swap = 0;
247 for (i = 254; i >= 0; i --) {
248 uint32_t kt;
249
250 kt = (k[31 - (i >> 3)] >> (i & 7)) & 1;
251 swap ^= kt;
252 cswap(x2, x3, swap);
253 cswap(z2, z3, swap);
254 swap = kt;
255
256 /* obsolete
257 print_int_mont("x2", x2);
258 print_int_mont("z2", z2);
259 print_int_mont("x3", x3);
260 print_int_mont("z3", z3);
261 */
262
263 c255_add(a, x2, z2);
264 c255_mul(aa, a, a);
265 c255_sub(b, x2, z2);
266 c255_mul(bb, b, b);
267 c255_sub(e, aa, bb);
268 c255_add(c, x3, z3);
269 c255_sub(d, x3, z3);
270 c255_mul(da, d, a);
271 c255_mul(cb, c, b);
272
273 /* obsolete
274 print_int_mont("a ", a);
275 print_int_mont("aa", aa);
276 print_int_mont("b ", b);
277 print_int_mont("bb", bb);
278 print_int_mont("e ", e);
279 print_int_mont("c ", c);
280 print_int_mont("d ", d);
281 print_int_mont("da", da);
282 print_int_mont("cb", cb);
283 */
284
285 c255_add(x3, da, cb);
286 c255_mul(x3, x3, x3);
287 c255_sub(z3, da, cb);
288 c255_mul(z3, z3, z3);
289 c255_mul(z3, z3, x1);
290 c255_mul(x2, aa, bb);
291 c255_mul(z2, C255_A24, e);
292 c255_add(z2, z2, aa);
293 c255_mul(z2, e, z2);
294
295 /* obsolete
296 print_int_mont("x2", x2);
297 print_int_mont("z2", z2);
298 print_int_mont("x3", x3);
299 print_int_mont("z3", z3);
300 */
301 }
302 cswap(x2, x3, swap);
303 cswap(z2, z3, swap);
304
305 /*
306 * Inverse z2 with a modular exponentiation. This is a simple
307 * square-and-multiply algorithm; we mutualise most non-squarings
308 * since the exponent contains almost only ones.
309 */
310 memcpy(a, z2, sizeof z2);
311 for (i = 0; i < 15; i ++) {
312 c255_mul(a, a, a);
313 c255_mul(a, a, z2);
314 }
315 memcpy(b, a, sizeof a);
316 for (i = 0; i < 14; i ++) {
317 int j;
318
319 for (j = 0; j < 16; j ++) {
320 c255_mul(b, b, b);
321 }
322 c255_mul(b, b, a);
323 }
324 for (i = 14; i >= 0; i --) {
325 c255_mul(b, b, b);
326 if ((0xFFEB >> i) & 1) {
327 c255_mul(b, z2, b);
328 }
329 }
330 c255_mul(b, x2, b);
331
332 /*
333 * To avoid a dependency on br_i31_from_monty(), we use
334 * a Montgomery multiplication with 1.
335 * memcpy(x2, b, sizeof b);
336 * br_i31_from_monty(x2, C255_P, P0I);
337 */
338 br_i31_zero(a, C255_P[0]);
339 a[1] = 1;
340 br_i31_montymul(x2, a, b, C255_P, P0I);
341
342 br_i31_encode(G, 32, x2);
343 byteswap(G);
344 return 1;
345 }
346
347 static size_t
api_mulgen(unsigned char * R,const unsigned char * x,size_t xlen,int curve)348 api_mulgen(unsigned char *R,
349 const unsigned char *x, size_t xlen, int curve)
350 {
351 const unsigned char *G;
352 size_t Glen;
353
354 G = api_generator(curve, &Glen);
355 memcpy(R, G, Glen);
356 api_mul(R, Glen, x, xlen, curve);
357 return Glen;
358 }
359
360 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)361 api_muladd(unsigned char *A, const unsigned char *B, size_t len,
362 const unsigned char *x, size_t xlen,
363 const unsigned char *y, size_t ylen, int curve)
364 {
365 /*
366 * We don't implement this method, since it is used for ECDSA
367 * only, and there is no ECDSA over Curve25519 (which instead
368 * uses EdDSA).
369 */
370 (void)A;
371 (void)B;
372 (void)len;
373 (void)x;
374 (void)xlen;
375 (void)y;
376 (void)ylen;
377 (void)curve;
378 return 0;
379 }
380
381 /* see bearssl_ec.h */
382 const br_ec_impl br_ec_c25519_i31 = {
383 (uint32_t)0x20000000,
384 &api_generator,
385 &api_order,
386 &api_xoff,
387 &api_mul,
388 &api_mulgen,
389 &api_muladd
390 };
391