1 /*
2 * Copyright 2017-2022 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright 2015-2016 Cryptography Research, Inc.
4 *
5 * Licensed under the Apache License 2.0 (the "License"). You may not use
6 * this file except in compliance with the License. You can obtain a copy
7 * in the file LICENSE in the source distribution or at
8 * https://www.openssl.org/source/license.html
9 *
10 * Originally written by Mike Hamburg
11 */
12 #include <openssl/crypto.h>
13 #include "word.h"
14 #include "field.h"
15
16 #include "point_448.h"
17 #include "ed448.h"
18 #include "crypto/ecx.h"
19 #include "curve448_local.h"
20
21 #define COFACTOR 4
22
23 #define C448_WNAF_FIXED_TABLE_BITS 5
24 #define C448_WNAF_VAR_TABLE_BITS 3
25
26 #define EDWARDS_D (-39081)
27
28 static const curve448_scalar_t precomputed_scalarmul_adjustment = {
29 {
30 {
31 SC_LIMB(0xc873d6d54a7bb0cfULL), SC_LIMB(0xe933d8d723a70aadULL),
32 SC_LIMB(0xbb124b65129c96fdULL), SC_LIMB(0x00000008335dc163ULL)
33 }
34 }
35 };
36
37 #define TWISTED_D (EDWARDS_D - 1)
38
39 #define WBITS C448_WORD_BITS /* NB this may be different from ARCH_WORD_BITS */
40
41 /* Inverse. */
gf_invert(gf y,const gf x,int assert_nonzero)42 static void gf_invert(gf y, const gf x, int assert_nonzero)
43 {
44 mask_t ret;
45 gf t1, t2;
46
47 gf_sqr(t1, x); /* o^2 */
48 ret = gf_isr(t2, t1); /* +-1/sqrt(o^2) = +-1/o */
49 (void)ret;
50 if (assert_nonzero)
51 assert(ret);
52 gf_sqr(t1, t2);
53 gf_mul(t2, t1, x); /* not direct to y in case of alias. */
54 gf_copy(y, t2);
55 }
56
57 /** identity = (0,1) */
58 const curve448_point_t ossl_curve448_point_identity =
59 { {{{{0}}}, {{{1}}}, {{{1}}}, {{{0}}}} };
60
point_double_internal(curve448_point_t p,const curve448_point_t q,int before_double)61 static void point_double_internal(curve448_point_t p, const curve448_point_t q,
62 int before_double)
63 {
64 gf a, b, c, d;
65
66 gf_sqr(c, q->x);
67 gf_sqr(a, q->y);
68 gf_add_nr(d, c, a); /* 2+e */
69 gf_add_nr(p->t, q->y, q->x); /* 2+e */
70 gf_sqr(b, p->t);
71 gf_subx_nr(b, b, d, 3); /* 4+e */
72 gf_sub_nr(p->t, a, c); /* 3+e */
73 gf_sqr(p->x, q->z);
74 gf_add_nr(p->z, p->x, p->x); /* 2+e */
75 gf_subx_nr(a, p->z, p->t, 4); /* 6+e */
76 if (GF_HEADROOM == 5)
77 gf_weak_reduce(a); /* or 1+e */
78 gf_mul(p->x, a, b);
79 gf_mul(p->z, p->t, a);
80 gf_mul(p->y, p->t, d);
81 if (!before_double)
82 gf_mul(p->t, b, d);
83 }
84
ossl_curve448_point_double(curve448_point_t p,const curve448_point_t q)85 void ossl_curve448_point_double(curve448_point_t p, const curve448_point_t q)
86 {
87 point_double_internal(p, q, 0);
88 }
89
90 /* Operations on [p]niels */
cond_neg_niels(niels_t n,mask_t neg)91 static ossl_inline void cond_neg_niels(niels_t n, mask_t neg)
92 {
93 gf_cond_swap(n->a, n->b, neg);
94 gf_cond_neg(n->c, neg);
95 }
96
pt_to_pniels(pniels_t b,const curve448_point_t a)97 static void pt_to_pniels(pniels_t b, const curve448_point_t a)
98 {
99 gf_sub(b->n->a, a->y, a->x);
100 gf_add(b->n->b, a->x, a->y);
101 gf_mulw(b->n->c, a->t, 2 * TWISTED_D);
102 gf_add(b->z, a->z, a->z);
103 }
104
pniels_to_pt(curve448_point_t e,const pniels_t d)105 static void pniels_to_pt(curve448_point_t e, const pniels_t d)
106 {
107 gf eu;
108
109 gf_add(eu, d->n->b, d->n->a);
110 gf_sub(e->y, d->n->b, d->n->a);
111 gf_mul(e->t, e->y, eu);
112 gf_mul(e->x, d->z, e->y);
113 gf_mul(e->y, d->z, eu);
114 gf_sqr(e->z, d->z);
115 }
116
niels_to_pt(curve448_point_t e,const niels_t n)117 static void niels_to_pt(curve448_point_t e, const niels_t n)
118 {
119 gf_add(e->y, n->b, n->a);
120 gf_sub(e->x, n->b, n->a);
121 gf_mul(e->t, e->y, e->x);
122 gf_copy(e->z, ONE);
123 }
124
add_niels_to_pt(curve448_point_t d,const niels_t e,int before_double)125 static void add_niels_to_pt(curve448_point_t d, const niels_t e,
126 int before_double)
127 {
128 gf a, b, c;
129
130 gf_sub_nr(b, d->y, d->x); /* 3+e */
131 gf_mul(a, e->a, b);
132 gf_add_nr(b, d->x, d->y); /* 2+e */
133 gf_mul(d->y, e->b, b);
134 gf_mul(d->x, e->c, d->t);
135 gf_add_nr(c, a, d->y); /* 2+e */
136 gf_sub_nr(b, d->y, a); /* 3+e */
137 gf_sub_nr(d->y, d->z, d->x); /* 3+e */
138 gf_add_nr(a, d->x, d->z); /* 2+e */
139 gf_mul(d->z, a, d->y);
140 gf_mul(d->x, d->y, b);
141 gf_mul(d->y, a, c);
142 if (!before_double)
143 gf_mul(d->t, b, c);
144 }
145
sub_niels_from_pt(curve448_point_t d,const niels_t e,int before_double)146 static void sub_niels_from_pt(curve448_point_t d, const niels_t e,
147 int before_double)
148 {
149 gf a, b, c;
150
151 gf_sub_nr(b, d->y, d->x); /* 3+e */
152 gf_mul(a, e->b, b);
153 gf_add_nr(b, d->x, d->y); /* 2+e */
154 gf_mul(d->y, e->a, b);
155 gf_mul(d->x, e->c, d->t);
156 gf_add_nr(c, a, d->y); /* 2+e */
157 gf_sub_nr(b, d->y, a); /* 3+e */
158 gf_add_nr(d->y, d->z, d->x); /* 2+e */
159 gf_sub_nr(a, d->z, d->x); /* 3+e */
160 gf_mul(d->z, a, d->y);
161 gf_mul(d->x, d->y, b);
162 gf_mul(d->y, a, c);
163 if (!before_double)
164 gf_mul(d->t, b, c);
165 }
166
add_pniels_to_pt(curve448_point_t p,const pniels_t pn,int before_double)167 static void add_pniels_to_pt(curve448_point_t p, const pniels_t pn,
168 int before_double)
169 {
170 gf L0;
171
172 gf_mul(L0, p->z, pn->z);
173 gf_copy(p->z, L0);
174 add_niels_to_pt(p, pn->n, before_double);
175 }
176
sub_pniels_from_pt(curve448_point_t p,const pniels_t pn,int before_double)177 static void sub_pniels_from_pt(curve448_point_t p, const pniels_t pn,
178 int before_double)
179 {
180 gf L0;
181
182 gf_mul(L0, p->z, pn->z);
183 gf_copy(p->z, L0);
184 sub_niels_from_pt(p, pn->n, before_double);
185 }
186
187 c448_bool_t
ossl_curve448_point_eq(const curve448_point_t p,const curve448_point_t q)188 ossl_curve448_point_eq(const curve448_point_t p,
189 const curve448_point_t q)
190 {
191 mask_t succ;
192 gf a, b;
193
194 /* equality mod 2-torsion compares x/y */
195 gf_mul(a, p->y, q->x);
196 gf_mul(b, q->y, p->x);
197 succ = gf_eq(a, b);
198
199 return mask_to_bool(succ);
200 }
201
202 c448_bool_t
ossl_curve448_point_valid(const curve448_point_t p)203 ossl_curve448_point_valid(const curve448_point_t p)
204 {
205 mask_t out;
206 gf a, b, c;
207
208 gf_mul(a, p->x, p->y);
209 gf_mul(b, p->z, p->t);
210 out = gf_eq(a, b);
211 gf_sqr(a, p->x);
212 gf_sqr(b, p->y);
213 gf_sub(a, b, a);
214 gf_sqr(b, p->t);
215 gf_mulw(c, b, TWISTED_D);
216 gf_sqr(b, p->z);
217 gf_add(b, b, c);
218 out &= gf_eq(a, b);
219 out &= ~gf_eq(p->z, ZERO);
220 return mask_to_bool(out);
221 }
222
constant_time_lookup_niels(niels_s * RESTRICT ni,const niels_t * table,int nelts,int idx)223 static ossl_inline void constant_time_lookup_niels(niels_s * RESTRICT ni,
224 const niels_t * table,
225 int nelts, int idx)
226 {
227 constant_time_lookup(ni, table, sizeof(niels_s), nelts, idx);
228 }
229
230 void
ossl_curve448_precomputed_scalarmul(curve448_point_t out,const curve448_precomputed_s * table,const curve448_scalar_t scalar)231 ossl_curve448_precomputed_scalarmul(curve448_point_t out,
232 const curve448_precomputed_s * table,
233 const curve448_scalar_t scalar)
234 {
235 unsigned int i, j, k;
236 const unsigned int n = COMBS_N, t = COMBS_T, s = COMBS_S;
237 niels_t ni;
238 curve448_scalar_t scalar1x;
239
240 ossl_curve448_scalar_add(scalar1x, scalar, precomputed_scalarmul_adjustment);
241 ossl_curve448_scalar_halve(scalar1x, scalar1x);
242
243 for (i = s; i > 0; i--) {
244 if (i != s)
245 point_double_internal(out, out, 0);
246
247 for (j = 0; j < n; j++) {
248 int tab = 0;
249 mask_t invert;
250
251 for (k = 0; k < t; k++) {
252 unsigned int bit = (i - 1) + s * (k + j * t);
253
254 if (bit < C448_SCALAR_BITS)
255 tab |=
256 (scalar1x->limb[bit / WBITS] >> (bit % WBITS) & 1) << k;
257 }
258
259 invert = (tab >> (t - 1)) - 1;
260 tab ^= invert;
261 tab &= (1 << (t - 1)) - 1;
262
263 constant_time_lookup_niels(ni, &table->table[j << (t - 1)],
264 1 << (t - 1), tab);
265
266 cond_neg_niels(ni, invert);
267 if ((i != s) || j != 0)
268 add_niels_to_pt(out, ni, j == n - 1 && i != 1);
269 else
270 niels_to_pt(out, ni);
271 }
272 }
273
274 OPENSSL_cleanse(ni, sizeof(ni));
275 OPENSSL_cleanse(scalar1x, sizeof(scalar1x));
276 }
277
278 void
ossl_curve448_point_mul_by_ratio_and_encode_like_eddsa(uint8_t enc[EDDSA_448_PUBLIC_BYTES],const curve448_point_t p)279 ossl_curve448_point_mul_by_ratio_and_encode_like_eddsa(
280 uint8_t enc[EDDSA_448_PUBLIC_BYTES],
281 const curve448_point_t p)
282 {
283 gf x, y, z, t;
284 curve448_point_t q;
285
286 /* The point is now on the twisted curve. Move it to untwisted. */
287 curve448_point_copy(q, p);
288
289 {
290 /* 4-isogeny: 2xy/(y^+x^2), (y^2-x^2)/(2z^2-y^2+x^2) */
291 gf u;
292
293 gf_sqr(x, q->x);
294 gf_sqr(t, q->y);
295 gf_add(u, x, t);
296 gf_add(z, q->y, q->x);
297 gf_sqr(y, z);
298 gf_sub(y, y, u);
299 gf_sub(z, t, x);
300 gf_sqr(x, q->z);
301 gf_add(t, x, x);
302 gf_sub(t, t, z);
303 gf_mul(x, t, y);
304 gf_mul(y, z, u);
305 gf_mul(z, u, t);
306 OPENSSL_cleanse(u, sizeof(u));
307 }
308
309 /* Affinize */
310 gf_invert(z, z, 1);
311 gf_mul(t, x, z);
312 gf_mul(x, y, z);
313
314 /* Encode */
315 enc[EDDSA_448_PRIVATE_BYTES - 1] = 0;
316 gf_serialize(enc, x, 1);
317 enc[EDDSA_448_PRIVATE_BYTES - 1] |= 0x80 & gf_lobit(t);
318
319 OPENSSL_cleanse(x, sizeof(x));
320 OPENSSL_cleanse(y, sizeof(y));
321 OPENSSL_cleanse(z, sizeof(z));
322 OPENSSL_cleanse(t, sizeof(t));
323 ossl_curve448_point_destroy(q);
324 }
325
326 c448_error_t
ossl_curve448_point_decode_like_eddsa_and_mul_by_ratio(curve448_point_t p,const uint8_t enc[EDDSA_448_PUBLIC_BYTES])327 ossl_curve448_point_decode_like_eddsa_and_mul_by_ratio(
328 curve448_point_t p,
329 const uint8_t enc[EDDSA_448_PUBLIC_BYTES])
330 {
331 uint8_t enc2[EDDSA_448_PUBLIC_BYTES];
332 mask_t low;
333 mask_t succ;
334
335 memcpy(enc2, enc, sizeof(enc2));
336
337 low = ~word_is_zero(enc2[EDDSA_448_PRIVATE_BYTES - 1] & 0x80);
338 enc2[EDDSA_448_PRIVATE_BYTES - 1] &= ~0x80;
339
340 succ = gf_deserialize(p->y, enc2, 1, 0);
341 succ &= word_is_zero(enc2[EDDSA_448_PRIVATE_BYTES - 1]);
342
343 gf_sqr(p->x, p->y);
344 gf_sub(p->z, ONE, p->x); /* num = 1-y^2 */
345 gf_mulw(p->t, p->x, EDWARDS_D); /* dy^2 */
346 gf_sub(p->t, ONE, p->t); /* denom = 1-dy^2 or 1-d + dy^2 */
347
348 gf_mul(p->x, p->z, p->t);
349 succ &= gf_isr(p->t, p->x); /* 1/sqrt(num * denom) */
350
351 gf_mul(p->x, p->t, p->z); /* sqrt(num / denom) */
352 gf_cond_neg(p->x, gf_lobit(p->x) ^ low);
353 gf_copy(p->z, ONE);
354
355 {
356 gf a, b, c, d;
357
358 /* 4-isogeny 2xy/(y^2-ax^2), (y^2+ax^2)/(2-y^2-ax^2) */
359 gf_sqr(c, p->x);
360 gf_sqr(a, p->y);
361 gf_add(d, c, a);
362 gf_add(p->t, p->y, p->x);
363 gf_sqr(b, p->t);
364 gf_sub(b, b, d);
365 gf_sub(p->t, a, c);
366 gf_sqr(p->x, p->z);
367 gf_add(p->z, p->x, p->x);
368 gf_sub(a, p->z, d);
369 gf_mul(p->x, a, b);
370 gf_mul(p->z, p->t, a);
371 gf_mul(p->y, p->t, d);
372 gf_mul(p->t, b, d);
373 OPENSSL_cleanse(a, sizeof(a));
374 OPENSSL_cleanse(b, sizeof(b));
375 OPENSSL_cleanse(c, sizeof(c));
376 OPENSSL_cleanse(d, sizeof(d));
377 }
378
379 OPENSSL_cleanse(enc2, sizeof(enc2));
380 assert(ossl_curve448_point_valid(p) || ~succ);
381
382 return c448_succeed_if(mask_to_bool(succ));
383 }
384
385 c448_error_t
ossl_x448_int(uint8_t out[X_PUBLIC_BYTES],const uint8_t base[X_PUBLIC_BYTES],const uint8_t scalar[X_PRIVATE_BYTES])386 ossl_x448_int(uint8_t out[X_PUBLIC_BYTES],
387 const uint8_t base[X_PUBLIC_BYTES],
388 const uint8_t scalar[X_PRIVATE_BYTES])
389 {
390 gf x1, x2, z2, x3, z3, t1, t2;
391 int t;
392 mask_t swap = 0;
393 mask_t nz;
394
395 (void)gf_deserialize(x1, base, 1, 0);
396 gf_copy(x2, ONE);
397 gf_copy(z2, ZERO);
398 gf_copy(x3, x1);
399 gf_copy(z3, ONE);
400
401 for (t = X_PRIVATE_BITS - 1; t >= 0; t--) {
402 uint8_t sb = scalar[t / 8];
403 mask_t k_t;
404
405 /* Scalar conditioning */
406 if (t / 8 == 0)
407 sb &= -(uint8_t)COFACTOR;
408 else if (t == X_PRIVATE_BITS - 1)
409 sb = -1;
410
411 k_t = (sb >> (t % 8)) & 1;
412 k_t = 0 - k_t; /* set to all 0s or all 1s */
413
414 swap ^= k_t;
415 gf_cond_swap(x2, x3, swap);
416 gf_cond_swap(z2, z3, swap);
417 swap = k_t;
418
419 /*
420 * The "_nr" below skips coefficient reduction. In the following
421 * comments, "2+e" is saying that the coefficients are at most 2+epsilon
422 * times the reduction limit.
423 */
424 gf_add_nr(t1, x2, z2); /* A = x2 + z2 */ /* 2+e */
425 gf_sub_nr(t2, x2, z2); /* B = x2 - z2 */ /* 3+e */
426 gf_sub_nr(z2, x3, z3); /* D = x3 - z3 */ /* 3+e */
427 gf_mul(x2, t1, z2); /* DA */
428 gf_add_nr(z2, z3, x3); /* C = x3 + z3 */ /* 2+e */
429 gf_mul(x3, t2, z2); /* CB */
430 gf_sub_nr(z3, x2, x3); /* DA-CB */ /* 3+e */
431 gf_sqr(z2, z3); /* (DA-CB)^2 */
432 gf_mul(z3, x1, z2); /* z3 = x1(DA-CB)^2 */
433 gf_add_nr(z2, x2, x3); /* (DA+CB) */ /* 2+e */
434 gf_sqr(x3, z2); /* x3 = (DA+CB)^2 */
435
436 gf_sqr(z2, t1); /* AA = A^2 */
437 gf_sqr(t1, t2); /* BB = B^2 */
438 gf_mul(x2, z2, t1); /* x2 = AA*BB */
439 gf_sub_nr(t2, z2, t1); /* E = AA-BB */ /* 3+e */
440
441 gf_mulw(t1, t2, -EDWARDS_D); /* E*-d = a24*E */
442 gf_add_nr(t1, t1, z2); /* AA + a24*E */ /* 2+e */
443 gf_mul(z2, t2, t1); /* z2 = E(AA+a24*E) */
444 }
445
446 /* Finish */
447 gf_cond_swap(x2, x3, swap);
448 gf_cond_swap(z2, z3, swap);
449 gf_invert(z2, z2, 0);
450 gf_mul(x1, x2, z2);
451 gf_serialize(out, x1, 1);
452 nz = ~gf_eq(x1, ZERO);
453
454 OPENSSL_cleanse(x1, sizeof(x1));
455 OPENSSL_cleanse(x2, sizeof(x2));
456 OPENSSL_cleanse(z2, sizeof(z2));
457 OPENSSL_cleanse(x3, sizeof(x3));
458 OPENSSL_cleanse(z3, sizeof(z3));
459 OPENSSL_cleanse(t1, sizeof(t1));
460 OPENSSL_cleanse(t2, sizeof(t2));
461
462 return c448_succeed_if(mask_to_bool(nz));
463 }
464
465 void
ossl_curve448_point_mul_by_ratio_and_encode_like_x448(uint8_t out[X_PUBLIC_BYTES],const curve448_point_t p)466 ossl_curve448_point_mul_by_ratio_and_encode_like_x448(uint8_t
467 out[X_PUBLIC_BYTES],
468 const curve448_point_t p)
469 {
470 curve448_point_t q;
471
472 curve448_point_copy(q, p);
473 gf_invert(q->t, q->x, 0); /* 1/x */
474 gf_mul(q->z, q->t, q->y); /* y/x */
475 gf_sqr(q->y, q->z); /* (y/x)^2 */
476 gf_serialize(out, q->y, 1);
477 ossl_curve448_point_destroy(q);
478 }
479
ossl_x448_derive_public_key(uint8_t out[X_PUBLIC_BYTES],const uint8_t scalar[X_PRIVATE_BYTES])480 void ossl_x448_derive_public_key(uint8_t out[X_PUBLIC_BYTES],
481 const uint8_t scalar[X_PRIVATE_BYTES])
482 {
483 /* Scalar conditioning */
484 uint8_t scalar2[X_PRIVATE_BYTES];
485 curve448_scalar_t the_scalar;
486 curve448_point_t p;
487 unsigned int i;
488
489 memcpy(scalar2, scalar, sizeof(scalar2));
490 scalar2[0] &= -(uint8_t)COFACTOR;
491
492 scalar2[X_PRIVATE_BYTES - 1] &= ~((0u - 1u) << ((X_PRIVATE_BITS + 7) % 8));
493 scalar2[X_PRIVATE_BYTES - 1] |= 1 << ((X_PRIVATE_BITS + 7) % 8);
494
495 ossl_curve448_scalar_decode_long(the_scalar, scalar2, sizeof(scalar2));
496
497 /* Compensate for the encoding ratio */
498 for (i = 1; i < X448_ENCODE_RATIO; i <<= 1)
499 ossl_curve448_scalar_halve(the_scalar, the_scalar);
500
501 ossl_curve448_precomputed_scalarmul(p, ossl_curve448_precomputed_base,
502 the_scalar);
503 ossl_curve448_point_mul_by_ratio_and_encode_like_x448(out, p);
504 ossl_curve448_point_destroy(p);
505 }
506
507 /* Control for variable-time scalar multiply algorithms. */
508 struct smvt_control {
509 int power, addend;
510 };
511
512 #if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ > 3))
513 # define NUMTRAILINGZEROS __builtin_ctz
514 #else
515 # define NUMTRAILINGZEROS numtrailingzeros
numtrailingzeros(uint32_t i)516 static uint32_t numtrailingzeros(uint32_t i)
517 {
518 uint32_t tmp;
519 uint32_t num = 31;
520
521 if (i == 0)
522 return 32;
523
524 tmp = i << 16;
525 if (tmp != 0) {
526 i = tmp;
527 num -= 16;
528 }
529 tmp = i << 8;
530 if (tmp != 0) {
531 i = tmp;
532 num -= 8;
533 }
534 tmp = i << 4;
535 if (tmp != 0) {
536 i = tmp;
537 num -= 4;
538 }
539 tmp = i << 2;
540 if (tmp != 0) {
541 i = tmp;
542 num -= 2;
543 }
544 tmp = i << 1;
545 if (tmp != 0)
546 num--;
547
548 return num;
549 }
550 #endif
551
recode_wnaf(struct smvt_control * control,const curve448_scalar_t scalar,unsigned int table_bits)552 static int recode_wnaf(struct smvt_control *control,
553 /* [nbits/(table_bits + 1) + 3] */
554 const curve448_scalar_t scalar,
555 unsigned int table_bits)
556 {
557 unsigned int table_size = C448_SCALAR_BITS / (table_bits + 1) + 3;
558 int position = table_size - 1; /* at the end */
559 uint64_t current = scalar->limb[0] & 0xFFFF;
560 uint32_t mask = (1 << (table_bits + 1)) - 1;
561 unsigned int w;
562 const unsigned int B_OVER_16 = sizeof(scalar->limb[0]) / 2;
563 unsigned int n, i;
564
565 /* place the end marker */
566 control[position].power = -1;
567 control[position].addend = 0;
568 position--;
569
570 /*
571 * PERF: Could negate scalar if it's large. But then would need more cases
572 * in the actual code that uses it, all for an expected reduction of like
573 * 1/5 op. Probably not worth it.
574 */
575
576 for (w = 1; w < (C448_SCALAR_BITS - 1) / 16 + 3; w++) {
577 if (w < (C448_SCALAR_BITS - 1) / 16 + 1) {
578 /* Refill the 16 high bits of current */
579 current += (uint32_t)((scalar->limb[w / B_OVER_16]
580 >> (16 * (w % B_OVER_16))) << 16);
581 }
582
583 while (current & 0xFFFF) {
584 uint32_t pos = NUMTRAILINGZEROS((uint32_t)current);
585 uint32_t odd = (uint32_t)current >> pos;
586 int32_t delta = odd & mask;
587
588 assert(position >= 0);
589 assert(pos < 32); /* can't fail since current & 0xFFFF != 0 */
590 if (odd & (1 << (table_bits + 1)))
591 delta -= (1 << (table_bits + 1));
592 current -= delta * (1 << pos);
593 control[position].power = pos + 16 * (w - 1);
594 control[position].addend = delta;
595 position--;
596 }
597 current >>= 16;
598 }
599 assert(current == 0);
600
601 position++;
602 n = table_size - position;
603 for (i = 0; i < n; i++)
604 control[i] = control[i + position];
605
606 return n - 1;
607 }
608
prepare_wnaf_table(pniels_t * output,const curve448_point_t working,unsigned int tbits)609 static void prepare_wnaf_table(pniels_t * output,
610 const curve448_point_t working,
611 unsigned int tbits)
612 {
613 curve448_point_t tmp;
614 int i;
615 pniels_t twop;
616
617 pt_to_pniels(output[0], working);
618
619 if (tbits == 0)
620 return;
621
622 ossl_curve448_point_double(tmp, working);
623 pt_to_pniels(twop, tmp);
624
625 add_pniels_to_pt(tmp, output[0], 0);
626 pt_to_pniels(output[1], tmp);
627
628 for (i = 2; i < 1 << tbits; i++) {
629 add_pniels_to_pt(tmp, twop, 0);
630 pt_to_pniels(output[i], tmp);
631 }
632
633 ossl_curve448_point_destroy(tmp);
634 OPENSSL_cleanse(twop, sizeof(twop));
635 }
636
637 void
ossl_curve448_base_double_scalarmul_non_secret(curve448_point_t combo,const curve448_scalar_t scalar1,const curve448_point_t base2,const curve448_scalar_t scalar2)638 ossl_curve448_base_double_scalarmul_non_secret(curve448_point_t combo,
639 const curve448_scalar_t scalar1,
640 const curve448_point_t base2,
641 const curve448_scalar_t scalar2)
642 {
643 const int table_bits_var = C448_WNAF_VAR_TABLE_BITS;
644 const int table_bits_pre = C448_WNAF_FIXED_TABLE_BITS;
645 struct smvt_control control_var[C448_SCALAR_BITS /
646 (C448_WNAF_VAR_TABLE_BITS + 1) + 3];
647 struct smvt_control control_pre[C448_SCALAR_BITS /
648 (C448_WNAF_FIXED_TABLE_BITS + 1) + 3];
649 int ncb_pre = recode_wnaf(control_pre, scalar1, table_bits_pre);
650 int ncb_var = recode_wnaf(control_var, scalar2, table_bits_var);
651 pniels_t precmp_var[1 << C448_WNAF_VAR_TABLE_BITS];
652 int contp = 0, contv = 0, i;
653
654 prepare_wnaf_table(precmp_var, base2, table_bits_var);
655 i = control_var[0].power;
656
657 if (i < 0) {
658 curve448_point_copy(combo, ossl_curve448_point_identity);
659 return;
660 }
661 if (i > control_pre[0].power) {
662 pniels_to_pt(combo, precmp_var[control_var[0].addend >> 1]);
663 contv++;
664 } else if (i == control_pre[0].power && i >= 0) {
665 pniels_to_pt(combo, precmp_var[control_var[0].addend >> 1]);
666 add_niels_to_pt(combo,
667 ossl_curve448_wnaf_base[control_pre[0].addend >> 1],
668 i);
669 contv++;
670 contp++;
671 } else {
672 i = control_pre[0].power;
673 niels_to_pt(combo, ossl_curve448_wnaf_base[control_pre[0].addend >> 1]);
674 contp++;
675 }
676
677 for (i--; i >= 0; i--) {
678 int cv = (i == control_var[contv].power);
679 int cp = (i == control_pre[contp].power);
680
681 point_double_internal(combo, combo, i && !(cv || cp));
682
683 if (cv) {
684 assert(control_var[contv].addend);
685
686 if (control_var[contv].addend > 0)
687 add_pniels_to_pt(combo,
688 precmp_var[control_var[contv].addend >> 1],
689 i && !cp);
690 else
691 sub_pniels_from_pt(combo,
692 precmp_var[(-control_var[contv].addend)
693 >> 1], i && !cp);
694 contv++;
695 }
696
697 if (cp) {
698 assert(control_pre[contp].addend);
699
700 if (control_pre[contp].addend > 0)
701 add_niels_to_pt(combo,
702 ossl_curve448_wnaf_base[control_pre[contp].addend
703 >> 1], i);
704 else
705 sub_niels_from_pt(combo,
706 ossl_curve448_wnaf_base[(-control_pre
707 [contp].addend) >> 1], i);
708 contp++;
709 }
710 }
711
712 /* This function is non-secret, but whatever this is cheap. */
713 OPENSSL_cleanse(control_var, sizeof(control_var));
714 OPENSSL_cleanse(control_pre, sizeof(control_pre));
715 OPENSSL_cleanse(precmp_var, sizeof(precmp_var));
716
717 assert(contv == ncb_var);
718 (void)ncb_var;
719 assert(contp == ncb_pre);
720 (void)ncb_pre;
721 }
722
ossl_curve448_point_destroy(curve448_point_t point)723 void ossl_curve448_point_destroy(curve448_point_t point)
724 {
725 OPENSSL_cleanse(point, sizeof(curve448_point_t));
726 }
727
ossl_x448(uint8_t out_shared_key[56],const uint8_t private_key[56],const uint8_t peer_public_value[56])728 int ossl_x448(uint8_t out_shared_key[56], const uint8_t private_key[56],
729 const uint8_t peer_public_value[56])
730 {
731 return ossl_x448_int(out_shared_key, peer_public_value, private_key)
732 == C448_SUCCESS;
733 }
734
ossl_x448_public_from_private(uint8_t out_public_value[56],const uint8_t private_key[56])735 void ossl_x448_public_from_private(uint8_t out_public_value[56],
736 const uint8_t private_key[56])
737 {
738 ossl_x448_derive_public_key(out_public_value, private_key);
739 }
740