1 /*
2 * Copyright 2017-2024 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 ossl_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 ossl_gf_sqr(t1, t2);
53 ossl_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 };
61
point_double_internal(curve448_point_t p,const curve448_point_t q,int before_double)62 static void point_double_internal(curve448_point_t p, const curve448_point_t q,
63 int before_double)
64 {
65 gf a, b, c, d;
66
67 ossl_gf_sqr(c, q->x);
68 ossl_gf_sqr(a, q->y);
69 gf_add_nr(d, c, a); /* 2+e */
70 gf_add_nr(p->t, q->y, q->x); /* 2+e */
71 ossl_gf_sqr(b, p->t);
72 gf_subx_nr(b, b, d, 3); /* 4+e */
73 gf_sub_nr(p->t, a, c); /* 3+e */
74 ossl_gf_sqr(p->x, q->z);
75 gf_add_nr(p->z, p->x, p->x); /* 2+e */
76 gf_subx_nr(a, p->z, p->t, 4); /* 6+e */
77 if (GF_HEADROOM == 5)
78 gf_weak_reduce(a); /* or 1+e */
79 ossl_gf_mul(p->x, a, b);
80 ossl_gf_mul(p->z, p->t, a);
81 ossl_gf_mul(p->y, p->t, d);
82 if (!before_double)
83 ossl_gf_mul(p->t, b, d);
84 }
85
ossl_curve448_point_double(curve448_point_t p,const curve448_point_t q)86 void ossl_curve448_point_double(curve448_point_t p, const curve448_point_t q)
87 {
88 point_double_internal(p, q, 0);
89 }
90
91 /* Operations on [p]niels */
cond_neg_niels(niels_t n,mask_t neg)92 static ossl_inline void cond_neg_niels(niels_t n, mask_t neg)
93 {
94 gf_cond_swap(n->a, n->b, neg);
95 gf_cond_neg(n->c, neg);
96 }
97
pt_to_pniels(pniels_t b,const curve448_point_t a)98 static void pt_to_pniels(pniels_t b, const curve448_point_t a)
99 {
100 gf_sub(b->n->a, a->y, a->x);
101 gf_add(b->n->b, a->x, a->y);
102 gf_mulw(b->n->c, a->t, 2 * TWISTED_D);
103 gf_add(b->z, a->z, a->z);
104 }
105
pniels_to_pt(curve448_point_t e,const pniels_t d)106 static void pniels_to_pt(curve448_point_t e, const pniels_t d)
107 {
108 gf eu;
109
110 gf_add(eu, d->n->b, d->n->a);
111 gf_sub(e->y, d->n->b, d->n->a);
112 ossl_gf_mul(e->t, e->y, eu);
113 ossl_gf_mul(e->x, d->z, e->y);
114 ossl_gf_mul(e->y, d->z, eu);
115 ossl_gf_sqr(e->z, d->z);
116 }
117
niels_to_pt(curve448_point_t e,const niels_t n)118 static void niels_to_pt(curve448_point_t e, const niels_t n)
119 {
120 gf_add(e->y, n->b, n->a);
121 gf_sub(e->x, n->b, n->a);
122 ossl_gf_mul(e->t, e->y, e->x);
123 gf_copy(e->z, ONE);
124 }
125
add_niels_to_pt(curve448_point_t d,const niels_t e,int before_double)126 static void add_niels_to_pt(curve448_point_t d, const niels_t e,
127 int before_double)
128 {
129 gf a, b, c;
130
131 gf_sub_nr(b, d->y, d->x); /* 3+e */
132 ossl_gf_mul(a, e->a, b);
133 gf_add_nr(b, d->x, d->y); /* 2+e */
134 ossl_gf_mul(d->y, e->b, b);
135 ossl_gf_mul(d->x, e->c, d->t);
136 gf_add_nr(c, a, d->y); /* 2+e */
137 gf_sub_nr(b, d->y, a); /* 3+e */
138 gf_sub_nr(d->y, d->z, d->x); /* 3+e */
139 gf_add_nr(a, d->x, d->z); /* 2+e */
140 ossl_gf_mul(d->z, a, d->y);
141 ossl_gf_mul(d->x, d->y, b);
142 ossl_gf_mul(d->y, a, c);
143 if (!before_double)
144 ossl_gf_mul(d->t, b, c);
145 }
146
sub_niels_from_pt(curve448_point_t d,const niels_t e,int before_double)147 static void sub_niels_from_pt(curve448_point_t d, const niels_t e,
148 int before_double)
149 {
150 gf a, b, c;
151
152 gf_sub_nr(b, d->y, d->x); /* 3+e */
153 ossl_gf_mul(a, e->b, b);
154 gf_add_nr(b, d->x, d->y); /* 2+e */
155 ossl_gf_mul(d->y, e->a, b);
156 ossl_gf_mul(d->x, e->c, d->t);
157 gf_add_nr(c, a, d->y); /* 2+e */
158 gf_sub_nr(b, d->y, a); /* 3+e */
159 gf_add_nr(d->y, d->z, d->x); /* 2+e */
160 gf_sub_nr(a, d->z, d->x); /* 3+e */
161 ossl_gf_mul(d->z, a, d->y);
162 ossl_gf_mul(d->x, d->y, b);
163 ossl_gf_mul(d->y, a, c);
164 if (!before_double)
165 ossl_gf_mul(d->t, b, c);
166 }
167
add_pniels_to_pt(curve448_point_t p,const pniels_t pn,int before_double)168 static void add_pniels_to_pt(curve448_point_t p, const pniels_t pn,
169 int before_double)
170 {
171 gf L0;
172
173 ossl_gf_mul(L0, p->z, pn->z);
174 gf_copy(p->z, L0);
175 add_niels_to_pt(p, pn->n, before_double);
176 }
177
sub_pniels_from_pt(curve448_point_t p,const pniels_t pn,int before_double)178 static void sub_pniels_from_pt(curve448_point_t p, const pniels_t pn,
179 int before_double)
180 {
181 gf L0;
182
183 ossl_gf_mul(L0, p->z, pn->z);
184 gf_copy(p->z, L0);
185 sub_niels_from_pt(p, pn->n, before_double);
186 }
187
188 c448_bool_t
ossl_curve448_point_eq(const curve448_point_t p,const curve448_point_t q)189 ossl_curve448_point_eq(const curve448_point_t p,
190 const curve448_point_t q)
191 {
192 mask_t succ;
193 gf a, b;
194
195 /* equality mod 2-torsion compares x/y */
196 ossl_gf_mul(a, p->y, q->x);
197 ossl_gf_mul(b, q->y, p->x);
198 succ = gf_eq(a, b);
199
200 return mask_to_bool(succ);
201 }
202
203 c448_bool_t
ossl_curve448_point_valid(const curve448_point_t p)204 ossl_curve448_point_valid(const curve448_point_t p)
205 {
206 mask_t out;
207 gf a, b, c;
208
209 ossl_gf_mul(a, p->x, p->y);
210 ossl_gf_mul(b, p->z, p->t);
211 out = gf_eq(a, b);
212 ossl_gf_sqr(a, p->x);
213 ossl_gf_sqr(b, p->y);
214 gf_sub(a, b, a);
215 ossl_gf_sqr(b, p->t);
216 gf_mulw(c, b, TWISTED_D);
217 ossl_gf_sqr(b, p->z);
218 gf_add(b, b, c);
219 out &= gf_eq(a, b);
220 out &= ~gf_eq(p->z, ZERO);
221 return mask_to_bool(out);
222 }
223
constant_time_lookup_niels(niels_s * RESTRICT ni,const niels_t * table,int nelts,int idx)224 static ossl_inline void constant_time_lookup_niels(niels_s * RESTRICT ni,
225 const niels_t *table,
226 int nelts, int idx)
227 {
228 constant_time_lookup(ni, table, sizeof(niels_s), nelts, idx);
229 }
230
231 void
ossl_curve448_precomputed_scalarmul(curve448_point_t out,const curve448_precomputed_s * table,const curve448_scalar_t scalar)232 ossl_curve448_precomputed_scalarmul(curve448_point_t out,
233 const curve448_precomputed_s *table,
234 const curve448_scalar_t scalar)
235 {
236 unsigned int i, j, k;
237 const unsigned int n = COMBS_N, t = COMBS_T, s = COMBS_S;
238 niels_t ni;
239 curve448_scalar_t scalar1x;
240
241 ossl_curve448_scalar_add(scalar1x, scalar, precomputed_scalarmul_adjustment);
242 ossl_curve448_scalar_halve(scalar1x, scalar1x);
243
244 for (i = s; i > 0; i--) {
245 if (i != s)
246 point_double_internal(out, out, 0);
247
248 for (j = 0; j < n; j++) {
249 int tab = 0;
250 mask_t invert;
251
252 for (k = 0; k < t; k++) {
253 unsigned int bit = (i - 1) + s * (k + j * t);
254
255 if (bit < C448_SCALAR_BITS)
256 tab |=
257 (scalar1x->limb[bit / WBITS] >> (bit % WBITS) & 1) << k;
258 }
259
260 invert = (tab >> (t - 1)) - 1;
261 tab ^= invert;
262 tab &= (1 << (t - 1)) - 1;
263
264 constant_time_lookup_niels(ni, &table->table[j << (t - 1)],
265 1 << (t - 1), tab);
266
267 cond_neg_niels(ni, invert);
268 if ((i != s) || j != 0)
269 add_niels_to_pt(out, ni, j == n - 1 && i != 1);
270 else
271 niels_to_pt(out, ni);
272 }
273 }
274
275 OPENSSL_cleanse(ni, sizeof(ni));
276 OPENSSL_cleanse(scalar1x, sizeof(scalar1x));
277 }
278
279 void
ossl_curve448_point_mul_by_ratio_and_encode_like_eddsa(uint8_t enc[EDDSA_448_PUBLIC_BYTES],const curve448_point_t p)280 ossl_curve448_point_mul_by_ratio_and_encode_like_eddsa(
281 uint8_t enc[EDDSA_448_PUBLIC_BYTES],
282 const curve448_point_t p)
283 {
284 gf x, y, z, t;
285 curve448_point_t q;
286
287 /* The point is now on the twisted curve. Move it to untwisted. */
288 curve448_point_copy(q, p);
289
290 {
291 /* 4-isogeny: 2xy/(y^+x^2), (y^2-x^2)/(2z^2-y^2+x^2) */
292 gf u;
293
294 ossl_gf_sqr(x, q->x);
295 ossl_gf_sqr(t, q->y);
296 gf_add(u, x, t);
297 gf_add(z, q->y, q->x);
298 ossl_gf_sqr(y, z);
299 gf_sub(y, y, u);
300 gf_sub(z, t, x);
301 ossl_gf_sqr(x, q->z);
302 gf_add(t, x, x);
303 gf_sub(t, t, z);
304 ossl_gf_mul(x, t, y);
305 ossl_gf_mul(y, z, u);
306 ossl_gf_mul(z, u, t);
307 OPENSSL_cleanse(u, sizeof(u));
308 }
309
310 /* Affinize */
311 gf_invert(z, z, 1);
312 ossl_gf_mul(t, x, z);
313 ossl_gf_mul(x, y, z);
314
315 /* Encode */
316 enc[EDDSA_448_PRIVATE_BYTES - 1] = 0;
317 gf_serialize(enc, x, 1);
318 enc[EDDSA_448_PRIVATE_BYTES - 1] |= 0x80 & gf_lobit(t);
319
320 OPENSSL_cleanse(x, sizeof(x));
321 OPENSSL_cleanse(y, sizeof(y));
322 OPENSSL_cleanse(z, sizeof(z));
323 OPENSSL_cleanse(t, sizeof(t));
324 ossl_curve448_point_destroy(q);
325 }
326
327 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])328 ossl_curve448_point_decode_like_eddsa_and_mul_by_ratio(
329 curve448_point_t p,
330 const uint8_t enc[EDDSA_448_PUBLIC_BYTES])
331 {
332 uint8_t enc2[EDDSA_448_PUBLIC_BYTES];
333 mask_t low;
334 mask_t succ;
335
336 memcpy(enc2, enc, sizeof(enc2));
337
338 low = ~word_is_zero(enc2[EDDSA_448_PRIVATE_BYTES - 1] & 0x80);
339 enc2[EDDSA_448_PRIVATE_BYTES - 1] &= ~0x80;
340
341 succ = gf_deserialize(p->y, enc2, 1, 0);
342 succ &= word_is_zero(enc2[EDDSA_448_PRIVATE_BYTES - 1]);
343
344 ossl_gf_sqr(p->x, p->y);
345 gf_sub(p->z, ONE, p->x); /* num = 1-y^2 */
346 gf_mulw(p->t, p->x, EDWARDS_D); /* dy^2 */
347 gf_sub(p->t, ONE, p->t); /* denom = 1-dy^2 or 1-d + dy^2 */
348
349 ossl_gf_mul(p->x, p->z, p->t);
350 succ &= gf_isr(p->t, p->x); /* 1/sqrt(num * denom) */
351
352 ossl_gf_mul(p->x, p->t, p->z); /* sqrt(num / denom) */
353 gf_cond_neg(p->x, gf_lobit(p->x) ^ low);
354 gf_copy(p->z, ONE);
355
356 {
357 gf a, b, c, d;
358
359 /* 4-isogeny 2xy/(y^2-ax^2), (y^2+ax^2)/(2-y^2-ax^2) */
360 ossl_gf_sqr(c, p->x);
361 ossl_gf_sqr(a, p->y);
362 gf_add(d, c, a);
363 gf_add(p->t, p->y, p->x);
364 ossl_gf_sqr(b, p->t);
365 gf_sub(b, b, d);
366 gf_sub(p->t, a, c);
367 ossl_gf_sqr(p->x, p->z);
368 gf_add(p->z, p->x, p->x);
369 gf_sub(a, p->z, d);
370 ossl_gf_mul(p->x, a, b);
371 ossl_gf_mul(p->z, p->t, a);
372 ossl_gf_mul(p->y, p->t, d);
373 ossl_gf_mul(p->t, b, d);
374 OPENSSL_cleanse(a, sizeof(a));
375 OPENSSL_cleanse(b, sizeof(b));
376 OPENSSL_cleanse(c, sizeof(c));
377 OPENSSL_cleanse(d, sizeof(d));
378 }
379
380 OPENSSL_cleanse(enc2, sizeof(enc2));
381 assert(ossl_curve448_point_valid(p) || ~succ);
382
383 return c448_succeed_if(mask_to_bool(succ));
384 }
385
386 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])387 ossl_x448_int(uint8_t out[X_PUBLIC_BYTES],
388 const uint8_t base[X_PUBLIC_BYTES],
389 const uint8_t scalar[X_PRIVATE_BYTES])
390 {
391 gf x1, x2, z2, x3, z3, t1, t2;
392 int t;
393 mask_t swap = 0;
394 mask_t nz;
395
396 (void)gf_deserialize(x1, base, 1, 0);
397 gf_copy(x2, ONE);
398 gf_copy(z2, ZERO);
399 gf_copy(x3, x1);
400 gf_copy(z3, ONE);
401
402 for (t = X_PRIVATE_BITS - 1; t >= 0; t--) {
403 uint8_t sb = scalar[t / 8];
404 mask_t k_t;
405
406 /* Scalar conditioning */
407 if (t / 8 == 0)
408 sb &= -(uint8_t)COFACTOR;
409 else if (t == X_PRIVATE_BITS - 1)
410 sb = -1;
411
412 k_t = (sb >> (t % 8)) & 1;
413 k_t = 0 - k_t; /* set to all 0s or all 1s */
414
415 swap ^= k_t;
416 gf_cond_swap(x2, x3, swap);
417 gf_cond_swap(z2, z3, swap);
418 swap = k_t;
419
420 /*
421 * The "_nr" below skips coefficient reduction. In the following
422 * comments, "2+e" is saying that the coefficients are at most 2+epsilon
423 * times the reduction limit.
424 */
425 gf_add_nr(t1, x2, z2); /* A = x2 + z2 */ /* 2+e */
426 gf_sub_nr(t2, x2, z2); /* B = x2 - z2 */ /* 3+e */
427 gf_sub_nr(z2, x3, z3); /* D = x3 - z3 */ /* 3+e */
428 ossl_gf_mul(x2, t1, z2); /* DA */
429 gf_add_nr(z2, z3, x3); /* C = x3 + z3 */ /* 2+e */
430 ossl_gf_mul(x3, t2, z2); /* CB */
431 gf_sub_nr(z3, x2, x3); /* DA-CB */ /* 3+e */
432 ossl_gf_sqr(z2, z3); /* (DA-CB)^2 */
433 ossl_gf_mul(z3, x1, z2); /* z3 = x1(DA-CB)^2 */
434 gf_add_nr(z2, x2, x3); /* (DA+CB) */ /* 2+e */
435 ossl_gf_sqr(x3, z2); /* x3 = (DA+CB)^2 */
436
437 ossl_gf_sqr(z2, t1); /* AA = A^2 */
438 ossl_gf_sqr(t1, t2); /* BB = B^2 */
439 ossl_gf_mul(x2, z2, t1); /* x2 = AA*BB */
440 gf_sub_nr(t2, z2, t1); /* E = AA-BB */ /* 3+e */
441
442 gf_mulw(t1, t2, -EDWARDS_D); /* E*-d = a24*E */
443 gf_add_nr(t1, t1, z2); /* AA + a24*E */ /* 2+e */
444 ossl_gf_mul(z2, t2, t1); /* z2 = E(AA+a24*E) */
445 }
446
447 /* Finish */
448 gf_cond_swap(x2, x3, swap);
449 gf_cond_swap(z2, z3, swap);
450 gf_invert(z2, z2, 0);
451 ossl_gf_mul(x1, x2, z2);
452 gf_serialize(out, x1, 1);
453 nz = ~gf_eq(x1, ZERO);
454
455 OPENSSL_cleanse(x1, sizeof(x1));
456 OPENSSL_cleanse(x2, sizeof(x2));
457 OPENSSL_cleanse(z2, sizeof(z2));
458 OPENSSL_cleanse(x3, sizeof(x3));
459 OPENSSL_cleanse(z3, sizeof(z3));
460 OPENSSL_cleanse(t1, sizeof(t1));
461 OPENSSL_cleanse(t2, sizeof(t2));
462
463 return c448_succeed_if(mask_to_bool(nz));
464 }
465
466 void
ossl_curve448_point_mul_by_ratio_and_encode_like_x448(uint8_t out[X_PUBLIC_BYTES],const curve448_point_t p)467 ossl_curve448_point_mul_by_ratio_and_encode_like_x448(uint8_t
468 out[X_PUBLIC_BYTES],
469 const curve448_point_t p)
470 {
471 curve448_point_t q;
472
473 curve448_point_copy(q, p);
474 gf_invert(q->t, q->x, 0); /* 1/x */
475 ossl_gf_mul(q->z, q->t, q->y); /* y/x */
476 ossl_gf_sqr(q->y, q->z); /* (y/x)^2 */
477 gf_serialize(out, q->y, 1);
478 ossl_curve448_point_destroy(q);
479 }
480
ossl_x448_derive_public_key(uint8_t out[X_PUBLIC_BYTES],const uint8_t scalar[X_PRIVATE_BYTES])481 void ossl_x448_derive_public_key(uint8_t out[X_PUBLIC_BYTES],
482 const uint8_t scalar[X_PRIVATE_BYTES])
483 {
484 /* Scalar conditioning */
485 uint8_t scalar2[X_PRIVATE_BYTES];
486 curve448_scalar_t the_scalar;
487 curve448_point_t p;
488 unsigned int i;
489
490 memcpy(scalar2, scalar, sizeof(scalar2));
491 scalar2[0] &= -(uint8_t)COFACTOR;
492
493 scalar2[X_PRIVATE_BYTES - 1] &= ~((0u - 1u) << ((X_PRIVATE_BITS + 7) % 8));
494 scalar2[X_PRIVATE_BYTES - 1] |= 1 << ((X_PRIVATE_BITS + 7) % 8);
495
496 ossl_curve448_scalar_decode_long(the_scalar, scalar2, sizeof(scalar2));
497
498 /* Compensate for the encoding ratio */
499 for (i = 1; i < X448_ENCODE_RATIO; i <<= 1)
500 ossl_curve448_scalar_halve(the_scalar, the_scalar);
501
502 ossl_curve448_precomputed_scalarmul(p, ossl_curve448_precomputed_base,
503 the_scalar);
504 ossl_curve448_point_mul_by_ratio_and_encode_like_x448(out, p);
505 ossl_curve448_point_destroy(p);
506 }
507
508 /* Control for variable-time scalar multiply algorithms. */
509 struct smvt_control {
510 int power, addend;
511 };
512
513 #if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ > 3))
514 # define NUMTRAILINGZEROS __builtin_ctz
515 #else
516 # define NUMTRAILINGZEROS numtrailingzeros
numtrailingzeros(uint32_t i)517 static uint32_t numtrailingzeros(uint32_t i)
518 {
519 uint32_t tmp;
520 uint32_t num = 31;
521
522 if (i == 0)
523 return 32;
524
525 tmp = i << 16;
526 if (tmp != 0) {
527 i = tmp;
528 num -= 16;
529 }
530 tmp = i << 8;
531 if (tmp != 0) {
532 i = tmp;
533 num -= 8;
534 }
535 tmp = i << 4;
536 if (tmp != 0) {
537 i = tmp;
538 num -= 4;
539 }
540 tmp = i << 2;
541 if (tmp != 0) {
542 i = tmp;
543 num -= 2;
544 }
545 tmp = i << 1;
546 if (tmp != 0)
547 num--;
548
549 return num;
550 }
551 #endif
552
recode_wnaf(struct smvt_control * control,const curve448_scalar_t scalar,unsigned int table_bits)553 static int recode_wnaf(struct smvt_control *control,
554 /* [nbits/(table_bits + 1) + 3] */
555 const curve448_scalar_t scalar,
556 unsigned int table_bits)
557 {
558 unsigned int table_size = C448_SCALAR_BITS / (table_bits + 1) + 3;
559 int position = table_size - 1; /* at the end */
560 uint64_t current = scalar->limb[0] & 0xFFFF;
561 uint32_t mask = (1 << (table_bits + 1)) - 1;
562 unsigned int w;
563 const unsigned int B_OVER_16 = sizeof(scalar->limb[0]) / 2;
564 unsigned int n, i;
565
566 /* place the end marker */
567 control[position].power = -1;
568 control[position].addend = 0;
569 position--;
570
571 /*
572 * PERF: Could negate scalar if it's large. But then would need more cases
573 * in the actual code that uses it, all for an expected reduction of like
574 * 1/5 op. Probably not worth it.
575 */
576
577 for (w = 1; w < (C448_SCALAR_BITS - 1) / 16 + 3; w++) {
578 if (w < (C448_SCALAR_BITS - 1) / 16 + 1) {
579 /* Refill the 16 high bits of current */
580 current += (uint32_t)((scalar->limb[w / B_OVER_16]
581 >> (16 * (w % B_OVER_16))) << 16);
582 }
583
584 while (current & 0xFFFF) {
585 uint32_t pos = NUMTRAILINGZEROS((uint32_t)current);
586 uint32_t odd = (uint32_t)current >> pos;
587 int32_t delta = odd & mask;
588
589 assert(position >= 0);
590 if (odd & (1 << (table_bits + 1)))
591 delta -= (1 << (table_bits + 1));
592 /*
593 * Coverity gets confused by the value of pos, thinking it might be
594 * 32. This would require current & 0xFFFF to be zero which isn't
595 * possible. Suppress this false positive, since adding a check
596 * isn't desirable.
597 */
598 /* coverity[overflow_before_widen] */
599 current -= delta * (1 << pos);
600 control[position].power = pos + 16 * (w - 1);
601 control[position].addend = delta;
602 position--;
603 }
604 current >>= 16;
605 }
606 assert(current == 0);
607
608 position++;
609 n = table_size - position;
610 for (i = 0; i < n; i++)
611 control[i] = control[i + position];
612
613 return n - 1;
614 }
615
prepare_wnaf_table(pniels_t * output,const curve448_point_t working,unsigned int tbits)616 static void prepare_wnaf_table(pniels_t *output,
617 const curve448_point_t working,
618 unsigned int tbits)
619 {
620 curve448_point_t tmp;
621 int i;
622 pniels_t twop;
623
624 pt_to_pniels(output[0], working);
625
626 if (tbits == 0)
627 return;
628
629 ossl_curve448_point_double(tmp, working);
630 pt_to_pniels(twop, tmp);
631
632 add_pniels_to_pt(tmp, output[0], 0);
633 pt_to_pniels(output[1], tmp);
634
635 for (i = 2; i < 1 << tbits; i++) {
636 add_pniels_to_pt(tmp, twop, 0);
637 pt_to_pniels(output[i], tmp);
638 }
639
640 ossl_curve448_point_destroy(tmp);
641 OPENSSL_cleanse(twop, sizeof(twop));
642 }
643
644 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)645 ossl_curve448_base_double_scalarmul_non_secret(curve448_point_t combo,
646 const curve448_scalar_t scalar1,
647 const curve448_point_t base2,
648 const curve448_scalar_t scalar2)
649 {
650 const int table_bits_var = C448_WNAF_VAR_TABLE_BITS;
651 const int table_bits_pre = C448_WNAF_FIXED_TABLE_BITS;
652 struct smvt_control control_var[C448_SCALAR_BITS /
653 (C448_WNAF_VAR_TABLE_BITS + 1) + 3];
654 struct smvt_control control_pre[C448_SCALAR_BITS /
655 (C448_WNAF_FIXED_TABLE_BITS + 1) + 3];
656 int ncb_pre = recode_wnaf(control_pre, scalar1, table_bits_pre);
657 int ncb_var = recode_wnaf(control_var, scalar2, table_bits_var);
658 pniels_t precmp_var[1 << C448_WNAF_VAR_TABLE_BITS];
659 int contp = 0, contv = 0, i;
660
661 prepare_wnaf_table(precmp_var, base2, table_bits_var);
662 i = control_var[0].power;
663
664 if (i < 0) {
665 curve448_point_copy(combo, ossl_curve448_point_identity);
666 return;
667 }
668 if (i > control_pre[0].power) {
669 pniels_to_pt(combo, precmp_var[control_var[0].addend >> 1]);
670 contv++;
671 } else if (i == control_pre[0].power && i >= 0) {
672 pniels_to_pt(combo, precmp_var[control_var[0].addend >> 1]);
673 add_niels_to_pt(combo,
674 ossl_curve448_wnaf_base[control_pre[0].addend >> 1],
675 i);
676 contv++;
677 contp++;
678 } else {
679 i = control_pre[0].power;
680 niels_to_pt(combo, ossl_curve448_wnaf_base[control_pre[0].addend >> 1]);
681 contp++;
682 }
683
684 for (i--; i >= 0; i--) {
685 int cv = (i == control_var[contv].power);
686 int cp = (i == control_pre[contp].power);
687
688 point_double_internal(combo, combo, i && !(cv || cp));
689
690 if (cv) {
691 assert(control_var[contv].addend);
692
693 if (control_var[contv].addend > 0)
694 add_pniels_to_pt(combo,
695 precmp_var[control_var[contv].addend >> 1],
696 i && !cp);
697 else
698 sub_pniels_from_pt(combo,
699 precmp_var[(-control_var[contv].addend)
700 >> 1], i && !cp);
701 contv++;
702 }
703
704 if (cp) {
705 assert(control_pre[contp].addend);
706
707 if (control_pre[contp].addend > 0)
708 add_niels_to_pt(combo,
709 ossl_curve448_wnaf_base[control_pre[contp].addend
710 >> 1], i);
711 else
712 sub_niels_from_pt(combo,
713 ossl_curve448_wnaf_base[(-control_pre
714 [contp].addend) >> 1], i);
715 contp++;
716 }
717 }
718
719 /* This function is non-secret, but whatever this is cheap. */
720 OPENSSL_cleanse(control_var, sizeof(control_var));
721 OPENSSL_cleanse(control_pre, sizeof(control_pre));
722 OPENSSL_cleanse(precmp_var, sizeof(precmp_var));
723
724 assert(contv == ncb_var);
725 (void)ncb_var;
726 assert(contp == ncb_pre);
727 (void)ncb_pre;
728 }
729
ossl_curve448_point_destroy(curve448_point_t point)730 void ossl_curve448_point_destroy(curve448_point_t point)
731 {
732 OPENSSL_cleanse(point, sizeof(curve448_point_t));
733 }
734
ossl_x448(uint8_t out_shared_key[56],const uint8_t private_key[56],const uint8_t peer_public_value[56])735 int ossl_x448(uint8_t out_shared_key[56], const uint8_t private_key[56],
736 const uint8_t peer_public_value[56])
737 {
738 return ossl_x448_int(out_shared_key, peer_public_value, private_key)
739 == C448_SUCCESS;
740 }
741
ossl_x448_public_from_private(uint8_t out_public_value[56],const uint8_t private_key[56])742 void ossl_x448_public_from_private(uint8_t out_public_value[56],
743 const uint8_t private_key[56])
744 {
745 ossl_x448_derive_public_key(out_public_value, private_key);
746 }
747
