1 /*
2  * Copyright 2017-2019 The OpenSSL Project Authors. All Rights Reserved.
3  * Copyright 2015-2016 Cryptography Research, Inc.
4  *
5  * Licensed under the OpenSSL license (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 "curve448_local.h"
19 
20 #define COFACTOR 4
21 
22 #define C448_WNAF_FIXED_TABLE_BITS 5
23 #define C448_WNAF_VAR_TABLE_BITS 3
24 
25 #define EDWARDS_D       (-39081)
26 
27 static const curve448_scalar_t precomputed_scalarmul_adjustment = {
28     {
29         {
30             SC_LIMB(0xc873d6d54a7bb0cfULL), SC_LIMB(0xe933d8d723a70aadULL),
31             SC_LIMB(0xbb124b65129c96fdULL), SC_LIMB(0x00000008335dc163ULL)
32         }
33     }
34 };
35 
36 #define TWISTED_D (EDWARDS_D - 1)
37 
38 #define WBITS C448_WORD_BITS   /* NB this may be different from ARCH_WORD_BITS */
39 
40 /* Inverse. */
gf_invert(gf y,const gf x,int assert_nonzero)41 static void gf_invert(gf y, const gf x, int assert_nonzero)
42 {
43     mask_t ret;
44     gf t1, t2;
45 
46     gf_sqr(t1, x);              /* o^2 */
47     ret = gf_isr(t2, t1);       /* +-1/sqrt(o^2) = +-1/o */
48     (void)ret;
49     if (assert_nonzero)
50         assert(ret);
51     gf_sqr(t1, t2);
52     gf_mul(t2, t1, x);          /* not direct to y in case of alias. */
53     gf_copy(y, t2);
54 }
55 
56 /** identity = (0,1) */
57 const curve448_point_t curve448_point_identity =
58     { {{{{0}}}, {{{1}}}, {{{1}}}, {{{0}}}} };
59 
point_double_internal(curve448_point_t p,const curve448_point_t q,int before_double)60 static void point_double_internal(curve448_point_t p, const curve448_point_t q,
61                                   int before_double)
62 {
63     gf a, b, c, d;
64 
65     gf_sqr(c, q->x);
66     gf_sqr(a, q->y);
67     gf_add_nr(d, c, a);         /* 2+e */
68     gf_add_nr(p->t, q->y, q->x); /* 2+e */
69     gf_sqr(b, p->t);
70     gf_subx_nr(b, b, d, 3);     /* 4+e */
71     gf_sub_nr(p->t, a, c);      /* 3+e */
72     gf_sqr(p->x, q->z);
73     gf_add_nr(p->z, p->x, p->x); /* 2+e */
74     gf_subx_nr(a, p->z, p->t, 4); /* 6+e */
75     if (GF_HEADROOM == 5)
76         gf_weak_reduce(a);      /* or 1+e */
77     gf_mul(p->x, a, b);
78     gf_mul(p->z, p->t, a);
79     gf_mul(p->y, p->t, d);
80     if (!before_double)
81         gf_mul(p->t, b, d);
82 }
83 
curve448_point_double(curve448_point_t p,const curve448_point_t q)84 void curve448_point_double(curve448_point_t p, const curve448_point_t q)
85 {
86     point_double_internal(p, q, 0);
87 }
88 
89 /* Operations on [p]niels */
cond_neg_niels(niels_t n,mask_t neg)90 static ossl_inline void cond_neg_niels(niels_t n, mask_t neg)
91 {
92     gf_cond_swap(n->a, n->b, neg);
93     gf_cond_neg(n->c, neg);
94 }
95 
pt_to_pniels(pniels_t b,const curve448_point_t a)96 static void pt_to_pniels(pniels_t b, const curve448_point_t a)
97 {
98     gf_sub(b->n->a, a->y, a->x);
99     gf_add(b->n->b, a->x, a->y);
100     gf_mulw(b->n->c, a->t, 2 * TWISTED_D);
101     gf_add(b->z, a->z, a->z);
102 }
103 
pniels_to_pt(curve448_point_t e,const pniels_t d)104 static void pniels_to_pt(curve448_point_t e, const pniels_t d)
105 {
106     gf eu;
107 
108     gf_add(eu, d->n->b, d->n->a);
109     gf_sub(e->y, d->n->b, d->n->a);
110     gf_mul(e->t, e->y, eu);
111     gf_mul(e->x, d->z, e->y);
112     gf_mul(e->y, d->z, eu);
113     gf_sqr(e->z, d->z);
114 }
115 
niels_to_pt(curve448_point_t e,const niels_t n)116 static void niels_to_pt(curve448_point_t e, const niels_t n)
117 {
118     gf_add(e->y, n->b, n->a);
119     gf_sub(e->x, n->b, n->a);
120     gf_mul(e->t, e->y, e->x);
121     gf_copy(e->z, ONE);
122 }
123 
add_niels_to_pt(curve448_point_t d,const niels_t e,int before_double)124 static void add_niels_to_pt(curve448_point_t d, const niels_t e,
125                             int before_double)
126 {
127     gf a, b, c;
128 
129     gf_sub_nr(b, d->y, d->x);   /* 3+e */
130     gf_mul(a, e->a, b);
131     gf_add_nr(b, d->x, d->y);   /* 2+e */
132     gf_mul(d->y, e->b, b);
133     gf_mul(d->x, e->c, d->t);
134     gf_add_nr(c, a, d->y);      /* 2+e */
135     gf_sub_nr(b, d->y, a);      /* 3+e */
136     gf_sub_nr(d->y, d->z, d->x); /* 3+e */
137     gf_add_nr(a, d->x, d->z);   /* 2+e */
138     gf_mul(d->z, a, d->y);
139     gf_mul(d->x, d->y, b);
140     gf_mul(d->y, a, c);
141     if (!before_double)
142         gf_mul(d->t, b, c);
143 }
144 
sub_niels_from_pt(curve448_point_t d,const niels_t e,int before_double)145 static void sub_niels_from_pt(curve448_point_t d, const niels_t e,
146                               int before_double)
147 {
148     gf a, b, c;
149 
150     gf_sub_nr(b, d->y, d->x);   /* 3+e */
151     gf_mul(a, e->b, b);
152     gf_add_nr(b, d->x, d->y);   /* 2+e */
153     gf_mul(d->y, e->a, b);
154     gf_mul(d->x, e->c, d->t);
155     gf_add_nr(c, a, d->y);      /* 2+e */
156     gf_sub_nr(b, d->y, a);      /* 3+e */
157     gf_add_nr(d->y, d->z, d->x); /* 2+e */
158     gf_sub_nr(a, d->z, d->x);   /* 3+e */
159     gf_mul(d->z, a, d->y);
160     gf_mul(d->x, d->y, b);
161     gf_mul(d->y, a, c);
162     if (!before_double)
163         gf_mul(d->t, b, c);
164 }
165 
add_pniels_to_pt(curve448_point_t p,const pniels_t pn,int before_double)166 static void add_pniels_to_pt(curve448_point_t p, const pniels_t pn,
167                              int before_double)
168 {
169     gf L0;
170 
171     gf_mul(L0, p->z, pn->z);
172     gf_copy(p->z, L0);
173     add_niels_to_pt(p, pn->n, before_double);
174 }
175 
sub_pniels_from_pt(curve448_point_t p,const pniels_t pn,int before_double)176 static void sub_pniels_from_pt(curve448_point_t p, const pniels_t pn,
177                                int before_double)
178 {
179     gf L0;
180 
181     gf_mul(L0, p->z, pn->z);
182     gf_copy(p->z, L0);
183     sub_niels_from_pt(p, pn->n, before_double);
184 }
185 
curve448_point_eq(const curve448_point_t p,const curve448_point_t q)186 c448_bool_t curve448_point_eq(const curve448_point_t p,
187                               const curve448_point_t q)
188 {
189     mask_t succ;
190     gf a, b;
191 
192     /* equality mod 2-torsion compares x/y */
193     gf_mul(a, p->y, q->x);
194     gf_mul(b, q->y, p->x);
195     succ = gf_eq(a, b);
196 
197     return mask_to_bool(succ);
198 }
199 
curve448_point_valid(const curve448_point_t p)200 c448_bool_t curve448_point_valid(const curve448_point_t p)
201 {
202     mask_t out;
203     gf a, b, c;
204 
205     gf_mul(a, p->x, p->y);
206     gf_mul(b, p->z, p->t);
207     out = gf_eq(a, b);
208     gf_sqr(a, p->x);
209     gf_sqr(b, p->y);
210     gf_sub(a, b, a);
211     gf_sqr(b, p->t);
212     gf_mulw(c, b, TWISTED_D);
213     gf_sqr(b, p->z);
214     gf_add(b, b, c);
215     out &= gf_eq(a, b);
216     out &= ~gf_eq(p->z, ZERO);
217     return mask_to_bool(out);
218 }
219 
constant_time_lookup_niels(niels_s * RESTRICT ni,const niels_t * table,int nelts,int idx)220 static ossl_inline void constant_time_lookup_niels(niels_s * RESTRICT ni,
221                                                    const niels_t * table,
222                                                    int nelts, int idx)
223 {
224     constant_time_lookup(ni, table, sizeof(niels_s), nelts, idx);
225 }
226 
curve448_precomputed_scalarmul(curve448_point_t out,const curve448_precomputed_s * table,const curve448_scalar_t scalar)227 void curve448_precomputed_scalarmul(curve448_point_t out,
228                                     const curve448_precomputed_s * table,
229                                     const curve448_scalar_t scalar)
230 {
231     unsigned int i, j, k;
232     const unsigned int n = COMBS_N, t = COMBS_T, s = COMBS_S;
233     niels_t ni;
234     curve448_scalar_t scalar1x;
235 
236     curve448_scalar_add(scalar1x, scalar, precomputed_scalarmul_adjustment);
237     curve448_scalar_halve(scalar1x, scalar1x);
238 
239     for (i = s; i > 0; i--) {
240         if (i != s)
241             point_double_internal(out, out, 0);
242 
243         for (j = 0; j < n; j++) {
244             int tab = 0;
245             mask_t invert;
246 
247             for (k = 0; k < t; k++) {
248                 unsigned int bit = (i - 1) + s * (k + j * t);
249 
250                 if (bit < C448_SCALAR_BITS)
251                     tab |=
252                         (scalar1x->limb[bit / WBITS] >> (bit % WBITS) & 1) << k;
253             }
254 
255             invert = (tab >> (t - 1)) - 1;
256             tab ^= invert;
257             tab &= (1 << (t - 1)) - 1;
258 
259             constant_time_lookup_niels(ni, &table->table[j << (t - 1)],
260                                        1 << (t - 1), tab);
261 
262             cond_neg_niels(ni, invert);
263             if ((i != s) || j != 0)
264                 add_niels_to_pt(out, ni, j == n - 1 && i != 1);
265             else
266                 niels_to_pt(out, ni);
267         }
268     }
269 
270     OPENSSL_cleanse(ni, sizeof(ni));
271     OPENSSL_cleanse(scalar1x, sizeof(scalar1x));
272 }
273 
curve448_point_mul_by_ratio_and_encode_like_eddsa(uint8_t enc[EDDSA_448_PUBLIC_BYTES],const curve448_point_t p)274 void curve448_point_mul_by_ratio_and_encode_like_eddsa(
275                                     uint8_t enc[EDDSA_448_PUBLIC_BYTES],
276                                     const curve448_point_t p)
277 {
278     gf x, y, z, t;
279     curve448_point_t q;
280 
281     /* The point is now on the twisted curve.  Move it to untwisted. */
282     curve448_point_copy(q, p);
283 
284     {
285         /* 4-isogeny: 2xy/(y^+x^2), (y^2-x^2)/(2z^2-y^2+x^2) */
286         gf u;
287 
288         gf_sqr(x, q->x);
289         gf_sqr(t, q->y);
290         gf_add(u, x, t);
291         gf_add(z, q->y, q->x);
292         gf_sqr(y, z);
293         gf_sub(y, y, u);
294         gf_sub(z, t, x);
295         gf_sqr(x, q->z);
296         gf_add(t, x, x);
297         gf_sub(t, t, z);
298         gf_mul(x, t, y);
299         gf_mul(y, z, u);
300         gf_mul(z, u, t);
301         OPENSSL_cleanse(u, sizeof(u));
302     }
303 
304     /* Affinize */
305     gf_invert(z, z, 1);
306     gf_mul(t, x, z);
307     gf_mul(x, y, z);
308 
309     /* Encode */
310     enc[EDDSA_448_PRIVATE_BYTES - 1] = 0;
311     gf_serialize(enc, x, 1);
312     enc[EDDSA_448_PRIVATE_BYTES - 1] |= 0x80 & gf_lobit(t);
313 
314     OPENSSL_cleanse(x, sizeof(x));
315     OPENSSL_cleanse(y, sizeof(y));
316     OPENSSL_cleanse(z, sizeof(z));
317     OPENSSL_cleanse(t, sizeof(t));
318     curve448_point_destroy(q);
319 }
320 
curve448_point_decode_like_eddsa_and_mul_by_ratio(curve448_point_t p,const uint8_t enc[EDDSA_448_PUBLIC_BYTES])321 c448_error_t curve448_point_decode_like_eddsa_and_mul_by_ratio(
322                                 curve448_point_t p,
323                                 const uint8_t enc[EDDSA_448_PUBLIC_BYTES])
324 {
325     uint8_t enc2[EDDSA_448_PUBLIC_BYTES];
326     mask_t low;
327     mask_t succ;
328 
329     memcpy(enc2, enc, sizeof(enc2));
330 
331     low = ~word_is_zero(enc2[EDDSA_448_PRIVATE_BYTES - 1] & 0x80);
332     enc2[EDDSA_448_PRIVATE_BYTES - 1] &= ~0x80;
333 
334     succ = gf_deserialize(p->y, enc2, 1, 0);
335     succ &= word_is_zero(enc2[EDDSA_448_PRIVATE_BYTES - 1]);
336 
337     gf_sqr(p->x, p->y);
338     gf_sub(p->z, ONE, p->x);    /* num = 1-y^2 */
339     gf_mulw(p->t, p->x, EDWARDS_D); /* dy^2 */
340     gf_sub(p->t, ONE, p->t);    /* denom = 1-dy^2 or 1-d + dy^2 */
341 
342     gf_mul(p->x, p->z, p->t);
343     succ &= gf_isr(p->t, p->x); /* 1/sqrt(num * denom) */
344 
345     gf_mul(p->x, p->t, p->z);   /* sqrt(num / denom) */
346     gf_cond_neg(p->x, gf_lobit(p->x) ^ low);
347     gf_copy(p->z, ONE);
348 
349     {
350         gf a, b, c, d;
351 
352         /* 4-isogeny 2xy/(y^2-ax^2), (y^2+ax^2)/(2-y^2-ax^2) */
353         gf_sqr(c, p->x);
354         gf_sqr(a, p->y);
355         gf_add(d, c, a);
356         gf_add(p->t, p->y, p->x);
357         gf_sqr(b, p->t);
358         gf_sub(b, b, d);
359         gf_sub(p->t, a, c);
360         gf_sqr(p->x, p->z);
361         gf_add(p->z, p->x, p->x);
362         gf_sub(a, p->z, d);
363         gf_mul(p->x, a, b);
364         gf_mul(p->z, p->t, a);
365         gf_mul(p->y, p->t, d);
366         gf_mul(p->t, b, d);
367         OPENSSL_cleanse(a, sizeof(a));
368         OPENSSL_cleanse(b, sizeof(b));
369         OPENSSL_cleanse(c, sizeof(c));
370         OPENSSL_cleanse(d, sizeof(d));
371     }
372 
373     OPENSSL_cleanse(enc2, sizeof(enc2));
374     assert(curve448_point_valid(p) || ~succ);
375 
376     return c448_succeed_if(mask_to_bool(succ));
377 }
378 
x448_int(uint8_t out[X_PUBLIC_BYTES],const uint8_t base[X_PUBLIC_BYTES],const uint8_t scalar[X_PRIVATE_BYTES])379 c448_error_t x448_int(uint8_t out[X_PUBLIC_BYTES],
380                       const uint8_t base[X_PUBLIC_BYTES],
381                       const uint8_t scalar[X_PRIVATE_BYTES])
382 {
383     gf x1, x2, z2, x3, z3, t1, t2;
384     int t;
385     mask_t swap = 0;
386     mask_t nz;
387 
388     (void)gf_deserialize(x1, base, 1, 0);
389     gf_copy(x2, ONE);
390     gf_copy(z2, ZERO);
391     gf_copy(x3, x1);
392     gf_copy(z3, ONE);
393 
394     for (t = X_PRIVATE_BITS - 1; t >= 0; t--) {
395         uint8_t sb = scalar[t / 8];
396         mask_t k_t;
397 
398         /* Scalar conditioning */
399         if (t / 8 == 0)
400             sb &= -(uint8_t)COFACTOR;
401         else if (t == X_PRIVATE_BITS - 1)
402             sb = -1;
403 
404         k_t = (sb >> (t % 8)) & 1;
405         k_t = 0 - k_t;             /* set to all 0s or all 1s */
406 
407         swap ^= k_t;
408         gf_cond_swap(x2, x3, swap);
409         gf_cond_swap(z2, z3, swap);
410         swap = k_t;
411 
412         /*
413          * The "_nr" below skips coefficient reduction. In the following
414          * comments, "2+e" is saying that the coefficients are at most 2+epsilon
415          * times the reduction limit.
416          */
417         gf_add_nr(t1, x2, z2);  /* A = x2 + z2 */ /* 2+e */
418         gf_sub_nr(t2, x2, z2);  /* B = x2 - z2 */ /* 3+e */
419         gf_sub_nr(z2, x3, z3);  /* D = x3 - z3 */ /* 3+e */
420         gf_mul(x2, t1, z2);     /* DA */
421         gf_add_nr(z2, z3, x3);  /* C = x3 + z3 */ /* 2+e */
422         gf_mul(x3, t2, z2);     /* CB */
423         gf_sub_nr(z3, x2, x3);  /* DA-CB */ /* 3+e */
424         gf_sqr(z2, z3);         /* (DA-CB)^2 */
425         gf_mul(z3, x1, z2);     /* z3 = x1(DA-CB)^2 */
426         gf_add_nr(z2, x2, x3);  /* (DA+CB) */ /* 2+e */
427         gf_sqr(x3, z2);         /* x3 = (DA+CB)^2 */
428 
429         gf_sqr(z2, t1);         /* AA = A^2 */
430         gf_sqr(t1, t2);         /* BB = B^2 */
431         gf_mul(x2, z2, t1);     /* x2 = AA*BB */
432         gf_sub_nr(t2, z2, t1);  /* E = AA-BB */ /* 3+e */
433 
434         gf_mulw(t1, t2, -EDWARDS_D); /* E*-d = a24*E */
435         gf_add_nr(t1, t1, z2);  /* AA + a24*E */ /* 2+e */
436         gf_mul(z2, t2, t1);     /* z2 = E(AA+a24*E) */
437     }
438 
439     /* Finish */
440     gf_cond_swap(x2, x3, swap);
441     gf_cond_swap(z2, z3, swap);
442     gf_invert(z2, z2, 0);
443     gf_mul(x1, x2, z2);
444     gf_serialize(out, x1, 1);
445     nz = ~gf_eq(x1, ZERO);
446 
447     OPENSSL_cleanse(x1, sizeof(x1));
448     OPENSSL_cleanse(x2, sizeof(x2));
449     OPENSSL_cleanse(z2, sizeof(z2));
450     OPENSSL_cleanse(x3, sizeof(x3));
451     OPENSSL_cleanse(z3, sizeof(z3));
452     OPENSSL_cleanse(t1, sizeof(t1));
453     OPENSSL_cleanse(t2, sizeof(t2));
454 
455     return c448_succeed_if(mask_to_bool(nz));
456 }
457 
curve448_point_mul_by_ratio_and_encode_like_x448(uint8_t out[X_PUBLIC_BYTES],const curve448_point_t p)458 void curve448_point_mul_by_ratio_and_encode_like_x448(uint8_t
459                                                       out[X_PUBLIC_BYTES],
460                                                       const curve448_point_t p)
461 {
462     curve448_point_t q;
463 
464     curve448_point_copy(q, p);
465     gf_invert(q->t, q->x, 0);   /* 1/x */
466     gf_mul(q->z, q->t, q->y);   /* y/x */
467     gf_sqr(q->y, q->z);         /* (y/x)^2 */
468     gf_serialize(out, q->y, 1);
469     curve448_point_destroy(q);
470 }
471 
x448_derive_public_key(uint8_t out[X_PUBLIC_BYTES],const uint8_t scalar[X_PRIVATE_BYTES])472 void x448_derive_public_key(uint8_t out[X_PUBLIC_BYTES],
473                             const uint8_t scalar[X_PRIVATE_BYTES])
474 {
475     /* Scalar conditioning */
476     uint8_t scalar2[X_PRIVATE_BYTES];
477     curve448_scalar_t the_scalar;
478     curve448_point_t p;
479     unsigned int i;
480 
481     memcpy(scalar2, scalar, sizeof(scalar2));
482     scalar2[0] &= -(uint8_t)COFACTOR;
483 
484     scalar2[X_PRIVATE_BYTES - 1] &= ~((0u - 1u) << ((X_PRIVATE_BITS + 7) % 8));
485     scalar2[X_PRIVATE_BYTES - 1] |= 1 << ((X_PRIVATE_BITS + 7) % 8);
486 
487     curve448_scalar_decode_long(the_scalar, scalar2, sizeof(scalar2));
488 
489     /* Compensate for the encoding ratio */
490     for (i = 1; i < X448_ENCODE_RATIO; i <<= 1)
491         curve448_scalar_halve(the_scalar, the_scalar);
492 
493     curve448_precomputed_scalarmul(p, curve448_precomputed_base, the_scalar);
494     curve448_point_mul_by_ratio_and_encode_like_x448(out, p);
495     curve448_point_destroy(p);
496 }
497 
498 /* Control for variable-time scalar multiply algorithms. */
499 struct smvt_control {
500     int power, addend;
501 };
502 
503 #if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ > 3))
504 # define NUMTRAILINGZEROS	__builtin_ctz
505 #else
506 # define NUMTRAILINGZEROS	numtrailingzeros
numtrailingzeros(uint32_t i)507 static uint32_t numtrailingzeros(uint32_t i)
508 {
509     uint32_t tmp;
510     uint32_t num = 31;
511 
512     if (i == 0)
513         return 32;
514 
515     tmp = i << 16;
516     if (tmp != 0) {
517         i = tmp;
518         num -= 16;
519     }
520     tmp = i << 8;
521     if (tmp != 0) {
522         i = tmp;
523         num -= 8;
524     }
525     tmp = i << 4;
526     if (tmp != 0) {
527         i = tmp;
528         num -= 4;
529     }
530     tmp = i << 2;
531     if (tmp != 0) {
532         i = tmp;
533         num -= 2;
534     }
535     tmp = i << 1;
536     if (tmp != 0)
537         num--;
538 
539     return num;
540 }
541 #endif
542 
recode_wnaf(struct smvt_control * control,const curve448_scalar_t scalar,unsigned int table_bits)543 static int recode_wnaf(struct smvt_control *control,
544                        /* [nbits/(table_bits + 1) + 3] */
545                        const curve448_scalar_t scalar,
546                        unsigned int table_bits)
547 {
548     unsigned int table_size = C448_SCALAR_BITS / (table_bits + 1) + 3;
549     int position = table_size - 1; /* at the end */
550     uint64_t current = scalar->limb[0] & 0xFFFF;
551     uint32_t mask = (1 << (table_bits + 1)) - 1;
552     unsigned int w;
553     const unsigned int B_OVER_16 = sizeof(scalar->limb[0]) / 2;
554     unsigned int n, i;
555 
556     /* place the end marker */
557     control[position].power = -1;
558     control[position].addend = 0;
559     position--;
560 
561     /*
562      * PERF: Could negate scalar if it's large.  But then would need more cases
563      * in the actual code that uses it, all for an expected reduction of like
564      * 1/5 op. Probably not worth it.
565      */
566 
567     for (w = 1; w < (C448_SCALAR_BITS - 1) / 16 + 3; w++) {
568         if (w < (C448_SCALAR_BITS - 1) / 16 + 1) {
569             /* Refill the 16 high bits of current */
570             current += (uint32_t)((scalar->limb[w / B_OVER_16]
571                        >> (16 * (w % B_OVER_16))) << 16);
572         }
573 
574         while (current & 0xFFFF) {
575             uint32_t pos = NUMTRAILINGZEROS((uint32_t)current);
576             uint32_t odd = (uint32_t)current >> pos;
577             int32_t delta = odd & mask;
578 
579             assert(position >= 0);
580             if (odd & (1 << (table_bits + 1)))
581                 delta -= (1 << (table_bits + 1));
582             current -= delta * (1 << pos);
583             control[position].power = pos + 16 * (w - 1);
584             control[position].addend = delta;
585             position--;
586         }
587         current >>= 16;
588     }
589     assert(current == 0);
590 
591     position++;
592     n = table_size - position;
593     for (i = 0; i < n; i++)
594         control[i] = control[i + position];
595 
596     return n - 1;
597 }
598 
prepare_wnaf_table(pniels_t * output,const curve448_point_t working,unsigned int tbits)599 static void prepare_wnaf_table(pniels_t * output,
600                                const curve448_point_t working,
601                                unsigned int tbits)
602 {
603     curve448_point_t tmp;
604     int i;
605     pniels_t twop;
606 
607     pt_to_pniels(output[0], working);
608 
609     if (tbits == 0)
610         return;
611 
612     curve448_point_double(tmp, working);
613     pt_to_pniels(twop, tmp);
614 
615     add_pniels_to_pt(tmp, output[0], 0);
616     pt_to_pniels(output[1], tmp);
617 
618     for (i = 2; i < 1 << tbits; i++) {
619         add_pniels_to_pt(tmp, twop, 0);
620         pt_to_pniels(output[i], tmp);
621     }
622 
623     curve448_point_destroy(tmp);
624     OPENSSL_cleanse(twop, sizeof(twop));
625 }
626 
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)627 void curve448_base_double_scalarmul_non_secret(curve448_point_t combo,
628                                                const curve448_scalar_t scalar1,
629                                                const curve448_point_t base2,
630                                                const curve448_scalar_t scalar2)
631 {
632     const int table_bits_var = C448_WNAF_VAR_TABLE_BITS;
633     const int table_bits_pre = C448_WNAF_FIXED_TABLE_BITS;
634     struct smvt_control control_var[C448_SCALAR_BITS /
635                                     (C448_WNAF_VAR_TABLE_BITS + 1) + 3];
636     struct smvt_control control_pre[C448_SCALAR_BITS /
637                                     (C448_WNAF_FIXED_TABLE_BITS + 1) + 3];
638     int ncb_pre = recode_wnaf(control_pre, scalar1, table_bits_pre);
639     int ncb_var = recode_wnaf(control_var, scalar2, table_bits_var);
640     pniels_t precmp_var[1 << C448_WNAF_VAR_TABLE_BITS];
641     int contp = 0, contv = 0, i;
642 
643     prepare_wnaf_table(precmp_var, base2, table_bits_var);
644     i = control_var[0].power;
645 
646     if (i < 0) {
647         curve448_point_copy(combo, curve448_point_identity);
648         return;
649     }
650     if (i > control_pre[0].power) {
651         pniels_to_pt(combo, precmp_var[control_var[0].addend >> 1]);
652         contv++;
653     } else if (i == control_pre[0].power && i >= 0) {
654         pniels_to_pt(combo, precmp_var[control_var[0].addend >> 1]);
655         add_niels_to_pt(combo, curve448_wnaf_base[control_pre[0].addend >> 1],
656                         i);
657         contv++;
658         contp++;
659     } else {
660         i = control_pre[0].power;
661         niels_to_pt(combo, curve448_wnaf_base[control_pre[0].addend >> 1]);
662         contp++;
663     }
664 
665     for (i--; i >= 0; i--) {
666         int cv = (i == control_var[contv].power);
667         int cp = (i == control_pre[contp].power);
668 
669         point_double_internal(combo, combo, i && !(cv || cp));
670 
671         if (cv) {
672             assert(control_var[contv].addend);
673 
674             if (control_var[contv].addend > 0)
675                 add_pniels_to_pt(combo,
676                                  precmp_var[control_var[contv].addend >> 1],
677                                  i && !cp);
678             else
679                 sub_pniels_from_pt(combo,
680                                    precmp_var[(-control_var[contv].addend)
681                                               >> 1], i && !cp);
682             contv++;
683         }
684 
685         if (cp) {
686             assert(control_pre[contp].addend);
687 
688             if (control_pre[contp].addend > 0)
689                 add_niels_to_pt(combo,
690                                 curve448_wnaf_base[control_pre[contp].addend
691                                                    >> 1], i);
692             else
693                 sub_niels_from_pt(combo,
694                                   curve448_wnaf_base[(-control_pre
695                                                       [contp].addend) >> 1], i);
696             contp++;
697         }
698     }
699 
700     /* This function is non-secret, but whatever this is cheap. */
701     OPENSSL_cleanse(control_var, sizeof(control_var));
702     OPENSSL_cleanse(control_pre, sizeof(control_pre));
703     OPENSSL_cleanse(precmp_var, sizeof(precmp_var));
704 
705     assert(contv == ncb_var);
706     (void)ncb_var;
707     assert(contp == ncb_pre);
708     (void)ncb_pre;
709 }
710 
curve448_point_destroy(curve448_point_t point)711 void curve448_point_destroy(curve448_point_t point)
712 {
713     OPENSSL_cleanse(point, sizeof(curve448_point_t));
714 }
715 
X448(uint8_t out_shared_key[56],const uint8_t private_key[56],const uint8_t peer_public_value[56])716 int X448(uint8_t out_shared_key[56], const uint8_t private_key[56],
717          const uint8_t peer_public_value[56])
718 {
719     return x448_int(out_shared_key, peer_public_value, private_key)
720            == C448_SUCCESS;
721 }
722 
X448_public_from_private(uint8_t out_public_value[56],const uint8_t private_key[56])723 void X448_public_from_private(uint8_t out_public_value[56],
724                               const uint8_t private_key[56])
725 {
726     x448_derive_public_key(out_public_value, private_key);
727 }
728