1 /**
2 * @file ed448goldilocks/decaf.c
3 * @author Mike Hamburg
4 *
5 * @copyright
6 * Copyright (c) 2015-2016 Cryptography Research, Inc. \n
7 * Released under the MIT License. See LICENSE.txt for license information.
8 *
9 * @brief Decaf high-level functions.
10 *
11 * @warning This file was automatically generated in Python.
12 * Please do not edit it.
13 */
14 #define _XOPEN_SOURCE 600 /* for posix_memalign */
15 #include "word.h"
16 #include "field.h"
17
18 #include <decaf.h>
19 #include <decaf/ed448.h>
20
21 /* Template stuff */
22 #define API_NS(_id) cryptonite_decaf_448_##_id
23 #define SCALAR_BITS CRYPTONITE_DECAF_448_SCALAR_BITS
24 #define SCALAR_SER_BYTES CRYPTONITE_DECAF_448_SCALAR_BYTES
25 #define SCALAR_LIMBS CRYPTONITE_DECAF_448_SCALAR_LIMBS
26 #define scalar_t API_NS(scalar_t)
27 #define point_t API_NS(point_t)
28 #define precomputed_s API_NS(precomputed_s)
29 #define IMAGINE_TWIST 0
30 #define COFACTOR 4
31
32 /* Comb config: number of combs, n, t, s. */
33 #define COMBS_N 5
34 #define COMBS_T 5
35 #define COMBS_S 18
36 #define CRYPTONITE_DECAF_WINDOW_BITS 5
37 #define CRYPTONITE_DECAF_WNAF_FIXED_TABLE_BITS 5
38 #define CRYPTONITE_DECAF_WNAF_VAR_TABLE_BITS 3
39
40 #define EDDSA_USE_SIGMA_ISOGENY 0
41
42 static const int EDWARDS_D = -39081;
43 static const scalar_t point_scalarmul_adjustment = {{{
44 SC_LIMB(0xc873d6d54a7bb0cf), SC_LIMB(0xe933d8d723a70aad), SC_LIMB(0xbb124b65129c96fd), SC_LIMB(0x00000008335dc163)
45 }}}, precomputed_scalarmul_adjustment = {{{
46 SC_LIMB(0xc873d6d54a7bb0cf), SC_LIMB(0xe933d8d723a70aad), SC_LIMB(0xbb124b65129c96fd), SC_LIMB(0x00000008335dc163)
47 }}};
48
49 const uint8_t cryptonite_decaf_x448_base_point[CRYPTONITE_DECAF_X448_PUBLIC_BYTES] = { 0x05 };
50
51 #if COFACTOR==8 || EDDSA_USE_SIGMA_ISOGENY
52 static const gf SQRT_ONE_MINUS_D = {FIELD_LITERAL(
53 /* NONE */
54 )};
55 #endif
56
57 /* End of template stuff */
58
59 /* Sanity */
60 #if (COFACTOR == 8) && !IMAGINE_TWIST && !UNSAFE_CURVE_HAS_POINTS_AT_INFINITY
61 /* FUTURE MAGIC: Curve41417 doesn't have these properties. */
62 #error "Currently require IMAGINE_TWIST (and thus p=5 mod 8) for cofactor 8"
63 /* OK, but why?
64 * Two reasons: #1: There are bugs when COFACTOR == && IMAGINE_TWIST
65 # #2:
66 */
67 #endif
68
69 #if IMAGINE_TWIST && (P_MOD_8 != 5)
70 #error "Cannot use IMAGINE_TWIST except for p == 5 mod 8"
71 #endif
72
73 #if (COFACTOR != 8) && (COFACTOR != 4)
74 #error "COFACTOR must be 4 or 8"
75 #endif
76
77 #if IMAGINE_TWIST
78 extern const gf SQRT_MINUS_ONE;
79 #endif
80
81 #define WBITS CRYPTONITE_DECAF_WORD_BITS /* NB this may be different from ARCH_WORD_BITS */
82
83 extern const point_t API_NS(point_base);
84
85 /* Projective Niels coordinates */
86 typedef struct { gf a, b, c; } niels_s, niels_t[1];
87 typedef struct { niels_t n; gf z; } VECTOR_ALIGNED pniels_s, pniels_t[1];
88
89 /* Precomputed base */
90 struct precomputed_s { niels_t table [COMBS_N<<(COMBS_T-1)]; };
91
92 extern const gf API_NS(precomputed_base_as_fe)[];
93 const precomputed_s *API_NS(precomputed_base) =
94 (const precomputed_s *) &API_NS(precomputed_base_as_fe);
95
96 const size_t API_NS(sizeof_precomputed_s) = sizeof(precomputed_s);
97 const size_t API_NS(alignof_precomputed_s) = sizeof(big_register_t);
98
99 /** Inverse. */
100 static void
cryptonite_gf_invert(gf y,const gf x,int assert_nonzero)101 cryptonite_gf_invert(gf y, const gf x, int assert_nonzero) {
102 gf t1, t2;
103 cryptonite_gf_sqr(t1, x); // o^2
104 mask_t ret = cryptonite_gf_isr(t2, t1); // +-1/sqrt(o^2) = +-1/o
105 (void)ret;
106 if (assert_nonzero) assert(ret);
107 cryptonite_gf_sqr(t1, t2);
108 cryptonite_gf_mul(t2, t1, x); // not direct to y in case of alias.
109 cryptonite_gf_copy(y, t2);
110 }
111
112 /** Return high bit of x = low bit of 2x mod p */
cryptonite_gf_lobit(const gf x)113 static mask_t cryptonite_gf_lobit(const gf x) {
114 gf y;
115 cryptonite_gf_copy(y,x);
116 cryptonite_gf_strong_reduce(y);
117 return -(y->limb[0]&1);
118 }
119
120 /** identity = (0,1) */
121 const point_t API_NS(point_identity) = {{{{{0}}},{{{1}}},{{{1}}},{{{0}}}}};
122
123 void API_NS(deisogenize) (
124 cryptonite_gf_s *__restrict__ s,
125 cryptonite_gf_s *__restrict__ minus_t_over_s,
126 const point_t p,
127 mask_t toggle_hibit_s,
128 mask_t toggle_hibit_t_over_s,
129 mask_t toggle_rotation
130 );
131
API_NS(deisogenize)132 void API_NS(deisogenize) (
133 cryptonite_gf_s *__restrict__ s,
134 cryptonite_gf_s *__restrict__ minus_t_over_s,
135 const point_t p,
136 mask_t toggle_hibit_s,
137 mask_t toggle_hibit_t_over_s,
138 mask_t toggle_rotation
139 ) {
140 #if COFACTOR == 4 && !IMAGINE_TWIST
141 (void) toggle_rotation;
142
143 gf b, d;
144 cryptonite_gf_s *c = s, *a = minus_t_over_s;
145 cryptonite_gf_mulw(a, p->y, 1-EDWARDS_D);
146 cryptonite_gf_mul(c, a, p->t); /* -dYT, with EDWARDS_D = d-1 */
147 cryptonite_gf_mul(a, p->x, p->z);
148 cryptonite_gf_sub(d, c, a); /* aXZ-dYT with a=-1 */
149 cryptonite_gf_add(a, p->z, p->y);
150 cryptonite_gf_sub(b, p->z, p->y);
151 cryptonite_gf_mul(c, b, a);
152 cryptonite_gf_mulw(b, c, -EDWARDS_D); /* (a-d)(Z+Y)(Z-Y) */
153 mask_t ok = cryptonite_gf_isr (a,b); /* r in the paper */
154 (void)ok; assert(ok | cryptonite_gf_eq(b,ZERO));
155 cryptonite_gf_mulw (b, a, -EDWARDS_D); /* u in the paper */
156
157 cryptonite_gf_mul(c,a,d); /* r(aZX-dYT) */
158 cryptonite_gf_mul(a,b,p->z); /* uZ */
159 cryptonite_gf_add(a,a,a); /* 2uZ */
160
161 mask_t tg = toggle_hibit_t_over_s ^ ~cryptonite_gf_hibit(minus_t_over_s);
162 cryptonite_gf_cond_neg(minus_t_over_s, tg); /* t/s <-? -t/s */
163 cryptonite_gf_cond_neg(c, tg); /* u <- -u if negative. */
164
165 cryptonite_gf_add(d,c,p->y);
166 cryptonite_gf_mul(s,b,d);
167 cryptonite_gf_cond_neg(s, toggle_hibit_s ^ cryptonite_gf_hibit(s));
168 #else
169 /* More complicated because of rotation */
170 /* MAGIC This code is wrong for certain non-Curve25519 curves;
171 * check if it's because of Cofactor==8 or IMAGINE_TWIST */
172
173 gf c, d;
174 cryptonite_gf_s *b = s, *a = minus_t_over_s;
175
176 #if IMAGINE_TWIST
177 gf x, t;
178 cryptonite_gf_div_qnr(x,p->x);
179 cryptonite_gf_div_qnr(t,p->t);
180 cryptonite_gf_add ( a, p->z, x );
181 cryptonite_gf_sub ( b, p->z, x );
182 cryptonite_gf_mul ( c, a, b ); /* "zx" = Z^2 - aX^2 = Z^2 - X^2 */
183 #else
184 const cryptonite_gf_s *x = p->x, *t = p->t;
185 cryptonite_gf_sqr ( a, p->z );
186 cryptonite_gf_sqr ( b, p->x );
187 cryptonite_gf_add ( c, a, b ); /* "zx" = Z^2 - aX^2 = Z^2 + X^2 */
188 #endif
189 /* Here: c = "zx" in the SAGE code = Z^2 - aX^2 */
190
191 cryptonite_gf_mul ( a, p->z, t ); /* "tz" = T*Z */
192 cryptonite_gf_sqr ( b, a );
193 cryptonite_gf_mul ( d, b, c ); /* (TZ)^2 * (Z^2-aX^2) */
194 mask_t ok = cryptonite_gf_isr(b, d);
195 (void)ok; assert(ok | cryptonite_gf_eq(d,ZERO));
196 cryptonite_gf_mul ( d, b, a ); /* "osx" = 1 / sqrt(z^2-ax^2) */
197 cryptonite_gf_mul ( a, b, c );
198 cryptonite_gf_mul ( b, a, d ); /* 1/tz */
199
200 mask_t rotate;
201 #if (COFACTOR == 8)
202 gf e;
203 cryptonite_gf_sqr(e, p->z);
204 cryptonite_gf_mul(a, e, b); /* z^2 / tz = z/t = 1/xy */
205 rotate = cryptonite_gf_hibit(a) ^ toggle_rotation;
206 /* Curve25519: cond select between zx * 1/tz or sqrt(1-d); y=-x */
207 cryptonite_gf_mul ( a, b, c );
208 cryptonite_gf_cond_sel ( a, a, SQRT_ONE_MINUS_D, rotate );
209 cryptonite_gf_cond_sel ( e, p->y, x, rotate );
210 #else
211 const cryptonite_gf_s *e = x;
212 (void)toggle_rotation;
213 rotate = 0;
214 #endif
215
216 cryptonite_gf_mul ( c, a, d ); // new "osx"
217 cryptonite_gf_mul ( a, c, p->z );
218 cryptonite_gf_add ( minus_t_over_s, a, a ); // 2 * "osx" * Z
219 cryptonite_gf_mul ( d, b, p->z );
220
221 mask_t tg = toggle_hibit_t_over_s ^~ cryptonite_gf_hibit(minus_t_over_s);
222 cryptonite_gf_cond_neg ( minus_t_over_s, tg );
223 cryptonite_gf_cond_neg ( c, rotate ^ tg );
224 cryptonite_gf_add ( d, d, c );
225 cryptonite_gf_mul ( s, d, e ); /* here "x" = y unless rotate */
226 cryptonite_gf_cond_neg ( s, toggle_hibit_s ^ cryptonite_gf_hibit(s) );
227 #endif
228 }
229
API_NS(point_encode)230 void API_NS(point_encode)( unsigned char ser[SER_BYTES], const point_t p ) {
231 gf s, mtos;
232 API_NS(deisogenize)(s,mtos,p,0,0,0);
233 cryptonite_gf_serialize(ser,s,0);
234 }
235
API_NS(point_decode)236 cryptonite_decaf_error_t API_NS(point_decode) (
237 point_t p,
238 const unsigned char ser[SER_BYTES],
239 cryptonite_decaf_bool_t allow_identity
240 ) {
241 gf s, a, b, c, d, e, f;
242 mask_t succ = cryptonite_gf_deserialize(s, ser, 0);
243 mask_t zero = cryptonite_gf_eq(s, ZERO);
244 succ &= bool_to_mask(allow_identity) | ~zero;
245 cryptonite_gf_sqr ( a, s ); /* s^2 */
246 #if IMAGINE_TWIST
247 cryptonite_gf_sub ( f, ONE, a ); /* f = 1-as^2 = 1-s^2*/
248 #else
249 cryptonite_gf_add ( f, ONE, a ); /* f = 1-as^2 = 1+s^2 */
250 #endif
251 succ &= ~ cryptonite_gf_eq( f, ZERO );
252 cryptonite_gf_sqr ( b, f ); /* (1-as^2)^2 = 1 - 2as^2 + a^2 s^4 */
253 cryptonite_gf_mulw ( c, a, 4*IMAGINE_TWIST-4*EDWARDS_D );
254 cryptonite_gf_add ( c, c, b ); /* t^2 = 1 + (2a-4d) s^2 + s^4 */
255 cryptonite_gf_mul ( d, f, s ); /* s * (1-as^2) for denoms */
256 cryptonite_gf_sqr ( e, d ); /* s^2 * (1-as^2)^2 */
257 cryptonite_gf_mul ( b, c, e ); /* t^2 * s^2 * (1-as^2)^2 */
258
259 succ &= cryptonite_gf_isr(e,b) | cryptonite_gf_eq(b,ZERO); /* e = 1/(t s (1-as^2)) */
260 cryptonite_gf_mul ( b, e, d ); /* 1 / t */
261 cryptonite_gf_mul ( d, e, c ); /* t / (s(1-as^2)) */
262 cryptonite_gf_mul ( e, d, f ); /* t / s */
263 mask_t negtos = cryptonite_gf_hibit(e);
264 cryptonite_gf_cond_neg(b, negtos);
265 cryptonite_gf_cond_neg(d, negtos);
266
267 #if IMAGINE_TWIST
268 cryptonite_gf_add ( p->z, ONE, a); /* Z = 1+as^2 = 1-s^2 */
269 #else
270 cryptonite_gf_sub ( p->z, ONE, a); /* Z = 1+as^2 = 1-s^2 */
271 #endif
272
273 #if COFACTOR == 8
274 cryptonite_gf_mul ( a, p->z, d); /* t(1+s^2) / s(1-s^2) = 2/xy */
275 succ &= ~cryptonite_gf_lobit(a); /* = ~cryptonite_gf_hibit(a/2), since cryptonite_gf_hibit(x) = cryptonite_gf_lobit(2x) */
276 #endif
277
278 cryptonite_gf_mul ( a, f, b ); /* y = (1-s^2) / t */
279 cryptonite_gf_mul ( p->y, p->z, a ); /* Y = yZ */
280 #if IMAGINE_TWIST
281 cryptonite_gf_add ( b, s, s );
282 cryptonite_gf_mul(p->x, b, SQRT_MINUS_ONE); /* Curve25519 */
283 #else
284 cryptonite_gf_add ( p->x, s, s );
285 #endif
286 cryptonite_gf_mul ( p->t, p->x, a ); /* T = 2s (1-as^2)/t */
287
288 #if UNSAFE_CURVE_HAS_POINTS_AT_INFINITY
289 /* This can't happen for any of the supported configurations.
290 *
291 * If it can happen (because s=1), it's because the curve has points
292 * at infinity, which means that there may be critical security bugs
293 * elsewhere in the library. In that case, it's better that you hit
294 * the assertion in point_valid, which will happen in the test suite
295 * since it tests s=1.
296 *
297 * This debugging option is to allow testing of IMAGINE_TWIST = 0 on
298 * Ed25519, without hitting that assertion. Don't use it in
299 * production.
300 */
301 succ &= ~cryptonite_gf_eq(p->z,ZERO);
302 #endif
303
304 p->y->limb[0] -= zero;
305 assert(API_NS(point_valid)(p) | ~succ);
306
307 return cryptonite_decaf_succeed_if(mask_to_bool(succ));
308 }
309
310 #if IMAGINE_TWIST
311 #define TWISTED_D (-(EDWARDS_D))
312 #else
313 #define TWISTED_D ((EDWARDS_D)-1)
314 #endif
315
316 #if TWISTED_D < 0
317 #define EFF_D (-(TWISTED_D))
318 #define NEG_D 1
319 #else
320 #define EFF_D TWISTED_D
321 #define NEG_D 0
322 #endif
323
API_NS(point_sub)324 void API_NS(point_sub) (
325 point_t p,
326 const point_t q,
327 const point_t r
328 ) {
329 gf a, b, c, d;
330 cryptonite_gf_sub_nr ( b, q->y, q->x ); /* 3+e */
331 cryptonite_gf_sub_nr ( d, r->y, r->x ); /* 3+e */
332 cryptonite_gf_add_nr ( c, r->y, r->x ); /* 2+e */
333 cryptonite_gf_mul ( a, c, b );
334 cryptonite_gf_add_nr ( b, q->y, q->x ); /* 2+e */
335 cryptonite_gf_mul ( p->y, d, b );
336 cryptonite_gf_mul ( b, r->t, q->t );
337 cryptonite_gf_mulw ( p->x, b, 2*EFF_D );
338 cryptonite_gf_add_nr ( b, a, p->y ); /* 2+e */
339 cryptonite_gf_sub_nr ( c, p->y, a ); /* 3+e */
340 cryptonite_gf_mul ( a, q->z, r->z );
341 cryptonite_gf_add_nr ( a, a, a ); /* 2+e */
342 if (GF_HEADROOM <= 3) cryptonite_gf_weak_reduce(a); /* or 1+e */
343 #if NEG_D
344 cryptonite_gf_sub_nr ( p->y, a, p->x ); /* 4+e or 3+e */
345 cryptonite_gf_add_nr ( a, a, p->x ); /* 3+e or 2+e */
346 #else
347 cryptonite_gf_add_nr ( p->y, a, p->x ); /* 3+e or 2+e */
348 cryptonite_gf_sub_nr ( a, a, p->x ); /* 4+e or 3+e */
349 #endif
350 cryptonite_gf_mul ( p->z, a, p->y );
351 cryptonite_gf_mul ( p->x, p->y, c );
352 cryptonite_gf_mul ( p->y, a, b );
353 cryptonite_gf_mul ( p->t, b, c );
354 }
355
API_NS(point_add)356 void API_NS(point_add) (
357 point_t p,
358 const point_t q,
359 const point_t r
360 ) {
361 gf a, b, c, d;
362 cryptonite_gf_sub_nr ( b, q->y, q->x ); /* 3+e */
363 cryptonite_gf_sub_nr ( c, r->y, r->x ); /* 3+e */
364 cryptonite_gf_add_nr ( d, r->y, r->x ); /* 2+e */
365 cryptonite_gf_mul ( a, c, b );
366 cryptonite_gf_add_nr ( b, q->y, q->x ); /* 2+e */
367 cryptonite_gf_mul ( p->y, d, b );
368 cryptonite_gf_mul ( b, r->t, q->t );
369 cryptonite_gf_mulw ( p->x, b, 2*EFF_D );
370 cryptonite_gf_add_nr ( b, a, p->y ); /* 2+e */
371 cryptonite_gf_sub_nr ( c, p->y, a ); /* 3+e */
372 cryptonite_gf_mul ( a, q->z, r->z );
373 cryptonite_gf_add_nr ( a, a, a ); /* 2+e */
374 if (GF_HEADROOM <= 3) cryptonite_gf_weak_reduce(a); /* or 1+e */
375 #if NEG_D
376 cryptonite_gf_add_nr ( p->y, a, p->x ); /* 3+e or 2+e */
377 cryptonite_gf_sub_nr ( a, a, p->x ); /* 4+e or 3+e */
378 #else
379 cryptonite_gf_sub_nr ( p->y, a, p->x ); /* 4+e or 3+e */
380 cryptonite_gf_add_nr ( a, a, p->x ); /* 3+e or 2+e */
381 #endif
382 cryptonite_gf_mul ( p->z, a, p->y );
383 cryptonite_gf_mul ( p->x, p->y, c );
384 cryptonite_gf_mul ( p->y, a, b );
385 cryptonite_gf_mul ( p->t, b, c );
386 }
387
388 static CRYPTONITE_DECAF_NOINLINE void
point_double_internal(point_t p,const point_t q,int before_double)389 point_double_internal (
390 point_t p,
391 const point_t q,
392 int before_double
393 ) {
394 gf a, b, c, d;
395 cryptonite_gf_sqr ( c, q->x );
396 cryptonite_gf_sqr ( a, q->y );
397 cryptonite_gf_add_nr ( d, c, a ); /* 2+e */
398 cryptonite_gf_add_nr ( p->t, q->y, q->x ); /* 2+e */
399 cryptonite_gf_sqr ( b, p->t );
400 cryptonite_gf_subx_nr ( b, b, d, 3 ); /* 4+e */
401 cryptonite_gf_sub_nr ( p->t, a, c ); /* 3+e */
402 cryptonite_gf_sqr ( p->x, q->z );
403 cryptonite_gf_add_nr ( p->z, p->x, p->x ); /* 2+e */
404 cryptonite_gf_subx_nr ( a, p->z, p->t, 4 ); /* 6+e */
405 if (GF_HEADROOM == 5) cryptonite_gf_weak_reduce(a); /* or 1+e */
406 cryptonite_gf_mul ( p->x, a, b );
407 cryptonite_gf_mul ( p->z, p->t, a );
408 cryptonite_gf_mul ( p->y, p->t, d );
409 if (!before_double) cryptonite_gf_mul ( p->t, b, d );
410 }
411
API_NS(point_double)412 void API_NS(point_double)(point_t p, const point_t q) {
413 point_double_internal(p,q,0);
414 }
415
API_NS(point_negate)416 void API_NS(point_negate) (
417 point_t nega,
418 const point_t a
419 ) {
420 cryptonite_gf_sub(nega->x, ZERO, a->x);
421 cryptonite_gf_copy(nega->y, a->y);
422 cryptonite_gf_copy(nega->z, a->z);
423 cryptonite_gf_sub(nega->t, ZERO, a->t);
424 }
425
426 /* Operations on [p]niels */
427 static CRYPTONITE_DECAF_INLINE void
cond_neg_niels(niels_t n,mask_t neg)428 cond_neg_niels (
429 niels_t n,
430 mask_t neg
431 ) {
432 cryptonite_gf_cond_swap(n->a, n->b, neg);
433 cryptonite_gf_cond_neg(n->c, neg);
434 }
435
pt_to_pniels(pniels_t b,const point_t a)436 static CRYPTONITE_DECAF_NOINLINE void pt_to_pniels (
437 pniels_t b,
438 const point_t a
439 ) {
440 cryptonite_gf_sub ( b->n->a, a->y, a->x );
441 cryptonite_gf_add ( b->n->b, a->x, a->y );
442 cryptonite_gf_mulw ( b->n->c, a->t, 2*TWISTED_D );
443 cryptonite_gf_add ( b->z, a->z, a->z );
444 }
445
pniels_to_pt(point_t e,const pniels_t d)446 static CRYPTONITE_DECAF_NOINLINE void pniels_to_pt (
447 point_t e,
448 const pniels_t d
449 ) {
450 gf eu;
451 cryptonite_gf_add ( eu, d->n->b, d->n->a );
452 cryptonite_gf_sub ( e->y, d->n->b, d->n->a );
453 cryptonite_gf_mul ( e->t, e->y, eu);
454 cryptonite_gf_mul ( e->x, d->z, e->y );
455 cryptonite_gf_mul ( e->y, d->z, eu );
456 cryptonite_gf_sqr ( e->z, d->z );
457 }
458
459 static CRYPTONITE_DECAF_NOINLINE void
niels_to_pt(point_t e,const niels_t n)460 niels_to_pt (
461 point_t e,
462 const niels_t n
463 ) {
464 cryptonite_gf_add ( e->y, n->b, n->a );
465 cryptonite_gf_sub ( e->x, n->b, n->a );
466 cryptonite_gf_mul ( e->t, e->y, e->x );
467 cryptonite_gf_copy ( e->z, ONE );
468 }
469
470 static CRYPTONITE_DECAF_NOINLINE void
add_niels_to_pt(point_t d,const niels_t e,int before_double)471 add_niels_to_pt (
472 point_t d,
473 const niels_t e,
474 int before_double
475 ) {
476 gf a, b, c;
477 cryptonite_gf_sub_nr ( b, d->y, d->x ); /* 3+e */
478 cryptonite_gf_mul ( a, e->a, b );
479 cryptonite_gf_add_nr ( b, d->x, d->y ); /* 2+e */
480 cryptonite_gf_mul ( d->y, e->b, b );
481 cryptonite_gf_mul ( d->x, e->c, d->t );
482 cryptonite_gf_add_nr ( c, a, d->y ); /* 2+e */
483 cryptonite_gf_sub_nr ( b, d->y, a ); /* 3+e */
484 cryptonite_gf_sub_nr ( d->y, d->z, d->x ); /* 3+e */
485 cryptonite_gf_add_nr ( a, d->x, d->z ); /* 2+e */
486 cryptonite_gf_mul ( d->z, a, d->y );
487 cryptonite_gf_mul ( d->x, d->y, b );
488 cryptonite_gf_mul ( d->y, a, c );
489 if (!before_double) cryptonite_gf_mul ( d->t, b, c );
490 }
491
492 static CRYPTONITE_DECAF_NOINLINE void
sub_niels_from_pt(point_t d,const niels_t e,int before_double)493 sub_niels_from_pt (
494 point_t d,
495 const niels_t e,
496 int before_double
497 ) {
498 gf a, b, c;
499 cryptonite_gf_sub_nr ( b, d->y, d->x ); /* 3+e */
500 cryptonite_gf_mul ( a, e->b, b );
501 cryptonite_gf_add_nr ( b, d->x, d->y ); /* 2+e */
502 cryptonite_gf_mul ( d->y, e->a, b );
503 cryptonite_gf_mul ( d->x, e->c, d->t );
504 cryptonite_gf_add_nr ( c, a, d->y ); /* 2+e */
505 cryptonite_gf_sub_nr ( b, d->y, a ); /* 3+e */
506 cryptonite_gf_add_nr ( d->y, d->z, d->x ); /* 2+e */
507 cryptonite_gf_sub_nr ( a, d->z, d->x ); /* 3+e */
508 cryptonite_gf_mul ( d->z, a, d->y );
509 cryptonite_gf_mul ( d->x, d->y, b );
510 cryptonite_gf_mul ( d->y, a, c );
511 if (!before_double) cryptonite_gf_mul ( d->t, b, c );
512 }
513
514 static void
add_pniels_to_pt(point_t p,const pniels_t pn,int before_double)515 add_pniels_to_pt (
516 point_t p,
517 const pniels_t pn,
518 int before_double
519 ) {
520 gf L0;
521 cryptonite_gf_mul ( L0, p->z, pn->z );
522 cryptonite_gf_copy ( p->z, L0 );
523 add_niels_to_pt( p, pn->n, before_double );
524 }
525
526 static void
sub_pniels_from_pt(point_t p,const pniels_t pn,int before_double)527 sub_pniels_from_pt (
528 point_t p,
529 const pniels_t pn,
530 int before_double
531 ) {
532 gf L0;
533 cryptonite_gf_mul ( L0, p->z, pn->z );
534 cryptonite_gf_copy ( p->z, L0 );
535 sub_niels_from_pt( p, pn->n, before_double );
536 }
537
538 static CRYPTONITE_DECAF_NOINLINE void
prepare_fixed_window(pniels_t * multiples,const point_t b,int ntable)539 prepare_fixed_window(
540 pniels_t *multiples,
541 const point_t b,
542 int ntable
543 ) {
544 point_t tmp;
545 pniels_t pn;
546 int i;
547
548 point_double_internal(tmp, b, 0);
549 pt_to_pniels(pn, tmp);
550 pt_to_pniels(multiples[0], b);
551 API_NS(point_copy)(tmp, b);
552 for (i=1; i<ntable; i++) {
553 add_pniels_to_pt(tmp, pn, 0);
554 pt_to_pniels(multiples[i], tmp);
555 }
556
557 cryptonite_decaf_bzero(pn,sizeof(pn));
558 cryptonite_decaf_bzero(tmp,sizeof(tmp));
559 }
560
API_NS(point_scalarmul)561 void API_NS(point_scalarmul) (
562 point_t a,
563 const point_t b,
564 const scalar_t scalar
565 ) {
566 const int WINDOW = CRYPTONITE_DECAF_WINDOW_BITS,
567 WINDOW_MASK = (1<<WINDOW)-1,
568 WINDOW_T_MASK = WINDOW_MASK >> 1,
569 NTABLE = 1<<(WINDOW-1);
570
571 scalar_t scalar1x;
572 API_NS(scalar_add)(scalar1x, scalar, point_scalarmul_adjustment);
573 API_NS(scalar_halve)(scalar1x,scalar1x);
574
575 /* Set up a precomputed table with odd multiples of b. */
576 pniels_t pn, multiples[NTABLE];
577 point_t tmp;
578 prepare_fixed_window(multiples, b, NTABLE);
579
580 /* Initialize. */
581 int i,j,first=1;
582 i = SCALAR_BITS - ((SCALAR_BITS-1) % WINDOW) - 1;
583
584 for (; i>=0; i-=WINDOW) {
585 /* Fetch another block of bits */
586 word_t bits = scalar1x->limb[i/WBITS] >> (i%WBITS);
587 if (i%WBITS >= WBITS-WINDOW && i/WBITS<SCALAR_LIMBS-1) {
588 bits ^= scalar1x->limb[i/WBITS+1] << (WBITS - (i%WBITS));
589 }
590 bits &= WINDOW_MASK;
591 mask_t inv = (bits>>(WINDOW-1))-1;
592 bits ^= inv;
593
594 /* Add in from table. Compute t only on last iteration. */
595 constant_time_lookup(pn, multiples, sizeof(pn), NTABLE, bits & WINDOW_T_MASK);
596 cond_neg_niels(pn->n, inv);
597 if (first) {
598 pniels_to_pt(tmp, pn);
599 first = 0;
600 } else {
601 /* Using Hisil et al's lookahead method instead of extensible here
602 * for no particular reason. Double WINDOW times, but only compute t on
603 * the last one.
604 */
605 for (j=0; j<WINDOW-1; j++)
606 point_double_internal(tmp, tmp, -1);
607 point_double_internal(tmp, tmp, 0);
608 add_pniels_to_pt(tmp, pn, i ? -1 : 0);
609 }
610 }
611
612 /* Write out the answer */
613 API_NS(point_copy)(a,tmp);
614
615 cryptonite_decaf_bzero(scalar1x,sizeof(scalar1x));
616 cryptonite_decaf_bzero(pn,sizeof(pn));
617 cryptonite_decaf_bzero(multiples,sizeof(multiples));
618 cryptonite_decaf_bzero(tmp,sizeof(tmp));
619 }
620
API_NS(point_double_scalarmul)621 void API_NS(point_double_scalarmul) (
622 point_t a,
623 const point_t b,
624 const scalar_t scalarb,
625 const point_t c,
626 const scalar_t scalarc
627 ) {
628 const int WINDOW = CRYPTONITE_DECAF_WINDOW_BITS,
629 WINDOW_MASK = (1<<WINDOW)-1,
630 WINDOW_T_MASK = WINDOW_MASK >> 1,
631 NTABLE = 1<<(WINDOW-1);
632
633 scalar_t scalar1x, scalar2x;
634 API_NS(scalar_add)(scalar1x, scalarb, point_scalarmul_adjustment);
635 API_NS(scalar_halve)(scalar1x,scalar1x);
636 API_NS(scalar_add)(scalar2x, scalarc, point_scalarmul_adjustment);
637 API_NS(scalar_halve)(scalar2x,scalar2x);
638
639 /* Set up a precomputed table with odd multiples of b. */
640 pniels_t pn, multiples1[NTABLE], multiples2[NTABLE];
641 point_t tmp;
642 prepare_fixed_window(multiples1, b, NTABLE);
643 prepare_fixed_window(multiples2, c, NTABLE);
644
645 /* Initialize. */
646 int i,j,first=1;
647 i = SCALAR_BITS - ((SCALAR_BITS-1) % WINDOW) - 1;
648
649 for (; i>=0; i-=WINDOW) {
650 /* Fetch another block of bits */
651 word_t bits1 = scalar1x->limb[i/WBITS] >> (i%WBITS),
652 bits2 = scalar2x->limb[i/WBITS] >> (i%WBITS);
653 if (i%WBITS >= WBITS-WINDOW && i/WBITS<SCALAR_LIMBS-1) {
654 bits1 ^= scalar1x->limb[i/WBITS+1] << (WBITS - (i%WBITS));
655 bits2 ^= scalar2x->limb[i/WBITS+1] << (WBITS - (i%WBITS));
656 }
657 bits1 &= WINDOW_MASK;
658 bits2 &= WINDOW_MASK;
659 mask_t inv1 = (bits1>>(WINDOW-1))-1;
660 mask_t inv2 = (bits2>>(WINDOW-1))-1;
661 bits1 ^= inv1;
662 bits2 ^= inv2;
663
664 /* Add in from table. Compute t only on last iteration. */
665 constant_time_lookup(pn, multiples1, sizeof(pn), NTABLE, bits1 & WINDOW_T_MASK);
666 cond_neg_niels(pn->n, inv1);
667 if (first) {
668 pniels_to_pt(tmp, pn);
669 first = 0;
670 } else {
671 /* Using Hisil et al's lookahead method instead of extensible here
672 * for no particular reason. Double WINDOW times, but only compute t on
673 * the last one.
674 */
675 for (j=0; j<WINDOW-1; j++)
676 point_double_internal(tmp, tmp, -1);
677 point_double_internal(tmp, tmp, 0);
678 add_pniels_to_pt(tmp, pn, 0);
679 }
680 constant_time_lookup(pn, multiples2, sizeof(pn), NTABLE, bits2 & WINDOW_T_MASK);
681 cond_neg_niels(pn->n, inv2);
682 add_pniels_to_pt(tmp, pn, i?-1:0);
683 }
684
685 /* Write out the answer */
686 API_NS(point_copy)(a,tmp);
687
688
689 cryptonite_decaf_bzero(scalar1x,sizeof(scalar1x));
690 cryptonite_decaf_bzero(scalar2x,sizeof(scalar2x));
691 cryptonite_decaf_bzero(pn,sizeof(pn));
692 cryptonite_decaf_bzero(multiples1,sizeof(multiples1));
693 cryptonite_decaf_bzero(multiples2,sizeof(multiples2));
694 cryptonite_decaf_bzero(tmp,sizeof(tmp));
695 }
696
API_NS(point_dual_scalarmul)697 void API_NS(point_dual_scalarmul) (
698 point_t a1,
699 point_t a2,
700 const point_t b,
701 const scalar_t scalar1,
702 const scalar_t scalar2
703 ) {
704 const int WINDOW = CRYPTONITE_DECAF_WINDOW_BITS,
705 WINDOW_MASK = (1<<WINDOW)-1,
706 WINDOW_T_MASK = WINDOW_MASK >> 1,
707 NTABLE = 1<<(WINDOW-1);
708
709 scalar_t scalar1x, scalar2x;
710 API_NS(scalar_add)(scalar1x, scalar1, point_scalarmul_adjustment);
711 API_NS(scalar_halve)(scalar1x,scalar1x);
712 API_NS(scalar_add)(scalar2x, scalar2, point_scalarmul_adjustment);
713 API_NS(scalar_halve)(scalar2x,scalar2x);
714
715 /* Set up a precomputed table with odd multiples of b. */
716 point_t multiples1[NTABLE], multiples2[NTABLE], working, tmp;
717 pniels_t pn;
718
719 API_NS(point_copy)(working, b);
720
721 /* Initialize. */
722 int i,j;
723
724 for (i=0; i<NTABLE; i++) {
725 API_NS(point_copy)(multiples1[i], API_NS(point_identity));
726 API_NS(point_copy)(multiples2[i], API_NS(point_identity));
727 }
728
729 for (i=0; i<SCALAR_BITS; i+=WINDOW) {
730 if (i) {
731 for (j=0; j<WINDOW-1; j++)
732 point_double_internal(working, working, -1);
733 point_double_internal(working, working, 0);
734 }
735
736 /* Fetch another block of bits */
737 word_t bits1 = scalar1x->limb[i/WBITS] >> (i%WBITS),
738 bits2 = scalar2x->limb[i/WBITS] >> (i%WBITS);
739 if (i%WBITS >= WBITS-WINDOW && i/WBITS<SCALAR_LIMBS-1) {
740 bits1 ^= scalar1x->limb[i/WBITS+1] << (WBITS - (i%WBITS));
741 bits2 ^= scalar2x->limb[i/WBITS+1] << (WBITS - (i%WBITS));
742 }
743 bits1 &= WINDOW_MASK;
744 bits2 &= WINDOW_MASK;
745 mask_t inv1 = (bits1>>(WINDOW-1))-1;
746 mask_t inv2 = (bits2>>(WINDOW-1))-1;
747 bits1 ^= inv1;
748 bits2 ^= inv2;
749
750 pt_to_pniels(pn, working);
751
752 constant_time_lookup(tmp, multiples1, sizeof(tmp), NTABLE, bits1 & WINDOW_T_MASK);
753 cond_neg_niels(pn->n, inv1);
754 /* add_pniels_to_pt(multiples1[bits1 & WINDOW_T_MASK], pn, 0); */
755 add_pniels_to_pt(tmp, pn, 0);
756 constant_time_insert(multiples1, tmp, sizeof(tmp), NTABLE, bits1 & WINDOW_T_MASK);
757
758
759 constant_time_lookup(tmp, multiples2, sizeof(tmp), NTABLE, bits2 & WINDOW_T_MASK);
760 cond_neg_niels(pn->n, inv1^inv2);
761 /* add_pniels_to_pt(multiples2[bits2 & WINDOW_T_MASK], pn, 0); */
762 add_pniels_to_pt(tmp, pn, 0);
763 constant_time_insert(multiples2, tmp, sizeof(tmp), NTABLE, bits2 & WINDOW_T_MASK);
764 }
765
766 if (NTABLE > 1) {
767 API_NS(point_copy)(working, multiples1[NTABLE-1]);
768 API_NS(point_copy)(tmp , multiples2[NTABLE-1]);
769
770 for (i=NTABLE-1; i>1; i--) {
771 API_NS(point_add)(multiples1[i-1], multiples1[i-1], multiples1[i]);
772 API_NS(point_add)(multiples2[i-1], multiples2[i-1], multiples2[i]);
773 API_NS(point_add)(working, working, multiples1[i-1]);
774 API_NS(point_add)(tmp, tmp, multiples2[i-1]);
775 }
776
777 API_NS(point_add)(multiples1[0], multiples1[0], multiples1[1]);
778 API_NS(point_add)(multiples2[0], multiples2[0], multiples2[1]);
779 point_double_internal(working, working, 0);
780 point_double_internal(tmp, tmp, 0);
781 API_NS(point_add)(a1, working, multiples1[0]);
782 API_NS(point_add)(a2, tmp, multiples2[0]);
783 } else {
784 API_NS(point_copy)(a1, multiples1[0]);
785 API_NS(point_copy)(a2, multiples2[0]);
786 }
787
788 cryptonite_decaf_bzero(scalar1x,sizeof(scalar1x));
789 cryptonite_decaf_bzero(scalar2x,sizeof(scalar2x));
790 cryptonite_decaf_bzero(pn,sizeof(pn));
791 cryptonite_decaf_bzero(multiples1,sizeof(multiples1));
792 cryptonite_decaf_bzero(multiples2,sizeof(multiples2));
793 cryptonite_decaf_bzero(tmp,sizeof(tmp));
794 cryptonite_decaf_bzero(working,sizeof(working));
795 }
796
API_NS(point_eq)797 cryptonite_decaf_bool_t API_NS(point_eq) ( const point_t p, const point_t q ) {
798 /* equality mod 2-torsion compares x/y */
799 gf a, b;
800 cryptonite_gf_mul ( a, p->y, q->x );
801 cryptonite_gf_mul ( b, q->y, p->x );
802 mask_t succ = cryptonite_gf_eq(a,b);
803
804 #if (COFACTOR == 8) && IMAGINE_TWIST
805 cryptonite_gf_mul ( a, p->y, q->y );
806 cryptonite_gf_mul ( b, q->x, p->x );
807 #if !(IMAGINE_TWIST)
808 cryptonite_gf_sub ( a, ZERO, a );
809 #else
810 /* Interesting note: the 4tor would normally be rotation.
811 * But because of the *i twist, it's actually
812 * (x,y) <-> (iy,ix)
813 */
814
815 /* No code, just a comment. */
816 #endif
817 succ |= cryptonite_gf_eq(a,b);
818 #endif
819
820 return mask_to_bool(succ);
821 }
822
API_NS(point_valid)823 cryptonite_decaf_bool_t API_NS(point_valid) (
824 const point_t p
825 ) {
826 gf a,b,c;
827 cryptonite_gf_mul(a,p->x,p->y);
828 cryptonite_gf_mul(b,p->z,p->t);
829 mask_t out = cryptonite_gf_eq(a,b);
830 cryptonite_gf_sqr(a,p->x);
831 cryptonite_gf_sqr(b,p->y);
832 cryptonite_gf_sub(a,b,a);
833 cryptonite_gf_sqr(b,p->t);
834 cryptonite_gf_mulw(c,b,TWISTED_D);
835 cryptonite_gf_sqr(b,p->z);
836 cryptonite_gf_add(b,b,c);
837 out &= cryptonite_gf_eq(a,b);
838 out &= ~cryptonite_gf_eq(p->z,ZERO);
839 return mask_to_bool(out);
840 }
841
API_NS(point_debugging_torque)842 void API_NS(point_debugging_torque) (
843 point_t q,
844 const point_t p
845 ) {
846 #if COFACTOR == 8 && IMAGINE_TWIST
847 gf tmp;
848 cryptonite_gf_mul(tmp,p->x,SQRT_MINUS_ONE);
849 cryptonite_gf_mul(q->x,p->y,SQRT_MINUS_ONE);
850 cryptonite_gf_copy(q->y,tmp);
851 cryptonite_gf_copy(q->z,p->z);
852 cryptonite_gf_sub(q->t,ZERO,p->t);
853 #else
854 cryptonite_gf_sub(q->x,ZERO,p->x);
855 cryptonite_gf_sub(q->y,ZERO,p->y);
856 cryptonite_gf_copy(q->z,p->z);
857 cryptonite_gf_copy(q->t,p->t);
858 #endif
859 }
860
API_NS(point_debugging_pscale)861 void API_NS(point_debugging_pscale) (
862 point_t q,
863 const point_t p,
864 const uint8_t factor[SER_BYTES]
865 ) {
866 gf gfac,tmp;
867 /* NB this means you'll never pscale by negative numbers for p521 */
868 ignore_result(cryptonite_gf_deserialize(gfac,factor,0));
869 cryptonite_gf_cond_sel(gfac,gfac,ONE,cryptonite_gf_eq(gfac,ZERO));
870 cryptonite_gf_mul(tmp,p->x,gfac);
871 cryptonite_gf_copy(q->x,tmp);
872 cryptonite_gf_mul(tmp,p->y,gfac);
873 cryptonite_gf_copy(q->y,tmp);
874 cryptonite_gf_mul(tmp,p->z,gfac);
875 cryptonite_gf_copy(q->z,tmp);
876 cryptonite_gf_mul(tmp,p->t,gfac);
877 cryptonite_gf_copy(q->t,tmp);
878 }
879
cryptonite_gf_batch_invert(gf * __restrict__ out,const gf * in,unsigned int n)880 static void cryptonite_gf_batch_invert (
881 gf *__restrict__ out,
882 const gf *in,
883 unsigned int n
884 ) {
885 gf t1;
886 assert(n>1);
887
888 cryptonite_gf_copy(out[1], in[0]);
889 int i;
890 for (i=1; i<(int) (n-1); i++) {
891 cryptonite_gf_mul(out[i+1], out[i], in[i]);
892 }
893 cryptonite_gf_mul(out[0], out[n-1], in[n-1]);
894
895 cryptonite_gf_invert(out[0], out[0], 1);
896
897 for (i=n-1; i>0; i--) {
898 cryptonite_gf_mul(t1, out[i], out[0]);
899 cryptonite_gf_copy(out[i], t1);
900 cryptonite_gf_mul(t1, out[0], in[i]);
901 cryptonite_gf_copy(out[0], t1);
902 }
903 }
904
batch_normalize_niels(niels_t * table,const gf * zs,gf * __restrict__ zis,int n)905 static void batch_normalize_niels (
906 niels_t *table,
907 const gf *zs,
908 gf *__restrict__ zis,
909 int n
910 ) {
911 int i;
912 gf product;
913 cryptonite_gf_batch_invert(zis, zs, n);
914
915 for (i=0; i<n; i++) {
916 cryptonite_gf_mul(product, table[i]->a, zis[i]);
917 cryptonite_gf_strong_reduce(product);
918 cryptonite_gf_copy(table[i]->a, product);
919
920 cryptonite_gf_mul(product, table[i]->b, zis[i]);
921 cryptonite_gf_strong_reduce(product);
922 cryptonite_gf_copy(table[i]->b, product);
923
924 cryptonite_gf_mul(product, table[i]->c, zis[i]);
925 cryptonite_gf_strong_reduce(product);
926 cryptonite_gf_copy(table[i]->c, product);
927 }
928
929 cryptonite_decaf_bzero(product,sizeof(product));
930 }
931
API_NS(precompute)932 void API_NS(precompute) (
933 precomputed_s *table,
934 const point_t base
935 ) {
936 const unsigned int n = COMBS_N, t = COMBS_T, s = COMBS_S;
937 assert(n*t*s >= SCALAR_BITS);
938
939 point_t working, start, doubles[t-1];
940 API_NS(point_copy)(working, base);
941 pniels_t pn_tmp;
942
943 gf zs[n<<(t-1)], zis[n<<(t-1)];
944
945 unsigned int i,j,k;
946
947 /* Compute n tables */
948 for (i=0; i<n; i++) {
949
950 /* Doubling phase */
951 for (j=0; j<t; j++) {
952 if (j) API_NS(point_add)(start, start, working);
953 else API_NS(point_copy)(start, working);
954
955 if (j==t-1 && i==n-1) break;
956
957 point_double_internal(working, working,0);
958 if (j<t-1) API_NS(point_copy)(doubles[j], working);
959
960 for (k=0; k<s-1; k++)
961 point_double_internal(working, working, k<s-2);
962 }
963
964 /* Gray-code phase */
965 for (j=0;; j++) {
966 int gray = j ^ (j>>1);
967 int idx = (((i+1)<<(t-1))-1) ^ gray;
968
969 pt_to_pniels(pn_tmp, start);
970 memcpy(table->table[idx], pn_tmp->n, sizeof(pn_tmp->n));
971 cryptonite_gf_copy(zs[idx], pn_tmp->z);
972
973 if (j >= (1u<<(t-1)) - 1) break;
974 int delta = (j+1) ^ ((j+1)>>1) ^ gray;
975
976 for (k=0; delta>1; k++)
977 delta >>=1;
978
979 if (gray & (1<<k)) {
980 API_NS(point_add)(start, start, doubles[k]);
981 } else {
982 API_NS(point_sub)(start, start, doubles[k]);
983 }
984 }
985 }
986
987 batch_normalize_niels(table->table,(const gf *)zs,zis,n<<(t-1));
988
989 cryptonite_decaf_bzero(zs,sizeof(zs));
990 cryptonite_decaf_bzero(zis,sizeof(zis));
991 cryptonite_decaf_bzero(pn_tmp,sizeof(pn_tmp));
992 cryptonite_decaf_bzero(working,sizeof(working));
993 cryptonite_decaf_bzero(start,sizeof(start));
994 cryptonite_decaf_bzero(doubles,sizeof(doubles));
995 }
996
997 static CRYPTONITE_DECAF_INLINE void
constant_time_lookup_niels(niels_s * __restrict__ ni,const niels_t * table,int nelts,int idx)998 constant_time_lookup_niels (
999 niels_s *__restrict__ ni,
1000 const niels_t *table,
1001 int nelts,
1002 int idx
1003 ) {
1004 constant_time_lookup(ni, table, sizeof(niels_s), nelts, idx);
1005 }
1006
API_NS(precomputed_scalarmul)1007 void API_NS(precomputed_scalarmul) (
1008 point_t out,
1009 const precomputed_s *table,
1010 const scalar_t scalar
1011 ) {
1012 int i;
1013 unsigned j,k;
1014 const unsigned int n = COMBS_N, t = COMBS_T, s = COMBS_S;
1015
1016 scalar_t scalar1x;
1017 API_NS(scalar_add)(scalar1x, scalar, precomputed_scalarmul_adjustment);
1018 API_NS(scalar_halve)(scalar1x,scalar1x);
1019
1020 niels_t ni;
1021
1022 for (i=s-1; i>=0; i--) {
1023 if (i != (int)s-1) point_double_internal(out,out,0);
1024
1025 for (j=0; j<n; j++) {
1026 int tab = 0;
1027
1028 for (k=0; k<t; k++) {
1029 unsigned int bit = i + s*(k + j*t);
1030 if (bit < SCALAR_BITS) {
1031 tab |= (scalar1x->limb[bit/WBITS] >> (bit%WBITS) & 1) << k;
1032 }
1033 }
1034
1035 mask_t invert = (tab>>(t-1))-1;
1036 tab ^= invert;
1037 tab &= (1<<(t-1)) - 1;
1038
1039 constant_time_lookup_niels(ni, &table->table[j<<(t-1)], 1<<(t-1), tab);
1040
1041 cond_neg_niels(ni, invert);
1042 if ((i!=(int)s-1)||j) {
1043 add_niels_to_pt(out, ni, j==n-1 && i);
1044 } else {
1045 niels_to_pt(out, ni);
1046 }
1047 }
1048 }
1049
1050 cryptonite_decaf_bzero(ni,sizeof(ni));
1051 cryptonite_decaf_bzero(scalar1x,sizeof(scalar1x));
1052 }
1053
API_NS(point_cond_sel)1054 void API_NS(point_cond_sel) (
1055 point_t out,
1056 const point_t a,
1057 const point_t b,
1058 cryptonite_decaf_bool_t pick_b
1059 ) {
1060 constant_time_select(out,a,b,sizeof(point_t),bool_to_mask(pick_b),0);
1061 }
1062
1063 /* FUTURE: restore Curve25519 Montgomery ladder? */
API_NS(direct_scalarmul)1064 cryptonite_decaf_error_t API_NS(direct_scalarmul) (
1065 uint8_t scaled[SER_BYTES],
1066 const uint8_t base[SER_BYTES],
1067 const scalar_t scalar,
1068 cryptonite_decaf_bool_t allow_identity,
1069 cryptonite_decaf_bool_t short_circuit
1070 ) {
1071 point_t basep;
1072 cryptonite_decaf_error_t succ = API_NS(point_decode)(basep, base, allow_identity);
1073 if (short_circuit && succ != CRYPTONITE_DECAF_SUCCESS) return succ;
1074 API_NS(point_cond_sel)(basep, API_NS(point_base), basep, succ);
1075 API_NS(point_scalarmul)(basep, basep, scalar);
1076 API_NS(point_encode)(scaled, basep);
1077 API_NS(point_destroy)(basep);
1078 return succ;
1079 }
1080
API_NS(point_mul_by_cofactor_and_encode_like_eddsa)1081 void API_NS(point_mul_by_cofactor_and_encode_like_eddsa) (
1082 uint8_t enc[CRYPTONITE_DECAF_EDDSA_448_PUBLIC_BYTES],
1083 const point_t p
1084 ) {
1085
1086 /* The point is now on the twisted curve. Move it to untwisted. */
1087 gf x, y, z, t;
1088 point_t q;
1089 #if COFACTOR == 8
1090 API_NS(point_double)(q,p);
1091 #else
1092 API_NS(point_copy)(q,p);
1093 #endif
1094
1095 #if EDDSA_USE_SIGMA_ISOGENY
1096 {
1097 /* Use 4-isogeny like ed25519:
1098 * 2*x*y*sqrt(d/a-1)/(ax^2 + y^2 - 2)
1099 * (y^2 - ax^2)/(y^2 + ax^2)
1100 * with a = -1, d = -EDWARDS_D:
1101 * -2xysqrt(EDWARDS_D-1)/(2z^2-y^2+x^2)
1102 * (y^2+x^2)/(y^2-x^2)
1103 */
1104 gf u;
1105 cryptonite_gf_sqr ( x, q->x ); // x^2
1106 cryptonite_gf_sqr ( t, q->y ); // y^2
1107 cryptonite_gf_add( u, x, t ); // x^2 + y^2
1108 cryptonite_gf_add( z, q->y, q->x );
1109 cryptonite_gf_sqr ( y, z);
1110 cryptonite_gf_sub ( y, u, y ); // -2xy
1111 cryptonite_gf_sub ( z, t, x ); // y^2 - x^2
1112 cryptonite_gf_sqr ( x, q->z );
1113 cryptonite_gf_add ( t, x, x);
1114 cryptonite_gf_sub ( t, t, z); // 2z^2 - y^2 + x^2
1115 cryptonite_gf_mul ( x, y, z ); // 2xy(y^2-x^2)
1116 cryptonite_gf_mul ( y, u, t ); // (x^2+y^2)(2z^2-y^2+x^2)
1117 cryptonite_gf_mul ( u, z, t );
1118 cryptonite_gf_copy( z, u );
1119 cryptonite_gf_mul ( u, x, SQRT_ONE_MINUS_D );
1120 cryptonite_gf_copy( x, u );
1121 cryptonite_decaf_bzero(u,sizeof(u));
1122 }
1123 #elif IMAGINE_TWIST
1124 {
1125 API_NS(point_double)(q,q);
1126 API_NS(point_double)(q,q);
1127 cryptonite_gf_mul_qnr(x, q->x);
1128 cryptonite_gf_copy(y, q->y);
1129 cryptonite_gf_copy(z, q->z);
1130 }
1131 #else
1132 {
1133 /* 4-isogeny: 2xy/(y^+x^2), (y^2-x^2)/(2z^2-y^2+x^2) */
1134 gf u;
1135 cryptonite_gf_sqr ( x, q->x );
1136 cryptonite_gf_sqr ( t, q->y );
1137 cryptonite_gf_add( u, x, t );
1138 cryptonite_gf_add( z, q->y, q->x );
1139 cryptonite_gf_sqr ( y, z);
1140 cryptonite_gf_sub ( y, u, y );
1141 cryptonite_gf_sub ( z, t, x );
1142 cryptonite_gf_sqr ( x, q->z );
1143 cryptonite_gf_add ( t, x, x);
1144 cryptonite_gf_sub ( t, t, z);
1145 cryptonite_gf_mul ( x, t, y );
1146 cryptonite_gf_mul ( y, z, u );
1147 cryptonite_gf_mul ( z, u, t );
1148 cryptonite_decaf_bzero(u,sizeof(u));
1149 }
1150 #endif
1151 /* Affinize */
1152 cryptonite_gf_invert(z,z,1);
1153 cryptonite_gf_mul(t,x,z);
1154 cryptonite_gf_mul(x,y,z);
1155
1156 /* Encode */
1157 enc[CRYPTONITE_DECAF_EDDSA_448_PRIVATE_BYTES-1] = 0;
1158 cryptonite_gf_serialize(enc, x, 1);
1159 enc[CRYPTONITE_DECAF_EDDSA_448_PRIVATE_BYTES-1] |= 0x80 & cryptonite_gf_lobit(t);
1160
1161 cryptonite_decaf_bzero(x,sizeof(x));
1162 cryptonite_decaf_bzero(y,sizeof(y));
1163 cryptonite_decaf_bzero(z,sizeof(z));
1164 cryptonite_decaf_bzero(t,sizeof(t));
1165 API_NS(point_destroy)(q);
1166 }
1167
1168
API_NS(point_decode_like_eddsa_and_ignore_cofactor)1169 cryptonite_decaf_error_t API_NS(point_decode_like_eddsa_and_ignore_cofactor) (
1170 point_t p,
1171 const uint8_t enc[CRYPTONITE_DECAF_EDDSA_448_PUBLIC_BYTES]
1172 ) {
1173 uint8_t enc2[CRYPTONITE_DECAF_EDDSA_448_PUBLIC_BYTES];
1174 memcpy(enc2,enc,sizeof(enc2));
1175
1176 mask_t low = ~word_is_zero(enc2[CRYPTONITE_DECAF_EDDSA_448_PRIVATE_BYTES-1] & 0x80);
1177 enc2[CRYPTONITE_DECAF_EDDSA_448_PRIVATE_BYTES-1] &= ~0x80;
1178
1179 mask_t succ = cryptonite_gf_deserialize(p->y, enc2, 1);
1180 #if 0 == 0
1181 succ &= word_is_zero(enc2[CRYPTONITE_DECAF_EDDSA_448_PRIVATE_BYTES-1]);
1182 #endif
1183
1184 cryptonite_gf_sqr(p->x,p->y);
1185 cryptonite_gf_sub(p->z,ONE,p->x); /* num = 1-y^2 */
1186 #if EDDSA_USE_SIGMA_ISOGENY
1187 cryptonite_gf_mulw(p->t,p->z,EDWARDS_D); /* d-dy^2 */
1188 cryptonite_gf_mulw(p->x,p->z,EDWARDS_D-1); /* num = (1-y^2)(d-1) */
1189 cryptonite_gf_copy(p->z,p->x);
1190 #else
1191 cryptonite_gf_mulw(p->t,p->x,EDWARDS_D); /* dy^2 */
1192 #endif
1193 cryptonite_gf_sub(p->t,ONE,p->t); /* denom = 1-dy^2 or 1-d + dy^2 */
1194
1195 cryptonite_gf_mul(p->x,p->z,p->t);
1196 succ &= cryptonite_gf_isr(p->t,p->x); /* 1/sqrt(num * denom) */
1197
1198 cryptonite_gf_mul(p->x,p->t,p->z); /* sqrt(num / denom) */
1199 cryptonite_gf_cond_neg(p->x,~cryptonite_gf_lobit(p->x)^low);
1200 cryptonite_gf_copy(p->z,ONE);
1201
1202 #if EDDSA_USE_SIGMA_ISOGENY
1203 {
1204 /* Use 4-isogeny like ed25519:
1205 * 2*x*y/sqrt(1-d/a)/(ax^2 + y^2 - 2)
1206 * (y^2 - ax^2)/(y^2 + ax^2)
1207 * (MAGIC: above formula may be off by a factor of -a
1208 * or something somewhere; check it for other a)
1209 *
1210 * with a = -1, d = -EDWARDS_D:
1211 * -2xy/sqrt(1-EDWARDS_D)/(2z^2-y^2+x^2)
1212 * (y^2+x^2)/(y^2-x^2)
1213 */
1214 gf a, b, c, d;
1215 cryptonite_gf_sqr ( c, p->x );
1216 cryptonite_gf_sqr ( a, p->y );
1217 cryptonite_gf_add ( d, c, a ); // x^2 + y^2
1218 cryptonite_gf_add ( p->t, p->y, p->x );
1219 cryptonite_gf_sqr ( b, p->t );
1220 cryptonite_gf_sub ( b, b, d ); // 2xy
1221 cryptonite_gf_sub ( p->t, a, c ); // y^2 - x^2
1222 cryptonite_gf_sqr ( p->x, p->z );
1223 cryptonite_gf_add ( p->z, p->x, p->x );
1224 cryptonite_gf_sub ( a, p->z, p->t ); // 2z^2 - y^2 + x^2
1225 cryptonite_gf_mul ( c, a, SQRT_ONE_MINUS_D );
1226 cryptonite_gf_mul ( p->x, b, p->t); // (2xy)(y^2-x^2)
1227 cryptonite_gf_mul ( p->z, p->t, c ); // (y^2-x^2)sd(2z^2 - y^2 + x^2)
1228 cryptonite_gf_mul ( p->y, d, c ); // (y^2+x^2)sd(2z^2 - y^2 + x^2)
1229 cryptonite_gf_mul ( p->t, d, b );
1230 cryptonite_decaf_bzero(a,sizeof(a));
1231 cryptonite_decaf_bzero(b,sizeof(b));
1232 cryptonite_decaf_bzero(c,sizeof(c));
1233 cryptonite_decaf_bzero(d,sizeof(d));
1234 }
1235 #elif IMAGINE_TWIST
1236 {
1237 cryptonite_gf_mul(p->t,p->x,SQRT_MINUS_ONE);
1238 cryptonite_gf_copy(p->x,p->t);
1239 cryptonite_gf_mul(p->t,p->x,p->y);
1240 }
1241 #else
1242 {
1243 /* 4-isogeny 2xy/(y^2-ax^2), (y^2+ax^2)/(2-y^2-ax^2) */
1244 gf a, b, c, d;
1245 cryptonite_gf_sqr ( c, p->x );
1246 cryptonite_gf_sqr ( a, p->y );
1247 cryptonite_gf_add ( d, c, a );
1248 cryptonite_gf_add ( p->t, p->y, p->x );
1249 cryptonite_gf_sqr ( b, p->t );
1250 cryptonite_gf_sub ( b, b, d );
1251 cryptonite_gf_sub ( p->t, a, c );
1252 cryptonite_gf_sqr ( p->x, p->z );
1253 cryptonite_gf_add ( p->z, p->x, p->x );
1254 cryptonite_gf_sub ( a, p->z, d );
1255 cryptonite_gf_mul ( p->x, a, b );
1256 cryptonite_gf_mul ( p->z, p->t, a );
1257 cryptonite_gf_mul ( p->y, p->t, d );
1258 cryptonite_gf_mul ( p->t, b, d );
1259 cryptonite_decaf_bzero(a,sizeof(a));
1260 cryptonite_decaf_bzero(b,sizeof(b));
1261 cryptonite_decaf_bzero(c,sizeof(c));
1262 cryptonite_decaf_bzero(d,sizeof(d));
1263 }
1264 #endif
1265
1266 cryptonite_decaf_bzero(enc2,sizeof(enc2));
1267 assert(API_NS(point_valid)(p) || ~succ);
1268 return cryptonite_decaf_succeed_if(mask_to_bool(succ));
1269 }
1270
cryptonite_decaf_x448(uint8_t out[X_PUBLIC_BYTES],const uint8_t base[X_PUBLIC_BYTES],const uint8_t scalar[X_PRIVATE_BYTES])1271 cryptonite_decaf_error_t cryptonite_decaf_x448 (
1272 uint8_t out[X_PUBLIC_BYTES],
1273 const uint8_t base[X_PUBLIC_BYTES],
1274 const uint8_t scalar[X_PRIVATE_BYTES]
1275 ) {
1276 gf x1, x2, z2, x3, z3, t1, t2;
1277 ignore_result(cryptonite_gf_deserialize(x1,base,1));
1278 cryptonite_gf_copy(x2,ONE);
1279 cryptonite_gf_copy(z2,ZERO);
1280 cryptonite_gf_copy(x3,x1);
1281 cryptonite_gf_copy(z3,ONE);
1282
1283 int t;
1284 mask_t swap = 0;
1285
1286 for (t = X_PRIVATE_BITS-1; t>=0; t--) {
1287 uint8_t sb = scalar[t/8];
1288
1289 /* Scalar conditioning */
1290 if (t/8==0) sb &= -(uint8_t)COFACTOR;
1291 else if (t == X_PRIVATE_BITS-1) sb = -1;
1292
1293 mask_t k_t = (sb>>(t%8)) & 1;
1294 k_t = -k_t; /* set to all 0s or all 1s */
1295
1296 swap ^= k_t;
1297 cryptonite_gf_cond_swap(x2,x3,swap);
1298 cryptonite_gf_cond_swap(z2,z3,swap);
1299 swap = k_t;
1300
1301 cryptonite_gf_add_nr(t1,x2,z2); /* A = x2 + z2 */ /* 2+e */
1302 cryptonite_gf_sub_nr(t2,x2,z2); /* B = x2 - z2 */ /* 3+e */
1303 cryptonite_gf_sub_nr(z2,x3,z3); /* D = x3 - z3 */ /* 3+e */
1304 cryptonite_gf_mul(x2,t1,z2); /* DA */
1305 cryptonite_gf_add_nr(z2,z3,x3); /* C = x3 + z3 */ /* 2+e */
1306 cryptonite_gf_mul(x3,t2,z2); /* CB */
1307 cryptonite_gf_sub_nr(z3,x2,x3); /* DA-CB */ /* 3+e */
1308 cryptonite_gf_sqr(z2,z3); /* (DA-CB)^2 */
1309 cryptonite_gf_mul(z3,x1,z2); /* z3 = x1(DA-CB)^2 */
1310 cryptonite_gf_add_nr(z2,x2,x3); /* (DA+CB) */ /* 2+e */
1311 cryptonite_gf_sqr(x3,z2); /* x3 = (DA+CB)^2 */
1312
1313 cryptonite_gf_sqr(z2,t1); /* AA = A^2 */
1314 cryptonite_gf_sqr(t1,t2); /* BB = B^2 */
1315 cryptonite_gf_mul(x2,z2,t1); /* x2 = AA*BB */
1316 cryptonite_gf_sub_nr(t2,z2,t1); /* E = AA-BB */ /* 3+e */
1317
1318 cryptonite_gf_mulw(t1,t2,-EDWARDS_D); /* E*-d = a24*E */
1319 cryptonite_gf_add_nr(t1,t1,z2); /* AA + a24*E */ /* 2+e */
1320 cryptonite_gf_mul(z2,t2,t1); /* z2 = E(AA+a24*E) */
1321 }
1322
1323 /* Finish */
1324 cryptonite_gf_cond_swap(x2,x3,swap);
1325 cryptonite_gf_cond_swap(z2,z3,swap);
1326 cryptonite_gf_invert(z2,z2,0);
1327 cryptonite_gf_mul(x1,x2,z2);
1328 cryptonite_gf_serialize(out,x1,1);
1329 mask_t nz = ~cryptonite_gf_eq(x1,ZERO);
1330
1331 cryptonite_decaf_bzero(x1,sizeof(x1));
1332 cryptonite_decaf_bzero(x2,sizeof(x2));
1333 cryptonite_decaf_bzero(z2,sizeof(z2));
1334 cryptonite_decaf_bzero(x3,sizeof(x3));
1335 cryptonite_decaf_bzero(z3,sizeof(z3));
1336 cryptonite_decaf_bzero(t1,sizeof(t1));
1337 cryptonite_decaf_bzero(t2,sizeof(t2));
1338
1339 return cryptonite_decaf_succeed_if(mask_to_bool(nz));
1340 }
1341
1342 /* Thanks Johan Pascal */
cryptonite_decaf_ed448_convert_public_key_to_x448(uint8_t x[CRYPTONITE_DECAF_X448_PUBLIC_BYTES],const uint8_t ed[CRYPTONITE_DECAF_EDDSA_448_PUBLIC_BYTES])1343 void cryptonite_decaf_ed448_convert_public_key_to_x448 (
1344 uint8_t x[CRYPTONITE_DECAF_X448_PUBLIC_BYTES],
1345 const uint8_t ed[CRYPTONITE_DECAF_EDDSA_448_PUBLIC_BYTES]
1346 ) {
1347 gf y;
1348 {
1349 uint8_t enc2[CRYPTONITE_DECAF_EDDSA_448_PUBLIC_BYTES];
1350 memcpy(enc2,ed,sizeof(enc2));
1351
1352 /* retrieve y from the ed compressed point */
1353 enc2[CRYPTONITE_DECAF_EDDSA_448_PUBLIC_BYTES-1] &= ~0x80;
1354 ignore_result(cryptonite_gf_deserialize(y, enc2, 0));
1355 cryptonite_decaf_bzero(enc2,sizeof(enc2));
1356 }
1357
1358 {
1359 gf n,d;
1360
1361 #if EDDSA_USE_SIGMA_ISOGENY
1362 /* u = (1+y)/(1-y)*/
1363 cryptonite_gf_add(n, y, ONE); /* n = y+1 */
1364 cryptonite_gf_sub(d, ONE, y); /* d = 1-y */
1365 cryptonite_gf_invert(d, d, 0); /* d = 1/(1-y) */
1366 cryptonite_gf_mul(y, n, d); /* u = (y+1)/(1-y) */
1367 cryptonite_gf_serialize(x,y,1);
1368 #else /* EDDSA_USE_SIGMA_ISOGENY */
1369 /* u = y^2 * (1-dy^2) / (1-y^2) */
1370 cryptonite_gf_sqr(n,y); /* y^2*/
1371 cryptonite_gf_sub(d,ONE,n); /* 1-y^2*/
1372 cryptonite_gf_invert(d,d,0); /* 1/(1-y^2)*/
1373 cryptonite_gf_mul(y,n,d); /* y^2 / (1-y^2) */
1374 cryptonite_gf_mulw(d,n,EDWARDS_D); /* dy^2*/
1375 cryptonite_gf_sub(d, ONE, d); /* 1-dy^2*/
1376 cryptonite_gf_mul(n, y, d); /* y^2 * (1-dy^2) / (1-y^2) */
1377 cryptonite_gf_serialize(x,n,1);
1378 #endif /* EDDSA_USE_SIGMA_ISOGENY */
1379
1380 cryptonite_decaf_bzero(y,sizeof(y));
1381 cryptonite_decaf_bzero(n,sizeof(n));
1382 cryptonite_decaf_bzero(d,sizeof(d));
1383 }
1384 }
1385
cryptonite_decaf_x448_generate_key(uint8_t out[X_PUBLIC_BYTES],const uint8_t scalar[X_PRIVATE_BYTES])1386 void cryptonite_decaf_x448_generate_key (
1387 uint8_t out[X_PUBLIC_BYTES],
1388 const uint8_t scalar[X_PRIVATE_BYTES]
1389 ) {
1390 cryptonite_decaf_x448_derive_public_key(out,scalar);
1391 }
1392
cryptonite_decaf_x448_derive_public_key(uint8_t out[X_PUBLIC_BYTES],const uint8_t scalar[X_PRIVATE_BYTES])1393 void cryptonite_decaf_x448_derive_public_key (
1394 uint8_t out[X_PUBLIC_BYTES],
1395 const uint8_t scalar[X_PRIVATE_BYTES]
1396 ) {
1397 /* Scalar conditioning */
1398 uint8_t scalar2[X_PRIVATE_BYTES];
1399 memcpy(scalar2,scalar,sizeof(scalar2));
1400 scalar2[0] &= -(uint8_t)COFACTOR;
1401
1402 scalar2[X_PRIVATE_BYTES-1] &= ~(-1u<<((X_PRIVATE_BITS+7)%8));
1403 scalar2[X_PRIVATE_BYTES-1] |= 1<<((X_PRIVATE_BITS+7)%8);
1404
1405 scalar_t the_scalar;
1406 API_NS(scalar_decode_long)(the_scalar,scalar2,sizeof(scalar2));
1407
1408 /* We're gonna isogenize by 2, so divide by 2.
1409 *
1410 * Why by 2, even though it's a 4-isogeny?
1411 *
1412 * The isogeny map looks like
1413 * Montgomery <-2-> Jacobi <-2-> Edwards
1414 *
1415 * Since the Jacobi base point is the PREimage of the iso to
1416 * the Montgomery curve, and we're going
1417 * Jacobi -> Edwards -> Jacobi -> Montgomery,
1418 * we pick up only a factor of 2 over Jacobi -> Montgomery.
1419 */
1420 API_NS(scalar_halve)(the_scalar,the_scalar);
1421 point_t p;
1422 API_NS(precomputed_scalarmul)(p,API_NS(precomputed_base),the_scalar);
1423
1424 /* Isogenize to Montgomery curve.
1425 *
1426 * Why isn't this just a separate function, eg cryptonite_decaf_encode_like_x448?
1427 * Basically because in general it does the wrong thing if there is a cofactor
1428 * component in the input. In this function though, there isn't a cofactor
1429 * component in the input.
1430 */
1431 cryptonite_gf_invert(p->t,p->x,0); /* 1/x */
1432 cryptonite_gf_mul(p->z,p->t,p->y); /* y/x */
1433 cryptonite_gf_sqr(p->y,p->z); /* (y/x)^2 */
1434 #if IMAGINE_TWIST
1435 cryptonite_gf_sub(p->y,ZERO,p->y);
1436 #endif
1437 cryptonite_gf_serialize(out,p->y,1);
1438
1439 cryptonite_decaf_bzero(scalar2,sizeof(scalar2));
1440 API_NS(scalar_destroy)(the_scalar);
1441 API_NS(point_destroy)(p);
1442 }
1443
1444 /**
1445 * @cond internal
1446 * Control for variable-time scalar multiply algorithms.
1447 */
1448 struct smvt_control {
1449 int power, addend;
1450 };
1451
recode_wnaf(struct smvt_control * control,const scalar_t scalar,unsigned int table_bits)1452 static int recode_wnaf (
1453 struct smvt_control *control, /* [nbits/(table_bits+1) + 3] */
1454 const scalar_t scalar,
1455 unsigned int table_bits
1456 ) {
1457 unsigned int table_size = SCALAR_BITS/(table_bits+1) + 3;
1458 int position = table_size - 1; /* at the end */
1459
1460 /* place the end marker */
1461 control[position].power = -1;
1462 control[position].addend = 0;
1463 position--;
1464
1465 /* PERF: Could negate scalar if it's large. But then would need more cases
1466 * in the actual code that uses it, all for an expected reduction of like 1/5 op.
1467 * Probably not worth it.
1468 */
1469
1470 uint64_t current = scalar->limb[0] & 0xFFFF;
1471 uint32_t mask = (1<<(table_bits+1))-1;
1472
1473 unsigned int w;
1474 const unsigned int B_OVER_16 = sizeof(scalar->limb[0]) / 2;
1475 for (w = 1; w<(SCALAR_BITS-1)/16+3; w++) {
1476 if (w < (SCALAR_BITS-1)/16+1) {
1477 /* Refill the 16 high bits of current */
1478 current += (uint32_t)((scalar->limb[w/B_OVER_16]>>(16*(w%B_OVER_16)))<<16);
1479 }
1480
1481 while (current & 0xFFFF) {
1482 assert(position >= 0);
1483 uint32_t pos = __builtin_ctz((uint32_t)current), odd = (uint32_t)current >> pos;
1484 int32_t delta = odd & mask;
1485 if (odd & 1<<(table_bits+1)) delta -= (1<<(table_bits+1));
1486 current -= delta << pos;
1487 control[position].power = pos + 16*(w-1);
1488 control[position].addend = delta;
1489 position--;
1490 }
1491 current >>= 16;
1492 }
1493 assert(current==0);
1494
1495 position++;
1496 unsigned int n = table_size - position;
1497 unsigned int i;
1498 for (i=0; i<n; i++) {
1499 control[i] = control[i+position];
1500 }
1501 return n-1;
1502 }
1503
1504 static void
prepare_wnaf_table(pniels_t * output,const point_t working,unsigned int tbits)1505 prepare_wnaf_table(
1506 pniels_t *output,
1507 const point_t working,
1508 unsigned int tbits
1509 ) {
1510 point_t tmp;
1511 int i;
1512 pt_to_pniels(output[0], working);
1513
1514 if (tbits == 0) return;
1515
1516 API_NS(point_double)(tmp,working);
1517 pniels_t twop;
1518 pt_to_pniels(twop, tmp);
1519
1520 add_pniels_to_pt(tmp, output[0],0);
1521 pt_to_pniels(output[1], tmp);
1522
1523 for (i=2; i < 1<<tbits; i++) {
1524 add_pniels_to_pt(tmp, twop,0);
1525 pt_to_pniels(output[i], tmp);
1526 }
1527
1528 API_NS(point_destroy)(tmp);
1529 cryptonite_decaf_bzero(twop,sizeof(twop));
1530 }
1531
1532 extern const gf API_NS(precomputed_wnaf_as_fe)[];
1533 static const niels_t *API_NS(wnaf_base) = (const niels_t *)API_NS(precomputed_wnaf_as_fe);
1534 const size_t API_NS(sizeof_precomputed_wnafs)
1535 = sizeof(niels_t)<<CRYPTONITE_DECAF_WNAF_FIXED_TABLE_BITS;
1536
1537 void API_NS(precompute_wnafs) (
1538 niels_t out[1<<CRYPTONITE_DECAF_WNAF_FIXED_TABLE_BITS],
1539 const point_t base
1540 );
1541
API_NS(precompute_wnafs)1542 void API_NS(precompute_wnafs) (
1543 niels_t out[1<<CRYPTONITE_DECAF_WNAF_FIXED_TABLE_BITS],
1544 const point_t base
1545 ) {
1546 pniels_t tmp[1<<CRYPTONITE_DECAF_WNAF_FIXED_TABLE_BITS];
1547 gf zs[1<<CRYPTONITE_DECAF_WNAF_FIXED_TABLE_BITS], zis[1<<CRYPTONITE_DECAF_WNAF_FIXED_TABLE_BITS];
1548 int i;
1549 prepare_wnaf_table(tmp,base,CRYPTONITE_DECAF_WNAF_FIXED_TABLE_BITS);
1550 for (i=0; i<1<<CRYPTONITE_DECAF_WNAF_FIXED_TABLE_BITS; i++) {
1551 memcpy(out[i], tmp[i]->n, sizeof(niels_t));
1552 cryptonite_gf_copy(zs[i], tmp[i]->z);
1553 }
1554 batch_normalize_niels(out, (const gf *)zs, zis, 1<<CRYPTONITE_DECAF_WNAF_FIXED_TABLE_BITS);
1555
1556 cryptonite_decaf_bzero(tmp,sizeof(tmp));
1557 cryptonite_decaf_bzero(zs,sizeof(zs));
1558 cryptonite_decaf_bzero(zis,sizeof(zis));
1559 }
1560
API_NS(base_double_scalarmul_non_secret)1561 void API_NS(base_double_scalarmul_non_secret) (
1562 point_t combo,
1563 const scalar_t scalar1,
1564 const point_t base2,
1565 const scalar_t scalar2
1566 ) {
1567 const int table_bits_var = CRYPTONITE_DECAF_WNAF_VAR_TABLE_BITS,
1568 table_bits_pre = CRYPTONITE_DECAF_WNAF_FIXED_TABLE_BITS;
1569 struct smvt_control control_var[SCALAR_BITS/(table_bits_var+1)+3];
1570 struct smvt_control control_pre[SCALAR_BITS/(table_bits_pre+1)+3];
1571
1572 int ncb_pre = recode_wnaf(control_pre, scalar1, table_bits_pre);
1573 int ncb_var = recode_wnaf(control_var, scalar2, table_bits_var);
1574
1575 pniels_t precmp_var[1<<table_bits_var];
1576 prepare_wnaf_table(precmp_var, base2, table_bits_var);
1577
1578 int contp=0, contv=0, i = control_var[0].power;
1579
1580 if (i < 0) {
1581 API_NS(point_copy)(combo, API_NS(point_identity));
1582 return;
1583 } else if (i > control_pre[0].power) {
1584 pniels_to_pt(combo, precmp_var[control_var[0].addend >> 1]);
1585 contv++;
1586 } else if (i == control_pre[0].power && i >=0 ) {
1587 pniels_to_pt(combo, precmp_var[control_var[0].addend >> 1]);
1588 add_niels_to_pt(combo, API_NS(wnaf_base)[control_pre[0].addend >> 1], i);
1589 contv++; contp++;
1590 } else {
1591 i = control_pre[0].power;
1592 niels_to_pt(combo, API_NS(wnaf_base)[control_pre[0].addend >> 1]);
1593 contp++;
1594 }
1595
1596 for (i--; i >= 0; i--) {
1597 int cv = (i==control_var[contv].power), cp = (i==control_pre[contp].power);
1598 point_double_internal(combo,combo,i && !(cv||cp));
1599
1600 if (cv) {
1601 assert(control_var[contv].addend);
1602
1603 if (control_var[contv].addend > 0) {
1604 add_pniels_to_pt(combo, precmp_var[control_var[contv].addend >> 1], i&&!cp);
1605 } else {
1606 sub_pniels_from_pt(combo, precmp_var[(-control_var[contv].addend) >> 1], i&&!cp);
1607 }
1608 contv++;
1609 }
1610
1611 if (cp) {
1612 assert(control_pre[contp].addend);
1613
1614 if (control_pre[contp].addend > 0) {
1615 add_niels_to_pt(combo, API_NS(wnaf_base)[control_pre[contp].addend >> 1], i);
1616 } else {
1617 sub_niels_from_pt(combo, API_NS(wnaf_base)[(-control_pre[contp].addend) >> 1], i);
1618 }
1619 contp++;
1620 }
1621 }
1622
1623 /* This function is non-secret, but whatever this is cheap. */
1624 cryptonite_decaf_bzero(control_var,sizeof(control_var));
1625 cryptonite_decaf_bzero(control_pre,sizeof(control_pre));
1626 cryptonite_decaf_bzero(precmp_var,sizeof(precmp_var));
1627
1628 assert(contv == ncb_var); (void)ncb_var;
1629 assert(contp == ncb_pre); (void)ncb_pre;
1630 }
1631
API_NS(point_destroy)1632 void API_NS(point_destroy) (
1633 point_t point
1634 ) {
1635 cryptonite_decaf_bzero(point, sizeof(point_t));
1636 }
1637
API_NS(precomputed_destroy)1638 void API_NS(precomputed_destroy) (
1639 precomputed_s *pre
1640 ) {
1641 cryptonite_decaf_bzero(pre, API_NS(sizeof_precomputed_s));
1642 }
1643