xref: /openssl/crypto/ec/ecp_nistz256.c (revision 7ed6de99)
1 /*
2  * Copyright 2014-2024 The OpenSSL Project Authors. All Rights Reserved.
3  * Copyright (c) 2014, Intel Corporation. All Rights Reserved.
4  * Copyright (c) 2015, CloudFlare, Inc.
5  *
6  * Licensed under the Apache License 2.0 (the "License").  You may not use
7  * this file except in compliance with the License.  You can obtain a copy
8  * in the file LICENSE in the source distribution or at
9  * https://www.openssl.org/source/license.html
10  *
11  * Originally written by Shay Gueron (1, 2), and Vlad Krasnov (1, 3)
12  * (1) Intel Corporation, Israel Development Center, Haifa, Israel
13  * (2) University of Haifa, Israel
14  * (3) CloudFlare, Inc.
15  *
16  * Reference:
17  * S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with
18  *                          256 Bit Primes"
19  */
20 
21 /*
22  * ECDSA low level APIs are deprecated for public use, but still ok for
23  * internal use.
24  */
25 #include "internal/deprecated.h"
26 
27 #include <string.h>
28 
29 #include "internal/cryptlib.h"
30 #include "crypto/bn.h"
31 #include "ec_local.h"
32 #include "internal/refcount.h"
33 
34 #if BN_BITS2 != 64
35 # define TOBN(hi,lo)    lo,hi
36 #else
37 # define TOBN(hi,lo)    ((BN_ULONG)hi<<32|lo)
38 #endif
39 
40 #define ALIGNPTR(p,N)   ((unsigned char *)p+N-(size_t)p%N)
41 #define P256_LIMBS      (256/BN_BITS2)
42 
43 typedef unsigned short u16;
44 
45 typedef struct {
46     BN_ULONG X[P256_LIMBS];
47     BN_ULONG Y[P256_LIMBS];
48     BN_ULONG Z[P256_LIMBS];
49 } P256_POINT;
50 
51 typedef struct {
52     BN_ULONG X[P256_LIMBS];
53     BN_ULONG Y[P256_LIMBS];
54 } P256_POINT_AFFINE;
55 
56 typedef P256_POINT_AFFINE PRECOMP256_ROW[64];
57 
58 /* structure for precomputed multiples of the generator */
59 struct nistz256_pre_comp_st {
60     const EC_GROUP *group;      /* Parent EC_GROUP object */
61     size_t w;                   /* Window size */
62     /*
63      * Constant time access to the X and Y coordinates of the pre-computed,
64      * generator multiplies, in the Montgomery domain. Pre-calculated
65      * multiplies are stored in affine form.
66      */
67     PRECOMP256_ROW *precomp;
68     void *precomp_storage;
69     CRYPTO_REF_COUNT references;
70 };
71 
72 /* Functions implemented in assembly */
73 /*
74  * Most of below mentioned functions *preserve* the property of inputs
75  * being fully reduced, i.e. being in [0, modulus) range. Simply put if
76  * inputs are fully reduced, then output is too. Note that reverse is
77  * not true, in sense that given partially reduced inputs output can be
78  * either, not unlikely reduced. And "most" in first sentence refers to
79  * the fact that given the calculations flow one can tolerate that
80  * addition, 1st function below, produces partially reduced result *if*
81  * multiplications by 2 and 3, which customarily use addition, fully
82  * reduce it. This effectively gives two options: a) addition produces
83  * fully reduced result [as long as inputs are, just like remaining
84  * functions]; b) addition is allowed to produce partially reduced
85  * result, but multiplications by 2 and 3 perform additional reduction
86  * step. Choice between the two can be platform-specific, but it was a)
87  * in all cases so far...
88  */
89 /* Modular add: res = a+b mod P   */
90 void ecp_nistz256_add(BN_ULONG res[P256_LIMBS],
91                       const BN_ULONG a[P256_LIMBS],
92                       const BN_ULONG b[P256_LIMBS]);
93 /* Modular mul by 2: res = 2*a mod P */
94 void ecp_nistz256_mul_by_2(BN_ULONG res[P256_LIMBS],
95                            const BN_ULONG a[P256_LIMBS]);
96 /* Modular mul by 3: res = 3*a mod P */
97 void ecp_nistz256_mul_by_3(BN_ULONG res[P256_LIMBS],
98                            const BN_ULONG a[P256_LIMBS]);
99 
100 /* Modular div by 2: res = a/2 mod P */
101 void ecp_nistz256_div_by_2(BN_ULONG res[P256_LIMBS],
102                            const BN_ULONG a[P256_LIMBS]);
103 /* Modular sub: res = a-b mod P   */
104 void ecp_nistz256_sub(BN_ULONG res[P256_LIMBS],
105                       const BN_ULONG a[P256_LIMBS],
106                       const BN_ULONG b[P256_LIMBS]);
107 /* Modular neg: res = -a mod P    */
108 void ecp_nistz256_neg(BN_ULONG res[P256_LIMBS], const BN_ULONG a[P256_LIMBS]);
109 /* Montgomery mul: res = a*b*2^-256 mod P */
110 void ecp_nistz256_mul_mont(BN_ULONG res[P256_LIMBS],
111                            const BN_ULONG a[P256_LIMBS],
112                            const BN_ULONG b[P256_LIMBS]);
113 /* Montgomery sqr: res = a*a*2^-256 mod P */
114 void ecp_nistz256_sqr_mont(BN_ULONG res[P256_LIMBS],
115                            const BN_ULONG a[P256_LIMBS]);
116 /* Convert a number from Montgomery domain, by multiplying with 1 */
117 void ecp_nistz256_from_mont(BN_ULONG res[P256_LIMBS],
118                             const BN_ULONG in[P256_LIMBS]);
119 /* Convert a number to Montgomery domain, by multiplying with 2^512 mod P*/
120 void ecp_nistz256_to_mont(BN_ULONG res[P256_LIMBS],
121                           const BN_ULONG in[P256_LIMBS]);
122 /* Functions that perform constant time access to the precomputed tables */
123 void ecp_nistz256_scatter_w5(P256_POINT *val,
124                              const P256_POINT *in_t, int idx);
125 void ecp_nistz256_gather_w5(P256_POINT *val,
126                             const P256_POINT *in_t, int idx);
127 void ecp_nistz256_scatter_w7(P256_POINT_AFFINE *val,
128                              const P256_POINT_AFFINE *in_t, int idx);
129 void ecp_nistz256_gather_w7(P256_POINT_AFFINE *val,
130                             const P256_POINT_AFFINE *in_t, int idx);
131 
132 /* One converted into the Montgomery domain */
133 static const BN_ULONG ONE[P256_LIMBS] = {
134     TOBN(0x00000000, 0x00000001), TOBN(0xffffffff, 0x00000000),
135     TOBN(0xffffffff, 0xffffffff), TOBN(0x00000000, 0xfffffffe)
136 };
137 
138 static NISTZ256_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group);
139 
140 /* Precomputed tables for the default generator */
141 extern const PRECOMP256_ROW ecp_nistz256_precomputed[37];
142 
143 /* Recode window to a signed digit, see ecp_nistputil.c for details */
_booth_recode_w5(unsigned int in)144 static unsigned int _booth_recode_w5(unsigned int in)
145 {
146     unsigned int s, d;
147 
148     s = ~((in >> 5) - 1);
149     d = (1 << 6) - in - 1;
150     d = (d & s) | (in & ~s);
151     d = (d >> 1) + (d & 1);
152 
153     return (d << 1) + (s & 1);
154 }
155 
_booth_recode_w7(unsigned int in)156 static unsigned int _booth_recode_w7(unsigned int in)
157 {
158     unsigned int s, d;
159 
160     s = ~((in >> 7) - 1);
161     d = (1 << 8) - in - 1;
162     d = (d & s) | (in & ~s);
163     d = (d >> 1) + (d & 1);
164 
165     return (d << 1) + (s & 1);
166 }
167 
copy_conditional(BN_ULONG dst[P256_LIMBS],const BN_ULONG src[P256_LIMBS],BN_ULONG move)168 static void copy_conditional(BN_ULONG dst[P256_LIMBS],
169                              const BN_ULONG src[P256_LIMBS], BN_ULONG move)
170 {
171     BN_ULONG mask1 = 0-move;
172     BN_ULONG mask2 = ~mask1;
173 
174     dst[0] = (src[0] & mask1) ^ (dst[0] & mask2);
175     dst[1] = (src[1] & mask1) ^ (dst[1] & mask2);
176     dst[2] = (src[2] & mask1) ^ (dst[2] & mask2);
177     dst[3] = (src[3] & mask1) ^ (dst[3] & mask2);
178     if (P256_LIMBS == 8) {
179         dst[4] = (src[4] & mask1) ^ (dst[4] & mask2);
180         dst[5] = (src[5] & mask1) ^ (dst[5] & mask2);
181         dst[6] = (src[6] & mask1) ^ (dst[6] & mask2);
182         dst[7] = (src[7] & mask1) ^ (dst[7] & mask2);
183     }
184 }
185 
is_zero(BN_ULONG in)186 static BN_ULONG is_zero(BN_ULONG in)
187 {
188     in |= (0 - in);
189     in = ~in;
190     in >>= BN_BITS2 - 1;
191     return in;
192 }
193 
is_equal(const BN_ULONG a[P256_LIMBS],const BN_ULONG b[P256_LIMBS])194 static BN_ULONG is_equal(const BN_ULONG a[P256_LIMBS],
195                          const BN_ULONG b[P256_LIMBS])
196 {
197     BN_ULONG res;
198 
199     res = a[0] ^ b[0];
200     res |= a[1] ^ b[1];
201     res |= a[2] ^ b[2];
202     res |= a[3] ^ b[3];
203     if (P256_LIMBS == 8) {
204         res |= a[4] ^ b[4];
205         res |= a[5] ^ b[5];
206         res |= a[6] ^ b[6];
207         res |= a[7] ^ b[7];
208     }
209 
210     return is_zero(res);
211 }
212 
is_one(const BIGNUM * z)213 static BN_ULONG is_one(const BIGNUM *z)
214 {
215     BN_ULONG res = 0;
216     BN_ULONG *a = bn_get_words(z);
217 
218     if (bn_get_top(z) == (P256_LIMBS - P256_LIMBS / 8)) {
219         res = a[0] ^ ONE[0];
220         res |= a[1] ^ ONE[1];
221         res |= a[2] ^ ONE[2];
222         res |= a[3] ^ ONE[3];
223         if (P256_LIMBS == 8) {
224             res |= a[4] ^ ONE[4];
225             res |= a[5] ^ ONE[5];
226             res |= a[6] ^ ONE[6];
227             /*
228              * no check for a[7] (being zero) on 32-bit platforms,
229              * because value of "one" takes only 7 limbs.
230              */
231         }
232         res = is_zero(res);
233     }
234 
235     return res;
236 }
237 
238 /*
239  * For reference, this macro is used only when new ecp_nistz256 assembly
240  * module is being developed.  For example, configure with
241  * -DECP_NISTZ256_REFERENCE_IMPLEMENTATION and implement only functions
242  * performing simplest arithmetic operations on 256-bit vectors. Then
243  * work on implementation of higher-level functions performing point
244  * operations. Then remove ECP_NISTZ256_REFERENCE_IMPLEMENTATION
245  * and never define it again. (The correct macro denoting presence of
246  * ecp_nistz256 module is ECP_NISTZ256_ASM.)
247  */
248 #ifndef ECP_NISTZ256_REFERENCE_IMPLEMENTATION
249 void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a);
250 void ecp_nistz256_point_add(P256_POINT *r,
251                             const P256_POINT *a, const P256_POINT *b);
252 void ecp_nistz256_point_add_affine(P256_POINT *r,
253                                    const P256_POINT *a,
254                                    const P256_POINT_AFFINE *b);
255 #else
256 /* Point double: r = 2*a */
ecp_nistz256_point_double(P256_POINT * r,const P256_POINT * a)257 static void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a)
258 {
259     BN_ULONG S[P256_LIMBS];
260     BN_ULONG M[P256_LIMBS];
261     BN_ULONG Zsqr[P256_LIMBS];
262     BN_ULONG tmp0[P256_LIMBS];
263 
264     const BN_ULONG *in_x = a->X;
265     const BN_ULONG *in_y = a->Y;
266     const BN_ULONG *in_z = a->Z;
267 
268     BN_ULONG *res_x = r->X;
269     BN_ULONG *res_y = r->Y;
270     BN_ULONG *res_z = r->Z;
271 
272     ecp_nistz256_mul_by_2(S, in_y);
273 
274     ecp_nistz256_sqr_mont(Zsqr, in_z);
275 
276     ecp_nistz256_sqr_mont(S, S);
277 
278     ecp_nistz256_mul_mont(res_z, in_z, in_y);
279     ecp_nistz256_mul_by_2(res_z, res_z);
280 
281     ecp_nistz256_add(M, in_x, Zsqr);
282     ecp_nistz256_sub(Zsqr, in_x, Zsqr);
283 
284     ecp_nistz256_sqr_mont(res_y, S);
285     ecp_nistz256_div_by_2(res_y, res_y);
286 
287     ecp_nistz256_mul_mont(M, M, Zsqr);
288     ecp_nistz256_mul_by_3(M, M);
289 
290     ecp_nistz256_mul_mont(S, S, in_x);
291     ecp_nistz256_mul_by_2(tmp0, S);
292 
293     ecp_nistz256_sqr_mont(res_x, M);
294 
295     ecp_nistz256_sub(res_x, res_x, tmp0);
296     ecp_nistz256_sub(S, S, res_x);
297 
298     ecp_nistz256_mul_mont(S, S, M);
299     ecp_nistz256_sub(res_y, S, res_y);
300 }
301 
302 /* Point addition: r = a+b */
ecp_nistz256_point_add(P256_POINT * r,const P256_POINT * a,const P256_POINT * b)303 static void ecp_nistz256_point_add(P256_POINT *r,
304                                    const P256_POINT *a, const P256_POINT *b)
305 {
306     BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS];
307     BN_ULONG U1[P256_LIMBS], S1[P256_LIMBS];
308     BN_ULONG Z1sqr[P256_LIMBS];
309     BN_ULONG Z2sqr[P256_LIMBS];
310     BN_ULONG H[P256_LIMBS], R[P256_LIMBS];
311     BN_ULONG Hsqr[P256_LIMBS];
312     BN_ULONG Rsqr[P256_LIMBS];
313     BN_ULONG Hcub[P256_LIMBS];
314 
315     BN_ULONG res_x[P256_LIMBS];
316     BN_ULONG res_y[P256_LIMBS];
317     BN_ULONG res_z[P256_LIMBS];
318 
319     BN_ULONG in1infty, in2infty;
320 
321     const BN_ULONG *in1_x = a->X;
322     const BN_ULONG *in1_y = a->Y;
323     const BN_ULONG *in1_z = a->Z;
324 
325     const BN_ULONG *in2_x = b->X;
326     const BN_ULONG *in2_y = b->Y;
327     const BN_ULONG *in2_z = b->Z;
328 
329     /*
330      * Infinity in encoded as (,,0)
331      */
332     in1infty = (in1_z[0] | in1_z[1] | in1_z[2] | in1_z[3]);
333     if (P256_LIMBS == 8)
334         in1infty |= (in1_z[4] | in1_z[5] | in1_z[6] | in1_z[7]);
335 
336     in2infty = (in2_z[0] | in2_z[1] | in2_z[2] | in2_z[3]);
337     if (P256_LIMBS == 8)
338         in2infty |= (in2_z[4] | in2_z[5] | in2_z[6] | in2_z[7]);
339 
340     in1infty = is_zero(in1infty);
341     in2infty = is_zero(in2infty);
342 
343     ecp_nistz256_sqr_mont(Z2sqr, in2_z);        /* Z2^2 */
344     ecp_nistz256_sqr_mont(Z1sqr, in1_z);        /* Z1^2 */
345 
346     ecp_nistz256_mul_mont(S1, Z2sqr, in2_z);    /* S1 = Z2^3 */
347     ecp_nistz256_mul_mont(S2, Z1sqr, in1_z);    /* S2 = Z1^3 */
348 
349     ecp_nistz256_mul_mont(S1, S1, in1_y);       /* S1 = Y1*Z2^3 */
350     ecp_nistz256_mul_mont(S2, S2, in2_y);       /* S2 = Y2*Z1^3 */
351     ecp_nistz256_sub(R, S2, S1);                /* R = S2 - S1 */
352 
353     ecp_nistz256_mul_mont(U1, in1_x, Z2sqr);    /* U1 = X1*Z2^2 */
354     ecp_nistz256_mul_mont(U2, in2_x, Z1sqr);    /* U2 = X2*Z1^2 */
355     ecp_nistz256_sub(H, U2, U1);                /* H = U2 - U1 */
356 
357     /*
358      * The formulae are incorrect if the points are equal so we check for
359      * this and do doubling if this happens.
360      *
361      * Points here are in Jacobian projective coordinates (Xi, Yi, Zi)
362      * that are bound to the affine coordinates (xi, yi) by the following
363      * equations:
364      *     - xi = Xi / (Zi)^2
365      *     - y1 = Yi / (Zi)^3
366      *
367      * For the sake of optimization, the algorithm operates over
368      * intermediate variables U1, U2 and S1, S2 that are derived from
369      * the projective coordinates:
370      *     - U1 = X1 * (Z2)^2 ; U2 = X2 * (Z1)^2
371      *     - S1 = Y1 * (Z2)^3 ; S2 = Y2 * (Z1)^3
372      *
373      * It is easy to prove that is_equal(U1, U2) implies that the affine
374      * x-coordinates are equal, or either point is at infinity.
375      * Likewise is_equal(S1, S2) implies that the affine y-coordinates are
376      * equal, or either point is at infinity.
377      *
378      * The special case of either point being the point at infinity (Z1 or Z2
379      * is zero), is handled separately later on in this function, so we avoid
380      * jumping to point_double here in those special cases.
381      *
382      * When both points are inverse of each other, we know that the affine
383      * x-coordinates are equal, and the y-coordinates have different sign.
384      * Therefore since U1 = U2, we know H = 0, and therefore Z3 = H*Z1*Z2
385      * will equal 0, thus the result is infinity, if we simply let this
386      * function continue normally.
387      *
388      * We use bitwise operations to avoid potential side-channels introduced by
389      * the short-circuiting behaviour of boolean operators.
390      */
391     if (is_equal(U1, U2) & ~in1infty & ~in2infty & is_equal(S1, S2)) {
392         /*
393          * This is obviously not constant-time but it should never happen during
394          * single point multiplication, so there is no timing leak for ECDH or
395          * ECDSA signing.
396          */
397         ecp_nistz256_point_double(r, a);
398         return;
399     }
400 
401     ecp_nistz256_sqr_mont(Rsqr, R);             /* R^2 */
402     ecp_nistz256_mul_mont(res_z, H, in1_z);     /* Z3 = H*Z1*Z2 */
403     ecp_nistz256_sqr_mont(Hsqr, H);             /* H^2 */
404     ecp_nistz256_mul_mont(res_z, res_z, in2_z); /* Z3 = H*Z1*Z2 */
405     ecp_nistz256_mul_mont(Hcub, Hsqr, H);       /* H^3 */
406 
407     ecp_nistz256_mul_mont(U2, U1, Hsqr);        /* U1*H^2 */
408     ecp_nistz256_mul_by_2(Hsqr, U2);            /* 2*U1*H^2 */
409 
410     ecp_nistz256_sub(res_x, Rsqr, Hsqr);
411     ecp_nistz256_sub(res_x, res_x, Hcub);
412 
413     ecp_nistz256_sub(res_y, U2, res_x);
414 
415     ecp_nistz256_mul_mont(S2, S1, Hcub);
416     ecp_nistz256_mul_mont(res_y, R, res_y);
417     ecp_nistz256_sub(res_y, res_y, S2);
418 
419     copy_conditional(res_x, in2_x, in1infty);
420     copy_conditional(res_y, in2_y, in1infty);
421     copy_conditional(res_z, in2_z, in1infty);
422 
423     copy_conditional(res_x, in1_x, in2infty);
424     copy_conditional(res_y, in1_y, in2infty);
425     copy_conditional(res_z, in1_z, in2infty);
426 
427     memcpy(r->X, res_x, sizeof(res_x));
428     memcpy(r->Y, res_y, sizeof(res_y));
429     memcpy(r->Z, res_z, sizeof(res_z));
430 }
431 
432 /* Point addition when b is known to be affine: r = a+b */
ecp_nistz256_point_add_affine(P256_POINT * r,const P256_POINT * a,const P256_POINT_AFFINE * b)433 static void ecp_nistz256_point_add_affine(P256_POINT *r,
434                                           const P256_POINT *a,
435                                           const P256_POINT_AFFINE *b)
436 {
437     BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS];
438     BN_ULONG Z1sqr[P256_LIMBS];
439     BN_ULONG H[P256_LIMBS], R[P256_LIMBS];
440     BN_ULONG Hsqr[P256_LIMBS];
441     BN_ULONG Rsqr[P256_LIMBS];
442     BN_ULONG Hcub[P256_LIMBS];
443 
444     BN_ULONG res_x[P256_LIMBS];
445     BN_ULONG res_y[P256_LIMBS];
446     BN_ULONG res_z[P256_LIMBS];
447 
448     BN_ULONG in1infty, in2infty;
449 
450     const BN_ULONG *in1_x = a->X;
451     const BN_ULONG *in1_y = a->Y;
452     const BN_ULONG *in1_z = a->Z;
453 
454     const BN_ULONG *in2_x = b->X;
455     const BN_ULONG *in2_y = b->Y;
456 
457     /*
458      * Infinity in encoded as (,,0)
459      */
460     in1infty = (in1_z[0] | in1_z[1] | in1_z[2] | in1_z[3]);
461     if (P256_LIMBS == 8)
462         in1infty |= (in1_z[4] | in1_z[5] | in1_z[6] | in1_z[7]);
463 
464     /*
465      * In affine representation we encode infinity as (0,0), which is
466      * not on the curve, so it is OK
467      */
468     in2infty = (in2_x[0] | in2_x[1] | in2_x[2] | in2_x[3] |
469                 in2_y[0] | in2_y[1] | in2_y[2] | in2_y[3]);
470     if (P256_LIMBS == 8)
471         in2infty |= (in2_x[4] | in2_x[5] | in2_x[6] | in2_x[7] |
472                      in2_y[4] | in2_y[5] | in2_y[6] | in2_y[7]);
473 
474     in1infty = is_zero(in1infty);
475     in2infty = is_zero(in2infty);
476 
477     ecp_nistz256_sqr_mont(Z1sqr, in1_z);        /* Z1^2 */
478 
479     ecp_nistz256_mul_mont(U2, in2_x, Z1sqr);    /* U2 = X2*Z1^2 */
480     ecp_nistz256_sub(H, U2, in1_x);             /* H = U2 - U1 */
481 
482     ecp_nistz256_mul_mont(S2, Z1sqr, in1_z);    /* S2 = Z1^3 */
483 
484     ecp_nistz256_mul_mont(res_z, H, in1_z);     /* Z3 = H*Z1*Z2 */
485 
486     ecp_nistz256_mul_mont(S2, S2, in2_y);       /* S2 = Y2*Z1^3 */
487     ecp_nistz256_sub(R, S2, in1_y);             /* R = S2 - S1 */
488 
489     ecp_nistz256_sqr_mont(Hsqr, H);             /* H^2 */
490     ecp_nistz256_sqr_mont(Rsqr, R);             /* R^2 */
491     ecp_nistz256_mul_mont(Hcub, Hsqr, H);       /* H^3 */
492 
493     ecp_nistz256_mul_mont(U2, in1_x, Hsqr);     /* U1*H^2 */
494     ecp_nistz256_mul_by_2(Hsqr, U2);            /* 2*U1*H^2 */
495 
496     ecp_nistz256_sub(res_x, Rsqr, Hsqr);
497     ecp_nistz256_sub(res_x, res_x, Hcub);
498     ecp_nistz256_sub(H, U2, res_x);
499 
500     ecp_nistz256_mul_mont(S2, in1_y, Hcub);
501     ecp_nistz256_mul_mont(H, H, R);
502     ecp_nistz256_sub(res_y, H, S2);
503 
504     copy_conditional(res_x, in2_x, in1infty);
505     copy_conditional(res_x, in1_x, in2infty);
506 
507     copy_conditional(res_y, in2_y, in1infty);
508     copy_conditional(res_y, in1_y, in2infty);
509 
510     copy_conditional(res_z, ONE, in1infty);
511     copy_conditional(res_z, in1_z, in2infty);
512 
513     memcpy(r->X, res_x, sizeof(res_x));
514     memcpy(r->Y, res_y, sizeof(res_y));
515     memcpy(r->Z, res_z, sizeof(res_z));
516 }
517 #endif
518 
519 /* r = in^-1 mod p */
ecp_nistz256_mod_inverse(BN_ULONG r[P256_LIMBS],const BN_ULONG in[P256_LIMBS])520 static void ecp_nistz256_mod_inverse(BN_ULONG r[P256_LIMBS],
521                                      const BN_ULONG in[P256_LIMBS])
522 {
523     /*
524      * The poly is ffffffff 00000001 00000000 00000000 00000000 ffffffff
525      * ffffffff ffffffff We use FLT and used poly-2 as exponent
526      */
527     BN_ULONG p2[P256_LIMBS];
528     BN_ULONG p4[P256_LIMBS];
529     BN_ULONG p8[P256_LIMBS];
530     BN_ULONG p16[P256_LIMBS];
531     BN_ULONG p32[P256_LIMBS];
532     BN_ULONG res[P256_LIMBS];
533     int i;
534 
535     ecp_nistz256_sqr_mont(res, in);
536     ecp_nistz256_mul_mont(p2, res, in);         /* 3*p */
537 
538     ecp_nistz256_sqr_mont(res, p2);
539     ecp_nistz256_sqr_mont(res, res);
540     ecp_nistz256_mul_mont(p4, res, p2);         /* f*p */
541 
542     ecp_nistz256_sqr_mont(res, p4);
543     ecp_nistz256_sqr_mont(res, res);
544     ecp_nistz256_sqr_mont(res, res);
545     ecp_nistz256_sqr_mont(res, res);
546     ecp_nistz256_mul_mont(p8, res, p4);         /* ff*p */
547 
548     ecp_nistz256_sqr_mont(res, p8);
549     for (i = 0; i < 7; i++)
550         ecp_nistz256_sqr_mont(res, res);
551     ecp_nistz256_mul_mont(p16, res, p8);        /* ffff*p */
552 
553     ecp_nistz256_sqr_mont(res, p16);
554     for (i = 0; i < 15; i++)
555         ecp_nistz256_sqr_mont(res, res);
556     ecp_nistz256_mul_mont(p32, res, p16);       /* ffffffff*p */
557 
558     ecp_nistz256_sqr_mont(res, p32);
559     for (i = 0; i < 31; i++)
560         ecp_nistz256_sqr_mont(res, res);
561     ecp_nistz256_mul_mont(res, res, in);
562 
563     for (i = 0; i < 32 * 4; i++)
564         ecp_nistz256_sqr_mont(res, res);
565     ecp_nistz256_mul_mont(res, res, p32);
566 
567     for (i = 0; i < 32; i++)
568         ecp_nistz256_sqr_mont(res, res);
569     ecp_nistz256_mul_mont(res, res, p32);
570 
571     for (i = 0; i < 16; i++)
572         ecp_nistz256_sqr_mont(res, res);
573     ecp_nistz256_mul_mont(res, res, p16);
574 
575     for (i = 0; i < 8; i++)
576         ecp_nistz256_sqr_mont(res, res);
577     ecp_nistz256_mul_mont(res, res, p8);
578 
579     ecp_nistz256_sqr_mont(res, res);
580     ecp_nistz256_sqr_mont(res, res);
581     ecp_nistz256_sqr_mont(res, res);
582     ecp_nistz256_sqr_mont(res, res);
583     ecp_nistz256_mul_mont(res, res, p4);
584 
585     ecp_nistz256_sqr_mont(res, res);
586     ecp_nistz256_sqr_mont(res, res);
587     ecp_nistz256_mul_mont(res, res, p2);
588 
589     ecp_nistz256_sqr_mont(res, res);
590     ecp_nistz256_sqr_mont(res, res);
591     ecp_nistz256_mul_mont(res, res, in);
592 
593     memcpy(r, res, sizeof(res));
594 }
595 
596 /*
597  * ecp_nistz256_bignum_to_field_elem copies the contents of |in| to |out| and
598  * returns one if it fits. Otherwise it returns zero.
599  */
ecp_nistz256_bignum_to_field_elem(BN_ULONG out[P256_LIMBS],const BIGNUM * in)600 __owur static int ecp_nistz256_bignum_to_field_elem(BN_ULONG out[P256_LIMBS],
601                                                     const BIGNUM *in)
602 {
603     return bn_copy_words(out, in, P256_LIMBS);
604 }
605 
606 /* r = sum(scalar[i]*point[i]) */
ecp_nistz256_windowed_mul(const EC_GROUP * group,P256_POINT * r,const BIGNUM ** scalar,const EC_POINT ** point,size_t num,BN_CTX * ctx)607 __owur static int ecp_nistz256_windowed_mul(const EC_GROUP *group,
608                                             P256_POINT *r,
609                                             const BIGNUM **scalar,
610                                             const EC_POINT **point,
611                                             size_t num, BN_CTX *ctx)
612 {
613     size_t i;
614     int j, ret = 0;
615     unsigned int idx;
616     unsigned char (*p_str)[33] = NULL;
617     const unsigned int window_size = 5;
618     const unsigned int mask = (1 << (window_size + 1)) - 1;
619     unsigned int wvalue;
620     P256_POINT *temp;           /* place for 5 temporary points */
621     const BIGNUM **scalars = NULL;
622     P256_POINT (*table)[16] = NULL;
623     void *table_storage = NULL;
624 
625     if ((num * 16 + 6) > OPENSSL_MALLOC_MAX_NELEMS(P256_POINT)
626         || (table_storage =
627             OPENSSL_malloc((num * 16 + 5) * sizeof(P256_POINT) + 64)) == NULL
628         || (p_str =
629             OPENSSL_malloc(num * 33 * sizeof(unsigned char))) == NULL
630         || (scalars = OPENSSL_malloc(num * sizeof(BIGNUM *))) == NULL)
631         goto err;
632 
633     table = (void *)ALIGNPTR(table_storage, 64);
634     temp = (P256_POINT *)(table + num);
635 
636     for (i = 0; i < num; i++) {
637         P256_POINT *row = table[i];
638 
639         /* This is an unusual input, we don't guarantee constant-timeness. */
640         if ((BN_num_bits(scalar[i]) > 256) || BN_is_negative(scalar[i])) {
641             BIGNUM *mod;
642 
643             if ((mod = BN_CTX_get(ctx)) == NULL)
644                 goto err;
645             if (!BN_nnmod(mod, scalar[i], group->order, ctx)) {
646                 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
647                 goto err;
648             }
649             scalars[i] = mod;
650         } else
651             scalars[i] = scalar[i];
652 
653         for (j = 0; j < bn_get_top(scalars[i]) * BN_BYTES; j += BN_BYTES) {
654             BN_ULONG d = bn_get_words(scalars[i])[j / BN_BYTES];
655 
656             p_str[i][j + 0] = (unsigned char)d;
657             p_str[i][j + 1] = (unsigned char)(d >> 8);
658             p_str[i][j + 2] = (unsigned char)(d >> 16);
659             p_str[i][j + 3] = (unsigned char)(d >>= 24);
660             if (BN_BYTES == 8) {
661                 d >>= 8;
662                 p_str[i][j + 4] = (unsigned char)d;
663                 p_str[i][j + 5] = (unsigned char)(d >> 8);
664                 p_str[i][j + 6] = (unsigned char)(d >> 16);
665                 p_str[i][j + 7] = (unsigned char)(d >> 24);
666             }
667         }
668         for (; j < 33; j++)
669             p_str[i][j] = 0;
670 
671         if (!ecp_nistz256_bignum_to_field_elem(temp[0].X, point[i]->X)
672             || !ecp_nistz256_bignum_to_field_elem(temp[0].Y, point[i]->Y)
673             || !ecp_nistz256_bignum_to_field_elem(temp[0].Z, point[i]->Z)) {
674             ERR_raise(ERR_LIB_EC, EC_R_COORDINATES_OUT_OF_RANGE);
675             goto err;
676         }
677 
678         /*
679          * row[0] is implicitly (0,0,0) (the point at infinity), therefore it
680          * is not stored. All other values are actually stored with an offset
681          * of -1 in table.
682          */
683 
684         ecp_nistz256_scatter_w5  (row, &temp[0], 1);
685         ecp_nistz256_point_double(&temp[1], &temp[0]);              /*1+1=2  */
686         ecp_nistz256_scatter_w5  (row, &temp[1], 2);
687         ecp_nistz256_point_add   (&temp[2], &temp[1], &temp[0]);    /*2+1=3  */
688         ecp_nistz256_scatter_w5  (row, &temp[2], 3);
689         ecp_nistz256_point_double(&temp[1], &temp[1]);              /*2*2=4  */
690         ecp_nistz256_scatter_w5  (row, &temp[1], 4);
691         ecp_nistz256_point_double(&temp[2], &temp[2]);              /*2*3=6  */
692         ecp_nistz256_scatter_w5  (row, &temp[2], 6);
693         ecp_nistz256_point_add   (&temp[3], &temp[1], &temp[0]);    /*4+1=5  */
694         ecp_nistz256_scatter_w5  (row, &temp[3], 5);
695         ecp_nistz256_point_add   (&temp[4], &temp[2], &temp[0]);    /*6+1=7  */
696         ecp_nistz256_scatter_w5  (row, &temp[4], 7);
697         ecp_nistz256_point_double(&temp[1], &temp[1]);              /*2*4=8  */
698         ecp_nistz256_scatter_w5  (row, &temp[1], 8);
699         ecp_nistz256_point_double(&temp[2], &temp[2]);              /*2*6=12 */
700         ecp_nistz256_scatter_w5  (row, &temp[2], 12);
701         ecp_nistz256_point_double(&temp[3], &temp[3]);              /*2*5=10 */
702         ecp_nistz256_scatter_w5  (row, &temp[3], 10);
703         ecp_nistz256_point_double(&temp[4], &temp[4]);              /*2*7=14 */
704         ecp_nistz256_scatter_w5  (row, &temp[4], 14);
705         ecp_nistz256_point_add   (&temp[2], &temp[2], &temp[0]);    /*12+1=13*/
706         ecp_nistz256_scatter_w5  (row, &temp[2], 13);
707         ecp_nistz256_point_add   (&temp[3], &temp[3], &temp[0]);    /*10+1=11*/
708         ecp_nistz256_scatter_w5  (row, &temp[3], 11);
709         ecp_nistz256_point_add   (&temp[4], &temp[4], &temp[0]);    /*14+1=15*/
710         ecp_nistz256_scatter_w5  (row, &temp[4], 15);
711         ecp_nistz256_point_add   (&temp[2], &temp[1], &temp[0]);    /*8+1=9  */
712         ecp_nistz256_scatter_w5  (row, &temp[2], 9);
713         ecp_nistz256_point_double(&temp[1], &temp[1]);              /*2*8=16 */
714         ecp_nistz256_scatter_w5  (row, &temp[1], 16);
715     }
716 
717     idx = 255;
718 
719     wvalue = p_str[0][(idx - 1) / 8];
720     wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
721 
722     /*
723      * We gather to temp[0], because we know it's position relative
724      * to table
725      */
726     ecp_nistz256_gather_w5(&temp[0], table[0], _booth_recode_w5(wvalue) >> 1);
727     memcpy(r, &temp[0], sizeof(temp[0]));
728 
729     while (idx >= 5) {
730         for (i = (idx == 255 ? 1 : 0); i < num; i++) {
731             unsigned int off = (idx - 1) / 8;
732 
733             wvalue = p_str[i][off] | p_str[i][off + 1] << 8;
734             wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
735 
736             wvalue = _booth_recode_w5(wvalue);
737 
738             ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1);
739 
740             ecp_nistz256_neg(temp[1].Y, temp[0].Y);
741             copy_conditional(temp[0].Y, temp[1].Y, (wvalue & 1));
742 
743             ecp_nistz256_point_add(r, r, &temp[0]);
744         }
745 
746         idx -= window_size;
747 
748         ecp_nistz256_point_double(r, r);
749         ecp_nistz256_point_double(r, r);
750         ecp_nistz256_point_double(r, r);
751         ecp_nistz256_point_double(r, r);
752         ecp_nistz256_point_double(r, r);
753     }
754 
755     /* Final window */
756     for (i = 0; i < num; i++) {
757         wvalue = p_str[i][0];
758         wvalue = (wvalue << 1) & mask;
759 
760         wvalue = _booth_recode_w5(wvalue);
761 
762         ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1);
763 
764         ecp_nistz256_neg(temp[1].Y, temp[0].Y);
765         copy_conditional(temp[0].Y, temp[1].Y, wvalue & 1);
766 
767         ecp_nistz256_point_add(r, r, &temp[0]);
768     }
769 
770     ret = 1;
771  err:
772     OPENSSL_free(table_storage);
773     OPENSSL_free(p_str);
774     OPENSSL_free(scalars);
775     return ret;
776 }
777 
778 /* Coordinates of G, for which we have precomputed tables */
779 static const BN_ULONG def_xG[P256_LIMBS] = {
780     TOBN(0x79e730d4, 0x18a9143c), TOBN(0x75ba95fc, 0x5fedb601),
781     TOBN(0x79fb732b, 0x77622510), TOBN(0x18905f76, 0xa53755c6)
782 };
783 
784 static const BN_ULONG def_yG[P256_LIMBS] = {
785     TOBN(0xddf25357, 0xce95560a), TOBN(0x8b4ab8e4, 0xba19e45c),
786     TOBN(0xd2e88688, 0xdd21f325), TOBN(0x8571ff18, 0x25885d85)
787 };
788 
789 /*
790  * ecp_nistz256_is_affine_G returns one if |generator| is the standard, P-256
791  * generator.
792  */
ecp_nistz256_is_affine_G(const EC_POINT * generator)793 static int ecp_nistz256_is_affine_G(const EC_POINT *generator)
794 {
795     return (bn_get_top(generator->X) == P256_LIMBS) &&
796         (bn_get_top(generator->Y) == P256_LIMBS) &&
797         is_equal(bn_get_words(generator->X), def_xG) &&
798         is_equal(bn_get_words(generator->Y), def_yG) &&
799         is_one(generator->Z);
800 }
801 
ecp_nistz256_mult_precompute(EC_GROUP * group,BN_CTX * ctx)802 __owur static int ecp_nistz256_mult_precompute(EC_GROUP *group, BN_CTX *ctx)
803 {
804     /*
805      * We precompute a table for a Booth encoded exponent (wNAF) based
806      * computation. Each table holds 64 values for safe access, with an
807      * implicit value of infinity at index zero. We use window of size 7, and
808      * therefore require ceil(256/7) = 37 tables.
809      */
810     const BIGNUM *order;
811     EC_POINT *P = NULL, *T = NULL;
812     const EC_POINT *generator;
813     NISTZ256_PRE_COMP *pre_comp;
814     BN_CTX *new_ctx = NULL;
815     int i, j, k, ret = 0;
816     size_t w;
817 
818     PRECOMP256_ROW *preComputedTable = NULL;
819     unsigned char *precomp_storage = NULL;
820 
821     /* if there is an old NISTZ256_PRE_COMP object, throw it away */
822     EC_pre_comp_free(group);
823     generator = EC_GROUP_get0_generator(group);
824     if (generator == NULL) {
825         ERR_raise(ERR_LIB_EC, EC_R_UNDEFINED_GENERATOR);
826         return 0;
827     }
828 
829     if (ecp_nistz256_is_affine_G(generator)) {
830         /*
831          * No need to calculate tables for the standard generator because we
832          * have them statically.
833          */
834         return 1;
835     }
836 
837     if ((pre_comp = ecp_nistz256_pre_comp_new(group)) == NULL)
838         return 0;
839 
840     if (ctx == NULL) {
841         ctx = new_ctx = BN_CTX_new_ex(group->libctx);
842         if (ctx == NULL)
843             goto err;
844     }
845 
846     BN_CTX_start(ctx);
847 
848     order = EC_GROUP_get0_order(group);
849     if (order == NULL)
850         goto err;
851 
852     if (BN_is_zero(order)) {
853         ERR_raise(ERR_LIB_EC, EC_R_UNKNOWN_ORDER);
854         goto err;
855     }
856 
857     w = 7;
858 
859     if ((precomp_storage =
860          OPENSSL_malloc(37 * 64 * sizeof(P256_POINT_AFFINE) + 64)) == NULL)
861         goto err;
862 
863     preComputedTable = (void *)ALIGNPTR(precomp_storage, 64);
864 
865     P = EC_POINT_new(group);
866     T = EC_POINT_new(group);
867     if (P == NULL || T == NULL)
868         goto err;
869 
870     /*
871      * The zero entry is implicitly infinity, and we skip it, storing other
872      * values with -1 offset.
873      */
874     if (!EC_POINT_copy(T, generator))
875         goto err;
876 
877     for (k = 0; k < 64; k++) {
878         if (!EC_POINT_copy(P, T))
879             goto err;
880         for (j = 0; j < 37; j++) {
881             P256_POINT_AFFINE temp;
882             /*
883              * It would be faster to use EC_POINTs_make_affine and
884              * make multiple points affine at the same time.
885              */
886             if (group->meth->make_affine == NULL
887                 || !group->meth->make_affine(group, P, ctx))
888                 goto err;
889             if (!ecp_nistz256_bignum_to_field_elem(temp.X, P->X) ||
890                 !ecp_nistz256_bignum_to_field_elem(temp.Y, P->Y)) {
891                 ERR_raise(ERR_LIB_EC, EC_R_COORDINATES_OUT_OF_RANGE);
892                 goto err;
893             }
894             ecp_nistz256_scatter_w7(preComputedTable[j], &temp, k);
895             for (i = 0; i < 7; i++) {
896                 if (!EC_POINT_dbl(group, P, P, ctx))
897                     goto err;
898             }
899         }
900         if (!EC_POINT_add(group, T, T, generator, ctx))
901             goto err;
902     }
903 
904     pre_comp->group = group;
905     pre_comp->w = w;
906     pre_comp->precomp = preComputedTable;
907     pre_comp->precomp_storage = precomp_storage;
908     precomp_storage = NULL;
909     SETPRECOMP(group, nistz256, pre_comp);
910     pre_comp = NULL;
911     ret = 1;
912 
913  err:
914     BN_CTX_end(ctx);
915     BN_CTX_free(new_ctx);
916 
917     EC_nistz256_pre_comp_free(pre_comp);
918     OPENSSL_free(precomp_storage);
919     EC_POINT_free(P);
920     EC_POINT_free(T);
921     return ret;
922 }
923 
ecp_nistz256_set_from_affine(EC_POINT * out,const EC_GROUP * group,const P256_POINT_AFFINE * in,BN_CTX * ctx)924 __owur static int ecp_nistz256_set_from_affine(EC_POINT *out, const EC_GROUP *group,
925                                                const P256_POINT_AFFINE *in,
926                                                BN_CTX *ctx)
927 {
928     int ret = 0;
929 
930     if ((ret = bn_set_words(out->X, in->X, P256_LIMBS))
931         && (ret = bn_set_words(out->Y, in->Y, P256_LIMBS))
932         && (ret = bn_set_words(out->Z, ONE, P256_LIMBS)))
933         out->Z_is_one = 1;
934 
935     return ret;
936 }
937 
938 /* r = scalar*G + sum(scalars[i]*points[i]) */
ecp_nistz256_points_mul(const EC_GROUP * group,EC_POINT * r,const BIGNUM * scalar,size_t num,const EC_POINT * points[],const BIGNUM * scalars[],BN_CTX * ctx)939 __owur static int ecp_nistz256_points_mul(const EC_GROUP *group,
940                                           EC_POINT *r,
941                                           const BIGNUM *scalar,
942                                           size_t num,
943                                           const EC_POINT *points[],
944                                           const BIGNUM *scalars[], BN_CTX *ctx)
945 {
946     int i = 0, ret = 0, no_precomp_for_generator = 0, p_is_infinity = 0;
947     unsigned char p_str[33] = { 0 };
948     const PRECOMP256_ROW *preComputedTable = NULL;
949     const NISTZ256_PRE_COMP *pre_comp = NULL;
950     const EC_POINT *generator = NULL;
951     const BIGNUM **new_scalars = NULL;
952     const EC_POINT **new_points = NULL;
953     unsigned int idx = 0;
954     const unsigned int window_size = 7;
955     const unsigned int mask = (1 << (window_size + 1)) - 1;
956     unsigned int wvalue;
957     ALIGN32 union {
958         P256_POINT p;
959         P256_POINT_AFFINE a;
960     } t, p;
961     BIGNUM *tmp_scalar;
962 
963     if ((num + 1) == 0 || (num + 1) > OPENSSL_MALLOC_MAX_NELEMS(void *)) {
964         ERR_raise(ERR_LIB_EC, ERR_R_PASSED_INVALID_ARGUMENT);
965         return 0;
966     }
967 
968     memset(&p, 0, sizeof(p));
969     BN_CTX_start(ctx);
970 
971     if (scalar) {
972         generator = EC_GROUP_get0_generator(group);
973         if (generator == NULL) {
974             ERR_raise(ERR_LIB_EC, EC_R_UNDEFINED_GENERATOR);
975             goto err;
976         }
977 
978         /* look if we can use precomputed multiples of generator */
979         pre_comp = group->pre_comp.nistz256;
980 
981         if (pre_comp) {
982             /*
983              * If there is a precomputed table for the generator, check that
984              * it was generated with the same generator.
985              */
986             EC_POINT *pre_comp_generator = EC_POINT_new(group);
987             if (pre_comp_generator == NULL)
988                 goto err;
989 
990             ecp_nistz256_gather_w7(&p.a, pre_comp->precomp[0], 1);
991             if (!ecp_nistz256_set_from_affine(pre_comp_generator,
992                                               group, &p.a, ctx)) {
993                 EC_POINT_free(pre_comp_generator);
994                 goto err;
995             }
996 
997             if (0 == EC_POINT_cmp(group, generator, pre_comp_generator, ctx))
998                 preComputedTable = (const PRECOMP256_ROW *)pre_comp->precomp;
999 
1000             EC_POINT_free(pre_comp_generator);
1001         }
1002 
1003         if (preComputedTable == NULL && ecp_nistz256_is_affine_G(generator)) {
1004             /*
1005              * If there is no precomputed data, but the generator is the
1006              * default, a hardcoded table of precomputed data is used. This
1007              * is because applications, such as Apache, do not use
1008              * EC_KEY_precompute_mult.
1009              */
1010             preComputedTable = ecp_nistz256_precomputed;
1011         }
1012 
1013         if (preComputedTable) {
1014             BN_ULONG infty;
1015 
1016             if ((BN_num_bits(scalar) > 256)
1017                 || BN_is_negative(scalar)) {
1018                 if ((tmp_scalar = BN_CTX_get(ctx)) == NULL)
1019                     goto err;
1020 
1021                 if (!BN_nnmod(tmp_scalar, scalar, group->order, ctx)) {
1022                     ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
1023                     goto err;
1024                 }
1025                 scalar = tmp_scalar;
1026             }
1027 
1028             for (i = 0; i < bn_get_top(scalar) * BN_BYTES; i += BN_BYTES) {
1029                 BN_ULONG d = bn_get_words(scalar)[i / BN_BYTES];
1030 
1031                 p_str[i + 0] = (unsigned char)d;
1032                 p_str[i + 1] = (unsigned char)(d >> 8);
1033                 p_str[i + 2] = (unsigned char)(d >> 16);
1034                 p_str[i + 3] = (unsigned char)(d >>= 24);
1035                 if (BN_BYTES == 8) {
1036                     d >>= 8;
1037                     p_str[i + 4] = (unsigned char)d;
1038                     p_str[i + 5] = (unsigned char)(d >> 8);
1039                     p_str[i + 6] = (unsigned char)(d >> 16);
1040                     p_str[i + 7] = (unsigned char)(d >> 24);
1041                 }
1042             }
1043 
1044             for (; i < 33; i++)
1045                 p_str[i] = 0;
1046 
1047             /* First window */
1048             wvalue = (p_str[0] << 1) & mask;
1049             idx += window_size;
1050 
1051             wvalue = _booth_recode_w7(wvalue);
1052 
1053             ecp_nistz256_gather_w7(&p.a, preComputedTable[0],
1054                                    wvalue >> 1);
1055 
1056             ecp_nistz256_neg(p.p.Z, p.p.Y);
1057             copy_conditional(p.p.Y, p.p.Z, wvalue & 1);
1058 
1059             /*
1060              * Since affine infinity is encoded as (0,0) and
1061              * Jacobian is (,,0), we need to harmonize them
1062              * by assigning "one" or zero to Z.
1063              */
1064             infty = (p.p.X[0] | p.p.X[1] | p.p.X[2] | p.p.X[3] |
1065                      p.p.Y[0] | p.p.Y[1] | p.p.Y[2] | p.p.Y[3]);
1066             if (P256_LIMBS == 8)
1067                 infty |= (p.p.X[4] | p.p.X[5] | p.p.X[6] | p.p.X[7] |
1068                           p.p.Y[4] | p.p.Y[5] | p.p.Y[6] | p.p.Y[7]);
1069 
1070             infty = 0 - is_zero(infty);
1071             infty = ~infty;
1072 
1073             p.p.Z[0] = ONE[0] & infty;
1074             p.p.Z[1] = ONE[1] & infty;
1075             p.p.Z[2] = ONE[2] & infty;
1076             p.p.Z[3] = ONE[3] & infty;
1077             if (P256_LIMBS == 8) {
1078                 p.p.Z[4] = ONE[4] & infty;
1079                 p.p.Z[5] = ONE[5] & infty;
1080                 p.p.Z[6] = ONE[6] & infty;
1081                 p.p.Z[7] = ONE[7] & infty;
1082             }
1083 
1084             for (i = 1; i < 37; i++) {
1085                 unsigned int off = (idx - 1) / 8;
1086                 wvalue = p_str[off] | p_str[off + 1] << 8;
1087                 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1088                 idx += window_size;
1089 
1090                 wvalue = _booth_recode_w7(wvalue);
1091 
1092                 ecp_nistz256_gather_w7(&t.a,
1093                                        preComputedTable[i], wvalue >> 1);
1094 
1095                 ecp_nistz256_neg(t.p.Z, t.a.Y);
1096                 copy_conditional(t.a.Y, t.p.Z, wvalue & 1);
1097 
1098                 ecp_nistz256_point_add_affine(&p.p, &p.p, &t.a);
1099             }
1100         } else {
1101             p_is_infinity = 1;
1102             no_precomp_for_generator = 1;
1103         }
1104     } else
1105         p_is_infinity = 1;
1106 
1107     if (no_precomp_for_generator) {
1108         /*
1109          * Without a precomputed table for the generator, it has to be
1110          * handled like a normal point.
1111          */
1112         new_scalars = OPENSSL_malloc((num + 1) * sizeof(BIGNUM *));
1113         if (new_scalars == NULL)
1114             goto err;
1115 
1116         new_points = OPENSSL_malloc((num + 1) * sizeof(EC_POINT *));
1117         if (new_points == NULL)
1118             goto err;
1119 
1120         memcpy(new_scalars, scalars, num * sizeof(BIGNUM *));
1121         new_scalars[num] = scalar;
1122         memcpy(new_points, points, num * sizeof(EC_POINT *));
1123         new_points[num] = generator;
1124 
1125         scalars = new_scalars;
1126         points = new_points;
1127         num++;
1128     }
1129 
1130     if (num) {
1131         P256_POINT *out = &t.p;
1132         if (p_is_infinity)
1133             out = &p.p;
1134 
1135         if (!ecp_nistz256_windowed_mul(group, out, scalars, points, num, ctx))
1136             goto err;
1137 
1138         if (!p_is_infinity)
1139             ecp_nistz256_point_add(&p.p, &p.p, out);
1140     }
1141 
1142     /* Not constant-time, but we're only operating on the public output. */
1143     if (!bn_set_words(r->X, p.p.X, P256_LIMBS) ||
1144         !bn_set_words(r->Y, p.p.Y, P256_LIMBS) ||
1145         !bn_set_words(r->Z, p.p.Z, P256_LIMBS)) {
1146         goto err;
1147     }
1148     r->Z_is_one = is_one(r->Z) & 1;
1149 
1150     ret = 1;
1151 
1152 err:
1153     BN_CTX_end(ctx);
1154     OPENSSL_free(new_points);
1155     OPENSSL_free(new_scalars);
1156     return ret;
1157 }
1158 
ecp_nistz256_get_affine(const EC_GROUP * group,const EC_POINT * point,BIGNUM * x,BIGNUM * y,BN_CTX * ctx)1159 __owur static int ecp_nistz256_get_affine(const EC_GROUP *group,
1160                                           const EC_POINT *point,
1161                                           BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
1162 {
1163     BN_ULONG z_inv2[P256_LIMBS];
1164     BN_ULONG z_inv3[P256_LIMBS];
1165     BN_ULONG x_aff[P256_LIMBS];
1166     BN_ULONG y_aff[P256_LIMBS];
1167     BN_ULONG point_x[P256_LIMBS], point_y[P256_LIMBS], point_z[P256_LIMBS];
1168     BN_ULONG x_ret[P256_LIMBS], y_ret[P256_LIMBS];
1169 
1170     if (EC_POINT_is_at_infinity(group, point)) {
1171         ERR_raise(ERR_LIB_EC, EC_R_POINT_AT_INFINITY);
1172         return 0;
1173     }
1174 
1175     if (!ecp_nistz256_bignum_to_field_elem(point_x, point->X) ||
1176         !ecp_nistz256_bignum_to_field_elem(point_y, point->Y) ||
1177         !ecp_nistz256_bignum_to_field_elem(point_z, point->Z)) {
1178         ERR_raise(ERR_LIB_EC, EC_R_COORDINATES_OUT_OF_RANGE);
1179         return 0;
1180     }
1181 
1182     ecp_nistz256_mod_inverse(z_inv3, point_z);
1183     ecp_nistz256_sqr_mont(z_inv2, z_inv3);
1184     ecp_nistz256_mul_mont(x_aff, z_inv2, point_x);
1185 
1186     if (x != NULL) {
1187         ecp_nistz256_from_mont(x_ret, x_aff);
1188         if (!bn_set_words(x, x_ret, P256_LIMBS))
1189             return 0;
1190     }
1191 
1192     if (y != NULL) {
1193         ecp_nistz256_mul_mont(z_inv3, z_inv3, z_inv2);
1194         ecp_nistz256_mul_mont(y_aff, z_inv3, point_y);
1195         ecp_nistz256_from_mont(y_ret, y_aff);
1196         if (!bn_set_words(y, y_ret, P256_LIMBS))
1197             return 0;
1198     }
1199 
1200     return 1;
1201 }
1202 
ecp_nistz256_pre_comp_new(const EC_GROUP * group)1203 static NISTZ256_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group)
1204 {
1205     NISTZ256_PRE_COMP *ret = NULL;
1206 
1207     if (!group)
1208         return NULL;
1209 
1210     ret = OPENSSL_zalloc(sizeof(*ret));
1211 
1212     if (ret == NULL)
1213         return ret;
1214 
1215     ret->group = group;
1216     ret->w = 6;                 /* default */
1217 
1218     if (!CRYPTO_NEW_REF(&ret->references, 1)) {
1219         OPENSSL_free(ret);
1220         return NULL;
1221     }
1222     return ret;
1223 }
1224 
EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP * p)1225 NISTZ256_PRE_COMP *EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP *p)
1226 {
1227     int i;
1228     if (p != NULL)
1229         CRYPTO_UP_REF(&p->references, &i);
1230     return p;
1231 }
1232 
EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP * pre)1233 void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP *pre)
1234 {
1235     int i;
1236 
1237     if (pre == NULL)
1238         return;
1239 
1240     CRYPTO_DOWN_REF(&pre->references, &i);
1241     REF_PRINT_COUNT("EC_nistz256", pre);
1242     if (i > 0)
1243         return;
1244     REF_ASSERT_ISNT(i < 0);
1245 
1246     OPENSSL_free(pre->precomp_storage);
1247     CRYPTO_FREE_REF(&pre->references);
1248     OPENSSL_free(pre);
1249 }
1250 
1251 
ecp_nistz256_window_have_precompute_mult(const EC_GROUP * group)1252 static int ecp_nistz256_window_have_precompute_mult(const EC_GROUP *group)
1253 {
1254     /* There is a hard-coded table for the default generator. */
1255     const EC_POINT *generator = EC_GROUP_get0_generator(group);
1256 
1257     if (generator != NULL && ecp_nistz256_is_affine_G(generator)) {
1258         /* There is a hard-coded table for the default generator. */
1259         return 1;
1260     }
1261 
1262     return HAVEPRECOMP(group, nistz256);
1263 }
1264 
1265 #if defined(__x86_64) || defined(__x86_64__) || \
1266     defined(_M_AMD64) || defined(_M_X64) || \
1267     defined(__powerpc64__) || defined(_ARCH_PP64) || \
1268     defined(__aarch64__)
1269 /*
1270  * Montgomery mul modulo Order(P): res = a*b*2^-256 mod Order(P)
1271  */
1272 void ecp_nistz256_ord_mul_mont(BN_ULONG res[P256_LIMBS],
1273                                const BN_ULONG a[P256_LIMBS],
1274                                const BN_ULONG b[P256_LIMBS]);
1275 void ecp_nistz256_ord_sqr_mont(BN_ULONG res[P256_LIMBS],
1276                                const BN_ULONG a[P256_LIMBS],
1277                                BN_ULONG rep);
1278 
ecp_nistz256_inv_mod_ord(const EC_GROUP * group,BIGNUM * r,const BIGNUM * x,BN_CTX * ctx)1279 static int ecp_nistz256_inv_mod_ord(const EC_GROUP *group, BIGNUM *r,
1280                                     const BIGNUM *x, BN_CTX *ctx)
1281 {
1282     /* RR = 2^512 mod ord(p256) */
1283     static const BN_ULONG RR[P256_LIMBS]  = {
1284         TOBN(0x83244c95,0xbe79eea2), TOBN(0x4699799c,0x49bd6fa6),
1285         TOBN(0x2845b239,0x2b6bec59), TOBN(0x66e12d94,0xf3d95620)
1286     };
1287     /* The constant 1 (unlike ONE that is one in Montgomery representation) */
1288     static const BN_ULONG one[P256_LIMBS] = {
1289         TOBN(0,1), TOBN(0,0), TOBN(0,0), TOBN(0,0)
1290     };
1291     /*
1292      * We don't use entry 0 in the table, so we omit it and address
1293      * with -1 offset.
1294      */
1295     BN_ULONG table[15][P256_LIMBS];
1296     BN_ULONG out[P256_LIMBS], t[P256_LIMBS];
1297     int i, ret = 0;
1298     enum {
1299         i_1 = 0, i_10,     i_11,     i_101, i_111, i_1010, i_1111,
1300         i_10101, i_101010, i_101111, i_x6,  i_x8,  i_x16,  i_x32
1301     };
1302 
1303     /*
1304      * Catch allocation failure early.
1305      */
1306     if (bn_wexpand(r, P256_LIMBS) == NULL) {
1307         ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
1308         goto err;
1309     }
1310 
1311     if ((BN_num_bits(x) > 256) || BN_is_negative(x)) {
1312         BIGNUM *tmp;
1313 
1314         if ((tmp = BN_CTX_get(ctx)) == NULL
1315             || !BN_nnmod(tmp, x, group->order, ctx)) {
1316             ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
1317             goto err;
1318         }
1319         x = tmp;
1320     }
1321 
1322     if (!ecp_nistz256_bignum_to_field_elem(t, x)) {
1323         ERR_raise(ERR_LIB_EC, EC_R_COORDINATES_OUT_OF_RANGE);
1324         goto err;
1325     }
1326 
1327     ecp_nistz256_ord_mul_mont(table[0], t, RR);
1328 #if 0
1329     /*
1330      * Original sparse-then-fixed-window algorithm, retained for reference.
1331      */
1332     for (i = 2; i < 16; i += 2) {
1333         ecp_nistz256_ord_sqr_mont(table[i-1], table[i/2-1], 1);
1334         ecp_nistz256_ord_mul_mont(table[i], table[i-1], table[0]);
1335     }
1336 
1337     /*
1338      * The top 128bit of the exponent are highly redudndant, so we
1339      * perform an optimized flow
1340      */
1341     ecp_nistz256_ord_sqr_mont(t, table[15-1], 4);   /* f0 */
1342     ecp_nistz256_ord_mul_mont(t, t, table[15-1]);   /* ff */
1343 
1344     ecp_nistz256_ord_sqr_mont(out, t, 8);           /* ff00 */
1345     ecp_nistz256_ord_mul_mont(out, out, t);         /* ffff */
1346 
1347     ecp_nistz256_ord_sqr_mont(t, out, 16);          /* ffff0000 */
1348     ecp_nistz256_ord_mul_mont(t, t, out);           /* ffffffff */
1349 
1350     ecp_nistz256_ord_sqr_mont(out, t, 64);          /* ffffffff0000000000000000 */
1351     ecp_nistz256_ord_mul_mont(out, out, t);         /* ffffffff00000000ffffffff */
1352 
1353     ecp_nistz256_ord_sqr_mont(out, out, 32);        /* ffffffff00000000ffffffff00000000 */
1354     ecp_nistz256_ord_mul_mont(out, out, t);         /* ffffffff00000000ffffffffffffffff */
1355 
1356     /*
1357      * The bottom 128 bit of the exponent are processed with fixed 4-bit window
1358      */
1359     for (i = 0; i < 32; i++) {
1360         /* expLo - the low 128 bits of the exponent we use (ord(p256) - 2),
1361          * split into nibbles */
1362         static const unsigned char expLo[32]  = {
1363             0xb,0xc,0xe,0x6,0xf,0xa,0xa,0xd,0xa,0x7,0x1,0x7,0x9,0xe,0x8,0x4,
1364             0xf,0x3,0xb,0x9,0xc,0xa,0xc,0x2,0xf,0xc,0x6,0x3,0x2,0x5,0x4,0xf
1365         };
1366 
1367         ecp_nistz256_ord_sqr_mont(out, out, 4);
1368         /* The exponent is public, no need in constant-time access */
1369         ecp_nistz256_ord_mul_mont(out, out, table[expLo[i]-1]);
1370     }
1371 #else
1372     /*
1373      * https://briansmith.org/ecc-inversion-addition-chains-01#p256_scalar_inversion
1374      *
1375      * Even though this code path spares 12 squarings, 4.5%, and 13
1376      * multiplications, 25%, on grand scale sign operation is not that
1377      * much faster, not more that 2%...
1378      */
1379 
1380     /* pre-calculate powers */
1381     ecp_nistz256_ord_sqr_mont(table[i_10], table[i_1], 1);
1382 
1383     ecp_nistz256_ord_mul_mont(table[i_11], table[i_1], table[i_10]);
1384 
1385     ecp_nistz256_ord_mul_mont(table[i_101], table[i_11], table[i_10]);
1386 
1387     ecp_nistz256_ord_mul_mont(table[i_111], table[i_101], table[i_10]);
1388 
1389     ecp_nistz256_ord_sqr_mont(table[i_1010], table[i_101], 1);
1390 
1391     ecp_nistz256_ord_mul_mont(table[i_1111], table[i_1010], table[i_101]);
1392 
1393     ecp_nistz256_ord_sqr_mont(table[i_10101], table[i_1010], 1);
1394     ecp_nistz256_ord_mul_mont(table[i_10101], table[i_10101], table[i_1]);
1395 
1396     ecp_nistz256_ord_sqr_mont(table[i_101010], table[i_10101], 1);
1397 
1398     ecp_nistz256_ord_mul_mont(table[i_101111], table[i_101010], table[i_101]);
1399 
1400     ecp_nistz256_ord_mul_mont(table[i_x6], table[i_101010], table[i_10101]);
1401 
1402     ecp_nistz256_ord_sqr_mont(table[i_x8], table[i_x6], 2);
1403     ecp_nistz256_ord_mul_mont(table[i_x8], table[i_x8], table[i_11]);
1404 
1405     ecp_nistz256_ord_sqr_mont(table[i_x16], table[i_x8], 8);
1406     ecp_nistz256_ord_mul_mont(table[i_x16], table[i_x16], table[i_x8]);
1407 
1408     ecp_nistz256_ord_sqr_mont(table[i_x32], table[i_x16], 16);
1409     ecp_nistz256_ord_mul_mont(table[i_x32], table[i_x32], table[i_x16]);
1410 
1411     /* calculations */
1412     ecp_nistz256_ord_sqr_mont(out, table[i_x32], 64);
1413     ecp_nistz256_ord_mul_mont(out, out, table[i_x32]);
1414 
1415     for (i = 0; i < 27; i++) {
1416         static const struct { unsigned char p, i; } chain[27] = {
1417             { 32, i_x32 }, { 6,  i_101111 }, { 5,  i_111    },
1418             { 4,  i_11  }, { 5,  i_1111   }, { 5,  i_10101  },
1419             { 4,  i_101 }, { 3,  i_101    }, { 3,  i_101    },
1420             { 5,  i_111 }, { 9,  i_101111 }, { 6,  i_1111   },
1421             { 2,  i_1   }, { 5,  i_1      }, { 6,  i_1111   },
1422             { 5,  i_111 }, { 4,  i_111    }, { 5,  i_111    },
1423             { 5,  i_101 }, { 3,  i_11     }, { 10, i_101111 },
1424             { 2,  i_11  }, { 5,  i_11     }, { 5,  i_11     },
1425             { 3,  i_1   }, { 7,  i_10101  }, { 6,  i_1111   }
1426         };
1427 
1428         ecp_nistz256_ord_sqr_mont(out, out, chain[i].p);
1429         ecp_nistz256_ord_mul_mont(out, out, table[chain[i].i]);
1430     }
1431 #endif
1432     ecp_nistz256_ord_mul_mont(out, out, one);
1433 
1434     /*
1435      * Can't fail, but check return code to be consistent anyway.
1436      */
1437     if (!bn_set_words(r, out, P256_LIMBS))
1438         goto err;
1439 
1440     ret = 1;
1441 err:
1442     return ret;
1443 }
1444 #else
1445 # define ecp_nistz256_inv_mod_ord NULL
1446 #endif
1447 
ecp_nistz256group_full_init(EC_GROUP * group,const unsigned char * params)1448 static int ecp_nistz256group_full_init(EC_GROUP *group,
1449                                        const unsigned char *params) {
1450     BN_CTX *ctx = NULL;
1451     BN_MONT_CTX *mont = NULL, *ordmont = NULL;
1452     const int param_len = 32;
1453     const int seed_len = 20;
1454     int ok = 0;
1455     uint32_t hi_order_n = 0xccd1c8aa;
1456     uint32_t lo_order_n = 0xee00bc4f;
1457     BIGNUM *p = NULL, *a = NULL, *b = NULL, *x = NULL, *y = NULL, *one = NULL,
1458         *order = NULL;
1459     EC_POINT *P = NULL;
1460 
1461     if ((ctx = BN_CTX_new_ex(group->libctx)) == NULL) {
1462         ERR_raise(ERR_LIB_EC, ERR_R_MALLOC_FAILURE);
1463         return 0;
1464     }
1465 
1466     if (!EC_GROUP_set_seed(group, params, seed_len)) {
1467         ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB);
1468         goto err;
1469     }
1470     params += seed_len;
1471 
1472     if ((p = BN_bin2bn(params + 0 * param_len, param_len, NULL)) == NULL
1473         || (a = BN_bin2bn(params + 1 * param_len, param_len, NULL)) == NULL
1474         || (b = BN_bin2bn(params + 2 * param_len, param_len, NULL)) == NULL) {
1475         ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
1476         goto err;
1477     }
1478 
1479     /*
1480      * Set up curve params and montgomery for field
1481      * Start by setting up montgomery and one
1482      */
1483     mont = BN_MONT_CTX_new();
1484     if (mont == NULL)
1485         goto err;
1486 
1487     if (!ossl_bn_mont_ctx_set(mont, p, 256, params + 6 * param_len, param_len,
1488                               1, 0))
1489         goto err;
1490 
1491     one = BN_new();
1492     if (one == NULL) {
1493         ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
1494         goto err;
1495     }
1496     if (!BN_to_montgomery(one, BN_value_one(), mont, ctx)){
1497         ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
1498         goto err;
1499     }
1500     group->field_data1 = mont;
1501     mont = NULL;
1502     group->field_data2 = one;
1503     one = NULL;
1504 
1505     if (!ossl_ec_GFp_simple_group_set_curve(group, p, a, b, ctx)) {
1506          ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB);
1507         goto err;
1508     }
1509 
1510     if ((P = EC_POINT_new(group)) == NULL) {
1511         ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB);
1512         goto err;
1513     }
1514 
1515     if ((x = BN_bin2bn(params + 3 * param_len, param_len, NULL)) == NULL
1516         || (y = BN_bin2bn(params + 4 * param_len, param_len, NULL)) == NULL) {
1517         ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
1518         goto err;
1519     }
1520     if (!EC_POINT_set_affine_coordinates(group, P, x, y, ctx)) {
1521         ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB);
1522         goto err;
1523     }
1524     if ((order = BN_bin2bn(params + 5 * param_len, param_len, NULL)) == NULL
1525         || !BN_set_word(x, (BN_ULONG)1)) { // cofactor is 1
1526         ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
1527         goto err;
1528     }
1529 
1530     /*
1531      * Set up generator and order and montgomery data
1532      */
1533     group->generator = EC_POINT_new(group);
1534     if (group->generator == NULL){
1535         ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB);
1536         goto err;
1537     }
1538     if (!EC_POINT_copy(group->generator, P))
1539         goto err;
1540     if (!BN_copy(group->order, order))
1541         goto err;
1542     if (!BN_set_word(group->cofactor, 1))
1543         goto err;
1544 
1545     ordmont = BN_MONT_CTX_new();
1546     if (ordmont  == NULL)
1547         goto err;
1548     if (!ossl_bn_mont_ctx_set(ordmont, order, 256, params + 7 * param_len,
1549                               param_len, lo_order_n, hi_order_n))
1550         goto err;
1551 
1552     group->mont_data = ordmont;
1553     ordmont = NULL;
1554 
1555     ok = 1;
1556 
1557  err:
1558     EC_POINT_free(P);
1559     BN_CTX_free(ctx);
1560     BN_MONT_CTX_free(mont);
1561     BN_MONT_CTX_free(ordmont);
1562     BN_free(p);
1563     BN_free(one);
1564     BN_free(a);
1565     BN_free(b);
1566     BN_free(order);
1567     BN_free(x);
1568     BN_free(y);
1569 
1570     return ok;
1571 }
1572 
EC_GFp_nistz256_method(void)1573 const EC_METHOD *EC_GFp_nistz256_method(void)
1574 {
1575     static const EC_METHOD ret = {
1576         EC_FLAGS_DEFAULT_OCT,
1577         NID_X9_62_prime_field,
1578         ossl_ec_GFp_mont_group_init,
1579         ossl_ec_GFp_mont_group_finish,
1580         ossl_ec_GFp_mont_group_clear_finish,
1581         ossl_ec_GFp_mont_group_copy,
1582         ossl_ec_GFp_mont_group_set_curve,
1583         ossl_ec_GFp_simple_group_get_curve,
1584         ossl_ec_GFp_simple_group_get_degree,
1585         ossl_ec_group_simple_order_bits,
1586         ossl_ec_GFp_simple_group_check_discriminant,
1587         ossl_ec_GFp_simple_point_init,
1588         ossl_ec_GFp_simple_point_finish,
1589         ossl_ec_GFp_simple_point_clear_finish,
1590         ossl_ec_GFp_simple_point_copy,
1591         ossl_ec_GFp_simple_point_set_to_infinity,
1592         ossl_ec_GFp_simple_point_set_affine_coordinates,
1593         ecp_nistz256_get_affine,
1594         0, 0, 0,
1595         ossl_ec_GFp_simple_add,
1596         ossl_ec_GFp_simple_dbl,
1597         ossl_ec_GFp_simple_invert,
1598         ossl_ec_GFp_simple_is_at_infinity,
1599         ossl_ec_GFp_simple_is_on_curve,
1600         ossl_ec_GFp_simple_cmp,
1601         ossl_ec_GFp_simple_make_affine,
1602         ossl_ec_GFp_simple_points_make_affine,
1603         ecp_nistz256_points_mul,                    /* mul */
1604         ecp_nistz256_mult_precompute,               /* precompute_mult */
1605         ecp_nistz256_window_have_precompute_mult,   /* have_precompute_mult */
1606         ossl_ec_GFp_mont_field_mul,
1607         ossl_ec_GFp_mont_field_sqr,
1608         0,                                          /* field_div */
1609         ossl_ec_GFp_mont_field_inv,
1610         ossl_ec_GFp_mont_field_encode,
1611         ossl_ec_GFp_mont_field_decode,
1612         ossl_ec_GFp_mont_field_set_to_one,
1613         ossl_ec_key_simple_priv2oct,
1614         ossl_ec_key_simple_oct2priv,
1615         0, /* set private */
1616         ossl_ec_key_simple_generate_key,
1617         ossl_ec_key_simple_check_key,
1618         ossl_ec_key_simple_generate_public_key,
1619         0, /* keycopy */
1620         0, /* keyfinish */
1621         ossl_ecdh_simple_compute_key,
1622         ossl_ecdsa_simple_sign_setup,
1623         ossl_ecdsa_simple_sign_sig,
1624         ossl_ecdsa_simple_verify_sig,
1625         ecp_nistz256_inv_mod_ord,                   /* can be #define-d NULL */
1626         0,                                          /* blind_coordinates */
1627         0,                                          /* ladder_pre */
1628         0,                                          /* ladder_step */
1629         0,                                          /* ladder_post */
1630         ecp_nistz256group_full_init
1631     };
1632 
1633     return &ret;
1634 }
1635