2 * Copyright 2014-2020 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright (c) 2014, Intel Corporation. All Rights Reserved.
4 * Copyright (c) 2015, CloudFlare, Inc.
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
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.
17 * S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with
22 * ECDSA low level APIs are deprecated for public use, but still ok for
25 #include "internal/deprecated.h"
29 #include "internal/cryptlib.h"
30 #include "crypto/bn.h"
32 #include "internal/refcount.h"
35 # define TOBN(hi,lo) lo,hi
37 # define TOBN(hi,lo) ((BN_ULONG)hi<<32|lo)
41 # define ALIGN32 __attribute((aligned(32)))
42 #elif defined(_MSC_VER)
43 # define ALIGN32 __declspec(align(32))
48 #define ALIGNPTR(p,N) ((unsigned char *)p+N-(size_t)p%N)
49 #define P256_LIMBS (256/BN_BITS2)
51 typedef unsigned short u16
;
54 BN_ULONG X
[P256_LIMBS
];
55 BN_ULONG Y
[P256_LIMBS
];
56 BN_ULONG Z
[P256_LIMBS
];
60 BN_ULONG X
[P256_LIMBS
];
61 BN_ULONG Y
[P256_LIMBS
];
64 typedef P256_POINT_AFFINE PRECOMP256_ROW
[64];
66 /* structure for precomputed multiples of the generator */
67 struct nistz256_pre_comp_st
{
68 const EC_GROUP
*group
; /* Parent EC_GROUP object */
69 size_t w
; /* Window size */
71 * Constant time access to the X and Y coordinates of the pre-computed,
72 * generator multiplies, in the Montgomery domain. Pre-calculated
73 * multiplies are stored in affine form.
75 PRECOMP256_ROW
*precomp
;
76 void *precomp_storage
;
77 CRYPTO_REF_COUNT references
;
81 /* Functions implemented in assembly */
83 * Most of below mentioned functions *preserve* the property of inputs
84 * being fully reduced, i.e. being in [0, modulus) range. Simply put if
85 * inputs are fully reduced, then output is too. Note that reverse is
86 * not true, in sense that given partially reduced inputs output can be
87 * either, not unlikely reduced. And "most" in first sentence refers to
88 * the fact that given the calculations flow one can tolerate that
89 * addition, 1st function below, produces partially reduced result *if*
90 * multiplications by 2 and 3, which customarily use addition, fully
91 * reduce it. This effectively gives two options: a) addition produces
92 * fully reduced result [as long as inputs are, just like remaining
93 * functions]; b) addition is allowed to produce partially reduced
94 * result, but multiplications by 2 and 3 perform additional reduction
95 * step. Choice between the two can be platform-specific, but it was a)
96 * in all cases so far...
98 /* Modular add: res = a+b mod P */
99 void ecp_nistz256_add(BN_ULONG res
[P256_LIMBS
],
100 const BN_ULONG a
[P256_LIMBS
],
101 const BN_ULONG b
[P256_LIMBS
]);
102 /* Modular mul by 2: res = 2*a mod P */
103 void ecp_nistz256_mul_by_2(BN_ULONG res
[P256_LIMBS
],
104 const BN_ULONG a
[P256_LIMBS
]);
105 /* Modular mul by 3: res = 3*a mod P */
106 void ecp_nistz256_mul_by_3(BN_ULONG res
[P256_LIMBS
],
107 const BN_ULONG a
[P256_LIMBS
]);
109 /* Modular div by 2: res = a/2 mod P */
110 void ecp_nistz256_div_by_2(BN_ULONG res
[P256_LIMBS
],
111 const BN_ULONG a
[P256_LIMBS
]);
112 /* Modular sub: res = a-b mod P */
113 void ecp_nistz256_sub(BN_ULONG res
[P256_LIMBS
],
114 const BN_ULONG a
[P256_LIMBS
],
115 const BN_ULONG b
[P256_LIMBS
]);
116 /* Modular neg: res = -a mod P */
117 void ecp_nistz256_neg(BN_ULONG res
[P256_LIMBS
], const BN_ULONG a
[P256_LIMBS
]);
118 /* Montgomery mul: res = a*b*2^-256 mod P */
119 void ecp_nistz256_mul_mont(BN_ULONG res
[P256_LIMBS
],
120 const BN_ULONG a
[P256_LIMBS
],
121 const BN_ULONG b
[P256_LIMBS
]);
122 /* Montgomery sqr: res = a*a*2^-256 mod P */
123 void ecp_nistz256_sqr_mont(BN_ULONG res
[P256_LIMBS
],
124 const BN_ULONG a
[P256_LIMBS
]);
125 /* Convert a number from Montgomery domain, by multiplying with 1 */
126 void ecp_nistz256_from_mont(BN_ULONG res
[P256_LIMBS
],
127 const BN_ULONG in
[P256_LIMBS
]);
128 /* Convert a number to Montgomery domain, by multiplying with 2^512 mod P*/
129 void ecp_nistz256_to_mont(BN_ULONG res
[P256_LIMBS
],
130 const BN_ULONG in
[P256_LIMBS
]);
131 /* Functions that perform constant time access to the precomputed tables */
132 void ecp_nistz256_scatter_w5(P256_POINT
*val
,
133 const P256_POINT
*in_t
, int idx
);
134 void ecp_nistz256_gather_w5(P256_POINT
*val
,
135 const P256_POINT
*in_t
, int idx
);
136 void ecp_nistz256_scatter_w7(P256_POINT_AFFINE
*val
,
137 const P256_POINT_AFFINE
*in_t
, int idx
);
138 void ecp_nistz256_gather_w7(P256_POINT_AFFINE
*val
,
139 const P256_POINT_AFFINE
*in_t
, int idx
);
141 /* One converted into the Montgomery domain */
142 static const BN_ULONG ONE
[P256_LIMBS
] = {
143 TOBN(0x00000000, 0x00000001), TOBN(0xffffffff, 0x00000000),
144 TOBN(0xffffffff, 0xffffffff), TOBN(0x00000000, 0xfffffffe)
147 static NISTZ256_PRE_COMP
*ecp_nistz256_pre_comp_new(const EC_GROUP
*group
);
149 /* Precomputed tables for the default generator */
150 extern const PRECOMP256_ROW ecp_nistz256_precomputed
[37];
152 /* Recode window to a signed digit, see ecp_nistputil.c for details */
153 static unsigned int _booth_recode_w5(unsigned int in
)
157 s
= ~((in
>> 5) - 1);
158 d
= (1 << 6) - in
- 1;
159 d
= (d
& s
) | (in
& ~s
);
160 d
= (d
>> 1) + (d
& 1);
162 return (d
<< 1) + (s
& 1);
165 static unsigned int _booth_recode_w7(unsigned int in
)
169 s
= ~((in
>> 7) - 1);
170 d
= (1 << 8) - in
- 1;
171 d
= (d
& s
) | (in
& ~s
);
172 d
= (d
>> 1) + (d
& 1);
174 return (d
<< 1) + (s
& 1);
177 static void copy_conditional(BN_ULONG dst
[P256_LIMBS
],
178 const BN_ULONG src
[P256_LIMBS
], BN_ULONG move
)
180 BN_ULONG mask1
= 0-move
;
181 BN_ULONG mask2
= ~mask1
;
183 dst
[0] = (src
[0] & mask1
) ^ (dst
[0] & mask2
);
184 dst
[1] = (src
[1] & mask1
) ^ (dst
[1] & mask2
);
185 dst
[2] = (src
[2] & mask1
) ^ (dst
[2] & mask2
);
186 dst
[3] = (src
[3] & mask1
) ^ (dst
[3] & mask2
);
187 if (P256_LIMBS
== 8) {
188 dst
[4] = (src
[4] & mask1
) ^ (dst
[4] & mask2
);
189 dst
[5] = (src
[5] & mask1
) ^ (dst
[5] & mask2
);
190 dst
[6] = (src
[6] & mask1
) ^ (dst
[6] & mask2
);
191 dst
[7] = (src
[7] & mask1
) ^ (dst
[7] & mask2
);
195 static BN_ULONG
is_zero(BN_ULONG in
)
203 static BN_ULONG
is_equal(const BN_ULONG a
[P256_LIMBS
],
204 const BN_ULONG b
[P256_LIMBS
])
212 if (P256_LIMBS
== 8) {
222 static BN_ULONG
is_one(const BIGNUM
*z
)
225 BN_ULONG
*a
= bn_get_words(z
);
227 if (bn_get_top(z
) == (P256_LIMBS
- P256_LIMBS
/ 8)) {
229 res
|= a
[1] ^ ONE
[1];
230 res
|= a
[2] ^ ONE
[2];
231 res
|= a
[3] ^ ONE
[3];
232 if (P256_LIMBS
== 8) {
233 res
|= a
[4] ^ ONE
[4];
234 res
|= a
[5] ^ ONE
[5];
235 res
|= a
[6] ^ ONE
[6];
237 * no check for a[7] (being zero) on 32-bit platforms,
238 * because value of "one" takes only 7 limbs.
248 * For reference, this macro is used only when new ecp_nistz256 assembly
249 * module is being developed. For example, configure with
250 * -DECP_NISTZ256_REFERENCE_IMPLEMENTATION and implement only functions
251 * performing simplest arithmetic operations on 256-bit vectors. Then
252 * work on implementation of higher-level functions performing point
253 * operations. Then remove ECP_NISTZ256_REFERENCE_IMPLEMENTATION
254 * and never define it again. (The correct macro denoting presence of
255 * ecp_nistz256 module is ECP_NISTZ256_ASM.)
257 #ifndef ECP_NISTZ256_REFERENCE_IMPLEMENTATION
258 void ecp_nistz256_point_double(P256_POINT
*r
, const P256_POINT
*a
);
259 void ecp_nistz256_point_add(P256_POINT
*r
,
260 const P256_POINT
*a
, const P256_POINT
*b
);
261 void ecp_nistz256_point_add_affine(P256_POINT
*r
,
263 const P256_POINT_AFFINE
*b
);
265 /* Point double: r = 2*a */
266 static void ecp_nistz256_point_double(P256_POINT
*r
, const P256_POINT
*a
)
268 BN_ULONG S
[P256_LIMBS
];
269 BN_ULONG M
[P256_LIMBS
];
270 BN_ULONG Zsqr
[P256_LIMBS
];
271 BN_ULONG tmp0
[P256_LIMBS
];
273 const BN_ULONG
*in_x
= a
->X
;
274 const BN_ULONG
*in_y
= a
->Y
;
275 const BN_ULONG
*in_z
= a
->Z
;
277 BN_ULONG
*res_x
= r
->X
;
278 BN_ULONG
*res_y
= r
->Y
;
279 BN_ULONG
*res_z
= r
->Z
;
281 ecp_nistz256_mul_by_2(S
, in_y
);
283 ecp_nistz256_sqr_mont(Zsqr
, in_z
);
285 ecp_nistz256_sqr_mont(S
, S
);
287 ecp_nistz256_mul_mont(res_z
, in_z
, in_y
);
288 ecp_nistz256_mul_by_2(res_z
, res_z
);
290 ecp_nistz256_add(M
, in_x
, Zsqr
);
291 ecp_nistz256_sub(Zsqr
, in_x
, Zsqr
);
293 ecp_nistz256_sqr_mont(res_y
, S
);
294 ecp_nistz256_div_by_2(res_y
, res_y
);
296 ecp_nistz256_mul_mont(M
, M
, Zsqr
);
297 ecp_nistz256_mul_by_3(M
, M
);
299 ecp_nistz256_mul_mont(S
, S
, in_x
);
300 ecp_nistz256_mul_by_2(tmp0
, S
);
302 ecp_nistz256_sqr_mont(res_x
, M
);
304 ecp_nistz256_sub(res_x
, res_x
, tmp0
);
305 ecp_nistz256_sub(S
, S
, res_x
);
307 ecp_nistz256_mul_mont(S
, S
, M
);
308 ecp_nistz256_sub(res_y
, S
, res_y
);
311 /* Point addition: r = a+b */
312 static void ecp_nistz256_point_add(P256_POINT
*r
,
313 const P256_POINT
*a
, const P256_POINT
*b
)
315 BN_ULONG U2
[P256_LIMBS
], S2
[P256_LIMBS
];
316 BN_ULONG U1
[P256_LIMBS
], S1
[P256_LIMBS
];
317 BN_ULONG Z1sqr
[P256_LIMBS
];
318 BN_ULONG Z2sqr
[P256_LIMBS
];
319 BN_ULONG H
[P256_LIMBS
], R
[P256_LIMBS
];
320 BN_ULONG Hsqr
[P256_LIMBS
];
321 BN_ULONG Rsqr
[P256_LIMBS
];
322 BN_ULONG Hcub
[P256_LIMBS
];
324 BN_ULONG res_x
[P256_LIMBS
];
325 BN_ULONG res_y
[P256_LIMBS
];
326 BN_ULONG res_z
[P256_LIMBS
];
328 BN_ULONG in1infty
, in2infty
;
330 const BN_ULONG
*in1_x
= a
->X
;
331 const BN_ULONG
*in1_y
= a
->Y
;
332 const BN_ULONG
*in1_z
= a
->Z
;
334 const BN_ULONG
*in2_x
= b
->X
;
335 const BN_ULONG
*in2_y
= b
->Y
;
336 const BN_ULONG
*in2_z
= b
->Z
;
339 * Infinity in encoded as (,,0)
341 in1infty
= (in1_z
[0] | in1_z
[1] | in1_z
[2] | in1_z
[3]);
343 in1infty
|= (in1_z
[4] | in1_z
[5] | in1_z
[6] | in1_z
[7]);
345 in2infty
= (in2_z
[0] | in2_z
[1] | in2_z
[2] | in2_z
[3]);
347 in2infty
|= (in2_z
[4] | in2_z
[5] | in2_z
[6] | in2_z
[7]);
349 in1infty
= is_zero(in1infty
);
350 in2infty
= is_zero(in2infty
);
352 ecp_nistz256_sqr_mont(Z2sqr
, in2_z
); /* Z2^2 */
353 ecp_nistz256_sqr_mont(Z1sqr
, in1_z
); /* Z1^2 */
355 ecp_nistz256_mul_mont(S1
, Z2sqr
, in2_z
); /* S1 = Z2^3 */
356 ecp_nistz256_mul_mont(S2
, Z1sqr
, in1_z
); /* S2 = Z1^3 */
358 ecp_nistz256_mul_mont(S1
, S1
, in1_y
); /* S1 = Y1*Z2^3 */
359 ecp_nistz256_mul_mont(S2
, S2
, in2_y
); /* S2 = Y2*Z1^3 */
360 ecp_nistz256_sub(R
, S2
, S1
); /* R = S2 - S1 */
362 ecp_nistz256_mul_mont(U1
, in1_x
, Z2sqr
); /* U1 = X1*Z2^2 */
363 ecp_nistz256_mul_mont(U2
, in2_x
, Z1sqr
); /* U2 = X2*Z1^2 */
364 ecp_nistz256_sub(H
, U2
, U1
); /* H = U2 - U1 */
367 * The formulae are incorrect if the points are equal so we check for
368 * this and do doubling if this happens.
370 * Points here are in Jacobian projective coordinates (Xi, Yi, Zi)
371 * that are bound to the affine coordinates (xi, yi) by the following
376 * For the sake of optimization, the algorithm operates over
377 * intermediate variables U1, U2 and S1, S2 that are derived from
378 * the projective coordinates:
379 * - U1 = X1 * (Z2)^2 ; U2 = X2 * (Z1)^2
380 * - S1 = Y1 * (Z2)^3 ; S2 = Y2 * (Z1)^3
382 * It is easy to prove that is_equal(U1, U2) implies that the affine
383 * x-coordinates are equal, or either point is at infinity.
384 * Likewise is_equal(S1, S2) implies that the affine y-coordinates are
385 * equal, or either point is at infinity.
387 * The special case of either point being the point at infinity (Z1 or Z2
388 * is zero), is handled separately later on in this function, so we avoid
389 * jumping to point_double here in those special cases.
391 * When both points are inverse of each other, we know that the affine
392 * x-coordinates are equal, and the y-coordinates have different sign.
393 * Therefore since U1 = U2, we know H = 0, and therefore Z3 = H*Z1*Z2
394 * will equal 0, thus the result is infinity, if we simply let this
395 * function continue normally.
397 * We use bitwise operations to avoid potential side-channels introduced by
398 * the short-circuiting behaviour of boolean operators.
400 if (is_equal(U1
, U2
) & ~in1infty
& ~in2infty
& is_equal(S1
, S2
)) {
402 * This is obviously not constant-time but it should never happen during
403 * single point multiplication, so there is no timing leak for ECDH or
406 ecp_nistz256_point_double(r
, a
);
410 ecp_nistz256_sqr_mont(Rsqr
, R
); /* R^2 */
411 ecp_nistz256_mul_mont(res_z
, H
, in1_z
); /* Z3 = H*Z1*Z2 */
412 ecp_nistz256_sqr_mont(Hsqr
, H
); /* H^2 */
413 ecp_nistz256_mul_mont(res_z
, res_z
, in2_z
); /* Z3 = H*Z1*Z2 */
414 ecp_nistz256_mul_mont(Hcub
, Hsqr
, H
); /* H^3 */
416 ecp_nistz256_mul_mont(U2
, U1
, Hsqr
); /* U1*H^2 */
417 ecp_nistz256_mul_by_2(Hsqr
, U2
); /* 2*U1*H^2 */
419 ecp_nistz256_sub(res_x
, Rsqr
, Hsqr
);
420 ecp_nistz256_sub(res_x
, res_x
, Hcub
);
422 ecp_nistz256_sub(res_y
, U2
, res_x
);
424 ecp_nistz256_mul_mont(S2
, S1
, Hcub
);
425 ecp_nistz256_mul_mont(res_y
, R
, res_y
);
426 ecp_nistz256_sub(res_y
, res_y
, S2
);
428 copy_conditional(res_x
, in2_x
, in1infty
);
429 copy_conditional(res_y
, in2_y
, in1infty
);
430 copy_conditional(res_z
, in2_z
, in1infty
);
432 copy_conditional(res_x
, in1_x
, in2infty
);
433 copy_conditional(res_y
, in1_y
, in2infty
);
434 copy_conditional(res_z
, in1_z
, in2infty
);
436 memcpy(r
->X
, res_x
, sizeof(res_x
));
437 memcpy(r
->Y
, res_y
, sizeof(res_y
));
438 memcpy(r
->Z
, res_z
, sizeof(res_z
));
441 /* Point addition when b is known to be affine: r = a+b */
442 static void ecp_nistz256_point_add_affine(P256_POINT
*r
,
444 const P256_POINT_AFFINE
*b
)
446 BN_ULONG U2
[P256_LIMBS
], S2
[P256_LIMBS
];
447 BN_ULONG Z1sqr
[P256_LIMBS
];
448 BN_ULONG H
[P256_LIMBS
], R
[P256_LIMBS
];
449 BN_ULONG Hsqr
[P256_LIMBS
];
450 BN_ULONG Rsqr
[P256_LIMBS
];
451 BN_ULONG Hcub
[P256_LIMBS
];
453 BN_ULONG res_x
[P256_LIMBS
];
454 BN_ULONG res_y
[P256_LIMBS
];
455 BN_ULONG res_z
[P256_LIMBS
];
457 BN_ULONG in1infty
, in2infty
;
459 const BN_ULONG
*in1_x
= a
->X
;
460 const BN_ULONG
*in1_y
= a
->Y
;
461 const BN_ULONG
*in1_z
= a
->Z
;
463 const BN_ULONG
*in2_x
= b
->X
;
464 const BN_ULONG
*in2_y
= b
->Y
;
467 * Infinity in encoded as (,,0)
469 in1infty
= (in1_z
[0] | in1_z
[1] | in1_z
[2] | in1_z
[3]);
471 in1infty
|= (in1_z
[4] | in1_z
[5] | in1_z
[6] | in1_z
[7]);
474 * In affine representation we encode infinity as (0,0), which is
475 * not on the curve, so it is OK
477 in2infty
= (in2_x
[0] | in2_x
[1] | in2_x
[2] | in2_x
[3] |
478 in2_y
[0] | in2_y
[1] | in2_y
[2] | in2_y
[3]);
480 in2infty
|= (in2_x
[4] | in2_x
[5] | in2_x
[6] | in2_x
[7] |
481 in2_y
[4] | in2_y
[5] | in2_y
[6] | in2_y
[7]);
483 in1infty
= is_zero(in1infty
);
484 in2infty
= is_zero(in2infty
);
486 ecp_nistz256_sqr_mont(Z1sqr
, in1_z
); /* Z1^2 */
488 ecp_nistz256_mul_mont(U2
, in2_x
, Z1sqr
); /* U2 = X2*Z1^2 */
489 ecp_nistz256_sub(H
, U2
, in1_x
); /* H = U2 - U1 */
491 ecp_nistz256_mul_mont(S2
, Z1sqr
, in1_z
); /* S2 = Z1^3 */
493 ecp_nistz256_mul_mont(res_z
, H
, in1_z
); /* Z3 = H*Z1*Z2 */
495 ecp_nistz256_mul_mont(S2
, S2
, in2_y
); /* S2 = Y2*Z1^3 */
496 ecp_nistz256_sub(R
, S2
, in1_y
); /* R = S2 - S1 */
498 ecp_nistz256_sqr_mont(Hsqr
, H
); /* H^2 */
499 ecp_nistz256_sqr_mont(Rsqr
, R
); /* R^2 */
500 ecp_nistz256_mul_mont(Hcub
, Hsqr
, H
); /* H^3 */
502 ecp_nistz256_mul_mont(U2
, in1_x
, Hsqr
); /* U1*H^2 */
503 ecp_nistz256_mul_by_2(Hsqr
, U2
); /* 2*U1*H^2 */
505 ecp_nistz256_sub(res_x
, Rsqr
, Hsqr
);
506 ecp_nistz256_sub(res_x
, res_x
, Hcub
);
507 ecp_nistz256_sub(H
, U2
, res_x
);
509 ecp_nistz256_mul_mont(S2
, in1_y
, Hcub
);
510 ecp_nistz256_mul_mont(H
, H
, R
);
511 ecp_nistz256_sub(res_y
, H
, S2
);
513 copy_conditional(res_x
, in2_x
, in1infty
);
514 copy_conditional(res_x
, in1_x
, in2infty
);
516 copy_conditional(res_y
, in2_y
, in1infty
);
517 copy_conditional(res_y
, in1_y
, in2infty
);
519 copy_conditional(res_z
, ONE
, in1infty
);
520 copy_conditional(res_z
, in1_z
, in2infty
);
522 memcpy(r
->X
, res_x
, sizeof(res_x
));
523 memcpy(r
->Y
, res_y
, sizeof(res_y
));
524 memcpy(r
->Z
, res_z
, sizeof(res_z
));
528 /* r = in^-1 mod p */
529 static void ecp_nistz256_mod_inverse(BN_ULONG r
[P256_LIMBS
],
530 const BN_ULONG in
[P256_LIMBS
])
533 * The poly is ffffffff 00000001 00000000 00000000 00000000 ffffffff
534 * ffffffff ffffffff We use FLT and used poly-2 as exponent
536 BN_ULONG p2
[P256_LIMBS
];
537 BN_ULONG p4
[P256_LIMBS
];
538 BN_ULONG p8
[P256_LIMBS
];
539 BN_ULONG p16
[P256_LIMBS
];
540 BN_ULONG p32
[P256_LIMBS
];
541 BN_ULONG res
[P256_LIMBS
];
544 ecp_nistz256_sqr_mont(res
, in
);
545 ecp_nistz256_mul_mont(p2
, res
, in
); /* 3*p */
547 ecp_nistz256_sqr_mont(res
, p2
);
548 ecp_nistz256_sqr_mont(res
, res
);
549 ecp_nistz256_mul_mont(p4
, res
, p2
); /* f*p */
551 ecp_nistz256_sqr_mont(res
, p4
);
552 ecp_nistz256_sqr_mont(res
, res
);
553 ecp_nistz256_sqr_mont(res
, res
);
554 ecp_nistz256_sqr_mont(res
, res
);
555 ecp_nistz256_mul_mont(p8
, res
, p4
); /* ff*p */
557 ecp_nistz256_sqr_mont(res
, p8
);
558 for (i
= 0; i
< 7; i
++)
559 ecp_nistz256_sqr_mont(res
, res
);
560 ecp_nistz256_mul_mont(p16
, res
, p8
); /* ffff*p */
562 ecp_nistz256_sqr_mont(res
, p16
);
563 for (i
= 0; i
< 15; i
++)
564 ecp_nistz256_sqr_mont(res
, res
);
565 ecp_nistz256_mul_mont(p32
, res
, p16
); /* ffffffff*p */
567 ecp_nistz256_sqr_mont(res
, p32
);
568 for (i
= 0; i
< 31; i
++)
569 ecp_nistz256_sqr_mont(res
, res
);
570 ecp_nistz256_mul_mont(res
, res
, in
);
572 for (i
= 0; i
< 32 * 4; i
++)
573 ecp_nistz256_sqr_mont(res
, res
);
574 ecp_nistz256_mul_mont(res
, res
, p32
);
576 for (i
= 0; i
< 32; i
++)
577 ecp_nistz256_sqr_mont(res
, res
);
578 ecp_nistz256_mul_mont(res
, res
, p32
);
580 for (i
= 0; i
< 16; i
++)
581 ecp_nistz256_sqr_mont(res
, res
);
582 ecp_nistz256_mul_mont(res
, res
, p16
);
584 for (i
= 0; i
< 8; i
++)
585 ecp_nistz256_sqr_mont(res
, res
);
586 ecp_nistz256_mul_mont(res
, res
, p8
);
588 ecp_nistz256_sqr_mont(res
, res
);
589 ecp_nistz256_sqr_mont(res
, res
);
590 ecp_nistz256_sqr_mont(res
, res
);
591 ecp_nistz256_sqr_mont(res
, res
);
592 ecp_nistz256_mul_mont(res
, res
, p4
);
594 ecp_nistz256_sqr_mont(res
, res
);
595 ecp_nistz256_sqr_mont(res
, res
);
596 ecp_nistz256_mul_mont(res
, res
, p2
);
598 ecp_nistz256_sqr_mont(res
, res
);
599 ecp_nistz256_sqr_mont(res
, res
);
600 ecp_nistz256_mul_mont(res
, res
, in
);
602 memcpy(r
, res
, sizeof(res
));
606 * ecp_nistz256_bignum_to_field_elem copies the contents of |in| to |out| and
607 * returns one if it fits. Otherwise it returns zero.
609 __owur
static int ecp_nistz256_bignum_to_field_elem(BN_ULONG out
[P256_LIMBS
],
612 return bn_copy_words(out
, in
, P256_LIMBS
);
615 /* r = sum(scalar[i]*point[i]) */
616 __owur
static int ecp_nistz256_windowed_mul(const EC_GROUP
*group
,
618 const BIGNUM
**scalar
,
619 const EC_POINT
**point
,
620 size_t num
, BN_CTX
*ctx
)
625 unsigned char (*p_str
)[33] = NULL
;
626 const unsigned int window_size
= 5;
627 const unsigned int mask
= (1 << (window_size
+ 1)) - 1;
629 P256_POINT
*temp
; /* place for 5 temporary points */
630 const BIGNUM
**scalars
= NULL
;
631 P256_POINT (*table
)[16] = NULL
;
632 void *table_storage
= NULL
;
634 if ((num
* 16 + 6) > OPENSSL_MALLOC_MAX_NELEMS(P256_POINT
)
636 OPENSSL_malloc((num
* 16 + 5) * sizeof(P256_POINT
) + 64)) == NULL
638 OPENSSL_malloc(num
* 33 * sizeof(unsigned char))) == NULL
639 || (scalars
= OPENSSL_malloc(num
* sizeof(BIGNUM
*))) == NULL
) {
640 ERR_raise(ERR_LIB_EC
, ERR_R_MALLOC_FAILURE
);
644 table
= (void *)ALIGNPTR(table_storage
, 64);
645 temp
= (P256_POINT
*)(table
+ num
);
647 for (i
= 0; i
< num
; i
++) {
648 P256_POINT
*row
= table
[i
];
650 /* This is an unusual input, we don't guarantee constant-timeness. */
651 if ((BN_num_bits(scalar
[i
]) > 256) || BN_is_negative(scalar
[i
])) {
654 if ((mod
= BN_CTX_get(ctx
)) == NULL
)
656 if (!BN_nnmod(mod
, scalar
[i
], group
->order
, ctx
)) {
657 ERR_raise(ERR_LIB_EC
, ERR_R_BN_LIB
);
662 scalars
[i
] = scalar
[i
];
664 for (j
= 0; j
< bn_get_top(scalars
[i
]) * BN_BYTES
; j
+= BN_BYTES
) {
665 BN_ULONG d
= bn_get_words(scalars
[i
])[j
/ BN_BYTES
];
667 p_str
[i
][j
+ 0] = (unsigned char)d
;
668 p_str
[i
][j
+ 1] = (unsigned char)(d
>> 8);
669 p_str
[i
][j
+ 2] = (unsigned char)(d
>> 16);
670 p_str
[i
][j
+ 3] = (unsigned char)(d
>>= 24);
673 p_str
[i
][j
+ 4] = (unsigned char)d
;
674 p_str
[i
][j
+ 5] = (unsigned char)(d
>> 8);
675 p_str
[i
][j
+ 6] = (unsigned char)(d
>> 16);
676 p_str
[i
][j
+ 7] = (unsigned char)(d
>> 24);
682 if (!ecp_nistz256_bignum_to_field_elem(temp
[0].X
, point
[i
]->X
)
683 || !ecp_nistz256_bignum_to_field_elem(temp
[0].Y
, point
[i
]->Y
)
684 || !ecp_nistz256_bignum_to_field_elem(temp
[0].Z
, point
[i
]->Z
)) {
685 ERR_raise(ERR_LIB_EC
, EC_R_COORDINATES_OUT_OF_RANGE
);
690 * row[0] is implicitly (0,0,0) (the point at infinity), therefore it
691 * is not stored. All other values are actually stored with an offset
695 ecp_nistz256_scatter_w5 (row
, &temp
[0], 1);
696 ecp_nistz256_point_double(&temp
[1], &temp
[0]); /*1+1=2 */
697 ecp_nistz256_scatter_w5 (row
, &temp
[1], 2);
698 ecp_nistz256_point_add (&temp
[2], &temp
[1], &temp
[0]); /*2+1=3 */
699 ecp_nistz256_scatter_w5 (row
, &temp
[2], 3);
700 ecp_nistz256_point_double(&temp
[1], &temp
[1]); /*2*2=4 */
701 ecp_nistz256_scatter_w5 (row
, &temp
[1], 4);
702 ecp_nistz256_point_double(&temp
[2], &temp
[2]); /*2*3=6 */
703 ecp_nistz256_scatter_w5 (row
, &temp
[2], 6);
704 ecp_nistz256_point_add (&temp
[3], &temp
[1], &temp
[0]); /*4+1=5 */
705 ecp_nistz256_scatter_w5 (row
, &temp
[3], 5);
706 ecp_nistz256_point_add (&temp
[4], &temp
[2], &temp
[0]); /*6+1=7 */
707 ecp_nistz256_scatter_w5 (row
, &temp
[4], 7);
708 ecp_nistz256_point_double(&temp
[1], &temp
[1]); /*2*4=8 */
709 ecp_nistz256_scatter_w5 (row
, &temp
[1], 8);
710 ecp_nistz256_point_double(&temp
[2], &temp
[2]); /*2*6=12 */
711 ecp_nistz256_scatter_w5 (row
, &temp
[2], 12);
712 ecp_nistz256_point_double(&temp
[3], &temp
[3]); /*2*5=10 */
713 ecp_nistz256_scatter_w5 (row
, &temp
[3], 10);
714 ecp_nistz256_point_double(&temp
[4], &temp
[4]); /*2*7=14 */
715 ecp_nistz256_scatter_w5 (row
, &temp
[4], 14);
716 ecp_nistz256_point_add (&temp
[2], &temp
[2], &temp
[0]); /*12+1=13*/
717 ecp_nistz256_scatter_w5 (row
, &temp
[2], 13);
718 ecp_nistz256_point_add (&temp
[3], &temp
[3], &temp
[0]); /*10+1=11*/
719 ecp_nistz256_scatter_w5 (row
, &temp
[3], 11);
720 ecp_nistz256_point_add (&temp
[4], &temp
[4], &temp
[0]); /*14+1=15*/
721 ecp_nistz256_scatter_w5 (row
, &temp
[4], 15);
722 ecp_nistz256_point_add (&temp
[2], &temp
[1], &temp
[0]); /*8+1=9 */
723 ecp_nistz256_scatter_w5 (row
, &temp
[2], 9);
724 ecp_nistz256_point_double(&temp
[1], &temp
[1]); /*2*8=16 */
725 ecp_nistz256_scatter_w5 (row
, &temp
[1], 16);
730 wvalue
= p_str
[0][(idx
- 1) / 8];
731 wvalue
= (wvalue
>> ((idx
- 1) % 8)) & mask
;
734 * We gather to temp[0], because we know it's position relative
737 ecp_nistz256_gather_w5(&temp
[0], table
[0], _booth_recode_w5(wvalue
) >> 1);
738 memcpy(r
, &temp
[0], sizeof(temp
[0]));
741 for (i
= (idx
== 255 ? 1 : 0); i
< num
; i
++) {
742 unsigned int off
= (idx
- 1) / 8;
744 wvalue
= p_str
[i
][off
] | p_str
[i
][off
+ 1] << 8;
745 wvalue
= (wvalue
>> ((idx
- 1) % 8)) & mask
;
747 wvalue
= _booth_recode_w5(wvalue
);
749 ecp_nistz256_gather_w5(&temp
[0], table
[i
], wvalue
>> 1);
751 ecp_nistz256_neg(temp
[1].Y
, temp
[0].Y
);
752 copy_conditional(temp
[0].Y
, temp
[1].Y
, (wvalue
& 1));
754 ecp_nistz256_point_add(r
, r
, &temp
[0]);
759 ecp_nistz256_point_double(r
, r
);
760 ecp_nistz256_point_double(r
, r
);
761 ecp_nistz256_point_double(r
, r
);
762 ecp_nistz256_point_double(r
, r
);
763 ecp_nistz256_point_double(r
, r
);
767 for (i
= 0; i
< num
; i
++) {
768 wvalue
= p_str
[i
][0];
769 wvalue
= (wvalue
<< 1) & mask
;
771 wvalue
= _booth_recode_w5(wvalue
);
773 ecp_nistz256_gather_w5(&temp
[0], table
[i
], wvalue
>> 1);
775 ecp_nistz256_neg(temp
[1].Y
, temp
[0].Y
);
776 copy_conditional(temp
[0].Y
, temp
[1].Y
, wvalue
& 1);
778 ecp_nistz256_point_add(r
, r
, &temp
[0]);
783 OPENSSL_free(table_storage
);
785 OPENSSL_free(scalars
);
789 /* Coordinates of G, for which we have precomputed tables */
790 static const BN_ULONG def_xG
[P256_LIMBS
] = {
791 TOBN(0x79e730d4, 0x18a9143c), TOBN(0x75ba95fc, 0x5fedb601),
792 TOBN(0x79fb732b, 0x77622510), TOBN(0x18905f76, 0xa53755c6)
795 static const BN_ULONG def_yG
[P256_LIMBS
] = {
796 TOBN(0xddf25357, 0xce95560a), TOBN(0x8b4ab8e4, 0xba19e45c),
797 TOBN(0xd2e88688, 0xdd21f325), TOBN(0x8571ff18, 0x25885d85)
801 * ecp_nistz256_is_affine_G returns one if |generator| is the standard, P-256
804 static int ecp_nistz256_is_affine_G(const EC_POINT
*generator
)
806 return (bn_get_top(generator
->X
) == P256_LIMBS
) &&
807 (bn_get_top(generator
->Y
) == P256_LIMBS
) &&
808 is_equal(bn_get_words(generator
->X
), def_xG
) &&
809 is_equal(bn_get_words(generator
->Y
), def_yG
) &&
810 is_one(generator
->Z
);
813 __owur
static int ecp_nistz256_mult_precompute(EC_GROUP
*group
, BN_CTX
*ctx
)
816 * We precompute a table for a Booth encoded exponent (wNAF) based
817 * computation. Each table holds 64 values for safe access, with an
818 * implicit value of infinity at index zero. We use window of size 7, and
819 * therefore require ceil(256/7) = 37 tables.
822 EC_POINT
*P
= NULL
, *T
= NULL
;
823 const EC_POINT
*generator
;
824 NISTZ256_PRE_COMP
*pre_comp
;
825 BN_CTX
*new_ctx
= NULL
;
826 int i
, j
, k
, ret
= 0;
829 PRECOMP256_ROW
*preComputedTable
= NULL
;
830 unsigned char *precomp_storage
= NULL
;
832 /* if there is an old NISTZ256_PRE_COMP object, throw it away */
833 EC_pre_comp_free(group
);
834 generator
= EC_GROUP_get0_generator(group
);
835 if (generator
== NULL
) {
836 ERR_raise(ERR_LIB_EC
, EC_R_UNDEFINED_GENERATOR
);
840 if (ecp_nistz256_is_affine_G(generator
)) {
842 * No need to calculate tables for the standard generator because we
843 * have them statically.
848 if ((pre_comp
= ecp_nistz256_pre_comp_new(group
)) == NULL
)
852 ctx
= new_ctx
= BN_CTX_new_ex(group
->libctx
);
859 order
= EC_GROUP_get0_order(group
);
863 if (BN_is_zero(order
)) {
864 ERR_raise(ERR_LIB_EC
, EC_R_UNKNOWN_ORDER
);
870 if ((precomp_storage
=
871 OPENSSL_malloc(37 * 64 * sizeof(P256_POINT_AFFINE
) + 64)) == NULL
) {
872 ERR_raise(ERR_LIB_EC
, ERR_R_MALLOC_FAILURE
);
876 preComputedTable
= (void *)ALIGNPTR(precomp_storage
, 64);
878 P
= EC_POINT_new(group
);
879 T
= EC_POINT_new(group
);
880 if (P
== NULL
|| T
== NULL
)
884 * The zero entry is implicitly infinity, and we skip it, storing other
885 * values with -1 offset.
887 if (!EC_POINT_copy(T
, generator
))
890 for (k
= 0; k
< 64; k
++) {
891 if (!EC_POINT_copy(P
, T
))
893 for (j
= 0; j
< 37; j
++) {
894 P256_POINT_AFFINE temp
;
896 * It would be faster to use EC_POINTs_make_affine and
897 * make multiple points affine at the same time.
899 if (group
->meth
->make_affine
== NULL
900 || !group
->meth
->make_affine(group
, P
, ctx
))
902 if (!ecp_nistz256_bignum_to_field_elem(temp
.X
, P
->X
) ||
903 !ecp_nistz256_bignum_to_field_elem(temp
.Y
, P
->Y
)) {
904 ERR_raise(ERR_LIB_EC
, EC_R_COORDINATES_OUT_OF_RANGE
);
907 ecp_nistz256_scatter_w7(preComputedTable
[j
], &temp
, k
);
908 for (i
= 0; i
< 7; i
++) {
909 if (!EC_POINT_dbl(group
, P
, P
, ctx
))
913 if (!EC_POINT_add(group
, T
, T
, generator
, ctx
))
917 pre_comp
->group
= group
;
919 pre_comp
->precomp
= preComputedTable
;
920 pre_comp
->precomp_storage
= precomp_storage
;
921 precomp_storage
= NULL
;
922 SETPRECOMP(group
, nistz256
, pre_comp
);
928 BN_CTX_free(new_ctx
);
930 EC_nistz256_pre_comp_free(pre_comp
);
931 OPENSSL_free(precomp_storage
);
937 __owur
static int ecp_nistz256_set_from_affine(EC_POINT
*out
, const EC_GROUP
*group
,
938 const P256_POINT_AFFINE
*in
,
943 if ((ret
= bn_set_words(out
->X
, in
->X
, P256_LIMBS
))
944 && (ret
= bn_set_words(out
->Y
, in
->Y
, P256_LIMBS
))
945 && (ret
= bn_set_words(out
->Z
, ONE
, P256_LIMBS
)))
951 /* r = scalar*G + sum(scalars[i]*points[i]) */
952 __owur
static int ecp_nistz256_points_mul(const EC_GROUP
*group
,
954 const BIGNUM
*scalar
,
956 const EC_POINT
*points
[],
957 const BIGNUM
*scalars
[], BN_CTX
*ctx
)
959 int i
= 0, ret
= 0, no_precomp_for_generator
= 0, p_is_infinity
= 0;
960 unsigned char p_str
[33] = { 0 };
961 const PRECOMP256_ROW
*preComputedTable
= NULL
;
962 const NISTZ256_PRE_COMP
*pre_comp
= NULL
;
963 const EC_POINT
*generator
= NULL
;
964 const BIGNUM
**new_scalars
= NULL
;
965 const EC_POINT
**new_points
= NULL
;
966 unsigned int idx
= 0;
967 const unsigned int window_size
= 7;
968 const unsigned int mask
= (1 << (window_size
+ 1)) - 1;
976 if ((num
+ 1) == 0 || (num
+ 1) > OPENSSL_MALLOC_MAX_NELEMS(void *)) {
977 ERR_raise(ERR_LIB_EC
, ERR_R_MALLOC_FAILURE
);
984 generator
= EC_GROUP_get0_generator(group
);
985 if (generator
== NULL
) {
986 ERR_raise(ERR_LIB_EC
, EC_R_UNDEFINED_GENERATOR
);
990 /* look if we can use precomputed multiples of generator */
991 pre_comp
= group
->pre_comp
.nistz256
;
995 * If there is a precomputed table for the generator, check that
996 * it was generated with the same generator.
998 EC_POINT
*pre_comp_generator
= EC_POINT_new(group
);
999 if (pre_comp_generator
== NULL
)
1002 ecp_nistz256_gather_w7(&p
.a
, pre_comp
->precomp
[0], 1);
1003 if (!ecp_nistz256_set_from_affine(pre_comp_generator
,
1004 group
, &p
.a
, ctx
)) {
1005 EC_POINT_free(pre_comp_generator
);
1009 if (0 == EC_POINT_cmp(group
, generator
, pre_comp_generator
, ctx
))
1010 preComputedTable
= (const PRECOMP256_ROW
*)pre_comp
->precomp
;
1012 EC_POINT_free(pre_comp_generator
);
1015 if (preComputedTable
== NULL
&& ecp_nistz256_is_affine_G(generator
)) {
1017 * If there is no precomputed data, but the generator is the
1018 * default, a hardcoded table of precomputed data is used. This
1019 * is because applications, such as Apache, do not use
1020 * EC_KEY_precompute_mult.
1022 preComputedTable
= ecp_nistz256_precomputed
;
1025 if (preComputedTable
) {
1028 if ((BN_num_bits(scalar
) > 256)
1029 || BN_is_negative(scalar
)) {
1030 if ((tmp_scalar
= BN_CTX_get(ctx
)) == NULL
)
1033 if (!BN_nnmod(tmp_scalar
, scalar
, group
->order
, ctx
)) {
1034 ERR_raise(ERR_LIB_EC
, ERR_R_BN_LIB
);
1037 scalar
= tmp_scalar
;
1040 for (i
= 0; i
< bn_get_top(scalar
) * BN_BYTES
; i
+= BN_BYTES
) {
1041 BN_ULONG d
= bn_get_words(scalar
)[i
/ BN_BYTES
];
1043 p_str
[i
+ 0] = (unsigned char)d
;
1044 p_str
[i
+ 1] = (unsigned char)(d
>> 8);
1045 p_str
[i
+ 2] = (unsigned char)(d
>> 16);
1046 p_str
[i
+ 3] = (unsigned char)(d
>>= 24);
1047 if (BN_BYTES
== 8) {
1049 p_str
[i
+ 4] = (unsigned char)d
;
1050 p_str
[i
+ 5] = (unsigned char)(d
>> 8);
1051 p_str
[i
+ 6] = (unsigned char)(d
>> 16);
1052 p_str
[i
+ 7] = (unsigned char)(d
>> 24);
1060 wvalue
= (p_str
[0] << 1) & mask
;
1063 wvalue
= _booth_recode_w7(wvalue
);
1065 ecp_nistz256_gather_w7(&p
.a
, preComputedTable
[0],
1068 ecp_nistz256_neg(p
.p
.Z
, p
.p
.Y
);
1069 copy_conditional(p
.p
.Y
, p
.p
.Z
, wvalue
& 1);
1072 * Since affine infinity is encoded as (0,0) and
1073 * Jacobian is (,,0), we need to harmonize them
1074 * by assigning "one" or zero to Z.
1076 infty
= (p
.p
.X
[0] | p
.p
.X
[1] | p
.p
.X
[2] | p
.p
.X
[3] |
1077 p
.p
.Y
[0] | p
.p
.Y
[1] | p
.p
.Y
[2] | p
.p
.Y
[3]);
1078 if (P256_LIMBS
== 8)
1079 infty
|= (p
.p
.X
[4] | p
.p
.X
[5] | p
.p
.X
[6] | p
.p
.X
[7] |
1080 p
.p
.Y
[4] | p
.p
.Y
[5] | p
.p
.Y
[6] | p
.p
.Y
[7]);
1082 infty
= 0 - is_zero(infty
);
1085 p
.p
.Z
[0] = ONE
[0] & infty
;
1086 p
.p
.Z
[1] = ONE
[1] & infty
;
1087 p
.p
.Z
[2] = ONE
[2] & infty
;
1088 p
.p
.Z
[3] = ONE
[3] & infty
;
1089 if (P256_LIMBS
== 8) {
1090 p
.p
.Z
[4] = ONE
[4] & infty
;
1091 p
.p
.Z
[5] = ONE
[5] & infty
;
1092 p
.p
.Z
[6] = ONE
[6] & infty
;
1093 p
.p
.Z
[7] = ONE
[7] & infty
;
1096 for (i
= 1; i
< 37; i
++) {
1097 unsigned int off
= (idx
- 1) / 8;
1098 wvalue
= p_str
[off
] | p_str
[off
+ 1] << 8;
1099 wvalue
= (wvalue
>> ((idx
- 1) % 8)) & mask
;
1102 wvalue
= _booth_recode_w7(wvalue
);
1104 ecp_nistz256_gather_w7(&t
.a
,
1105 preComputedTable
[i
], wvalue
>> 1);
1107 ecp_nistz256_neg(t
.p
.Z
, t
.a
.Y
);
1108 copy_conditional(t
.a
.Y
, t
.p
.Z
, wvalue
& 1);
1110 ecp_nistz256_point_add_affine(&p
.p
, &p
.p
, &t
.a
);
1114 no_precomp_for_generator
= 1;
1119 if (no_precomp_for_generator
) {
1121 * Without a precomputed table for the generator, it has to be
1122 * handled like a normal point.
1124 new_scalars
= OPENSSL_malloc((num
+ 1) * sizeof(BIGNUM
*));
1125 if (new_scalars
== NULL
) {
1126 ERR_raise(ERR_LIB_EC
, ERR_R_MALLOC_FAILURE
);
1130 new_points
= OPENSSL_malloc((num
+ 1) * sizeof(EC_POINT
*));
1131 if (new_points
== NULL
) {
1132 ERR_raise(ERR_LIB_EC
, ERR_R_MALLOC_FAILURE
);
1136 memcpy(new_scalars
, scalars
, num
* sizeof(BIGNUM
*));
1137 new_scalars
[num
] = scalar
;
1138 memcpy(new_points
, points
, num
* sizeof(EC_POINT
*));
1139 new_points
[num
] = generator
;
1141 scalars
= new_scalars
;
1142 points
= new_points
;
1147 P256_POINT
*out
= &t
.p
;
1151 if (!ecp_nistz256_windowed_mul(group
, out
, scalars
, points
, num
, ctx
))
1155 ecp_nistz256_point_add(&p
.p
, &p
.p
, out
);
1158 /* Not constant-time, but we're only operating on the public output. */
1159 if (!bn_set_words(r
->X
, p
.p
.X
, P256_LIMBS
) ||
1160 !bn_set_words(r
->Y
, p
.p
.Y
, P256_LIMBS
) ||
1161 !bn_set_words(r
->Z
, p
.p
.Z
, P256_LIMBS
)) {
1164 r
->Z_is_one
= is_one(r
->Z
) & 1;
1170 OPENSSL_free(new_points
);
1171 OPENSSL_free(new_scalars
);
1175 __owur
static int ecp_nistz256_get_affine(const EC_GROUP
*group
,
1176 const EC_POINT
*point
,
1177 BIGNUM
*x
, BIGNUM
*y
, BN_CTX
*ctx
)
1179 BN_ULONG z_inv2
[P256_LIMBS
];
1180 BN_ULONG z_inv3
[P256_LIMBS
];
1181 BN_ULONG x_aff
[P256_LIMBS
];
1182 BN_ULONG y_aff
[P256_LIMBS
];
1183 BN_ULONG point_x
[P256_LIMBS
], point_y
[P256_LIMBS
], point_z
[P256_LIMBS
];
1184 BN_ULONG x_ret
[P256_LIMBS
], y_ret
[P256_LIMBS
];
1186 if (EC_POINT_is_at_infinity(group
, point
)) {
1187 ERR_raise(ERR_LIB_EC
, EC_R_POINT_AT_INFINITY
);
1191 if (!ecp_nistz256_bignum_to_field_elem(point_x
, point
->X
) ||
1192 !ecp_nistz256_bignum_to_field_elem(point_y
, point
->Y
) ||
1193 !ecp_nistz256_bignum_to_field_elem(point_z
, point
->Z
)) {
1194 ERR_raise(ERR_LIB_EC
, EC_R_COORDINATES_OUT_OF_RANGE
);
1198 ecp_nistz256_mod_inverse(z_inv3
, point_z
);
1199 ecp_nistz256_sqr_mont(z_inv2
, z_inv3
);
1200 ecp_nistz256_mul_mont(x_aff
, z_inv2
, point_x
);
1203 ecp_nistz256_from_mont(x_ret
, x_aff
);
1204 if (!bn_set_words(x
, x_ret
, P256_LIMBS
))
1209 ecp_nistz256_mul_mont(z_inv3
, z_inv3
, z_inv2
);
1210 ecp_nistz256_mul_mont(y_aff
, z_inv3
, point_y
);
1211 ecp_nistz256_from_mont(y_ret
, y_aff
);
1212 if (!bn_set_words(y
, y_ret
, P256_LIMBS
))
1219 static NISTZ256_PRE_COMP
*ecp_nistz256_pre_comp_new(const EC_GROUP
*group
)
1221 NISTZ256_PRE_COMP
*ret
= NULL
;
1226 ret
= OPENSSL_zalloc(sizeof(*ret
));
1229 ERR_raise(ERR_LIB_EC
, ERR_R_MALLOC_FAILURE
);
1234 ret
->w
= 6; /* default */
1235 ret
->references
= 1;
1237 ret
->lock
= CRYPTO_THREAD_lock_new();
1238 if (ret
->lock
== NULL
) {
1239 ERR_raise(ERR_LIB_EC
, ERR_R_MALLOC_FAILURE
);
1246 NISTZ256_PRE_COMP
*EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP
*p
)
1250 CRYPTO_UP_REF(&p
->references
, &i
, p
->lock
);
1254 void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP
*pre
)
1261 CRYPTO_DOWN_REF(&pre
->references
, &i
, pre
->lock
);
1262 REF_PRINT_COUNT("EC_nistz256", pre
);
1265 REF_ASSERT_ISNT(i
< 0);
1267 OPENSSL_free(pre
->precomp_storage
);
1268 CRYPTO_THREAD_lock_free(pre
->lock
);
1273 static int ecp_nistz256_window_have_precompute_mult(const EC_GROUP
*group
)
1275 /* There is a hard-coded table for the default generator. */
1276 const EC_POINT
*generator
= EC_GROUP_get0_generator(group
);
1278 if (generator
!= NULL
&& ecp_nistz256_is_affine_G(generator
)) {
1279 /* There is a hard-coded table for the default generator. */
1283 return HAVEPRECOMP(group
, nistz256
);
1286 #if defined(__x86_64) || defined(__x86_64__) || \
1287 defined(_M_AMD64) || defined(_M_X64) || \
1288 defined(__powerpc64__) || defined(_ARCH_PP64) || \
1289 defined(__aarch64__)
1291 * Montgomery mul modulo Order(P): res = a*b*2^-256 mod Order(P)
1293 void ecp_nistz256_ord_mul_mont(BN_ULONG res
[P256_LIMBS
],
1294 const BN_ULONG a
[P256_LIMBS
],
1295 const BN_ULONG b
[P256_LIMBS
]);
1296 void ecp_nistz256_ord_sqr_mont(BN_ULONG res
[P256_LIMBS
],
1297 const BN_ULONG a
[P256_LIMBS
],
1300 static int ecp_nistz256_inv_mod_ord(const EC_GROUP
*group
, BIGNUM
*r
,
1301 const BIGNUM
*x
, BN_CTX
*ctx
)
1303 /* RR = 2^512 mod ord(p256) */
1304 static const BN_ULONG RR
[P256_LIMBS
] = {
1305 TOBN(0x83244c95,0xbe79eea2), TOBN(0x4699799c,0x49bd6fa6),
1306 TOBN(0x2845b239,0x2b6bec59), TOBN(0x66e12d94,0xf3d95620)
1308 /* The constant 1 (unlike ONE that is one in Montgomery representation) */
1309 static const BN_ULONG one
[P256_LIMBS
] = {
1310 TOBN(0,1), TOBN(0,0), TOBN(0,0), TOBN(0,0)
1313 * We don't use entry 0 in the table, so we omit it and address
1316 BN_ULONG table
[15][P256_LIMBS
];
1317 BN_ULONG out
[P256_LIMBS
], t
[P256_LIMBS
];
1320 i_1
= 0, i_10
, i_11
, i_101
, i_111
, i_1010
, i_1111
,
1321 i_10101
, i_101010
, i_101111
, i_x6
, i_x8
, i_x16
, i_x32
1325 * Catch allocation failure early.
1327 if (bn_wexpand(r
, P256_LIMBS
) == NULL
) {
1328 ERR_raise(ERR_LIB_EC
, ERR_R_BN_LIB
);
1332 if ((BN_num_bits(x
) > 256) || BN_is_negative(x
)) {
1335 if ((tmp
= BN_CTX_get(ctx
)) == NULL
1336 || !BN_nnmod(tmp
, x
, group
->order
, ctx
)) {
1337 ERR_raise(ERR_LIB_EC
, ERR_R_BN_LIB
);
1343 if (!ecp_nistz256_bignum_to_field_elem(t
, x
)) {
1344 ERR_raise(ERR_LIB_EC
, EC_R_COORDINATES_OUT_OF_RANGE
);
1348 ecp_nistz256_ord_mul_mont(table
[0], t
, RR
);
1351 * Original sparse-then-fixed-window algorithm, retained for reference.
1353 for (i
= 2; i
< 16; i
+= 2) {
1354 ecp_nistz256_ord_sqr_mont(table
[i
-1], table
[i
/2-1], 1);
1355 ecp_nistz256_ord_mul_mont(table
[i
], table
[i
-1], table
[0]);
1359 * The top 128bit of the exponent are highly redudndant, so we
1360 * perform an optimized flow
1362 ecp_nistz256_ord_sqr_mont(t
, table
[15-1], 4); /* f0 */
1363 ecp_nistz256_ord_mul_mont(t
, t
, table
[15-1]); /* ff */
1365 ecp_nistz256_ord_sqr_mont(out
, t
, 8); /* ff00 */
1366 ecp_nistz256_ord_mul_mont(out
, out
, t
); /* ffff */
1368 ecp_nistz256_ord_sqr_mont(t
, out
, 16); /* ffff0000 */
1369 ecp_nistz256_ord_mul_mont(t
, t
, out
); /* ffffffff */
1371 ecp_nistz256_ord_sqr_mont(out
, t
, 64); /* ffffffff0000000000000000 */
1372 ecp_nistz256_ord_mul_mont(out
, out
, t
); /* ffffffff00000000ffffffff */
1374 ecp_nistz256_ord_sqr_mont(out
, out
, 32); /* ffffffff00000000ffffffff00000000 */
1375 ecp_nistz256_ord_mul_mont(out
, out
, t
); /* ffffffff00000000ffffffffffffffff */
1378 * The bottom 128 bit of the exponent are processed with fixed 4-bit window
1380 for(i
= 0; i
< 32; i
++) {
1381 /* expLo - the low 128 bits of the exponent we use (ord(p256) - 2),
1382 * split into nibbles */
1383 static const unsigned char expLo
[32] = {
1384 0xb,0xc,0xe,0x6,0xf,0xa,0xa,0xd,0xa,0x7,0x1,0x7,0x9,0xe,0x8,0x4,
1385 0xf,0x3,0xb,0x9,0xc,0xa,0xc,0x2,0xf,0xc,0x6,0x3,0x2,0x5,0x4,0xf
1388 ecp_nistz256_ord_sqr_mont(out
, out
, 4);
1389 /* The exponent is public, no need in constant-time access */
1390 ecp_nistz256_ord_mul_mont(out
, out
, table
[expLo
[i
]-1]);
1394 * https://briansmith.org/ecc-inversion-addition-chains-01#p256_scalar_inversion
1396 * Even though this code path spares 12 squarings, 4.5%, and 13
1397 * multiplications, 25%, on grand scale sign operation is not that
1398 * much faster, not more that 2%...
1401 /* pre-calculate powers */
1402 ecp_nistz256_ord_sqr_mont(table
[i_10
], table
[i_1
], 1);
1404 ecp_nistz256_ord_mul_mont(table
[i_11
], table
[i_1
], table
[i_10
]);
1406 ecp_nistz256_ord_mul_mont(table
[i_101
], table
[i_11
], table
[i_10
]);
1408 ecp_nistz256_ord_mul_mont(table
[i_111
], table
[i_101
], table
[i_10
]);
1410 ecp_nistz256_ord_sqr_mont(table
[i_1010
], table
[i_101
], 1);
1412 ecp_nistz256_ord_mul_mont(table
[i_1111
], table
[i_1010
], table
[i_101
]);
1414 ecp_nistz256_ord_sqr_mont(table
[i_10101
], table
[i_1010
], 1);
1415 ecp_nistz256_ord_mul_mont(table
[i_10101
], table
[i_10101
], table
[i_1
]);
1417 ecp_nistz256_ord_sqr_mont(table
[i_101010
], table
[i_10101
], 1);
1419 ecp_nistz256_ord_mul_mont(table
[i_101111
], table
[i_101010
], table
[i_101
]);
1421 ecp_nistz256_ord_mul_mont(table
[i_x6
], table
[i_101010
], table
[i_10101
]);
1423 ecp_nistz256_ord_sqr_mont(table
[i_x8
], table
[i_x6
], 2);
1424 ecp_nistz256_ord_mul_mont(table
[i_x8
], table
[i_x8
], table
[i_11
]);
1426 ecp_nistz256_ord_sqr_mont(table
[i_x16
], table
[i_x8
], 8);
1427 ecp_nistz256_ord_mul_mont(table
[i_x16
], table
[i_x16
], table
[i_x8
]);
1429 ecp_nistz256_ord_sqr_mont(table
[i_x32
], table
[i_x16
], 16);
1430 ecp_nistz256_ord_mul_mont(table
[i_x32
], table
[i_x32
], table
[i_x16
]);
1433 ecp_nistz256_ord_sqr_mont(out
, table
[i_x32
], 64);
1434 ecp_nistz256_ord_mul_mont(out
, out
, table
[i_x32
]);
1436 for (i
= 0; i
< 27; i
++) {
1437 static const struct { unsigned char p
, i
; } chain
[27] = {
1438 { 32, i_x32
}, { 6, i_101111
}, { 5, i_111
},
1439 { 4, i_11
}, { 5, i_1111
}, { 5, i_10101
},
1440 { 4, i_101
}, { 3, i_101
}, { 3, i_101
},
1441 { 5, i_111
}, { 9, i_101111
}, { 6, i_1111
},
1442 { 2, i_1
}, { 5, i_1
}, { 6, i_1111
},
1443 { 5, i_111
}, { 4, i_111
}, { 5, i_111
},
1444 { 5, i_101
}, { 3, i_11
}, { 10, i_101111
},
1445 { 2, i_11
}, { 5, i_11
}, { 5, i_11
},
1446 { 3, i_1
}, { 7, i_10101
}, { 6, i_1111
}
1449 ecp_nistz256_ord_sqr_mont(out
, out
, chain
[i
].p
);
1450 ecp_nistz256_ord_mul_mont(out
, out
, table
[chain
[i
].i
]);
1453 ecp_nistz256_ord_mul_mont(out
, out
, one
);
1456 * Can't fail, but check return code to be consistent anyway.
1458 if (!bn_set_words(r
, out
, P256_LIMBS
))
1466 # define ecp_nistz256_inv_mod_ord NULL
1469 const EC_METHOD
*EC_GFp_nistz256_method(void)
1471 static const EC_METHOD ret
= {
1472 EC_FLAGS_DEFAULT_OCT
,
1473 NID_X9_62_prime_field
,
1474 ec_GFp_mont_group_init
,
1475 ec_GFp_mont_group_finish
,
1476 ec_GFp_mont_group_clear_finish
,
1477 ec_GFp_mont_group_copy
,
1478 ec_GFp_mont_group_set_curve
,
1479 ec_GFp_simple_group_get_curve
,
1480 ec_GFp_simple_group_get_degree
,
1481 ec_group_simple_order_bits
,
1482 ec_GFp_simple_group_check_discriminant
,
1483 ec_GFp_simple_point_init
,
1484 ec_GFp_simple_point_finish
,
1485 ec_GFp_simple_point_clear_finish
,
1486 ec_GFp_simple_point_copy
,
1487 ec_GFp_simple_point_set_to_infinity
,
1488 ec_GFp_simple_point_set_affine_coordinates
,
1489 ecp_nistz256_get_affine
,
1493 ec_GFp_simple_invert
,
1494 ec_GFp_simple_is_at_infinity
,
1495 ec_GFp_simple_is_on_curve
,
1497 ec_GFp_simple_make_affine
,
1498 ec_GFp_simple_points_make_affine
,
1499 ecp_nistz256_points_mul
, /* mul */
1500 ecp_nistz256_mult_precompute
, /* precompute_mult */
1501 ecp_nistz256_window_have_precompute_mult
, /* have_precompute_mult */
1502 ec_GFp_mont_field_mul
,
1503 ec_GFp_mont_field_sqr
,
1505 ec_GFp_mont_field_inv
,
1506 ec_GFp_mont_field_encode
,
1507 ec_GFp_mont_field_decode
,
1508 ec_GFp_mont_field_set_to_one
,
1509 ec_key_simple_priv2oct
,
1510 ec_key_simple_oct2priv
,
1511 0, /* set private */
1512 ec_key_simple_generate_key
,
1513 ec_key_simple_check_key
,
1514 ec_key_simple_generate_public_key
,
1517 ecdh_simple_compute_key
,
1518 ecdsa_simple_sign_setup
,
1519 ecdsa_simple_sign_sig
,
1520 ecdsa_simple_verify_sig
,
1521 ecp_nistz256_inv_mod_ord
, /* can be #define-d NULL */
1522 0, /* blind_coordinates */
1524 0, /* ladder_step */