2 * Copyright 2002-2016 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
5 * Licensed under the OpenSSL license (the "License"). You may not use
6 * this file except in compliance with the License. You can obtain a copy
7 * in the file LICENSE in the source distribution or at
8 * https://www.openssl.org/source/license.html
11 #include <openssl/err.h>
13 #include "internal/bn_int.h"
16 #ifndef OPENSSL_NO_EC2M
18 const EC_METHOD
*EC_GF2m_simple_method(void)
20 static const EC_METHOD ret
= {
22 NID_X9_62_characteristic_two_field
,
23 ec_GF2m_simple_group_init
,
24 ec_GF2m_simple_group_finish
,
25 ec_GF2m_simple_group_clear_finish
,
26 ec_GF2m_simple_group_copy
,
27 ec_GF2m_simple_group_set_curve
,
28 ec_GF2m_simple_group_get_curve
,
29 ec_GF2m_simple_group_get_degree
,
30 ec_group_simple_order_bits
,
31 ec_GF2m_simple_group_check_discriminant
,
32 ec_GF2m_simple_point_init
,
33 ec_GF2m_simple_point_finish
,
34 ec_GF2m_simple_point_clear_finish
,
35 ec_GF2m_simple_point_copy
,
36 ec_GF2m_simple_point_set_to_infinity
,
37 0 /* set_Jprojective_coordinates_GFp */ ,
38 0 /* get_Jprojective_coordinates_GFp */ ,
39 ec_GF2m_simple_point_set_affine_coordinates
,
40 ec_GF2m_simple_point_get_affine_coordinates
,
44 ec_GF2m_simple_invert
,
45 ec_GF2m_simple_is_at_infinity
,
46 ec_GF2m_simple_is_on_curve
,
48 ec_GF2m_simple_make_affine
,
49 ec_GF2m_simple_points_make_affine
,
52 * the following three method functions are defined in ec2_mult.c
55 ec_GF2m_precompute_mult
,
56 ec_GF2m_have_precompute_mult
,
58 ec_GF2m_simple_field_mul
,
59 ec_GF2m_simple_field_sqr
,
60 ec_GF2m_simple_field_div
,
61 0 /* field_encode */ ,
62 0 /* field_decode */ ,
63 0, /* field_set_to_one */
64 ec_key_simple_priv2oct
,
65 ec_key_simple_oct2priv
,
67 ec_key_simple_generate_key
,
68 ec_key_simple_check_key
,
69 ec_key_simple_generate_public_key
,
72 ecdh_simple_compute_key
79 * Initialize a GF(2^m)-based EC_GROUP structure. Note that all other members
80 * are handled by EC_GROUP_new.
82 int ec_GF2m_simple_group_init(EC_GROUP
*group
)
84 group
->field
= BN_new();
88 if (group
->field
== NULL
|| group
->a
== NULL
|| group
->b
== NULL
) {
89 BN_free(group
->field
);
98 * Free a GF(2^m)-based EC_GROUP structure. Note that all other members are
99 * handled by EC_GROUP_free.
101 void ec_GF2m_simple_group_finish(EC_GROUP
*group
)
103 BN_free(group
->field
);
109 * Clear and free a GF(2^m)-based EC_GROUP structure. Note that all other
110 * members are handled by EC_GROUP_clear_free.
112 void ec_GF2m_simple_group_clear_finish(EC_GROUP
*group
)
114 BN_clear_free(group
->field
);
115 BN_clear_free(group
->a
);
116 BN_clear_free(group
->b
);
126 * Copy a GF(2^m)-based EC_GROUP structure. Note that all other members are
127 * handled by EC_GROUP_copy.
129 int ec_GF2m_simple_group_copy(EC_GROUP
*dest
, const EC_GROUP
*src
)
131 if (!BN_copy(dest
->field
, src
->field
))
133 if (!BN_copy(dest
->a
, src
->a
))
135 if (!BN_copy(dest
->b
, src
->b
))
137 dest
->poly
[0] = src
->poly
[0];
138 dest
->poly
[1] = src
->poly
[1];
139 dest
->poly
[2] = src
->poly
[2];
140 dest
->poly
[3] = src
->poly
[3];
141 dest
->poly
[4] = src
->poly
[4];
142 dest
->poly
[5] = src
->poly
[5];
143 if (bn_wexpand(dest
->a
, (int)(dest
->poly
[0] + BN_BITS2
- 1) / BN_BITS2
) ==
146 if (bn_wexpand(dest
->b
, (int)(dest
->poly
[0] + BN_BITS2
- 1) / BN_BITS2
) ==
149 bn_set_all_zero(dest
->a
);
150 bn_set_all_zero(dest
->b
);
154 /* Set the curve parameters of an EC_GROUP structure. */
155 int ec_GF2m_simple_group_set_curve(EC_GROUP
*group
,
156 const BIGNUM
*p
, const BIGNUM
*a
,
157 const BIGNUM
*b
, BN_CTX
*ctx
)
162 if (!BN_copy(group
->field
, p
))
164 i
= BN_GF2m_poly2arr(group
->field
, group
->poly
, 6) - 1;
165 if ((i
!= 5) && (i
!= 3)) {
166 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE
, EC_R_UNSUPPORTED_FIELD
);
171 if (!BN_GF2m_mod_arr(group
->a
, a
, group
->poly
))
173 if (bn_wexpand(group
->a
, (int)(group
->poly
[0] + BN_BITS2
- 1) / BN_BITS2
)
176 bn_set_all_zero(group
->a
);
179 if (!BN_GF2m_mod_arr(group
->b
, b
, group
->poly
))
181 if (bn_wexpand(group
->b
, (int)(group
->poly
[0] + BN_BITS2
- 1) / BN_BITS2
)
184 bn_set_all_zero(group
->b
);
192 * Get the curve parameters of an EC_GROUP structure. If p, a, or b are NULL
193 * then there values will not be set but the method will return with success.
195 int ec_GF2m_simple_group_get_curve(const EC_GROUP
*group
, BIGNUM
*p
,
196 BIGNUM
*a
, BIGNUM
*b
, BN_CTX
*ctx
)
201 if (!BN_copy(p
, group
->field
))
206 if (!BN_copy(a
, group
->a
))
211 if (!BN_copy(b
, group
->b
))
222 * Gets the degree of the field. For a curve over GF(2^m) this is the value
225 int ec_GF2m_simple_group_get_degree(const EC_GROUP
*group
)
227 return BN_num_bits(group
->field
) - 1;
231 * Checks the discriminant of the curve. y^2 + x*y = x^3 + a*x^2 + b is an
232 * elliptic curve <=> b != 0 (mod p)
234 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP
*group
,
239 BN_CTX
*new_ctx
= NULL
;
242 ctx
= new_ctx
= BN_CTX_new();
244 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT
,
245 ERR_R_MALLOC_FAILURE
);
254 if (!BN_GF2m_mod_arr(b
, group
->b
, group
->poly
))
258 * check the discriminant: y^2 + x*y = x^3 + a*x^2 + b is an elliptic
259 * curve <=> b != 0 (mod p)
269 BN_CTX_free(new_ctx
);
273 /* Initializes an EC_POINT. */
274 int ec_GF2m_simple_point_init(EC_POINT
*point
)
280 if (point
->X
== NULL
|| point
->Y
== NULL
|| point
->Z
== NULL
) {
289 /* Frees an EC_POINT. */
290 void ec_GF2m_simple_point_finish(EC_POINT
*point
)
297 /* Clears and frees an EC_POINT. */
298 void ec_GF2m_simple_point_clear_finish(EC_POINT
*point
)
300 BN_clear_free(point
->X
);
301 BN_clear_free(point
->Y
);
302 BN_clear_free(point
->Z
);
307 * Copy the contents of one EC_POINT into another. Assumes dest is
310 int ec_GF2m_simple_point_copy(EC_POINT
*dest
, const EC_POINT
*src
)
312 if (!BN_copy(dest
->X
, src
->X
))
314 if (!BN_copy(dest
->Y
, src
->Y
))
316 if (!BN_copy(dest
->Z
, src
->Z
))
318 dest
->Z_is_one
= src
->Z_is_one
;
324 * Set an EC_POINT to the point at infinity. A point at infinity is
325 * represented by having Z=0.
327 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP
*group
,
336 * Set the coordinates of an EC_POINT using affine coordinates. Note that
337 * the simple implementation only uses affine coordinates.
339 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP
*group
,
342 const BIGNUM
*y
, BN_CTX
*ctx
)
345 if (x
== NULL
|| y
== NULL
) {
346 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES
,
347 ERR_R_PASSED_NULL_PARAMETER
);
351 if (!BN_copy(point
->X
, x
))
353 BN_set_negative(point
->X
, 0);
354 if (!BN_copy(point
->Y
, y
))
356 BN_set_negative(point
->Y
, 0);
357 if (!BN_copy(point
->Z
, BN_value_one()))
359 BN_set_negative(point
->Z
, 0);
368 * Gets the affine coordinates of an EC_POINT. Note that the simple
369 * implementation only uses affine coordinates.
371 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP
*group
,
372 const EC_POINT
*point
,
373 BIGNUM
*x
, BIGNUM
*y
,
378 if (EC_POINT_is_at_infinity(group
, point
)) {
379 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES
,
380 EC_R_POINT_AT_INFINITY
);
384 if (BN_cmp(point
->Z
, BN_value_one())) {
385 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES
,
386 ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
390 if (!BN_copy(x
, point
->X
))
392 BN_set_negative(x
, 0);
395 if (!BN_copy(y
, point
->Y
))
397 BN_set_negative(y
, 0);
406 * Computes a + b and stores the result in r. r could be a or b, a could be
407 * b. Uses algorithm A.10.2 of IEEE P1363.
409 int ec_GF2m_simple_add(const EC_GROUP
*group
, EC_POINT
*r
, const EC_POINT
*a
,
410 const EC_POINT
*b
, BN_CTX
*ctx
)
412 BN_CTX
*new_ctx
= NULL
;
413 BIGNUM
*x0
, *y0
, *x1
, *y1
, *x2
, *y2
, *s
, *t
;
416 if (EC_POINT_is_at_infinity(group
, a
)) {
417 if (!EC_POINT_copy(r
, b
))
422 if (EC_POINT_is_at_infinity(group
, b
)) {
423 if (!EC_POINT_copy(r
, a
))
429 ctx
= new_ctx
= BN_CTX_new();
435 x0
= BN_CTX_get(ctx
);
436 y0
= BN_CTX_get(ctx
);
437 x1
= BN_CTX_get(ctx
);
438 y1
= BN_CTX_get(ctx
);
439 x2
= BN_CTX_get(ctx
);
440 y2
= BN_CTX_get(ctx
);
447 if (!BN_copy(x0
, a
->X
))
449 if (!BN_copy(y0
, a
->Y
))
452 if (!EC_POINT_get_affine_coordinates_GF2m(group
, a
, x0
, y0
, ctx
))
456 if (!BN_copy(x1
, b
->X
))
458 if (!BN_copy(y1
, b
->Y
))
461 if (!EC_POINT_get_affine_coordinates_GF2m(group
, b
, x1
, y1
, ctx
))
465 if (BN_GF2m_cmp(x0
, x1
)) {
466 if (!BN_GF2m_add(t
, x0
, x1
))
468 if (!BN_GF2m_add(s
, y0
, y1
))
470 if (!group
->meth
->field_div(group
, s
, s
, t
, ctx
))
472 if (!group
->meth
->field_sqr(group
, x2
, s
, ctx
))
474 if (!BN_GF2m_add(x2
, x2
, group
->a
))
476 if (!BN_GF2m_add(x2
, x2
, s
))
478 if (!BN_GF2m_add(x2
, x2
, t
))
481 if (BN_GF2m_cmp(y0
, y1
) || BN_is_zero(x1
)) {
482 if (!EC_POINT_set_to_infinity(group
, r
))
487 if (!group
->meth
->field_div(group
, s
, y1
, x1
, ctx
))
489 if (!BN_GF2m_add(s
, s
, x1
))
492 if (!group
->meth
->field_sqr(group
, x2
, s
, ctx
))
494 if (!BN_GF2m_add(x2
, x2
, s
))
496 if (!BN_GF2m_add(x2
, x2
, group
->a
))
500 if (!BN_GF2m_add(y2
, x1
, x2
))
502 if (!group
->meth
->field_mul(group
, y2
, y2
, s
, ctx
))
504 if (!BN_GF2m_add(y2
, y2
, x2
))
506 if (!BN_GF2m_add(y2
, y2
, y1
))
509 if (!EC_POINT_set_affine_coordinates_GF2m(group
, r
, x2
, y2
, ctx
))
516 BN_CTX_free(new_ctx
);
521 * Computes 2 * a and stores the result in r. r could be a. Uses algorithm
522 * A.10.2 of IEEE P1363.
524 int ec_GF2m_simple_dbl(const EC_GROUP
*group
, EC_POINT
*r
, const EC_POINT
*a
,
527 return ec_GF2m_simple_add(group
, r
, a
, a
, ctx
);
530 int ec_GF2m_simple_invert(const EC_GROUP
*group
, EC_POINT
*point
, BN_CTX
*ctx
)
532 if (EC_POINT_is_at_infinity(group
, point
) || BN_is_zero(point
->Y
))
533 /* point is its own inverse */
536 if (!EC_POINT_make_affine(group
, point
, ctx
))
538 return BN_GF2m_add(point
->Y
, point
->X
, point
->Y
);
541 /* Indicates whether the given point is the point at infinity. */
542 int ec_GF2m_simple_is_at_infinity(const EC_GROUP
*group
,
543 const EC_POINT
*point
)
545 return BN_is_zero(point
->Z
);
549 * Determines whether the given EC_POINT is an actual point on the curve defined
550 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation:
551 * y^2 + x*y = x^3 + a*x^2 + b.
553 int ec_GF2m_simple_is_on_curve(const EC_GROUP
*group
, const EC_POINT
*point
,
557 BN_CTX
*new_ctx
= NULL
;
559 int (*field_mul
) (const EC_GROUP
*, BIGNUM
*, const BIGNUM
*,
560 const BIGNUM
*, BN_CTX
*);
561 int (*field_sqr
) (const EC_GROUP
*, BIGNUM
*, const BIGNUM
*, BN_CTX
*);
563 if (EC_POINT_is_at_infinity(group
, point
))
566 field_mul
= group
->meth
->field_mul
;
567 field_sqr
= group
->meth
->field_sqr
;
569 /* only support affine coordinates */
570 if (!point
->Z_is_one
)
574 ctx
= new_ctx
= BN_CTX_new();
580 y2
= BN_CTX_get(ctx
);
581 lh
= BN_CTX_get(ctx
);
586 * We have a curve defined by a Weierstrass equation
587 * y^2 + x*y = x^3 + a*x^2 + b.
588 * <=> x^3 + a*x^2 + x*y + b + y^2 = 0
589 * <=> ((x + a) * x + y ) * x + b + y^2 = 0
591 if (!BN_GF2m_add(lh
, point
->X
, group
->a
))
593 if (!field_mul(group
, lh
, lh
, point
->X
, ctx
))
595 if (!BN_GF2m_add(lh
, lh
, point
->Y
))
597 if (!field_mul(group
, lh
, lh
, point
->X
, ctx
))
599 if (!BN_GF2m_add(lh
, lh
, group
->b
))
601 if (!field_sqr(group
, y2
, point
->Y
, ctx
))
603 if (!BN_GF2m_add(lh
, lh
, y2
))
605 ret
= BN_is_zero(lh
);
609 BN_CTX_free(new_ctx
);
614 * Indicates whether two points are equal.
617 * 0 equal (in affine coordinates)
620 int ec_GF2m_simple_cmp(const EC_GROUP
*group
, const EC_POINT
*a
,
621 const EC_POINT
*b
, BN_CTX
*ctx
)
623 BIGNUM
*aX
, *aY
, *bX
, *bY
;
624 BN_CTX
*new_ctx
= NULL
;
627 if (EC_POINT_is_at_infinity(group
, a
)) {
628 return EC_POINT_is_at_infinity(group
, b
) ? 0 : 1;
631 if (EC_POINT_is_at_infinity(group
, b
))
634 if (a
->Z_is_one
&& b
->Z_is_one
) {
635 return ((BN_cmp(a
->X
, b
->X
) == 0) && BN_cmp(a
->Y
, b
->Y
) == 0) ? 0 : 1;
639 ctx
= new_ctx
= BN_CTX_new();
645 aX
= BN_CTX_get(ctx
);
646 aY
= BN_CTX_get(ctx
);
647 bX
= BN_CTX_get(ctx
);
648 bY
= BN_CTX_get(ctx
);
652 if (!EC_POINT_get_affine_coordinates_GF2m(group
, a
, aX
, aY
, ctx
))
654 if (!EC_POINT_get_affine_coordinates_GF2m(group
, b
, bX
, bY
, ctx
))
656 ret
= ((BN_cmp(aX
, bX
) == 0) && BN_cmp(aY
, bY
) == 0) ? 0 : 1;
661 BN_CTX_free(new_ctx
);
665 /* Forces the given EC_POINT to internally use affine coordinates. */
666 int ec_GF2m_simple_make_affine(const EC_GROUP
*group
, EC_POINT
*point
,
669 BN_CTX
*new_ctx
= NULL
;
673 if (point
->Z_is_one
|| EC_POINT_is_at_infinity(group
, point
))
677 ctx
= new_ctx
= BN_CTX_new();
688 if (!EC_POINT_get_affine_coordinates_GF2m(group
, point
, x
, y
, ctx
))
690 if (!BN_copy(point
->X
, x
))
692 if (!BN_copy(point
->Y
, y
))
694 if (!BN_one(point
->Z
))
703 BN_CTX_free(new_ctx
);
708 * Forces each of the EC_POINTs in the given array to use affine coordinates.
710 int ec_GF2m_simple_points_make_affine(const EC_GROUP
*group
, size_t num
,
711 EC_POINT
*points
[], BN_CTX
*ctx
)
715 for (i
= 0; i
< num
; i
++) {
716 if (!group
->meth
->make_affine(group
, points
[i
], ctx
))
723 /* Wrapper to simple binary polynomial field multiplication implementation. */
724 int ec_GF2m_simple_field_mul(const EC_GROUP
*group
, BIGNUM
*r
,
725 const BIGNUM
*a
, const BIGNUM
*b
, BN_CTX
*ctx
)
727 return BN_GF2m_mod_mul_arr(r
, a
, b
, group
->poly
, ctx
);
730 /* Wrapper to simple binary polynomial field squaring implementation. */
731 int ec_GF2m_simple_field_sqr(const EC_GROUP
*group
, BIGNUM
*r
,
732 const BIGNUM
*a
, BN_CTX
*ctx
)
734 return BN_GF2m_mod_sqr_arr(r
, a
, group
->poly
, ctx
);
737 /* Wrapper to simple binary polynomial field division implementation. */
738 int ec_GF2m_simple_field_div(const EC_GROUP
*group
, BIGNUM
*r
,
739 const BIGNUM
*a
, const BIGNUM
*b
, BN_CTX
*ctx
)
741 return BN_GF2m_mod_div(r
, a
, b
, group
->field
, ctx
);