2 * Copyright 2002-2016 The OpenSSL Project Authors. All Rights Reserved.
4 * Licensed under the OpenSSL license (the "License"). You may not use
5 * this file except in compliance with the License. You can obtain a copy
6 * in the file LICENSE in the source distribution or at
7 * https://www.openssl.org/source/license.html
10 /* ====================================================================
11 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
13 * The Elliptic Curve Public-Key Crypto Library (ECC Code) included
14 * herein is developed by SUN MICROSYSTEMS, INC., and is contributed
15 * to the OpenSSL project.
17 * The ECC Code is licensed pursuant to the OpenSSL open source
18 * license provided below.
20 * The software is originally written by Sheueling Chang Shantz and
21 * Douglas Stebila of Sun Microsystems Laboratories.
25 #include <openssl/err.h>
27 #include "internal/bn_int.h"
30 #ifndef OPENSSL_NO_EC2M
32 const EC_METHOD
*EC_GF2m_simple_method(void)
34 static const EC_METHOD ret
= {
36 NID_X9_62_characteristic_two_field
,
37 ec_GF2m_simple_group_init
,
38 ec_GF2m_simple_group_finish
,
39 ec_GF2m_simple_group_clear_finish
,
40 ec_GF2m_simple_group_copy
,
41 ec_GF2m_simple_group_set_curve
,
42 ec_GF2m_simple_group_get_curve
,
43 ec_GF2m_simple_group_get_degree
,
44 ec_group_simple_order_bits
,
45 ec_GF2m_simple_group_check_discriminant
,
46 ec_GF2m_simple_point_init
,
47 ec_GF2m_simple_point_finish
,
48 ec_GF2m_simple_point_clear_finish
,
49 ec_GF2m_simple_point_copy
,
50 ec_GF2m_simple_point_set_to_infinity
,
51 0 /* set_Jprojective_coordinates_GFp */ ,
52 0 /* get_Jprojective_coordinates_GFp */ ,
53 ec_GF2m_simple_point_set_affine_coordinates
,
54 ec_GF2m_simple_point_get_affine_coordinates
,
58 ec_GF2m_simple_invert
,
59 ec_GF2m_simple_is_at_infinity
,
60 ec_GF2m_simple_is_on_curve
,
62 ec_GF2m_simple_make_affine
,
63 ec_GF2m_simple_points_make_affine
,
66 * the following three method functions are defined in ec2_mult.c
69 ec_GF2m_precompute_mult
,
70 ec_GF2m_have_precompute_mult
,
72 ec_GF2m_simple_field_mul
,
73 ec_GF2m_simple_field_sqr
,
74 ec_GF2m_simple_field_div
,
75 0 /* field_encode */ ,
76 0 /* field_decode */ ,
77 0, /* field_set_to_one */
78 ec_key_simple_priv2oct
,
79 ec_key_simple_oct2priv
,
81 ec_key_simple_generate_key
,
82 ec_key_simple_check_key
,
83 ec_key_simple_generate_public_key
,
86 ecdh_simple_compute_key
93 * Initialize a GF(2^m)-based EC_GROUP structure. Note that all other members
94 * are handled by EC_GROUP_new.
96 int ec_GF2m_simple_group_init(EC_GROUP
*group
)
98 group
->field
= BN_new();
102 if (group
->field
== NULL
|| group
->a
== NULL
|| group
->b
== NULL
) {
103 BN_free(group
->field
);
112 * Free a GF(2^m)-based EC_GROUP structure. Note that all other members are
113 * handled by EC_GROUP_free.
115 void ec_GF2m_simple_group_finish(EC_GROUP
*group
)
117 BN_free(group
->field
);
123 * Clear and free a GF(2^m)-based EC_GROUP structure. Note that all other
124 * members are handled by EC_GROUP_clear_free.
126 void ec_GF2m_simple_group_clear_finish(EC_GROUP
*group
)
128 BN_clear_free(group
->field
);
129 BN_clear_free(group
->a
);
130 BN_clear_free(group
->b
);
140 * Copy a GF(2^m)-based EC_GROUP structure. Note that all other members are
141 * handled by EC_GROUP_copy.
143 int ec_GF2m_simple_group_copy(EC_GROUP
*dest
, const EC_GROUP
*src
)
145 if (!BN_copy(dest
->field
, src
->field
))
147 if (!BN_copy(dest
->a
, src
->a
))
149 if (!BN_copy(dest
->b
, src
->b
))
151 dest
->poly
[0] = src
->poly
[0];
152 dest
->poly
[1] = src
->poly
[1];
153 dest
->poly
[2] = src
->poly
[2];
154 dest
->poly
[3] = src
->poly
[3];
155 dest
->poly
[4] = src
->poly
[4];
156 dest
->poly
[5] = src
->poly
[5];
157 if (bn_wexpand(dest
->a
, (int)(dest
->poly
[0] + BN_BITS2
- 1) / BN_BITS2
) ==
160 if (bn_wexpand(dest
->b
, (int)(dest
->poly
[0] + BN_BITS2
- 1) / BN_BITS2
) ==
163 bn_set_all_zero(dest
->a
);
164 bn_set_all_zero(dest
->b
);
168 /* Set the curve parameters of an EC_GROUP structure. */
169 int ec_GF2m_simple_group_set_curve(EC_GROUP
*group
,
170 const BIGNUM
*p
, const BIGNUM
*a
,
171 const BIGNUM
*b
, BN_CTX
*ctx
)
176 if (!BN_copy(group
->field
, p
))
178 i
= BN_GF2m_poly2arr(group
->field
, group
->poly
, 6) - 1;
179 if ((i
!= 5) && (i
!= 3)) {
180 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE
, EC_R_UNSUPPORTED_FIELD
);
185 if (!BN_GF2m_mod_arr(group
->a
, a
, group
->poly
))
187 if (bn_wexpand(group
->a
, (int)(group
->poly
[0] + BN_BITS2
- 1) / BN_BITS2
)
190 bn_set_all_zero(group
->a
);
193 if (!BN_GF2m_mod_arr(group
->b
, b
, group
->poly
))
195 if (bn_wexpand(group
->b
, (int)(group
->poly
[0] + BN_BITS2
- 1) / BN_BITS2
)
198 bn_set_all_zero(group
->b
);
206 * Get the curve parameters of an EC_GROUP structure. If p, a, or b are NULL
207 * then there values will not be set but the method will return with success.
209 int ec_GF2m_simple_group_get_curve(const EC_GROUP
*group
, BIGNUM
*p
,
210 BIGNUM
*a
, BIGNUM
*b
, BN_CTX
*ctx
)
215 if (!BN_copy(p
, group
->field
))
220 if (!BN_copy(a
, group
->a
))
225 if (!BN_copy(b
, group
->b
))
236 * Gets the degree of the field. For a curve over GF(2^m) this is the value
239 int ec_GF2m_simple_group_get_degree(const EC_GROUP
*group
)
241 return BN_num_bits(group
->field
) - 1;
245 * Checks the discriminant of the curve. y^2 + x*y = x^3 + a*x^2 + b is an
246 * elliptic curve <=> b != 0 (mod p)
248 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP
*group
,
253 BN_CTX
*new_ctx
= NULL
;
256 ctx
= new_ctx
= BN_CTX_new();
258 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT
,
259 ERR_R_MALLOC_FAILURE
);
268 if (!BN_GF2m_mod_arr(b
, group
->b
, group
->poly
))
272 * check the discriminant: y^2 + x*y = x^3 + a*x^2 + b is an elliptic
273 * curve <=> b != 0 (mod p)
283 BN_CTX_free(new_ctx
);
287 /* Initializes an EC_POINT. */
288 int ec_GF2m_simple_point_init(EC_POINT
*point
)
294 if (point
->X
== NULL
|| point
->Y
== NULL
|| point
->Z
== NULL
) {
303 /* Frees an EC_POINT. */
304 void ec_GF2m_simple_point_finish(EC_POINT
*point
)
311 /* Clears and frees an EC_POINT. */
312 void ec_GF2m_simple_point_clear_finish(EC_POINT
*point
)
314 BN_clear_free(point
->X
);
315 BN_clear_free(point
->Y
);
316 BN_clear_free(point
->Z
);
321 * Copy the contents of one EC_POINT into another. Assumes dest is
324 int ec_GF2m_simple_point_copy(EC_POINT
*dest
, const EC_POINT
*src
)
326 if (!BN_copy(dest
->X
, src
->X
))
328 if (!BN_copy(dest
->Y
, src
->Y
))
330 if (!BN_copy(dest
->Z
, src
->Z
))
332 dest
->Z_is_one
= src
->Z_is_one
;
338 * Set an EC_POINT to the point at infinity. A point at infinity is
339 * represented by having Z=0.
341 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP
*group
,
350 * Set the coordinates of an EC_POINT using affine coordinates. Note that
351 * the simple implementation only uses affine coordinates.
353 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP
*group
,
356 const BIGNUM
*y
, BN_CTX
*ctx
)
359 if (x
== NULL
|| y
== NULL
) {
360 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES
,
361 ERR_R_PASSED_NULL_PARAMETER
);
365 if (!BN_copy(point
->X
, x
))
367 BN_set_negative(point
->X
, 0);
368 if (!BN_copy(point
->Y
, y
))
370 BN_set_negative(point
->Y
, 0);
371 if (!BN_copy(point
->Z
, BN_value_one()))
373 BN_set_negative(point
->Z
, 0);
382 * Gets the affine coordinates of an EC_POINT. Note that the simple
383 * implementation only uses affine coordinates.
385 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP
*group
,
386 const EC_POINT
*point
,
387 BIGNUM
*x
, BIGNUM
*y
,
392 if (EC_POINT_is_at_infinity(group
, point
)) {
393 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES
,
394 EC_R_POINT_AT_INFINITY
);
398 if (BN_cmp(point
->Z
, BN_value_one())) {
399 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES
,
400 ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
404 if (!BN_copy(x
, point
->X
))
406 BN_set_negative(x
, 0);
409 if (!BN_copy(y
, point
->Y
))
411 BN_set_negative(y
, 0);
420 * Computes a + b and stores the result in r. r could be a or b, a could be
421 * b. Uses algorithm A.10.2 of IEEE P1363.
423 int ec_GF2m_simple_add(const EC_GROUP
*group
, EC_POINT
*r
, const EC_POINT
*a
,
424 const EC_POINT
*b
, BN_CTX
*ctx
)
426 BN_CTX
*new_ctx
= NULL
;
427 BIGNUM
*x0
, *y0
, *x1
, *y1
, *x2
, *y2
, *s
, *t
;
430 if (EC_POINT_is_at_infinity(group
, a
)) {
431 if (!EC_POINT_copy(r
, b
))
436 if (EC_POINT_is_at_infinity(group
, b
)) {
437 if (!EC_POINT_copy(r
, a
))
443 ctx
= new_ctx
= BN_CTX_new();
449 x0
= BN_CTX_get(ctx
);
450 y0
= BN_CTX_get(ctx
);
451 x1
= BN_CTX_get(ctx
);
452 y1
= BN_CTX_get(ctx
);
453 x2
= BN_CTX_get(ctx
);
454 y2
= BN_CTX_get(ctx
);
461 if (!BN_copy(x0
, a
->X
))
463 if (!BN_copy(y0
, a
->Y
))
466 if (!EC_POINT_get_affine_coordinates_GF2m(group
, a
, x0
, y0
, ctx
))
470 if (!BN_copy(x1
, b
->X
))
472 if (!BN_copy(y1
, b
->Y
))
475 if (!EC_POINT_get_affine_coordinates_GF2m(group
, b
, x1
, y1
, ctx
))
479 if (BN_GF2m_cmp(x0
, x1
)) {
480 if (!BN_GF2m_add(t
, x0
, x1
))
482 if (!BN_GF2m_add(s
, y0
, y1
))
484 if (!group
->meth
->field_div(group
, s
, s
, t
, ctx
))
486 if (!group
->meth
->field_sqr(group
, x2
, s
, ctx
))
488 if (!BN_GF2m_add(x2
, x2
, group
->a
))
490 if (!BN_GF2m_add(x2
, x2
, s
))
492 if (!BN_GF2m_add(x2
, x2
, t
))
495 if (BN_GF2m_cmp(y0
, y1
) || BN_is_zero(x1
)) {
496 if (!EC_POINT_set_to_infinity(group
, r
))
501 if (!group
->meth
->field_div(group
, s
, y1
, x1
, ctx
))
503 if (!BN_GF2m_add(s
, s
, x1
))
506 if (!group
->meth
->field_sqr(group
, x2
, s
, ctx
))
508 if (!BN_GF2m_add(x2
, x2
, s
))
510 if (!BN_GF2m_add(x2
, x2
, group
->a
))
514 if (!BN_GF2m_add(y2
, x1
, x2
))
516 if (!group
->meth
->field_mul(group
, y2
, y2
, s
, ctx
))
518 if (!BN_GF2m_add(y2
, y2
, x2
))
520 if (!BN_GF2m_add(y2
, y2
, y1
))
523 if (!EC_POINT_set_affine_coordinates_GF2m(group
, r
, x2
, y2
, ctx
))
530 BN_CTX_free(new_ctx
);
535 * Computes 2 * a and stores the result in r. r could be a. Uses algorithm
536 * A.10.2 of IEEE P1363.
538 int ec_GF2m_simple_dbl(const EC_GROUP
*group
, EC_POINT
*r
, const EC_POINT
*a
,
541 return ec_GF2m_simple_add(group
, r
, a
, a
, ctx
);
544 int ec_GF2m_simple_invert(const EC_GROUP
*group
, EC_POINT
*point
, BN_CTX
*ctx
)
546 if (EC_POINT_is_at_infinity(group
, point
) || BN_is_zero(point
->Y
))
547 /* point is its own inverse */
550 if (!EC_POINT_make_affine(group
, point
, ctx
))
552 return BN_GF2m_add(point
->Y
, point
->X
, point
->Y
);
555 /* Indicates whether the given point is the point at infinity. */
556 int ec_GF2m_simple_is_at_infinity(const EC_GROUP
*group
,
557 const EC_POINT
*point
)
559 return BN_is_zero(point
->Z
);
563 * Determines whether the given EC_POINT is an actual point on the curve defined
564 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation:
565 * y^2 + x*y = x^3 + a*x^2 + b.
567 int ec_GF2m_simple_is_on_curve(const EC_GROUP
*group
, const EC_POINT
*point
,
571 BN_CTX
*new_ctx
= NULL
;
573 int (*field_mul
) (const EC_GROUP
*, BIGNUM
*, const BIGNUM
*,
574 const BIGNUM
*, BN_CTX
*);
575 int (*field_sqr
) (const EC_GROUP
*, BIGNUM
*, const BIGNUM
*, BN_CTX
*);
577 if (EC_POINT_is_at_infinity(group
, point
))
580 field_mul
= group
->meth
->field_mul
;
581 field_sqr
= group
->meth
->field_sqr
;
583 /* only support affine coordinates */
584 if (!point
->Z_is_one
)
588 ctx
= new_ctx
= BN_CTX_new();
594 y2
= BN_CTX_get(ctx
);
595 lh
= BN_CTX_get(ctx
);
600 * We have a curve defined by a Weierstrass equation
601 * y^2 + x*y = x^3 + a*x^2 + b.
602 * <=> x^3 + a*x^2 + x*y + b + y^2 = 0
603 * <=> ((x + a) * x + y ) * x + b + y^2 = 0
605 if (!BN_GF2m_add(lh
, point
->X
, group
->a
))
607 if (!field_mul(group
, lh
, lh
, point
->X
, ctx
))
609 if (!BN_GF2m_add(lh
, lh
, point
->Y
))
611 if (!field_mul(group
, lh
, lh
, point
->X
, ctx
))
613 if (!BN_GF2m_add(lh
, lh
, group
->b
))
615 if (!field_sqr(group
, y2
, point
->Y
, ctx
))
617 if (!BN_GF2m_add(lh
, lh
, y2
))
619 ret
= BN_is_zero(lh
);
623 BN_CTX_free(new_ctx
);
628 * Indicates whether two points are equal.
631 * 0 equal (in affine coordinates)
634 int ec_GF2m_simple_cmp(const EC_GROUP
*group
, const EC_POINT
*a
,
635 const EC_POINT
*b
, BN_CTX
*ctx
)
637 BIGNUM
*aX
, *aY
, *bX
, *bY
;
638 BN_CTX
*new_ctx
= NULL
;
641 if (EC_POINT_is_at_infinity(group
, a
)) {
642 return EC_POINT_is_at_infinity(group
, b
) ? 0 : 1;
645 if (EC_POINT_is_at_infinity(group
, b
))
648 if (a
->Z_is_one
&& b
->Z_is_one
) {
649 return ((BN_cmp(a
->X
, b
->X
) == 0) && BN_cmp(a
->Y
, b
->Y
) == 0) ? 0 : 1;
653 ctx
= new_ctx
= BN_CTX_new();
659 aX
= BN_CTX_get(ctx
);
660 aY
= BN_CTX_get(ctx
);
661 bX
= BN_CTX_get(ctx
);
662 bY
= BN_CTX_get(ctx
);
666 if (!EC_POINT_get_affine_coordinates_GF2m(group
, a
, aX
, aY
, ctx
))
668 if (!EC_POINT_get_affine_coordinates_GF2m(group
, b
, bX
, bY
, ctx
))
670 ret
= ((BN_cmp(aX
, bX
) == 0) && BN_cmp(aY
, bY
) == 0) ? 0 : 1;
675 BN_CTX_free(new_ctx
);
679 /* Forces the given EC_POINT to internally use affine coordinates. */
680 int ec_GF2m_simple_make_affine(const EC_GROUP
*group
, EC_POINT
*point
,
683 BN_CTX
*new_ctx
= NULL
;
687 if (point
->Z_is_one
|| EC_POINT_is_at_infinity(group
, point
))
691 ctx
= new_ctx
= BN_CTX_new();
702 if (!EC_POINT_get_affine_coordinates_GF2m(group
, point
, x
, y
, ctx
))
704 if (!BN_copy(point
->X
, x
))
706 if (!BN_copy(point
->Y
, y
))
708 if (!BN_one(point
->Z
))
717 BN_CTX_free(new_ctx
);
722 * Forces each of the EC_POINTs in the given array to use affine coordinates.
724 int ec_GF2m_simple_points_make_affine(const EC_GROUP
*group
, size_t num
,
725 EC_POINT
*points
[], BN_CTX
*ctx
)
729 for (i
= 0; i
< num
; i
++) {
730 if (!group
->meth
->make_affine(group
, points
[i
], ctx
))
737 /* Wrapper to simple binary polynomial field multiplication implementation. */
738 int ec_GF2m_simple_field_mul(const EC_GROUP
*group
, BIGNUM
*r
,
739 const BIGNUM
*a
, const BIGNUM
*b
, BN_CTX
*ctx
)
741 return BN_GF2m_mod_mul_arr(r
, a
, b
, group
->poly
, ctx
);
744 /* Wrapper to simple binary polynomial field squaring implementation. */
745 int ec_GF2m_simple_field_sqr(const EC_GROUP
*group
, BIGNUM
*r
,
746 const BIGNUM
*a
, BN_CTX
*ctx
)
748 return BN_GF2m_mod_sqr_arr(r
, a
, group
->poly
, ctx
);
751 /* Wrapper to simple binary polynomial field division implementation. */
752 int ec_GF2m_simple_field_div(const EC_GROUP
*group
, BIGNUM
*r
,
753 const BIGNUM
*a
, const BIGNUM
*b
, BN_CTX
*ctx
)
755 return BN_GF2m_mod_div(r
, a
, b
, group
->field
, ctx
);