2 * Copyright 2001-2018 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
5 * Licensed under the Apache License 2.0 (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
13 #include <openssl/err.h>
14 #include <openssl/opensslv.h>
18 /* functions for EC_GROUP objects */
20 EC_GROUP
*EC_GROUP_new_ex(OPENSSL_CTX
*libctx
, const EC_METHOD
*meth
)
25 ECerr(EC_F_EC_GROUP_NEW_EX
, EC_R_SLOT_FULL
);
28 if (meth
->group_init
== 0) {
29 ECerr(EC_F_EC_GROUP_NEW_EX
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
33 ret
= OPENSSL_zalloc(sizeof(*ret
));
35 ECerr(EC_F_EC_GROUP_NEW_EX
, ERR_R_MALLOC_FAILURE
);
41 if ((ret
->meth
->flags
& EC_FLAGS_CUSTOM_CURVE
) == 0) {
42 ret
->order
= BN_new();
43 if (ret
->order
== NULL
)
45 ret
->cofactor
= BN_new();
46 if (ret
->cofactor
== NULL
)
49 ret
->asn1_flag
= OPENSSL_EC_NAMED_CURVE
;
50 ret
->asn1_form
= POINT_CONVERSION_UNCOMPRESSED
;
51 if (!meth
->group_init(ret
))
57 BN_free(ret
->cofactor
);
63 EC_GROUP
*EC_GROUP_new(const EC_METHOD
*meth
)
65 return EC_GROUP_new_ex(NULL
, meth
);
69 void EC_pre_comp_free(EC_GROUP
*group
)
71 switch (group
->pre_comp_type
) {
75 #ifdef ECP_NISTZ256_ASM
76 EC_nistz256_pre_comp_free(group
->pre_comp
.nistz256
);
79 #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
81 EC_nistp224_pre_comp_free(group
->pre_comp
.nistp224
);
84 EC_nistp256_pre_comp_free(group
->pre_comp
.nistp256
);
87 EC_nistp521_pre_comp_free(group
->pre_comp
.nistp521
);
96 EC_ec_pre_comp_free(group
->pre_comp
.ec
);
99 group
->pre_comp
.ec
= NULL
;
102 void EC_GROUP_free(EC_GROUP
*group
)
107 if (group
->meth
->group_finish
!= 0)
108 group
->meth
->group_finish(group
);
110 EC_pre_comp_free(group
);
111 BN_MONT_CTX_free(group
->mont_data
);
112 EC_POINT_free(group
->generator
);
113 BN_free(group
->order
);
114 BN_free(group
->cofactor
);
115 OPENSSL_free(group
->seed
);
119 void EC_GROUP_clear_free(EC_GROUP
*group
)
124 if (group
->meth
->group_clear_finish
!= 0)
125 group
->meth
->group_clear_finish(group
);
126 else if (group
->meth
->group_finish
!= 0)
127 group
->meth
->group_finish(group
);
129 EC_pre_comp_free(group
);
130 BN_MONT_CTX_free(group
->mont_data
);
131 EC_POINT_clear_free(group
->generator
);
132 BN_clear_free(group
->order
);
133 BN_clear_free(group
->cofactor
);
134 OPENSSL_clear_free(group
->seed
, group
->seed_len
);
135 OPENSSL_clear_free(group
, sizeof(*group
));
138 int EC_GROUP_copy(EC_GROUP
*dest
, const EC_GROUP
*src
)
140 if (dest
->meth
->group_copy
== 0) {
141 ECerr(EC_F_EC_GROUP_COPY
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
144 if (dest
->meth
!= src
->meth
) {
145 ECerr(EC_F_EC_GROUP_COPY
, EC_R_INCOMPATIBLE_OBJECTS
);
151 dest
->libctx
= src
->libctx
;
152 dest
->curve_name
= src
->curve_name
;
154 /* Copy precomputed */
155 dest
->pre_comp_type
= src
->pre_comp_type
;
156 switch (src
->pre_comp_type
) {
158 dest
->pre_comp
.ec
= NULL
;
161 #ifdef ECP_NISTZ256_ASM
162 dest
->pre_comp
.nistz256
= EC_nistz256_pre_comp_dup(src
->pre_comp
.nistz256
);
165 #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
167 dest
->pre_comp
.nistp224
= EC_nistp224_pre_comp_dup(src
->pre_comp
.nistp224
);
170 dest
->pre_comp
.nistp256
= EC_nistp256_pre_comp_dup(src
->pre_comp
.nistp256
);
173 dest
->pre_comp
.nistp521
= EC_nistp521_pre_comp_dup(src
->pre_comp
.nistp521
);
182 dest
->pre_comp
.ec
= EC_ec_pre_comp_dup(src
->pre_comp
.ec
);
186 if (src
->mont_data
!= NULL
) {
187 if (dest
->mont_data
== NULL
) {
188 dest
->mont_data
= BN_MONT_CTX_new();
189 if (dest
->mont_data
== NULL
)
192 if (!BN_MONT_CTX_copy(dest
->mont_data
, src
->mont_data
))
195 /* src->generator == NULL */
196 BN_MONT_CTX_free(dest
->mont_data
);
197 dest
->mont_data
= NULL
;
200 if (src
->generator
!= NULL
) {
201 if (dest
->generator
== NULL
) {
202 dest
->generator
= EC_POINT_new(dest
);
203 if (dest
->generator
== NULL
)
206 if (!EC_POINT_copy(dest
->generator
, src
->generator
))
209 /* src->generator == NULL */
210 EC_POINT_clear_free(dest
->generator
);
211 dest
->generator
= NULL
;
214 if ((src
->meth
->flags
& EC_FLAGS_CUSTOM_CURVE
) == 0) {
215 if (!BN_copy(dest
->order
, src
->order
))
217 if (!BN_copy(dest
->cofactor
, src
->cofactor
))
221 dest
->asn1_flag
= src
->asn1_flag
;
222 dest
->asn1_form
= src
->asn1_form
;
225 OPENSSL_free(dest
->seed
);
226 if ((dest
->seed
= OPENSSL_malloc(src
->seed_len
)) == NULL
) {
227 ECerr(EC_F_EC_GROUP_COPY
, ERR_R_MALLOC_FAILURE
);
230 if (!memcpy(dest
->seed
, src
->seed
, src
->seed_len
))
232 dest
->seed_len
= src
->seed_len
;
234 OPENSSL_free(dest
->seed
);
239 return dest
->meth
->group_copy(dest
, src
);
242 EC_GROUP
*EC_GROUP_dup(const EC_GROUP
*a
)
250 if ((t
= EC_GROUP_new_ex(a
->libctx
, a
->meth
)) == NULL
)
252 if (!EC_GROUP_copy(t
, a
))
265 const EC_METHOD
*EC_GROUP_method_of(const EC_GROUP
*group
)
270 int EC_METHOD_get_field_type(const EC_METHOD
*meth
)
272 return meth
->field_type
;
275 static int ec_precompute_mont_data(EC_GROUP
*);
278 * Try computing cofactor from the generator order (n) and field cardinality (q).
279 * This works for all curves of cryptographic interest.
281 * Hasse thm: q + 1 - 2*sqrt(q) <= n*h <= q + 1 + 2*sqrt(q)
282 * h_min = (q + 1 - 2*sqrt(q))/n
283 * h_max = (q + 1 + 2*sqrt(q))/n
284 * h_max - h_min = 4*sqrt(q)/n
285 * So if n > 4*sqrt(q) holds, there is only one possible value for h:
286 * h = \lfloor (h_min + h_max)/2 \rceil = \lfloor (q + 1)/n \rceil
288 * Otherwise, zero cofactor and return success.
290 static int ec_guess_cofactor(EC_GROUP
*group
) {
296 * If the cofactor is too large, we cannot guess it.
297 * The RHS of below is a strict overestimate of lg(4 * sqrt(q))
299 if (BN_num_bits(group
->order
) <= (BN_num_bits(group
->field
) + 1) / 2 + 3) {
301 BN_zero(group
->cofactor
);
306 if ((ctx
= BN_CTX_new_ex(group
->libctx
)) == NULL
)
310 if ((q
= BN_CTX_get(ctx
)) == NULL
)
313 /* set q = 2**m for binary fields; q = p otherwise */
314 if (group
->meth
->field_type
== NID_X9_62_characteristic_two_field
) {
316 if (!BN_set_bit(q
, BN_num_bits(group
->field
) - 1))
319 if (!BN_copy(q
, group
->field
))
323 /* compute h = \lfloor (q + 1)/n \rceil = \lfloor (q + 1 + n/2)/n \rfloor */
324 if (!BN_rshift1(group
->cofactor
, group
->order
) /* n/2 */
325 || !BN_add(group
->cofactor
, group
->cofactor
, q
) /* q + n/2 */
327 || !BN_add(group
->cofactor
, group
->cofactor
, BN_value_one())
328 /* (q + 1 + n/2)/n */
329 || !BN_div(group
->cofactor
, NULL
, group
->cofactor
, group
->order
, ctx
))
338 int EC_GROUP_set_generator(EC_GROUP
*group
, const EC_POINT
*generator
,
339 const BIGNUM
*order
, const BIGNUM
*cofactor
)
341 if (generator
== NULL
) {
342 ECerr(EC_F_EC_GROUP_SET_GENERATOR
, ERR_R_PASSED_NULL_PARAMETER
);
346 /* require group->field >= 1 */
347 if (group
->field
== NULL
|| BN_is_zero(group
->field
)
348 || BN_is_negative(group
->field
)) {
349 ECerr(EC_F_EC_GROUP_SET_GENERATOR
, EC_R_INVALID_FIELD
);
354 * - require order >= 1
355 * - enforce upper bound due to Hasse thm: order can be no more than one bit
356 * longer than field cardinality
358 if (order
== NULL
|| BN_is_zero(order
) || BN_is_negative(order
)
359 || BN_num_bits(order
) > BN_num_bits(group
->field
) + 1) {
360 ECerr(EC_F_EC_GROUP_SET_GENERATOR
, EC_R_INVALID_GROUP_ORDER
);
365 * Unfortunately the cofactor is an optional field in many standards.
366 * Internally, the lib uses 0 cofactor as a marker for "unknown cofactor".
367 * So accept cofactor == NULL or cofactor >= 0.
369 if (cofactor
!= NULL
&& BN_is_negative(cofactor
)) {
370 ECerr(EC_F_EC_GROUP_SET_GENERATOR
, EC_R_UNKNOWN_COFACTOR
);
374 if (group
->generator
== NULL
) {
375 group
->generator
= EC_POINT_new(group
);
376 if (group
->generator
== NULL
)
379 if (!EC_POINT_copy(group
->generator
, generator
))
382 if (!BN_copy(group
->order
, order
))
385 /* Either take the provided positive cofactor, or try to compute it */
386 if (cofactor
!= NULL
&& !BN_is_zero(cofactor
)) {
387 if (!BN_copy(group
->cofactor
, cofactor
))
389 } else if (!ec_guess_cofactor(group
)) {
390 BN_zero(group
->cofactor
);
395 * Some groups have an order with
396 * factors of two, which makes the Montgomery setup fail.
397 * |group->mont_data| will be NULL in this case.
399 if (BN_is_odd(group
->order
)) {
400 return ec_precompute_mont_data(group
);
403 BN_MONT_CTX_free(group
->mont_data
);
404 group
->mont_data
= NULL
;
408 const EC_POINT
*EC_GROUP_get0_generator(const EC_GROUP
*group
)
410 return group
->generator
;
413 BN_MONT_CTX
*EC_GROUP_get_mont_data(const EC_GROUP
*group
)
415 return group
->mont_data
;
418 int EC_GROUP_get_order(const EC_GROUP
*group
, BIGNUM
*order
, BN_CTX
*ctx
)
420 if (group
->order
== NULL
)
422 if (!BN_copy(order
, group
->order
))
425 return !BN_is_zero(order
);
428 const BIGNUM
*EC_GROUP_get0_order(const EC_GROUP
*group
)
433 int EC_GROUP_order_bits(const EC_GROUP
*group
)
435 return group
->meth
->group_order_bits(group
);
438 int EC_GROUP_get_cofactor(const EC_GROUP
*group
, BIGNUM
*cofactor
,
442 if (group
->cofactor
== NULL
)
444 if (!BN_copy(cofactor
, group
->cofactor
))
447 return !BN_is_zero(group
->cofactor
);
450 const BIGNUM
*EC_GROUP_get0_cofactor(const EC_GROUP
*group
)
452 return group
->cofactor
;
455 void EC_GROUP_set_curve_name(EC_GROUP
*group
, int nid
)
457 group
->curve_name
= nid
;
460 int EC_GROUP_get_curve_name(const EC_GROUP
*group
)
462 return group
->curve_name
;
465 const BIGNUM
*EC_GROUP_get0_field(const EC_GROUP
*group
)
470 void EC_GROUP_set_asn1_flag(EC_GROUP
*group
, int flag
)
472 group
->asn1_flag
= flag
;
475 int EC_GROUP_get_asn1_flag(const EC_GROUP
*group
)
477 return group
->asn1_flag
;
480 void EC_GROUP_set_point_conversion_form(EC_GROUP
*group
,
481 point_conversion_form_t form
)
483 group
->asn1_form
= form
;
486 point_conversion_form_t
EC_GROUP_get_point_conversion_form(const EC_GROUP
489 return group
->asn1_form
;
492 size_t EC_GROUP_set_seed(EC_GROUP
*group
, const unsigned char *p
, size_t len
)
494 OPENSSL_free(group
->seed
);
501 if ((group
->seed
= OPENSSL_malloc(len
)) == NULL
) {
502 ECerr(EC_F_EC_GROUP_SET_SEED
, ERR_R_MALLOC_FAILURE
);
505 memcpy(group
->seed
, p
, len
);
506 group
->seed_len
= len
;
511 unsigned char *EC_GROUP_get0_seed(const EC_GROUP
*group
)
516 size_t EC_GROUP_get_seed_len(const EC_GROUP
*group
)
518 return group
->seed_len
;
521 int EC_GROUP_set_curve(EC_GROUP
*group
, const BIGNUM
*p
, const BIGNUM
*a
,
522 const BIGNUM
*b
, BN_CTX
*ctx
)
524 if (group
->meth
->group_set_curve
== 0) {
525 ECerr(EC_F_EC_GROUP_SET_CURVE
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
528 return group
->meth
->group_set_curve(group
, p
, a
, b
, ctx
);
531 int EC_GROUP_get_curve(const EC_GROUP
*group
, BIGNUM
*p
, BIGNUM
*a
, BIGNUM
*b
,
534 if (group
->meth
->group_get_curve
== NULL
) {
535 ECerr(EC_F_EC_GROUP_GET_CURVE
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
538 return group
->meth
->group_get_curve(group
, p
, a
, b
, ctx
);
542 int EC_GROUP_set_curve_GFp(EC_GROUP
*group
, const BIGNUM
*p
, const BIGNUM
*a
,
543 const BIGNUM
*b
, BN_CTX
*ctx
)
545 return EC_GROUP_set_curve(group
, p
, a
, b
, ctx
);
548 int EC_GROUP_get_curve_GFp(const EC_GROUP
*group
, BIGNUM
*p
, BIGNUM
*a
,
549 BIGNUM
*b
, BN_CTX
*ctx
)
551 return EC_GROUP_get_curve(group
, p
, a
, b
, ctx
);
554 # ifndef OPENSSL_NO_EC2M
555 int EC_GROUP_set_curve_GF2m(EC_GROUP
*group
, const BIGNUM
*p
, const BIGNUM
*a
,
556 const BIGNUM
*b
, BN_CTX
*ctx
)
558 return EC_GROUP_set_curve(group
, p
, a
, b
, ctx
);
561 int EC_GROUP_get_curve_GF2m(const EC_GROUP
*group
, BIGNUM
*p
, BIGNUM
*a
,
562 BIGNUM
*b
, BN_CTX
*ctx
)
564 return EC_GROUP_get_curve(group
, p
, a
, b
, ctx
);
569 int EC_GROUP_get_degree(const EC_GROUP
*group
)
571 if (group
->meth
->group_get_degree
== 0) {
572 ECerr(EC_F_EC_GROUP_GET_DEGREE
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
575 return group
->meth
->group_get_degree(group
);
578 int EC_GROUP_check_discriminant(const EC_GROUP
*group
, BN_CTX
*ctx
)
580 if (group
->meth
->group_check_discriminant
== 0) {
581 ECerr(EC_F_EC_GROUP_CHECK_DISCRIMINANT
,
582 ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
585 return group
->meth
->group_check_discriminant(group
, ctx
);
588 int EC_GROUP_cmp(const EC_GROUP
*a
, const EC_GROUP
*b
, BN_CTX
*ctx
)
591 BIGNUM
*a1
, *a2
, *a3
, *b1
, *b2
, *b3
;
593 BN_CTX
*ctx_new
= NULL
;
596 ctx_new
= ctx
= BN_CTX_new();
601 /* compare the field types */
602 if (EC_METHOD_get_field_type(EC_GROUP_method_of(a
)) !=
603 EC_METHOD_get_field_type(EC_GROUP_method_of(b
)))
605 /* compare the curve name (if present in both) */
606 if (EC_GROUP_get_curve_name(a
) && EC_GROUP_get_curve_name(b
) &&
607 EC_GROUP_get_curve_name(a
) != EC_GROUP_get_curve_name(b
))
609 if (a
->meth
->flags
& EC_FLAGS_CUSTOM_CURVE
)
613 a1
= BN_CTX_get(ctx
);
614 a2
= BN_CTX_get(ctx
);
615 a3
= BN_CTX_get(ctx
);
616 b1
= BN_CTX_get(ctx
);
617 b2
= BN_CTX_get(ctx
);
618 b3
= BN_CTX_get(ctx
);
622 BN_CTX_free(ctx_new
);
628 * XXX This approach assumes that the external representation of curves
629 * over the same field type is the same.
631 if (!a
->meth
->group_get_curve(a
, a1
, a2
, a3
, ctx
) ||
632 !b
->meth
->group_get_curve(b
, b1
, b2
, b3
, ctx
))
635 /* return 1 if the curve parameters are different */
636 if (r
|| BN_cmp(a1
, b1
) != 0 || BN_cmp(a2
, b2
) != 0 || BN_cmp(a3
, b3
) != 0)
639 /* XXX EC_POINT_cmp() assumes that the methods are equal */
640 /* return 1 if the generators are different */
641 if (r
|| EC_POINT_cmp(a
, EC_GROUP_get0_generator(a
),
642 EC_GROUP_get0_generator(b
), ctx
) != 0)
646 const BIGNUM
*ao
, *bo
, *ac
, *bc
;
647 /* compare the orders */
648 ao
= EC_GROUP_get0_order(a
);
649 bo
= EC_GROUP_get0_order(b
);
650 if (ao
== NULL
|| bo
== NULL
) {
651 /* return an error if either order is NULL */
655 if (BN_cmp(ao
, bo
) != 0) {
656 /* return 1 if orders are different */
661 * It gets here if the curve parameters and generator matched.
662 * Now check the optional cofactors (if both are present).
664 ac
= EC_GROUP_get0_cofactor(a
);
665 bc
= EC_GROUP_get0_cofactor(b
);
666 /* Returns 1 (mismatch) if both cofactors are specified and different */
667 if (!BN_is_zero(ac
) && !BN_is_zero(bc
) && BN_cmp(ac
, bc
) != 0)
669 /* Returns 0 if the parameters matched */
674 BN_CTX_free(ctx_new
);
679 /* functions for EC_POINT objects */
681 EC_POINT
*EC_POINT_new(const EC_GROUP
*group
)
686 ECerr(EC_F_EC_POINT_NEW
, ERR_R_PASSED_NULL_PARAMETER
);
689 if (group
->meth
->point_init
== NULL
) {
690 ECerr(EC_F_EC_POINT_NEW
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
694 ret
= OPENSSL_zalloc(sizeof(*ret
));
696 ECerr(EC_F_EC_POINT_NEW
, ERR_R_MALLOC_FAILURE
);
700 ret
->meth
= group
->meth
;
701 ret
->curve_name
= group
->curve_name
;
703 if (!ret
->meth
->point_init(ret
)) {
711 void EC_POINT_free(EC_POINT
*point
)
716 if (point
->meth
->point_finish
!= 0)
717 point
->meth
->point_finish(point
);
721 void EC_POINT_clear_free(EC_POINT
*point
)
726 if (point
->meth
->point_clear_finish
!= 0)
727 point
->meth
->point_clear_finish(point
);
728 else if (point
->meth
->point_finish
!= 0)
729 point
->meth
->point_finish(point
);
730 OPENSSL_clear_free(point
, sizeof(*point
));
733 int EC_POINT_copy(EC_POINT
*dest
, const EC_POINT
*src
)
735 if (dest
->meth
->point_copy
== 0) {
736 ECerr(EC_F_EC_POINT_COPY
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
739 if (dest
->meth
!= src
->meth
740 || (dest
->curve_name
!= src
->curve_name
741 && dest
->curve_name
!= 0
742 && src
->curve_name
!= 0)) {
743 ECerr(EC_F_EC_POINT_COPY
, EC_R_INCOMPATIBLE_OBJECTS
);
748 return dest
->meth
->point_copy(dest
, src
);
751 EC_POINT
*EC_POINT_dup(const EC_POINT
*a
, const EC_GROUP
*group
)
759 t
= EC_POINT_new(group
);
762 r
= EC_POINT_copy(t
, a
);
770 const EC_METHOD
*EC_POINT_method_of(const EC_POINT
*point
)
775 int EC_POINT_set_to_infinity(const EC_GROUP
*group
, EC_POINT
*point
)
777 if (group
->meth
->point_set_to_infinity
== 0) {
778 ECerr(EC_F_EC_POINT_SET_TO_INFINITY
,
779 ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
782 if (group
->meth
!= point
->meth
) {
783 ECerr(EC_F_EC_POINT_SET_TO_INFINITY
, EC_R_INCOMPATIBLE_OBJECTS
);
786 return group
->meth
->point_set_to_infinity(group
, point
);
789 int EC_POINT_set_Jprojective_coordinates_GFp(const EC_GROUP
*group
,
790 EC_POINT
*point
, const BIGNUM
*x
,
791 const BIGNUM
*y
, const BIGNUM
*z
,
794 if (group
->meth
->point_set_Jprojective_coordinates_GFp
== 0) {
795 ECerr(EC_F_EC_POINT_SET_JPROJECTIVE_COORDINATES_GFP
,
796 ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
799 if (!ec_point_is_compat(point
, group
)) {
800 ECerr(EC_F_EC_POINT_SET_JPROJECTIVE_COORDINATES_GFP
,
801 EC_R_INCOMPATIBLE_OBJECTS
);
804 return group
->meth
->point_set_Jprojective_coordinates_GFp(group
, point
, x
,
808 int EC_POINT_get_Jprojective_coordinates_GFp(const EC_GROUP
*group
,
809 const EC_POINT
*point
, BIGNUM
*x
,
810 BIGNUM
*y
, BIGNUM
*z
,
813 if (group
->meth
->point_get_Jprojective_coordinates_GFp
== 0) {
814 ECerr(EC_F_EC_POINT_GET_JPROJECTIVE_COORDINATES_GFP
,
815 ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
818 if (!ec_point_is_compat(point
, group
)) {
819 ECerr(EC_F_EC_POINT_GET_JPROJECTIVE_COORDINATES_GFP
,
820 EC_R_INCOMPATIBLE_OBJECTS
);
823 return group
->meth
->point_get_Jprojective_coordinates_GFp(group
, point
, x
,
827 int EC_POINT_set_affine_coordinates(const EC_GROUP
*group
, EC_POINT
*point
,
828 const BIGNUM
*x
, const BIGNUM
*y
,
831 if (group
->meth
->point_set_affine_coordinates
== NULL
) {
832 ECerr(EC_F_EC_POINT_SET_AFFINE_COORDINATES
,
833 ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
836 if (!ec_point_is_compat(point
, group
)) {
837 ECerr(EC_F_EC_POINT_SET_AFFINE_COORDINATES
, EC_R_INCOMPATIBLE_OBJECTS
);
840 if (!group
->meth
->point_set_affine_coordinates(group
, point
, x
, y
, ctx
))
843 if (EC_POINT_is_on_curve(group
, point
, ctx
) <= 0) {
844 ECerr(EC_F_EC_POINT_SET_AFFINE_COORDINATES
, EC_R_POINT_IS_NOT_ON_CURVE
);
851 int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP
*group
,
852 EC_POINT
*point
, const BIGNUM
*x
,
853 const BIGNUM
*y
, BN_CTX
*ctx
)
855 return EC_POINT_set_affine_coordinates(group
, point
, x
, y
, ctx
);
858 # ifndef OPENSSL_NO_EC2M
859 int EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP
*group
,
860 EC_POINT
*point
, const BIGNUM
*x
,
861 const BIGNUM
*y
, BN_CTX
*ctx
)
863 return EC_POINT_set_affine_coordinates(group
, point
, x
, y
, ctx
);
868 int EC_POINT_get_affine_coordinates(const EC_GROUP
*group
,
869 const EC_POINT
*point
, BIGNUM
*x
, BIGNUM
*y
,
872 if (group
->meth
->point_get_affine_coordinates
== NULL
) {
873 ECerr(EC_F_EC_POINT_GET_AFFINE_COORDINATES
,
874 ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
877 if (!ec_point_is_compat(point
, group
)) {
878 ECerr(EC_F_EC_POINT_GET_AFFINE_COORDINATES
, EC_R_INCOMPATIBLE_OBJECTS
);
881 if (EC_POINT_is_at_infinity(group
, point
)) {
882 ECerr(EC_F_EC_POINT_GET_AFFINE_COORDINATES
, EC_R_POINT_AT_INFINITY
);
885 return group
->meth
->point_get_affine_coordinates(group
, point
, x
, y
, ctx
);
889 int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP
*group
,
890 const EC_POINT
*point
, BIGNUM
*x
,
891 BIGNUM
*y
, BN_CTX
*ctx
)
893 return EC_POINT_get_affine_coordinates(group
, point
, x
, y
, ctx
);
896 # ifndef OPENSSL_NO_EC2M
897 int EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP
*group
,
898 const EC_POINT
*point
, BIGNUM
*x
,
899 BIGNUM
*y
, BN_CTX
*ctx
)
901 return EC_POINT_get_affine_coordinates(group
, point
, x
, y
, ctx
);
906 int EC_POINT_add(const EC_GROUP
*group
, EC_POINT
*r
, const EC_POINT
*a
,
907 const EC_POINT
*b
, BN_CTX
*ctx
)
909 if (group
->meth
->add
== 0) {
910 ECerr(EC_F_EC_POINT_ADD
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
913 if (!ec_point_is_compat(r
, group
) || !ec_point_is_compat(a
, group
)
914 || !ec_point_is_compat(b
, group
)) {
915 ECerr(EC_F_EC_POINT_ADD
, EC_R_INCOMPATIBLE_OBJECTS
);
918 return group
->meth
->add(group
, r
, a
, b
, ctx
);
921 int EC_POINT_dbl(const EC_GROUP
*group
, EC_POINT
*r
, const EC_POINT
*a
,
924 if (group
->meth
->dbl
== 0) {
925 ECerr(EC_F_EC_POINT_DBL
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
928 if (!ec_point_is_compat(r
, group
) || !ec_point_is_compat(a
, group
)) {
929 ECerr(EC_F_EC_POINT_DBL
, EC_R_INCOMPATIBLE_OBJECTS
);
932 return group
->meth
->dbl(group
, r
, a
, ctx
);
935 int EC_POINT_invert(const EC_GROUP
*group
, EC_POINT
*a
, BN_CTX
*ctx
)
937 if (group
->meth
->invert
== 0) {
938 ECerr(EC_F_EC_POINT_INVERT
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
941 if (!ec_point_is_compat(a
, group
)) {
942 ECerr(EC_F_EC_POINT_INVERT
, EC_R_INCOMPATIBLE_OBJECTS
);
945 return group
->meth
->invert(group
, a
, ctx
);
948 int EC_POINT_is_at_infinity(const EC_GROUP
*group
, const EC_POINT
*point
)
950 if (group
->meth
->is_at_infinity
== 0) {
951 ECerr(EC_F_EC_POINT_IS_AT_INFINITY
,
952 ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
955 if (!ec_point_is_compat(point
, group
)) {
956 ECerr(EC_F_EC_POINT_IS_AT_INFINITY
, EC_R_INCOMPATIBLE_OBJECTS
);
959 return group
->meth
->is_at_infinity(group
, point
);
963 * Check whether an EC_POINT is on the curve or not. Note that the return
964 * value for this function should NOT be treated as a boolean. Return values:
965 * 1: The point is on the curve
966 * 0: The point is not on the curve
967 * -1: An error occurred
969 int EC_POINT_is_on_curve(const EC_GROUP
*group
, const EC_POINT
*point
,
972 if (group
->meth
->is_on_curve
== 0) {
973 ECerr(EC_F_EC_POINT_IS_ON_CURVE
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
976 if (!ec_point_is_compat(point
, group
)) {
977 ECerr(EC_F_EC_POINT_IS_ON_CURVE
, EC_R_INCOMPATIBLE_OBJECTS
);
980 return group
->meth
->is_on_curve(group
, point
, ctx
);
983 int EC_POINT_cmp(const EC_GROUP
*group
, const EC_POINT
*a
, const EC_POINT
*b
,
986 if (group
->meth
->point_cmp
== 0) {
987 ECerr(EC_F_EC_POINT_CMP
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
990 if (!ec_point_is_compat(a
, group
) || !ec_point_is_compat(b
, group
)) {
991 ECerr(EC_F_EC_POINT_CMP
, EC_R_INCOMPATIBLE_OBJECTS
);
994 return group
->meth
->point_cmp(group
, a
, b
, ctx
);
997 int EC_POINT_make_affine(const EC_GROUP
*group
, EC_POINT
*point
, BN_CTX
*ctx
)
999 if (group
->meth
->make_affine
== 0) {
1000 ECerr(EC_F_EC_POINT_MAKE_AFFINE
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
1003 if (!ec_point_is_compat(point
, group
)) {
1004 ECerr(EC_F_EC_POINT_MAKE_AFFINE
, EC_R_INCOMPATIBLE_OBJECTS
);
1007 return group
->meth
->make_affine(group
, point
, ctx
);
1010 int EC_POINTs_make_affine(const EC_GROUP
*group
, size_t num
,
1011 EC_POINT
*points
[], BN_CTX
*ctx
)
1015 if (group
->meth
->points_make_affine
== 0) {
1016 ECerr(EC_F_EC_POINTS_MAKE_AFFINE
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
1019 for (i
= 0; i
< num
; i
++) {
1020 if (!ec_point_is_compat(points
[i
], group
)) {
1021 ECerr(EC_F_EC_POINTS_MAKE_AFFINE
, EC_R_INCOMPATIBLE_OBJECTS
);
1025 return group
->meth
->points_make_affine(group
, num
, points
, ctx
);
1029 * Functions for point multiplication. If group->meth->mul is 0, we use the
1030 * wNAF-based implementations in ec_mult.c; otherwise we dispatch through
1034 int EC_POINTs_mul(const EC_GROUP
*group
, EC_POINT
*r
, const BIGNUM
*scalar
,
1035 size_t num
, const EC_POINT
*points
[],
1036 const BIGNUM
*scalars
[], BN_CTX
*ctx
)
1041 BN_CTX
*new_ctx
= NULL
;
1044 ctx
= new_ctx
= BN_CTX_secure_new();
1047 ECerr(EC_F_EC_POINTS_MUL
, ERR_R_INTERNAL_ERROR
);
1051 if ((scalar
== NULL
) && (num
== 0)) {
1052 return EC_POINT_set_to_infinity(group
, r
);
1055 if (!ec_point_is_compat(r
, group
)) {
1056 ECerr(EC_F_EC_POINTS_MUL
, EC_R_INCOMPATIBLE_OBJECTS
);
1059 for (i
= 0; i
< num
; i
++) {
1060 if (!ec_point_is_compat(points
[i
], group
)) {
1061 ECerr(EC_F_EC_POINTS_MUL
, EC_R_INCOMPATIBLE_OBJECTS
);
1066 if (group
->meth
->mul
!= NULL
)
1067 ret
= group
->meth
->mul(group
, r
, scalar
, num
, points
, scalars
, ctx
);
1070 ret
= ec_wNAF_mul(group
, r
, scalar
, num
, points
, scalars
, ctx
);
1073 BN_CTX_free(new_ctx
);
1078 int EC_POINT_mul(const EC_GROUP
*group
, EC_POINT
*r
, const BIGNUM
*g_scalar
,
1079 const EC_POINT
*point
, const BIGNUM
*p_scalar
, BN_CTX
*ctx
)
1081 /* just a convenient interface to EC_POINTs_mul() */
1083 const EC_POINT
*points
[1];
1084 const BIGNUM
*scalars
[1];
1087 scalars
[0] = p_scalar
;
1089 return EC_POINTs_mul(group
, r
, g_scalar
,
1091 && p_scalar
!= NULL
), points
, scalars
, ctx
);
1094 int EC_GROUP_precompute_mult(EC_GROUP
*group
, BN_CTX
*ctx
)
1096 if (group
->meth
->mul
== 0)
1098 return ec_wNAF_precompute_mult(group
, ctx
);
1100 if (group
->meth
->precompute_mult
!= 0)
1101 return group
->meth
->precompute_mult(group
, ctx
);
1103 return 1; /* nothing to do, so report success */
1106 int EC_GROUP_have_precompute_mult(const EC_GROUP
*group
)
1108 if (group
->meth
->mul
== 0)
1110 return ec_wNAF_have_precompute_mult(group
);
1112 if (group
->meth
->have_precompute_mult
!= 0)
1113 return group
->meth
->have_precompute_mult(group
);
1115 return 0; /* cannot tell whether precomputation has
1120 * ec_precompute_mont_data sets |group->mont_data| from |group->order| and
1121 * returns one on success. On error it returns zero.
1123 static int ec_precompute_mont_data(EC_GROUP
*group
)
1125 BN_CTX
*ctx
= BN_CTX_new_ex(group
->libctx
);
1128 BN_MONT_CTX_free(group
->mont_data
);
1129 group
->mont_data
= NULL
;
1134 group
->mont_data
= BN_MONT_CTX_new();
1135 if (group
->mont_data
== NULL
)
1138 if (!BN_MONT_CTX_set(group
->mont_data
, group
->order
, ctx
)) {
1139 BN_MONT_CTX_free(group
->mont_data
);
1140 group
->mont_data
= NULL
;
1153 int EC_KEY_set_ex_data(EC_KEY
*key
, int idx
, void *arg
)
1155 return CRYPTO_set_ex_data(&key
->ex_data
, idx
, arg
);
1158 void *EC_KEY_get_ex_data(const EC_KEY
*key
, int idx
)
1160 return CRYPTO_get_ex_data(&key
->ex_data
, idx
);
1164 int ec_group_simple_order_bits(const EC_GROUP
*group
)
1166 if (group
->order
== NULL
)
1168 return BN_num_bits(group
->order
);
1171 static int ec_field_inverse_mod_ord(const EC_GROUP
*group
, BIGNUM
*r
,
1172 const BIGNUM
*x
, BN_CTX
*ctx
)
1177 BN_CTX
*new_ctx
= NULL
;
1180 ctx
= new_ctx
= BN_CTX_secure_new();
1185 if (group
->mont_data
== NULL
)
1189 if ((e
= BN_CTX_get(ctx
)) == NULL
)
1193 * We want inverse in constant time, therefore we utilize the fact
1194 * order must be prime and use Fermats Little Theorem instead.
1196 if (!BN_set_word(e
, 2))
1198 if (!BN_sub(e
, group
->order
, e
))
1201 * Exponent e is public.
1202 * No need for scatter-gather or BN_FLG_CONSTTIME.
1204 if (!BN_mod_exp_mont(r
, x
, e
, group
->order
, ctx
, group
->mont_data
))
1212 BN_CTX_free(new_ctx
);
1218 * Default behavior, if group->meth->field_inverse_mod_ord is NULL:
1219 * - When group->order is even, this function returns an error.
1220 * - When group->order is otherwise composite, the correctness
1221 * of the output is not guaranteed.
1222 * - When x is outside the range [1, group->order), the correctness
1223 * of the output is not guaranteed.
1224 * - Otherwise, this function returns the multiplicative inverse in the
1225 * range [1, group->order).
1227 * EC_METHODs must implement their own field_inverse_mod_ord for
1228 * other functionality.
1230 int ec_group_do_inverse_ord(const EC_GROUP
*group
, BIGNUM
*res
,
1231 const BIGNUM
*x
, BN_CTX
*ctx
)
1233 if (group
->meth
->field_inverse_mod_ord
!= NULL
)
1234 return group
->meth
->field_inverse_mod_ord(group
, res
, x
, ctx
);
1236 return ec_field_inverse_mod_ord(group
, res
, x
, ctx
);
1240 * Coordinate blinding for EC_POINT.
1242 * The underlying EC_METHOD can optionally implement this function:
1243 * underlying implementations should return 0 on errors, or 1 on
1246 * This wrapper returns 1 in case the underlying EC_METHOD does not
1247 * support coordinate blinding.
1249 int ec_point_blind_coordinates(const EC_GROUP
*group
, EC_POINT
*p
, BN_CTX
*ctx
)
1251 if (group
->meth
->blind_coordinates
== NULL
)
1252 return 1; /* ignore if not implemented */
1254 return group
->meth
->blind_coordinates(group
, p
, ctx
);