3 * Originally written by Bodo Moeller for the OpenSSL project.
6 * \file crypto/ec/ec.h Include file for the OpenSSL EC functions
7 * \author Originally written by Bodo Moeller for the OpenSSL project
9 /* ====================================================================
10 * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved.
12 * Redistribution and use in source and binary forms, with or without
13 * modification, are permitted provided that the following conditions
16 * 1. Redistributions of source code must retain the above copyright
17 * notice, this list of conditions and the following disclaimer.
19 * 2. Redistributions in binary form must reproduce the above copyright
20 * notice, this list of conditions and the following disclaimer in
21 * the documentation and/or other materials provided with the
24 * 3. All advertising materials mentioning features or use of this
25 * software must display the following acknowledgment:
26 * "This product includes software developed by the OpenSSL Project
27 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
29 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
30 * endorse or promote products derived from this software without
31 * prior written permission. For written permission, please contact
32 * openssl-core@openssl.org.
34 * 5. Products derived from this software may not be called "OpenSSL"
35 * nor may "OpenSSL" appear in their names without prior written
36 * permission of the OpenSSL Project.
38 * 6. Redistributions of any form whatsoever must retain the following
40 * "This product includes software developed by the OpenSSL Project
41 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
43 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
44 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
45 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
46 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
47 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
48 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
49 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
50 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
51 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
52 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
53 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
54 * OF THE POSSIBILITY OF SUCH DAMAGE.
55 * ====================================================================
57 * This product includes cryptographic software written by Eric Young
58 * (eay@cryptsoft.com). This product includes software written by Tim
59 * Hudson (tjh@cryptsoft.com).
62 /* ====================================================================
63 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
65 * Portions of the attached software ("Contribution") are developed by
66 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
68 * The Contribution is licensed pursuant to the OpenSSL open source
69 * license provided above.
71 * The elliptic curve binary polynomial software is originally written by
72 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
79 # include <openssl/opensslconf.h>
82 # error EC is disabled.
85 # include <openssl/asn1.h>
86 # include <openssl/symhacks.h>
87 # ifdef OPENSSL_USE_DEPRECATED
88 # include <openssl/bn.h>
93 # elif defined(__SUNPRO_C)
94 # if __SUNPRO_C >= 0x520
95 # pragma error_messages (off,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE)
99 # ifndef OPENSSL_ECC_MAX_FIELD_BITS
100 # define OPENSSL_ECC_MAX_FIELD_BITS 661
103 /** Enum for the point conversion form as defined in X9.62 (ECDSA)
104 * for the encoding of a elliptic curve point (x,y) */
106 /** the point is encoded as z||x, where the octet z specifies
107 * which solution of the quadratic equation y is */
108 POINT_CONVERSION_COMPRESSED = 2,
109 /** the point is encoded as z||x||y, where z is the octet 0x04 */
110 POINT_CONVERSION_UNCOMPRESSED = 4,
111 /** the point is encoded as z||x||y, where the octet z specifies
112 * which solution of the quadratic equation y is */
113 POINT_CONVERSION_HYBRID = 6
114 } point_conversion_form_t;
116 typedef struct ec_method_st EC_METHOD;
118 typedef struct ec_group_st
122 -- curve coefficients
123 -- optional generator with associated information (order, cofactor)
124 -- optional extra data (precomputed table for fast computation of multiples of generator)
129 typedef struct ec_point_st EC_POINT;
131 /********************************************************************/
132 /* EC_METHODs for curves over GF(p) */
133 /********************************************************************/
135 /** Returns the basic GFp ec methods which provides the basis for the
137 * \return EC_METHOD object
139 const EC_METHOD *EC_GFp_simple_method(void);
141 /** Returns GFp methods using montgomery multiplication.
142 * \return EC_METHOD object
144 const EC_METHOD *EC_GFp_mont_method(void);
146 /** Returns GFp methods using optimized methods for NIST recommended curves
147 * \return EC_METHOD object
149 const EC_METHOD *EC_GFp_nist_method(void);
151 # ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
152 # ifndef OPENSSL_SYS_WIN32
153 /** Returns 64-bit optimized methods for nistp224
154 * \return EC_METHOD object
156 const EC_METHOD *EC_GFp_nistp224_method(void);
158 /** Returns 64-bit optimized methods for nistp256
159 * \return EC_METHOD object
161 const EC_METHOD *EC_GFp_nistp256_method(void);
163 /** Returns 64-bit optimized methods for nistp521
164 * \return EC_METHOD object
166 const EC_METHOD *EC_GFp_nistp521_method(void);
170 # ifndef OPENSSL_NO_EC2M
171 /********************************************************************/
172 /* EC_METHOD for curves over GF(2^m) */
173 /********************************************************************/
175 /** Returns the basic GF2m ec method
176 * \return EC_METHOD object
178 const EC_METHOD *EC_GF2m_simple_method(void);
182 /********************************************************************/
183 /* EC_GROUP functions */
184 /********************************************************************/
186 /** Creates a new EC_GROUP object
187 * \param meth EC_METHOD to use
188 * \return newly created EC_GROUP object or NULL in case of an error.
190 EC_GROUP *EC_GROUP_new(const EC_METHOD *meth);
192 /** Frees a EC_GROUP object
193 * \param group EC_GROUP object to be freed.
195 void EC_GROUP_free(EC_GROUP *group);
197 /** Clears and frees a EC_GROUP object
198 * \param group EC_GROUP object to be cleared and freed.
200 void EC_GROUP_clear_free(EC_GROUP *group);
202 /** Copies EC_GROUP objects. Note: both EC_GROUPs must use the same EC_METHOD.
203 * \param dst destination EC_GROUP object
204 * \param src source EC_GROUP object
205 * \return 1 on success and 0 if an error occurred.
207 int EC_GROUP_copy(EC_GROUP *dst, const EC_GROUP *src);
209 /** Creates a new EC_GROUP object and copies the copies the content
210 * form src to the newly created EC_KEY object
211 * \param src source EC_GROUP object
212 * \return newly created EC_GROUP object or NULL in case of an error.
214 EC_GROUP *EC_GROUP_dup(const EC_GROUP *src);
216 /** Returns the EC_METHOD of the EC_GROUP object.
217 * \param group EC_GROUP object
218 * \return EC_METHOD used in this EC_GROUP object.
220 const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group);
222 /** Returns the field type of the EC_METHOD.
223 * \param meth EC_METHOD object
224 * \return NID of the underlying field type OID.
226 int EC_METHOD_get_field_type(const EC_METHOD *meth);
228 /** Sets the generator and it's order/cofactor of a EC_GROUP object.
229 * \param group EC_GROUP object
230 * \param generator EC_POINT object with the generator.
231 * \param order the order of the group generated by the generator.
232 * \param cofactor the index of the sub-group generated by the generator
233 * in the group of all points on the elliptic curve.
234 * \return 1 on success and 0 if an error occurred
236 int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator,
237 const BIGNUM *order, const BIGNUM *cofactor);
239 /** Returns the generator of a EC_GROUP object.
240 * \param group EC_GROUP object
241 * \return the currently used generator (possibly NULL).
243 const EC_POINT *EC_GROUP_get0_generator(const EC_GROUP *group);
245 /** Returns the montgomery data for order(Generator)
246 * \param group EC_GROUP object
247 * \return the currently used generator (possibly NULL).
249 BN_MONT_CTX *EC_GROUP_get_mont_data(const EC_GROUP *group);
251 /** Gets the order of a EC_GROUP
252 * \param group EC_GROUP object
253 * \param order BIGNUM to which the order is copied
254 * \param ctx BN_CTX object (optional)
255 * \return 1 on success and 0 if an error occurred
257 int EC_GROUP_get_order(const EC_GROUP *group, BIGNUM *order, BN_CTX *ctx);
259 /** Gets the cofactor of a EC_GROUP
260 * \param group EC_GROUP object
261 * \param cofactor BIGNUM to which the cofactor is copied
262 * \param ctx BN_CTX object (optional)
263 * \return 1 on success and 0 if an error occurred
265 int EC_GROUP_get_cofactor(const EC_GROUP *group, BIGNUM *cofactor,
268 /** Sets the name of a EC_GROUP object
269 * \param group EC_GROUP object
270 * \param nid NID of the curve name OID
272 void EC_GROUP_set_curve_name(EC_GROUP *group, int nid);
274 /** Returns the curve name of a EC_GROUP object
275 * \param group EC_GROUP object
276 * \return NID of the curve name OID or 0 if not set.
278 int EC_GROUP_get_curve_name(const EC_GROUP *group);
280 void EC_GROUP_set_asn1_flag(EC_GROUP *group, int flag);
281 int EC_GROUP_get_asn1_flag(const EC_GROUP *group);
283 void EC_GROUP_set_point_conversion_form(EC_GROUP *group,
284 point_conversion_form_t form);
285 point_conversion_form_t EC_GROUP_get_point_conversion_form(const EC_GROUP *);
287 unsigned char *EC_GROUP_get0_seed(const EC_GROUP *x);
288 size_t EC_GROUP_get_seed_len(const EC_GROUP *);
289 size_t EC_GROUP_set_seed(EC_GROUP *, const unsigned char *, size_t len);
291 /** Sets the parameter of a ec over GFp defined by y^2 = x^3 + a*x + b
292 * \param group EC_GROUP object
293 * \param p BIGNUM with the prime number
294 * \param a BIGNUM with parameter a of the equation
295 * \param b BIGNUM with parameter b of the equation
296 * \param ctx BN_CTX object (optional)
297 * \return 1 on success and 0 if an error occurred
299 int EC_GROUP_set_curve_GFp(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a,
300 const BIGNUM *b, BN_CTX *ctx);
302 /** Gets the parameter of the ec over GFp defined by y^2 = x^3 + a*x + b
303 * \param group EC_GROUP object
304 * \param p BIGNUM for the prime number
305 * \param a BIGNUM for parameter a of the equation
306 * \param b BIGNUM for parameter b of the equation
307 * \param ctx BN_CTX object (optional)
308 * \return 1 on success and 0 if an error occurred
310 int EC_GROUP_get_curve_GFp(const EC_GROUP *group, BIGNUM *p, BIGNUM *a,
311 BIGNUM *b, BN_CTX *ctx);
313 # ifndef OPENSSL_NO_EC2M
314 /** Sets the parameter of a ec over GF2m defined by y^2 + x*y = x^3 + a*x^2 + b
315 * \param group EC_GROUP object
316 * \param p BIGNUM with the polynomial defining the underlying field
317 * \param a BIGNUM with parameter a of the equation
318 * \param b BIGNUM with parameter b of the equation
319 * \param ctx BN_CTX object (optional)
320 * \return 1 on success and 0 if an error occurred
322 int EC_GROUP_set_curve_GF2m(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a,
323 const BIGNUM *b, BN_CTX *ctx);
325 /** Gets the parameter of the ec over GF2m defined by y^2 + x*y = x^3 + a*x^2 + b
326 * \param group EC_GROUP object
327 * \param p BIGNUM for the polynomial defining the underlying field
328 * \param a BIGNUM for parameter a of the equation
329 * \param b BIGNUM for parameter b of the equation
330 * \param ctx BN_CTX object (optional)
331 * \return 1 on success and 0 if an error occurred
333 int EC_GROUP_get_curve_GF2m(const EC_GROUP *group, BIGNUM *p, BIGNUM *a,
334 BIGNUM *b, BN_CTX *ctx);
336 /** Returns the number of bits needed to represent a field element
337 * \param group EC_GROUP object
338 * \return number of bits needed to represent a field element
340 int EC_GROUP_get_degree(const EC_GROUP *group);
342 /** Checks whether the parameter in the EC_GROUP define a valid ec group
343 * \param group EC_GROUP object
344 * \param ctx BN_CTX object (optional)
345 * \return 1 if group is a valid ec group and 0 otherwise
347 int EC_GROUP_check(const EC_GROUP *group, BN_CTX *ctx);
349 /** Checks whether the discriminant of the elliptic curve is zero or not
350 * \param group EC_GROUP object
351 * \param ctx BN_CTX object (optional)
352 * \return 1 if the discriminant is not zero and 0 otherwise
354 int EC_GROUP_check_discriminant(const EC_GROUP *group, BN_CTX *ctx);
356 /** Compares two EC_GROUP objects
357 * \param a first EC_GROUP object
358 * \param b second EC_GROUP object
359 * \param ctx BN_CTX object (optional)
360 * \return 0 if both groups are equal and 1 otherwise
362 int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx);
365 * EC_GROUP_new_GF*() calls EC_GROUP_new() and EC_GROUP_set_GF*() after
366 * choosing an appropriate EC_METHOD
369 /** Creates a new EC_GROUP object with the specified parameters defined
370 * over GFp (defined by the equation y^2 = x^3 + a*x + b)
371 * \param p BIGNUM with the prime number
372 * \param a BIGNUM with the parameter a of the equation
373 * \param b BIGNUM with the parameter b of the equation
374 * \param ctx BN_CTX object (optional)
375 * \return newly created EC_GROUP object with the specified parameters
377 EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a,
378 const BIGNUM *b, BN_CTX *ctx);
379 # ifndef OPENSSL_NO_EC2M
380 /** Creates a new EC_GROUP object with the specified parameters defined
381 * over GF2m (defined by the equation y^2 + x*y = x^3 + a*x^2 + b)
382 * \param p BIGNUM with the polynomial defining the underlying field
383 * \param a BIGNUM with the parameter a of the equation
384 * \param b BIGNUM with the parameter b of the equation
385 * \param ctx BN_CTX object (optional)
386 * \return newly created EC_GROUP object with the specified parameters
388 EC_GROUP *EC_GROUP_new_curve_GF2m(const BIGNUM *p, const BIGNUM *a,
389 const BIGNUM *b, BN_CTX *ctx);
391 /** Creates a EC_GROUP object with a curve specified by a NID
392 * \param nid NID of the OID of the curve name
393 * \return newly created EC_GROUP object with specified curve or NULL
394 * if an error occurred
396 EC_GROUP *EC_GROUP_new_by_curve_name(int nid);
398 /********************************************************************/
399 /* handling of internal curves */
400 /********************************************************************/
408 * EC_builtin_curves(EC_builtin_curve *r, size_t size) returns number of all
409 * available curves or zero if a error occurred. In case r ist not zero
410 * nitems EC_builtin_curve structures are filled with the data of the first
411 * nitems internal groups
413 size_t EC_get_builtin_curves(EC_builtin_curve *r, size_t nitems);
415 const char *EC_curve_nid2nist(int nid);
416 int EC_curve_nist2nid(const char *name);
418 /********************************************************************/
419 /* EC_POINT functions */
420 /********************************************************************/
422 /** Creates a new EC_POINT object for the specified EC_GROUP
423 * \param group EC_GROUP the underlying EC_GROUP object
424 * \return newly created EC_POINT object or NULL if an error occurred
426 EC_POINT *EC_POINT_new(const EC_GROUP *group);
428 /** Frees a EC_POINT object
429 * \param point EC_POINT object to be freed
431 void EC_POINT_free(EC_POINT *point);
433 /** Clears and frees a EC_POINT object
434 * \param point EC_POINT object to be cleared and freed
436 void EC_POINT_clear_free(EC_POINT *point);
438 /** Copies EC_POINT object
439 * \param dst destination EC_POINT object
440 * \param src source EC_POINT object
441 * \return 1 on success and 0 if an error occurred
443 int EC_POINT_copy(EC_POINT *dst, const EC_POINT *src);
445 /** Creates a new EC_POINT object and copies the content of the supplied
447 * \param src source EC_POINT object
448 * \param group underlying the EC_GROUP object
449 * \return newly created EC_POINT object or NULL if an error occurred
451 EC_POINT *EC_POINT_dup(const EC_POINT *src, const EC_GROUP *group);
453 /** Returns the EC_METHOD used in EC_POINT object
454 * \param point EC_POINT object
455 * \return the EC_METHOD used
457 const EC_METHOD *EC_POINT_method_of(const EC_POINT *point);
459 /** Sets a point to infinity (neutral element)
460 * \param group underlying EC_GROUP object
461 * \param point EC_POINT to set to infinity
462 * \return 1 on success and 0 if an error occurred
464 int EC_POINT_set_to_infinity(const EC_GROUP *group, EC_POINT *point);
466 /** Sets the jacobian projective coordinates of a EC_POINT over GFp
467 * \param group underlying EC_GROUP object
468 * \param p EC_POINT object
469 * \param x BIGNUM with the x-coordinate
470 * \param y BIGNUM with the y-coordinate
471 * \param z BIGNUM with the z-coordinate
472 * \param ctx BN_CTX object (optional)
473 * \return 1 on success and 0 if an error occurred
475 int EC_POINT_set_Jprojective_coordinates_GFp(const EC_GROUP *group,
476 EC_POINT *p, const BIGNUM *x,
477 const BIGNUM *y, const BIGNUM *z,
480 /** Gets the jacobian projective coordinates of a EC_POINT over GFp
481 * \param group underlying EC_GROUP object
482 * \param p EC_POINT object
483 * \param x BIGNUM for the x-coordinate
484 * \param y BIGNUM for the y-coordinate
485 * \param z BIGNUM for the z-coordinate
486 * \param ctx BN_CTX object (optional)
487 * \return 1 on success and 0 if an error occurred
489 int EC_POINT_get_Jprojective_coordinates_GFp(const EC_GROUP *group,
490 const EC_POINT *p, BIGNUM *x,
491 BIGNUM *y, BIGNUM *z,
494 /** Sets the affine coordinates of a EC_POINT over GFp
495 * \param group underlying EC_GROUP object
496 * \param p EC_POINT object
497 * \param x BIGNUM with the x-coordinate
498 * \param y BIGNUM with the y-coordinate
499 * \param ctx BN_CTX object (optional)
500 * \return 1 on success and 0 if an error occurred
502 int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *p,
503 const BIGNUM *x, const BIGNUM *y,
506 /** Gets the affine coordinates of a EC_POINT over GFp
507 * \param group underlying EC_GROUP object
508 * \param p EC_POINT object
509 * \param x BIGNUM for the x-coordinate
510 * \param y BIGNUM for the y-coordinate
511 * \param ctx BN_CTX object (optional)
512 * \return 1 on success and 0 if an error occurred
514 int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group,
515 const EC_POINT *p, BIGNUM *x,
516 BIGNUM *y, BN_CTX *ctx);
518 /** Sets the x9.62 compressed coordinates of a EC_POINT over GFp
519 * \param group underlying EC_GROUP object
520 * \param p EC_POINT object
521 * \param x BIGNUM with x-coordinate
522 * \param y_bit integer with the y-Bit (either 0 or 1)
523 * \param ctx BN_CTX object (optional)
524 * \return 1 on success and 0 if an error occurred
526 int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *group,
527 EC_POINT *p, const BIGNUM *x,
528 int y_bit, BN_CTX *ctx);
529 # ifndef OPENSSL_NO_EC2M
530 /** Sets the affine coordinates of a EC_POINT over GF2m
531 * \param group underlying EC_GROUP object
532 * \param p EC_POINT object
533 * \param x BIGNUM with the x-coordinate
534 * \param y BIGNUM with the y-coordinate
535 * \param ctx BN_CTX object (optional)
536 * \return 1 on success and 0 if an error occurred
538 int EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP *group, EC_POINT *p,
539 const BIGNUM *x, const BIGNUM *y,
542 /** Gets the affine coordinates of a EC_POINT over GF2m
543 * \param group underlying EC_GROUP object
544 * \param p EC_POINT object
545 * \param x BIGNUM for the x-coordinate
546 * \param y BIGNUM for the y-coordinate
547 * \param ctx BN_CTX object (optional)
548 * \return 1 on success and 0 if an error occurred
550 int EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *group,
551 const EC_POINT *p, BIGNUM *x,
552 BIGNUM *y, BN_CTX *ctx);
554 /** Sets the x9.62 compressed coordinates of a EC_POINT over GF2m
555 * \param group underlying EC_GROUP object
556 * \param p EC_POINT object
557 * \param x BIGNUM with x-coordinate
558 * \param y_bit integer with the y-Bit (either 0 or 1)
559 * \param ctx BN_CTX object (optional)
560 * \return 1 on success and 0 if an error occurred
562 int EC_POINT_set_compressed_coordinates_GF2m(const EC_GROUP *group,
563 EC_POINT *p, const BIGNUM *x,
564 int y_bit, BN_CTX *ctx);
566 /** Encodes a EC_POINT object to a octet string
567 * \param group underlying EC_GROUP object
568 * \param p EC_POINT object
569 * \param form point conversion form
570 * \param buf memory buffer for the result. If NULL the function returns
571 * required buffer size.
572 * \param len length of the memory buffer
573 * \param ctx BN_CTX object (optional)
574 * \return the length of the encoded octet string or 0 if an error occurred
576 size_t EC_POINT_point2oct(const EC_GROUP *group, const EC_POINT *p,
577 point_conversion_form_t form,
578 unsigned char *buf, size_t len, BN_CTX *ctx);
580 /** Decodes a EC_POINT from a octet string
581 * \param group underlying EC_GROUP object
582 * \param p EC_POINT object
583 * \param buf memory buffer with the encoded ec point
584 * \param len length of the encoded ec point
585 * \param ctx BN_CTX object (optional)
586 * \return 1 on success and 0 if an error occurred
588 int EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *p,
589 const unsigned char *buf, size_t len, BN_CTX *ctx);
591 /* other interfaces to point2oct/oct2point: */
592 BIGNUM *EC_POINT_point2bn(const EC_GROUP *, const EC_POINT *,
593 point_conversion_form_t form, BIGNUM *, BN_CTX *);
594 EC_POINT *EC_POINT_bn2point(const EC_GROUP *, const BIGNUM *,
595 EC_POINT *, BN_CTX *);
596 char *EC_POINT_point2hex(const EC_GROUP *, const EC_POINT *,
597 point_conversion_form_t form, BN_CTX *);
598 EC_POINT *EC_POINT_hex2point(const EC_GROUP *, const char *,
599 EC_POINT *, BN_CTX *);
601 /********************************************************************/
602 /* functions for doing EC_POINT arithmetic */
603 /********************************************************************/
605 /** Computes the sum of two EC_POINT
606 * \param group underlying EC_GROUP object
607 * \param r EC_POINT object for the result (r = a + b)
608 * \param a EC_POINT object with the first summand
609 * \param b EC_POINT object with the second summand
610 * \param ctx BN_CTX object (optional)
611 * \return 1 on success and 0 if an error occurred
613 int EC_POINT_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
614 const EC_POINT *b, BN_CTX *ctx);
616 /** Computes the double of a EC_POINT
617 * \param group underlying EC_GROUP object
618 * \param r EC_POINT object for the result (r = 2 * a)
619 * \param a EC_POINT object
620 * \param ctx BN_CTX object (optional)
621 * \return 1 on success and 0 if an error occurred
623 int EC_POINT_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
626 /** Computes the inverse of a EC_POINT
627 * \param group underlying EC_GROUP object
628 * \param a EC_POINT object to be inverted (it's used for the result as well)
629 * \param ctx BN_CTX object (optional)
630 * \return 1 on success and 0 if an error occurred
632 int EC_POINT_invert(const EC_GROUP *group, EC_POINT *a, BN_CTX *ctx);
634 /** Checks whether the point is the neutral element of the group
635 * \param group the underlying EC_GROUP object
636 * \param p EC_POINT object
637 * \return 1 if the point is the neutral element and 0 otherwise
639 int EC_POINT_is_at_infinity(const EC_GROUP *group, const EC_POINT *p);
641 /** Checks whether the point is on the curve
642 * \param group underlying EC_GROUP object
643 * \param point EC_POINT object to check
644 * \param ctx BN_CTX object (optional)
645 * \return 1 if point if on the curve and 0 otherwise
647 int EC_POINT_is_on_curve(const EC_GROUP *group, const EC_POINT *point,
650 /** Compares two EC_POINTs
651 * \param group underlying EC_GROUP object
652 * \param a first EC_POINT object
653 * \param b second EC_POINT object
654 * \param ctx BN_CTX object (optional)
655 * \return 0 if both points are equal and a value != 0 otherwise
657 int EC_POINT_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b,
660 int EC_POINT_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx);
661 int EC_POINTs_make_affine(const EC_GROUP *group, size_t num,
662 EC_POINT *points[], BN_CTX *ctx);
664 /** Computes r = generator * n sum_{i=0}^{num-1} p[i] * m[i]
665 * \param group underlying EC_GROUP object
666 * \param r EC_POINT object for the result
667 * \param n BIGNUM with the multiplier for the group generator (optional)
668 * \param num number futher summands
669 * \param p array of size num of EC_POINT objects
670 * \param m array of size num of BIGNUM objects
671 * \param ctx BN_CTX object (optional)
672 * \return 1 on success and 0 if an error occurred
674 int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *n,
675 size_t num, const EC_POINT *p[], const BIGNUM *m[],
678 /** Computes r = generator * n + q * m
679 * \param group underlying EC_GROUP object
680 * \param r EC_POINT object for the result
681 * \param n BIGNUM with the multiplier for the group generator (optional)
682 * \param q EC_POINT object with the first factor of the second summand
683 * \param m BIGNUM with the second factor of the second summand
684 * \param ctx BN_CTX object (optional)
685 * \return 1 on success and 0 if an error occurred
687 int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *n,
688 const EC_POINT *q, const BIGNUM *m, BN_CTX *ctx);
690 /** Stores multiples of generator for faster point multiplication
691 * \param group EC_GROUP object
692 * \param ctx BN_CTX object (optional)
693 * \return 1 on success and 0 if an error occurred
695 int EC_GROUP_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
697 /** Reports whether a precomputation has been done
698 * \param group EC_GROUP object
699 * \return 1 if a pre-computation has been done and 0 otherwise
701 int EC_GROUP_have_precompute_mult(const EC_GROUP *group);
703 /********************************************************************/
705 /********************************************************************/
708 * EC_GROUP_get_basis_type() returns the NID of the basis type used to
709 * represent the field elements
711 int EC_GROUP_get_basis_type(const EC_GROUP *);
712 # ifndef OPENSSL_NO_EC2M
713 int EC_GROUP_get_trinomial_basis(const EC_GROUP *, unsigned int *k);
714 int EC_GROUP_get_pentanomial_basis(const EC_GROUP *, unsigned int *k1,
715 unsigned int *k2, unsigned int *k3);
718 # define OPENSSL_EC_EXPLICIT_CURVE 0x000
719 # define OPENSSL_EC_NAMED_CURVE 0x001
721 typedef struct ecpk_parameters_st ECPKPARAMETERS;
723 EC_GROUP *d2i_ECPKParameters(EC_GROUP **, const unsigned char **in, long len);
724 int i2d_ECPKParameters(const EC_GROUP *, unsigned char **out);
726 # define d2i_ECPKParameters_bio(bp,x) ASN1_d2i_bio_of(EC_GROUP,NULL,d2i_ECPKParameters,bp,x)
727 # define i2d_ECPKParameters_bio(bp,x) ASN1_i2d_bio_of_const(EC_GROUP,i2d_ECPKParameters,bp,x)
728 # define d2i_ECPKParameters_fp(fp,x) (EC_GROUP *)ASN1_d2i_fp(NULL, \
729 (char *(*)())d2i_ECPKParameters,(fp),(unsigned char **)(x))
730 # define i2d_ECPKParameters_fp(fp,x) ASN1_i2d_fp(i2d_ECPKParameters,(fp), \
731 (unsigned char *)(x))
733 int ECPKParameters_print(BIO *bp, const EC_GROUP *x, int off);
734 # ifndef OPENSSL_NO_STDIO
735 int ECPKParameters_print_fp(FILE *fp, const EC_GROUP *x, int off);
738 /********************************************************************/
739 /* EC_KEY functions */
740 /********************************************************************/
742 typedef struct ec_key_st EC_KEY;
744 /* some values for the encoding_flag */
745 # define EC_PKEY_NO_PARAMETERS 0x001
746 # define EC_PKEY_NO_PUBKEY 0x002
748 /* some values for the flags field */
749 # define EC_FLAG_NON_FIPS_ALLOW 0x1
750 # define EC_FLAG_FIPS_CHECKED 0x2
752 /** Creates a new EC_KEY object.
753 * \return EC_KEY object or NULL if an error occurred.
755 EC_KEY *EC_KEY_new(void);
757 int EC_KEY_get_flags(const EC_KEY *key);
759 void EC_KEY_set_flags(EC_KEY *key, int flags);
761 void EC_KEY_clear_flags(EC_KEY *key, int flags);
763 /** Creates a new EC_KEY object using a named curve as underlying
765 * \param nid NID of the named curve.
766 * \return EC_KEY object or NULL if an error occurred.
768 EC_KEY *EC_KEY_new_by_curve_name(int nid);
770 /** Frees a EC_KEY object.
771 * \param key EC_KEY object to be freed.
773 void EC_KEY_free(EC_KEY *key);
775 /** Copies a EC_KEY object.
776 * \param dst destination EC_KEY object
777 * \param src src EC_KEY object
778 * \return dst or NULL if an error occurred.
780 EC_KEY *EC_KEY_copy(EC_KEY *dst, const EC_KEY *src);
782 /** Creates a new EC_KEY object and copies the content from src to it.
783 * \param src the source EC_KEY object
784 * \return newly created EC_KEY object or NULL if an error occurred.
786 EC_KEY *EC_KEY_dup(const EC_KEY *src);
788 /** Increases the internal reference count of a EC_KEY object.
789 * \param key EC_KEY object
790 * \return 1 on success and 0 if an error occurred.
792 int EC_KEY_up_ref(EC_KEY *key);
794 /** Returns the EC_GROUP object of a EC_KEY object
795 * \param key EC_KEY object
796 * \return the EC_GROUP object (possibly NULL).
798 const EC_GROUP *EC_KEY_get0_group(const EC_KEY *key);
800 /** Sets the EC_GROUP of a EC_KEY object.
801 * \param key EC_KEY object
802 * \param group EC_GROUP to use in the EC_KEY object (note: the EC_KEY
803 * object will use an own copy of the EC_GROUP).
804 * \return 1 on success and 0 if an error occurred.
806 int EC_KEY_set_group(EC_KEY *key, const EC_GROUP *group);
808 /** Returns the private key of a EC_KEY object.
809 * \param key EC_KEY object
810 * \return a BIGNUM with the private key (possibly NULL).
812 const BIGNUM *EC_KEY_get0_private_key(const EC_KEY *key);
814 /** Sets the private key of a EC_KEY object.
815 * \param key EC_KEY object
816 * \param prv BIGNUM with the private key (note: the EC_KEY object
817 * will use an own copy of the BIGNUM).
818 * \return 1 on success and 0 if an error occurred.
820 int EC_KEY_set_private_key(EC_KEY *key, const BIGNUM *prv);
822 /** Returns the public key of a EC_KEY object.
823 * \param key the EC_KEY object
824 * \return a EC_POINT object with the public key (possibly NULL)
826 const EC_POINT *EC_KEY_get0_public_key(const EC_KEY *key);
828 /** Sets the public key of a EC_KEY object.
829 * \param key EC_KEY object
830 * \param pub EC_POINT object with the public key (note: the EC_KEY object
831 * will use an own copy of the EC_POINT object).
832 * \return 1 on success and 0 if an error occurred.
834 int EC_KEY_set_public_key(EC_KEY *key, const EC_POINT *pub);
836 unsigned EC_KEY_get_enc_flags(const EC_KEY *key);
837 void EC_KEY_set_enc_flags(EC_KEY *eckey, unsigned int flags);
838 point_conversion_form_t EC_KEY_get_conv_form(const EC_KEY *key);
839 void EC_KEY_set_conv_form(EC_KEY *eckey, point_conversion_form_t cform);
840 /* functions to set/get method specific data */
841 void *EC_KEY_get_key_method_data(EC_KEY *key,
842 void *(*dup_func) (void *),
843 void (*free_func) (void *),
844 void (*clear_free_func) (void *));
845 /** Sets the key method data of an EC_KEY object, if none has yet been set.
846 * \param key EC_KEY object
847 * \param data opaque data to install.
848 * \param dup_func a function that duplicates |data|.
849 * \param free_func a function that frees |data|.
850 * \param clear_free_func a function that wipes and frees |data|.
851 * \return the previously set data pointer, or NULL if |data| was inserted.
853 void *EC_KEY_insert_key_method_data(EC_KEY *key, void *data,
854 void *(*dup_func) (void *),
855 void (*free_func) (void *),
856 void (*clear_free_func) (void *));
857 /* wrapper functions for the underlying EC_GROUP object */
858 void EC_KEY_set_asn1_flag(EC_KEY *eckey, int asn1_flag);
860 /** Creates a table of pre-computed multiples of the generator to
861 * accelerate further EC_KEY operations.
862 * \param key EC_KEY object
863 * \param ctx BN_CTX object (optional)
864 * \return 1 on success and 0 if an error occurred.
866 int EC_KEY_precompute_mult(EC_KEY *key, BN_CTX *ctx);
868 /** Creates a new ec private (and optional a new public) key.
869 * \param key EC_KEY object
870 * \return 1 on success and 0 if an error occurred.
872 int EC_KEY_generate_key(EC_KEY *key);
874 /** Verifies that a private and/or public key is valid.
875 * \param key the EC_KEY object
876 * \return 1 on success and 0 otherwise.
878 int EC_KEY_check_key(const EC_KEY *key);
880 /** Sets a public key from affine coordindates performing
881 * necessary NIST PKV tests.
882 * \param key the EC_KEY object
883 * \param x public key x coordinate
884 * \param y public key y coordinate
885 * \return 1 on success and 0 otherwise.
887 int EC_KEY_set_public_key_affine_coordinates(EC_KEY *key, BIGNUM *x,
890 /********************************************************************/
891 /* de- and encoding functions for SEC1 ECPrivateKey */
892 /********************************************************************/
894 /** Decodes a private key from a memory buffer.
895 * \param key a pointer to a EC_KEY object which should be used (or NULL)
896 * \param in pointer to memory with the DER encoded private key
897 * \param len length of the DER encoded private key
898 * \return the decoded private key or NULL if an error occurred.
900 EC_KEY *d2i_ECPrivateKey(EC_KEY **key, const unsigned char **in, long len);
902 /** Encodes a private key object and stores the result in a buffer.
903 * \param key the EC_KEY object to encode
904 * \param out the buffer for the result (if NULL the function returns number
906 * \return 1 on success and 0 if an error occurred.
908 int i2d_ECPrivateKey(EC_KEY *key, unsigned char **out);
910 /********************************************************************/
911 /* de- and encoding functions for EC parameters */
912 /********************************************************************/
914 /** Decodes ec parameter from a memory buffer.
915 * \param key a pointer to a EC_KEY object which should be used (or NULL)
916 * \param in pointer to memory with the DER encoded ec parameters
917 * \param len length of the DER encoded ec parameters
918 * \return a EC_KEY object with the decoded parameters or NULL if an error
921 EC_KEY *d2i_ECParameters(EC_KEY **key, const unsigned char **in, long len);
923 /** Encodes ec parameter and stores the result in a buffer.
924 * \param key the EC_KEY object with ec parameters to encode
925 * \param out the buffer for the result (if NULL the function returns number
927 * \return 1 on success and 0 if an error occurred.
929 int i2d_ECParameters(EC_KEY *key, unsigned char **out);
931 /********************************************************************/
932 /* de- and encoding functions for EC public key */
933 /* (octet string, not DER -- hence 'o2i' and 'i2o') */
934 /********************************************************************/
936 /** Decodes a ec public key from a octet string.
937 * \param key a pointer to a EC_KEY object which should be used
938 * \param in memory buffer with the encoded public key
939 * \param len length of the encoded public key
940 * \return EC_KEY object with decoded public key or NULL if an error
943 EC_KEY *o2i_ECPublicKey(EC_KEY **key, const unsigned char **in, long len);
945 /** Encodes a ec public key in an octet string.
946 * \param key the EC_KEY object with the public key
947 * \param out the buffer for the result (if NULL the function returns number
949 * \return 1 on success and 0 if an error occurred
951 int i2o_ECPublicKey(EC_KEY *key, unsigned char **out);
953 /** Prints out the ec parameters on human readable form.
954 * \param bp BIO object to which the information is printed
955 * \param key EC_KEY object
956 * \return 1 on success and 0 if an error occurred
958 int ECParameters_print(BIO *bp, const EC_KEY *key);
960 /** Prints out the contents of a EC_KEY object
961 * \param bp BIO object to which the information is printed
962 * \param key EC_KEY object
963 * \param off line offset
964 * \return 1 on success and 0 if an error occurred
966 int EC_KEY_print(BIO *bp, const EC_KEY *key, int off);
968 # ifndef OPENSSL_NO_STDIO
969 /** Prints out the ec parameters on human readable form.
970 * \param fp file descriptor to which the information is printed
971 * \param key EC_KEY object
972 * \return 1 on success and 0 if an error occurred
974 int ECParameters_print_fp(FILE *fp, const EC_KEY *key);
976 /** Prints out the contents of a EC_KEY object
977 * \param fp file descriptor to which the information is printed
978 * \param key EC_KEY object
979 * \param off line offset
980 * \return 1 on success and 0 if an error occurred
982 int EC_KEY_print_fp(FILE *fp, const EC_KEY *key, int off);
986 # define ECParameters_dup(x) ASN1_dup_of(EC_KEY,i2d_ECParameters,d2i_ECParameters,x)
989 # if defined(__SUNPRO_C)
990 # if __SUNPRO_C >= 0x520
991 # pragma error_messages (default,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE)
996 # define EVP_PKEY_CTX_set_ec_paramgen_curve_nid(ctx, nid) \
997 EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, \
998 EVP_PKEY_OP_PARAMGEN|EVP_PKEY_OP_KEYGEN, \
999 EVP_PKEY_CTRL_EC_PARAMGEN_CURVE_NID, nid, NULL)
1001 # define EVP_PKEY_CTX_set_ec_param_enc(ctx, flag) \
1002 EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, \
1003 EVP_PKEY_OP_PARAMGEN|EVP_PKEY_OP_KEYGEN, \
1004 EVP_PKEY_CTRL_EC_PARAM_ENC, flag, NULL)
1006 # define EVP_PKEY_CTX_set_ecdh_cofactor_mode(ctx, flag) \
1007 EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, \
1008 EVP_PKEY_OP_DERIVE, \
1009 EVP_PKEY_CTRL_EC_ECDH_COFACTOR, flag, NULL)
1011 # define EVP_PKEY_CTX_get_ecdh_cofactor_mode(ctx) \
1012 EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, \
1013 EVP_PKEY_OP_DERIVE, \
1014 EVP_PKEY_CTRL_EC_ECDH_COFACTOR, -2, NULL)
1016 # define EVP_PKEY_CTX_set_ecdh_kdf_type(ctx, kdf) \
1017 EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, \
1018 EVP_PKEY_OP_DERIVE, \
1019 EVP_PKEY_CTRL_EC_KDF_TYPE, kdf, NULL)
1021 # define EVP_PKEY_CTX_get_ecdh_kdf_type(ctx) \
1022 EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, \
1023 EVP_PKEY_OP_DERIVE, \
1024 EVP_PKEY_CTRL_EC_KDF_TYPE, -2, NULL)
1026 # define EVP_PKEY_CTX_set_ecdh_kdf_md(ctx, md) \
1027 EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, \
1028 EVP_PKEY_OP_DERIVE, \
1029 EVP_PKEY_CTRL_EC_KDF_MD, 0, (void *)md)
1031 # define EVP_PKEY_CTX_get_ecdh_kdf_md(ctx, pmd) \
1032 EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, \
1033 EVP_PKEY_OP_DERIVE, \
1034 EVP_PKEY_CTRL_GET_EC_KDF_MD, 0, (void *)pmd)
1036 # define EVP_PKEY_CTX_set_ecdh_kdf_outlen(ctx, len) \
1037 EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, \
1038 EVP_PKEY_OP_DERIVE, \
1039 EVP_PKEY_CTRL_EC_KDF_OUTLEN, len, NULL)
1041 # define EVP_PKEY_CTX_get_ecdh_kdf_outlen(ctx, plen) \
1042 EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, \
1043 EVP_PKEY_OP_DERIVE, \
1044 EVP_PKEY_CTRL_GET_EC_KDF_OUTLEN, 0, (void *)plen)
1046 # define EVP_PKEY_CTX_set0_ecdh_kdf_ukm(ctx, p, plen) \
1047 EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, \
1048 EVP_PKEY_OP_DERIVE, \
1049 EVP_PKEY_CTRL_EC_KDF_UKM, plen, (void *)p)
1051 # define EVP_PKEY_CTX_get0_ecdh_kdf_ukm(ctx, p) \
1052 EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, \
1053 EVP_PKEY_OP_DERIVE, \
1054 EVP_PKEY_CTRL_GET_EC_KDF_UKM, 0, (void *)p)
1056 # define EVP_PKEY_CTRL_EC_PARAMGEN_CURVE_NID (EVP_PKEY_ALG_CTRL + 1)
1057 # define EVP_PKEY_CTRL_EC_PARAM_ENC (EVP_PKEY_ALG_CTRL + 2)
1058 # define EVP_PKEY_CTRL_EC_ECDH_COFACTOR (EVP_PKEY_ALG_CTRL + 3)
1059 # define EVP_PKEY_CTRL_EC_KDF_TYPE (EVP_PKEY_ALG_CTRL + 4)
1060 # define EVP_PKEY_CTRL_EC_KDF_MD (EVP_PKEY_ALG_CTRL + 5)
1061 # define EVP_PKEY_CTRL_GET_EC_KDF_MD (EVP_PKEY_ALG_CTRL + 6)
1062 # define EVP_PKEY_CTRL_EC_KDF_OUTLEN (EVP_PKEY_ALG_CTRL + 7)
1063 # define EVP_PKEY_CTRL_GET_EC_KDF_OUTLEN (EVP_PKEY_ALG_CTRL + 8)
1064 # define EVP_PKEY_CTRL_EC_KDF_UKM (EVP_PKEY_ALG_CTRL + 9)
1065 # define EVP_PKEY_CTRL_GET_EC_KDF_UKM (EVP_PKEY_ALG_CTRL + 10)
1067 # define EVP_PKEY_ECDH_KDF_NONE 1
1068 # define EVP_PKEY_ECDH_KDF_X9_62 2
1070 /* BEGIN ERROR CODES */
1072 * The following lines are auto generated by the script mkerr.pl. Any changes
1073 * made after this point may be overwritten when the script is next run.
1075 void ERR_load_EC_strings(void);
1077 /* Error codes for the EC functions. */
1079 /* Function codes. */
1080 # define EC_F_BN_TO_FELEM 224
1081 # define EC_F_COMPUTE_WNAF 143
1082 # define EC_F_D2I_ECPARAMETERS 144
1083 # define EC_F_D2I_ECPKPARAMETERS 145
1084 # define EC_F_D2I_ECPRIVATEKEY 146
1085 # define EC_F_DO_EC_KEY_PRINT 221
1086 # define EC_F_ECDH_CMS_DECRYPT 238
1087 # define EC_F_ECDH_CMS_SET_SHARED_INFO 239
1088 # define EC_F_ECKEY_PARAM2TYPE 223
1089 # define EC_F_ECKEY_PARAM_DECODE 212
1090 # define EC_F_ECKEY_PRIV_DECODE 213
1091 # define EC_F_ECKEY_PRIV_ENCODE 214
1092 # define EC_F_ECKEY_PUB_DECODE 215
1093 # define EC_F_ECKEY_PUB_ENCODE 216
1094 # define EC_F_ECKEY_TYPE2PARAM 220
1095 # define EC_F_ECPARAMETERS_PRINT 147
1096 # define EC_F_ECPARAMETERS_PRINT_FP 148
1097 # define EC_F_ECPKPARAMETERS_PRINT 149
1098 # define EC_F_ECPKPARAMETERS_PRINT_FP 150
1099 # define EC_F_ECP_NIST_MOD_192 203
1100 # define EC_F_ECP_NIST_MOD_224 204
1101 # define EC_F_ECP_NIST_MOD_256 205
1102 # define EC_F_ECP_NIST_MOD_521 206
1103 # define EC_F_EC_ASN1_GROUP2CURVE 153
1104 # define EC_F_EC_ASN1_GROUP2FIELDID 154
1105 # define EC_F_EC_ASN1_GROUP2PARAMETERS 155
1106 # define EC_F_EC_ASN1_GROUP2PKPARAMETERS 156
1107 # define EC_F_EC_ASN1_PARAMETERS2GROUP 157
1108 # define EC_F_EC_ASN1_PKPARAMETERS2GROUP 158
1109 # define EC_F_EC_EX_DATA_SET_DATA 211
1110 # define EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY 208
1111 # define EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT 159
1112 # define EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE 195
1113 # define EC_F_EC_GF2M_SIMPLE_OCT2POINT 160
1114 # define EC_F_EC_GF2M_SIMPLE_POINT2OCT 161
1115 # define EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES 162
1116 # define EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES 163
1117 # define EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES 164
1118 # define EC_F_EC_GFP_MONT_FIELD_DECODE 133
1119 # define EC_F_EC_GFP_MONT_FIELD_ENCODE 134
1120 # define EC_F_EC_GFP_MONT_FIELD_MUL 131
1121 # define EC_F_EC_GFP_MONT_FIELD_SET_TO_ONE 209
1122 # define EC_F_EC_GFP_MONT_FIELD_SQR 132
1123 # define EC_F_EC_GFP_MONT_GROUP_SET_CURVE 189
1124 # define EC_F_EC_GFP_MONT_GROUP_SET_CURVE_GFP 135
1125 # define EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE 225
1126 # define EC_F_EC_GFP_NISTP224_POINTS_MUL 228
1127 # define EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES 226
1128 # define EC_F_EC_GFP_NISTP256_GROUP_SET_CURVE 230
1129 # define EC_F_EC_GFP_NISTP256_POINTS_MUL 231
1130 # define EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES 232
1131 # define EC_F_EC_GFP_NISTP521_GROUP_SET_CURVE 233
1132 # define EC_F_EC_GFP_NISTP521_POINTS_MUL 234
1133 # define EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES 235
1134 # define EC_F_EC_GFP_NIST_FIELD_MUL 200
1135 # define EC_F_EC_GFP_NIST_FIELD_SQR 201
1136 # define EC_F_EC_GFP_NIST_GROUP_SET_CURVE 202
1137 # define EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT 165
1138 # define EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE 166
1139 # define EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE_GFP 100
1140 # define EC_F_EC_GFP_SIMPLE_GROUP_SET_GENERATOR 101
1141 # define EC_F_EC_GFP_SIMPLE_MAKE_AFFINE 102
1142 # define EC_F_EC_GFP_SIMPLE_OCT2POINT 103
1143 # define EC_F_EC_GFP_SIMPLE_POINT2OCT 104
1144 # define EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE 137
1145 # define EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES 167
1146 # define EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES_GFP 105
1147 # define EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES 168
1148 # define EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES_GFP 128
1149 # define EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES 169
1150 # define EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP 129
1151 # define EC_F_EC_GROUP_CHECK 170
1152 # define EC_F_EC_GROUP_CHECK_DISCRIMINANT 171
1153 # define EC_F_EC_GROUP_COPY 106
1154 # define EC_F_EC_GROUP_GET0_GENERATOR 139
1155 # define EC_F_EC_GROUP_GET_COFACTOR 140
1156 # define EC_F_EC_GROUP_GET_CURVE_GF2M 172
1157 # define EC_F_EC_GROUP_GET_CURVE_GFP 130
1158 # define EC_F_EC_GROUP_GET_DEGREE 173
1159 # define EC_F_EC_GROUP_GET_ORDER 141
1160 # define EC_F_EC_GROUP_GET_PENTANOMIAL_BASIS 193
1161 # define EC_F_EC_GROUP_GET_TRINOMIAL_BASIS 194
1162 # define EC_F_EC_GROUP_NEW 108
1163 # define EC_F_EC_GROUP_NEW_BY_CURVE_NAME 174
1164 # define EC_F_EC_GROUP_NEW_FROM_DATA 175
1165 # define EC_F_EC_GROUP_PRECOMPUTE_MULT 142
1166 # define EC_F_EC_GROUP_SET_CURVE_GF2M 176
1167 # define EC_F_EC_GROUP_SET_CURVE_GFP 109
1168 # define EC_F_EC_GROUP_SET_EXTRA_DATA 110
1169 # define EC_F_EC_GROUP_SET_GENERATOR 111
1170 # define EC_F_EC_KEY_CHECK_KEY 177
1171 # define EC_F_EC_KEY_COPY 178
1172 # define EC_F_EC_KEY_GENERATE_KEY 179
1173 # define EC_F_EC_KEY_NEW 182
1174 # define EC_F_EC_KEY_PRINT 180
1175 # define EC_F_EC_KEY_PRINT_FP 181
1176 # define EC_F_EC_KEY_SET_PUBLIC_KEY_AFFINE_COORDINATES 229
1177 # define EC_F_EC_POINTS_MAKE_AFFINE 136
1178 # define EC_F_EC_POINT_ADD 112
1179 # define EC_F_EC_POINT_CMP 113
1180 # define EC_F_EC_POINT_COPY 114
1181 # define EC_F_EC_POINT_DBL 115
1182 # define EC_F_EC_POINT_GET_AFFINE_COORDINATES_GF2M 183
1183 # define EC_F_EC_POINT_GET_AFFINE_COORDINATES_GFP 116
1184 # define EC_F_EC_POINT_GET_JPROJECTIVE_COORDINATES_GFP 117
1185 # define EC_F_EC_POINT_INVERT 210
1186 # define EC_F_EC_POINT_IS_AT_INFINITY 118
1187 # define EC_F_EC_POINT_IS_ON_CURVE 119
1188 # define EC_F_EC_POINT_MAKE_AFFINE 120
1189 # define EC_F_EC_POINT_MUL 184
1190 # define EC_F_EC_POINT_NEW 121
1191 # define EC_F_EC_POINT_OCT2POINT 122
1192 # define EC_F_EC_POINT_POINT2OCT 123
1193 # define EC_F_EC_POINT_SET_AFFINE_COORDINATES_GF2M 185
1194 # define EC_F_EC_POINT_SET_AFFINE_COORDINATES_GFP 124
1195 # define EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GF2M 186
1196 # define EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GFP 125
1197 # define EC_F_EC_POINT_SET_JPROJECTIVE_COORDINATES_GFP 126
1198 # define EC_F_EC_POINT_SET_TO_INFINITY 127
1199 # define EC_F_EC_PRE_COMP_DUP 207
1200 # define EC_F_EC_PRE_COMP_NEW 196
1201 # define EC_F_EC_WNAF_MUL 187
1202 # define EC_F_EC_WNAF_PRECOMPUTE_MULT 188
1203 # define EC_F_I2D_ECPARAMETERS 190
1204 # define EC_F_I2D_ECPKPARAMETERS 191
1205 # define EC_F_I2D_ECPRIVATEKEY 192
1206 # define EC_F_I2O_ECPUBLICKEY 151
1207 # define EC_F_NISTP224_PRE_COMP_NEW 227
1208 # define EC_F_NISTP256_PRE_COMP_NEW 236
1209 # define EC_F_NISTP521_PRE_COMP_NEW 237
1210 # define EC_F_ECP_NISTZ256_GET_AFFINE 240
1211 # define EC_F_ECP_NISTZ256_POINTS_MUL 241
1212 # define EC_F_ECP_NISTZ256_WINDOWED_MUL 242
1213 # define EC_F_ECP_NISTZ256_MULT_PRECOMPUTE 243
1214 # define EC_F_ECP_NISTZ256_PRE_COMP_NEW 244
1215 # define EC_F_O2I_ECPUBLICKEY 152
1216 # define EC_F_OLD_EC_PRIV_DECODE 222
1217 # define EC_F_PKEY_EC_CTRL 197
1218 # define EC_F_PKEY_EC_CTRL_STR 198
1219 # define EC_F_PKEY_EC_DERIVE 217
1220 # define EC_F_PKEY_EC_KEYGEN 199
1221 # define EC_F_PKEY_EC_PARAMGEN 219
1222 # define EC_F_PKEY_EC_SIGN 218
1225 # define EC_R_ASN1_ERROR 115
1226 # define EC_R_ASN1_UNKNOWN_FIELD 116
1227 # define EC_R_BIGNUM_OUT_OF_RANGE 144
1228 # define EC_R_BUFFER_TOO_SMALL 100
1229 # define EC_R_COORDINATES_OUT_OF_RANGE 146
1230 # define EC_R_D2I_ECPKPARAMETERS_FAILURE 117
1231 # define EC_R_DECODE_ERROR 142
1232 # define EC_R_DISCRIMINANT_IS_ZERO 118
1233 # define EC_R_EC_GROUP_NEW_BY_NAME_FAILURE 119
1234 # define EC_R_FIELD_TOO_LARGE 143
1235 # define EC_R_GF2M_NOT_SUPPORTED 147
1236 # define EC_R_GROUP2PKPARAMETERS_FAILURE 120
1237 # define EC_R_I2D_ECPKPARAMETERS_FAILURE 121
1238 # define EC_R_INCOMPATIBLE_OBJECTS 101
1239 # define EC_R_INVALID_ARGUMENT 112
1240 # define EC_R_INVALID_COMPRESSED_POINT 110
1241 # define EC_R_INVALID_COMPRESSION_BIT 109
1242 # define EC_R_INVALID_CURVE 141
1243 # define EC_R_INVALID_DIGEST 151
1244 # define EC_R_INVALID_DIGEST_TYPE 138
1245 # define EC_R_INVALID_ENCODING 102
1246 # define EC_R_INVALID_FIELD 103
1247 # define EC_R_INVALID_FORM 104
1248 # define EC_R_INVALID_GROUP_ORDER 122
1249 # define EC_R_INVALID_PENTANOMIAL_BASIS 132
1250 # define EC_R_INVALID_PRIVATE_KEY 123
1251 # define EC_R_INVALID_TRINOMIAL_BASIS 137
1252 # define EC_R_KDF_PARAMETER_ERROR 148
1253 # define EC_R_KEYS_NOT_SET 140
1254 # define EC_R_MISSING_PARAMETERS 124
1255 # define EC_R_MISSING_PRIVATE_KEY 125
1256 # define EC_R_NOT_A_NIST_PRIME 135
1257 # define EC_R_NOT_A_SUPPORTED_NIST_PRIME 136
1258 # define EC_R_NOT_IMPLEMENTED 126
1259 # define EC_R_NOT_INITIALIZED 111
1260 # define EC_R_NO_FIELD_MOD 133
1261 # define EC_R_NO_PARAMETERS_SET 139
1262 # define EC_R_PASSED_NULL_PARAMETER 134
1263 # define EC_R_PEER_KEY_ERROR 149
1264 # define EC_R_PKPARAMETERS2GROUP_FAILURE 127
1265 # define EC_R_POINT_AT_INFINITY 106
1266 # define EC_R_POINT_IS_NOT_ON_CURVE 107
1267 # define EC_R_SHARED_INFO_ERROR 150
1268 # define EC_R_SLOT_FULL 108
1269 # define EC_R_UNDEFINED_GENERATOR 113
1270 # define EC_R_UNDEFINED_ORDER 128
1271 # define EC_R_UNKNOWN_GROUP 129
1272 # define EC_R_UNKNOWN_ORDER 114
1273 # define EC_R_UNSUPPORTED_FIELD 131
1274 # define EC_R_WRONG_CURVE_PARAMETERS 145
1275 # define EC_R_WRONG_ORDER 130