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 #ifndef OPENSSL_NO_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)
100 #ifndef OPENSSL_ECC_MAX_FIELD_BITS
101 # define OPENSSL_ECC_MAX_FIELD_BITS 661
104 /** Enum for the point conversion form as defined in X9.62 (ECDSA)
105 * for the encoding of a elliptic curve point (x,y) */
107 /** the point is encoded as z||x, where the octet z specifies
108 * which solution of the quadratic equation y is */
109 POINT_CONVERSION_COMPRESSED = 2,
110 /** the point is encoded as z||x||y, where z is the octet 0x02 */
111 POINT_CONVERSION_UNCOMPRESSED = 4,
112 /** the point is encoded as z||x||y, where the octet z specifies
113 * which solution of the quadratic equation y is */
114 POINT_CONVERSION_HYBRID = 6
115 } point_conversion_form_t;
118 typedef struct ec_method_st EC_METHOD;
120 typedef struct ec_group_st
124 -- curve coefficients
125 -- optional generator with associated information (order, cofactor)
126 -- optional extra data (precomputed table for fast computation of multiples of generator)
131 typedef struct ec_point_st EC_POINT;
134 /********************************************************************/
135 /* EC_METHODs for curves over GF(p) */
136 /********************************************************************/
138 /** Returns the basic GFp ec methods which provides the basis for the
140 * \return EC_METHOD object
142 const EC_METHOD *EC_GFp_simple_method(void);
144 /** Returns GFp methods using montgomery multiplication.
145 * \return EC_METHOD object
147 const EC_METHOD *EC_GFp_mont_method(void);
149 /** Returns GFp methods using optimized methods for NIST recommended curves
150 * \return EC_METHOD object
152 const EC_METHOD *EC_GFp_nist_method(void);
154 #ifdef EC_NISTP224_64_GCC_128
155 /** Returns 64-bit optimized methods for nistp224
156 * \return EC_METHOD object
158 const EC_METHOD *EC_GFp_nistp224_method(void);
161 /********************************************************************/
162 /* EC_METHOD for curves over GF(2^m) */
163 /********************************************************************/
165 /** Returns the basic GF2m ec method
166 * \return EC_METHOD object
168 const EC_METHOD *EC_GF2m_simple_method(void);
171 /********************************************************************/
172 /* EC_GROUP functions */
173 /********************************************************************/
175 /** Creates a new EC_GROUP object
176 * \param meth EC_METHOD to use
177 * \return newly created EC_GROUP object or NULL in case of an error.
179 EC_GROUP *EC_GROUP_new(const EC_METHOD *meth);
181 /** Frees a EC_GROUP object
182 * \param group EC_GROUP object to be freed.
184 void EC_GROUP_free(EC_GROUP *group);
186 /** Clears and frees a EC_GROUP object
187 * \param group EC_GROUP object to be cleared and freed.
189 void EC_GROUP_clear_free(EC_GROUP *group);
191 /** Copies EC_GROUP objects. Note: both EC_GROUPs must use the same EC_METHOD.
192 * \param dst destination EC_GROUP object
193 * \param src source EC_GROUP object
194 * \return 1 on success and 0 if an error occurred.
196 int EC_GROUP_copy(EC_GROUP *dst, const EC_GROUP *src);
198 /** Creates a new EC_GROUP object and copies the copies the content
199 * form src to the newly created EC_KEY object
200 * \param src source EC_GROUP object
201 * \return newly created EC_GROUP object or NULL in case of an error.
203 EC_GROUP *EC_GROUP_dup(const EC_GROUP *src);
205 /** Returns the EC_METHOD of the EC_GROUP object.
206 * \param group EC_GROUP object
207 * \return EC_METHOD used in this EC_GROUP object.
209 const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group);
211 /** Returns the field type of the EC_METHOD.
212 * \param meth EC_METHOD object
213 * \return NID of the underlying field type OID.
215 int EC_METHOD_get_field_type(const EC_METHOD *meth);
217 /** Sets the generator and it's order/cofactor of a EC_GROUP object.
218 * \param group EC_GROUP object
219 * \param generator EC_POINT object with the generator.
220 * \param order the order of the group generated by the generator.
221 * \param cofactor the index of the sub-group generated by the generator
222 * in the group of all points on the elliptic curve.
223 * \return 1 on success and 0 if an error occured
225 int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator, const BIGNUM *order, const BIGNUM *cofactor);
227 /** Returns the generator of a EC_GROUP object.
228 * \param group EC_GROUP object
229 * \return the currently used generator (possibly NULL).
231 const EC_POINT *EC_GROUP_get0_generator(const EC_GROUP *group);
233 /** Gets the order of a EC_GROUP
234 * \param group EC_GROUP object
235 * \param order BIGNUM to which the order is copied
236 * \param ctx BN_CTX object (optional)
237 * \return 1 on success and 0 if an error occured
239 int EC_GROUP_get_order(const EC_GROUP *group, BIGNUM *order, BN_CTX *ctx);
241 /** Gets the cofactor of a EC_GROUP
242 * \param group EC_GROUP object
243 * \param cofactor BIGNUM to which the cofactor is copied
244 * \param ctx BN_CTX object (optional)
245 * \return 1 on success and 0 if an error occured
247 int EC_GROUP_get_cofactor(const EC_GROUP *group, BIGNUM *cofactor, BN_CTX *ctx);
249 /** Sets the name of a EC_GROUP object
250 * \param group EC_GROUP object
251 * \param nid NID of the curve name OID
253 void EC_GROUP_set_curve_name(EC_GROUP *group, int nid);
255 /** Returns the curve name of a EC_GROUP object
256 * \param group EC_GROUP object
257 * \return NID of the curve name OID or 0 if not set.
259 int EC_GROUP_get_curve_name(const EC_GROUP *group);
261 void EC_GROUP_set_asn1_flag(EC_GROUP *group, int flag);
262 int EC_GROUP_get_asn1_flag(const EC_GROUP *group);
264 void EC_GROUP_set_point_conversion_form(EC_GROUP *, point_conversion_form_t);
265 point_conversion_form_t EC_GROUP_get_point_conversion_form(const EC_GROUP *);
267 unsigned char *EC_GROUP_get0_seed(const EC_GROUP *);
268 size_t EC_GROUP_get_seed_len(const EC_GROUP *);
269 size_t EC_GROUP_set_seed(EC_GROUP *, const unsigned char *, size_t len);
271 /** Sets the parameter of a ec over GFp defined by y^2 = x^3 + a*x + b
272 * \param group EC_GROUP object
273 * \param p BIGNUM with the prime number
274 * \param a BIGNUM with parameter a of the equation
275 * \param b BIGNUM with parameter b of the equation
276 * \param ctx BN_CTX object (optional)
277 * \return 1 on success and 0 if an error occured
279 int EC_GROUP_set_curve_GFp(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
281 /** Gets the parameter of the ec over GFp defined by y^2 = x^3 + a*x + b
282 * \param group EC_GROUP object
283 * \param p BIGNUM for the prime number
284 * \param a BIGNUM for parameter a of the equation
285 * \param b BIGNUM for parameter b of the equation
286 * \param ctx BN_CTX object (optional)
287 * \return 1 on success and 0 if an error occured
289 int EC_GROUP_get_curve_GFp(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
291 /** Sets the parameter of a ec over GF2m defined by y^2 + x*y = x^3 + a*x^2 + b
292 * \param group EC_GROUP object
293 * \param p BIGNUM with the polynomial defining the underlying field
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 occured
299 int EC_GROUP_set_curve_GF2m(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
301 /** Gets the parameter of the ec over GF2m defined by y^2 + x*y = x^3 + a*x^2 + b
302 * \param group EC_GROUP object
303 * \param p BIGNUM for the polynomial defining the underlying field
304 * \param a BIGNUM for parameter a of the equation
305 * \param b BIGNUM for parameter b of the equation
306 * \param ctx BN_CTX object (optional)
307 * \return 1 on success and 0 if an error occured
309 int EC_GROUP_get_curve_GF2m(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
311 /** Returns the number of bits needed to represent a field element
312 * \param group EC_GROUP object
313 * \return number of bits needed to represent a field element
315 int EC_GROUP_get_degree(const EC_GROUP *group);
317 /** Checks whether the parameter in the EC_GROUP define a valid ec group
318 * \param group EC_GROUP object
319 * \param ctx BN_CTX object (optional)
320 * \return 1 if group is a valid ec group and 0 otherwise
322 int EC_GROUP_check(const EC_GROUP *group, BN_CTX *ctx);
324 /** Checks whether the discriminant of the elliptic curve is zero or not
325 * \param group EC_GROUP object
326 * \param ctx BN_CTX object (optional)
327 * \return 1 if the discriminant is not zero and 0 otherwise
329 int EC_GROUP_check_discriminant(const EC_GROUP *group, BN_CTX *ctx);
331 /** Compares two EC_GROUP objects
332 * \param a first EC_GROUP object
333 * \param b second EC_GROUP object
334 * \param ctx BN_CTX object (optional)
335 * \return 0 if both groups are equal and 1 otherwise
337 int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx);
339 /* EC_GROUP_new_GF*() calls EC_GROUP_new() and EC_GROUP_set_GF*()
340 * after choosing an appropriate EC_METHOD */
342 /** Creates a new EC_GROUP object with the specified parameters defined
343 * over GFp (defined by the equation y^2 = x^3 + a*x + b)
344 * \param p BIGNUM with the prime number
345 * \param a BIGNUM with the parameter a of the equation
346 * \param b BIGNUM with the parameter b of the equation
347 * \param ctx BN_CTX object (optional)
348 * \return newly created EC_GROUP object with the specified parameters
350 EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
352 /** Creates a new EC_GROUP object with the specified parameters defined
353 * over GF2m (defined by the equation y^2 + x*y = x^3 + a*x^2 + b)
354 * \param p BIGNUM with the polynomial defining the underlying field
355 * \param a BIGNUM with the parameter a of the equation
356 * \param b BIGNUM with the parameter b of the equation
357 * \param ctx BN_CTX object (optional)
358 * \return newly created EC_GROUP object with the specified parameters
360 EC_GROUP *EC_GROUP_new_curve_GF2m(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
362 /** Creates a EC_GROUP object with a curve specified by a NID
363 * \param nid NID of the OID of the curve name
364 * \return newly created EC_GROUP object with specified curve or NULL
365 * if an error occurred
367 EC_GROUP *EC_GROUP_new_by_curve_name(int nid);
370 /********************************************************************/
371 /* handling of internal curves */
372 /********************************************************************/
379 /* EC_builtin_curves(EC_builtin_curve *r, size_t size) returns number
380 * of all available curves or zero if a error occurred.
381 * In case r ist not zero nitems EC_builtin_curve structures
382 * are filled with the data of the first nitems internal groups */
383 size_t EC_get_builtin_curves(EC_builtin_curve *r, size_t nitems);
386 /********************************************************************/
387 /* EC_POINT functions */
388 /********************************************************************/
390 /** Creates a new EC_POINT object for the specified EC_GROUP
391 * \param group EC_GROUP the underlying EC_GROUP object
392 * \return newly created EC_POINT object or NULL if an error occurred
394 EC_POINT *EC_POINT_new(const EC_GROUP *group);
396 /** Frees a EC_POINT object
397 * \param point EC_POINT object to be freed
399 void EC_POINT_free(EC_POINT *point);
401 /** Clears and frees a EC_POINT object
402 * \param point EC_POINT object to be cleared and freed
404 void EC_POINT_clear_free(EC_POINT *point);
406 /** Copies EC_POINT object
407 * \param dst destination EC_POINT object
408 * \param src source EC_POINT object
409 * \return 1 on success and 0 if an error occured
411 int EC_POINT_copy(EC_POINT *dst, const EC_POINT *src);
413 /** Creates a new EC_POINT object and copies the content of the supplied
415 * \param src source EC_POINT object
416 * \param group underlying the EC_GROUP object
417 * \return newly created EC_POINT object or NULL if an error occurred
419 EC_POINT *EC_POINT_dup(const EC_POINT *src, const EC_GROUP *group);
421 /** Returns the EC_METHOD used in EC_POINT object
422 * \param point EC_POINT object
423 * \return the EC_METHOD used
425 const EC_METHOD *EC_POINT_method_of(const EC_POINT *point);
427 /** Sets a point to infinity (neutral element)
428 * \param group underlying EC_GROUP object
429 * \param point EC_POINT to set to infinity
430 * \return 1 on success and 0 if an error occured
432 int EC_POINT_set_to_infinity(const EC_GROUP *group, EC_POINT *point);
434 /** Sets the jacobian projective coordinates of a EC_POINT over GFp
435 * \param group underlying EC_GROUP object
436 * \param p EC_POINT object
437 * \param x BIGNUM with the x-coordinate
438 * \param y BIGNUM with the y-coordinate
439 * \param z BIGNUM with the z-coordinate
440 * \param ctx BN_CTX object (optional)
441 * \return 1 on success and 0 if an error occured
443 int EC_POINT_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *p,
444 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx);
446 /** Gets the jacobian projective coordinates of a EC_POINT over GFp
447 * \param group underlying EC_GROUP object
448 * \param p EC_POINT object
449 * \param x BIGNUM for the x-coordinate
450 * \param y BIGNUM for the y-coordinate
451 * \param z BIGNUM for the z-coordinate
452 * \param ctx BN_CTX object (optional)
453 * \return 1 on success and 0 if an error occured
455 int EC_POINT_get_Jprojective_coordinates_GFp(const EC_GROUP *group,
456 const EC_POINT *p, BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx);
458 /** Sets the affine coordinates of a EC_POINT over GFp
459 * \param group underlying EC_GROUP object
460 * \param p EC_POINT object
461 * \param x BIGNUM with the x-coordinate
462 * \param y BIGNUM with the y-coordinate
463 * \param ctx BN_CTX object (optional)
464 * \return 1 on success and 0 if an error occured
466 int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *p,
467 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx);
469 /** Gets the affine coordinates of a EC_POINT over GFp
470 * \param group underlying EC_GROUP object
471 * \param p EC_POINT object
472 * \param x BIGNUM for the x-coordinate
473 * \param y BIGNUM for the y-coordinate
474 * \param ctx BN_CTX object (optional)
475 * \return 1 on success and 0 if an error occured
477 int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group,
478 const EC_POINT *p, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
480 /** Sets the x9.62 compressed coordinates of a EC_POINT over GFp
481 * \param group underlying EC_GROUP object
482 * \param p EC_POINT object
483 * \param x BIGNUM with x-coordinate
484 * \param y_bit integer with the y-Bit (either 0 or 1)
485 * \param ctx BN_CTX object (optional)
486 * \return 1 on success and 0 if an error occured
488 int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *group, EC_POINT *p,
489 const BIGNUM *x, int y_bit, BN_CTX *ctx);
491 /** Sets the affine coordinates of a EC_POINT over GF2m
492 * \param group underlying EC_GROUP object
493 * \param p EC_POINT object
494 * \param x BIGNUM with the x-coordinate
495 * \param y BIGNUM with the y-coordinate
496 * \param ctx BN_CTX object (optional)
497 * \return 1 on success and 0 if an error occured
499 int EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP *group, EC_POINT *p,
500 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx);
502 /** Gets the affine coordinates of a EC_POINT over GF2m
503 * \param group underlying EC_GROUP object
504 * \param p EC_POINT object
505 * \param x BIGNUM for the x-coordinate
506 * \param y BIGNUM for the y-coordinate
507 * \param ctx BN_CTX object (optional)
508 * \return 1 on success and 0 if an error occured
510 int EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *group,
511 const EC_POINT *p, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
513 /** Sets the x9.62 compressed coordinates of a EC_POINT over GF2m
514 * \param group underlying EC_GROUP object
515 * \param p EC_POINT object
516 * \param x BIGNUM with x-coordinate
517 * \param y_bit integer with the y-Bit (either 0 or 1)
518 * \param ctx BN_CTX object (optional)
519 * \return 1 on success and 0 if an error occured
521 int EC_POINT_set_compressed_coordinates_GF2m(const EC_GROUP *group, EC_POINT *p,
522 const BIGNUM *x, int y_bit, BN_CTX *ctx);
524 /** Encodes a EC_POINT object to a octet string
525 * \param group underlying EC_GROUP object
526 * \param p EC_POINT object
527 * \param form point conversion form
528 * \param buf memory buffer for the result. If NULL the function returns
529 * required buffer size.
530 * \param len length of the memory buffer
531 * \param ctx BN_CTX object (optional)
532 * \return the length of the encoded octet string or 0 if an error occurred
534 size_t EC_POINT_point2oct(const EC_GROUP *group, const EC_POINT *p,
535 point_conversion_form_t form,
536 unsigned char *buf, size_t len, BN_CTX *ctx);
538 /** Decodes a EC_POINT from a octet string
539 * \param group underlying EC_GROUP object
540 * \param p EC_POINT object
541 * \param buf memory buffer with the encoded ec point
542 * \param len length of the encoded ec point
543 * \param ctx BN_CTX object (optional)
544 * \return 1 on success and 0 if an error occured
546 int EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *p,
547 const unsigned char *buf, size_t len, BN_CTX *ctx);
549 /* other interfaces to point2oct/oct2point: */
550 BIGNUM *EC_POINT_point2bn(const EC_GROUP *, const EC_POINT *,
551 point_conversion_form_t form, BIGNUM *, BN_CTX *);
552 EC_POINT *EC_POINT_bn2point(const EC_GROUP *, const BIGNUM *,
553 EC_POINT *, BN_CTX *);
554 char *EC_POINT_point2hex(const EC_GROUP *, const EC_POINT *,
555 point_conversion_form_t form, BN_CTX *);
556 EC_POINT *EC_POINT_hex2point(const EC_GROUP *, const char *,
557 EC_POINT *, BN_CTX *);
560 /********************************************************************/
561 /* functions for doing EC_POINT arithmetic */
562 /********************************************************************/
564 /** Computes the sum of two EC_POINT
565 * \param group underlying EC_GROUP object
566 * \param r EC_POINT object for the result (r = a + b)
567 * \param a EC_POINT object with the first summand
568 * \param b EC_POINT object with the second summand
569 * \param ctx BN_CTX object (optional)
570 * \return 1 on success and 0 if an error occured
572 int EC_POINT_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx);
574 /** Computes the double of a EC_POINT
575 * \param group underlying EC_GROUP object
576 * \param r EC_POINT object for the result (r = 2 * a)
577 * \param a EC_POINT object
578 * \param ctx BN_CTX object (optional)
579 * \return 1 on success and 0 if an error occured
581 int EC_POINT_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx);
583 /** Computes the inverse of a EC_POINT
584 * \param group underlying EC_GROUP object
585 * \param a EC_POINT object to be inverted (it's used for the result as well)
586 * \param ctx BN_CTX object (optional)
587 * \return 1 on success and 0 if an error occured
589 int EC_POINT_invert(const EC_GROUP *group, EC_POINT *a, BN_CTX *ctx);
591 /** Checks whether the point is the neutral element of the group
592 * \param group the underlying EC_GROUP object
593 * \param p EC_POINT object
594 * \return 1 if the point is the neutral element and 0 otherwise
596 int EC_POINT_is_at_infinity(const EC_GROUP *group, const EC_POINT *p);
598 /** Checks whether the point is on the curve
599 * \param group underlying EC_GROUP object
600 * \param point EC_POINT object to check
601 * \param ctx BN_CTX object (optional)
602 * \return 1 if point if on the curve and 0 otherwise
604 int EC_POINT_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx);
606 /** Compares two EC_POINTs
607 * \param group underlying EC_GROUP object
608 * \param a first EC_POINT object
609 * \param b second EC_POINT object
610 * \param ctx BN_CTX object (optional)
611 * \return 0 if both points are equal and a value != 0 otherwise
613 int EC_POINT_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx);
615 int EC_POINT_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
616 int EC_POINTs_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
618 /** Computes r = generator * n sum_{i=0}^num p[i] * m[i]
619 * \param group underlying EC_GROUP object
620 * \param r EC_POINT object for the result
621 * \param n BIGNUM with the multiplier for the group generator (optional)
622 * \param num number futher summands
623 * \param p array of size num of EC_POINT objects
624 * \param m array of size num of BIGNUM objects
625 * \param ctx BN_CTX object (optional)
626 * \return 1 on success and 0 if an error occured
628 int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *n, size_t num, const EC_POINT *p[], const BIGNUM *m[], BN_CTX *ctx);
630 /** Computes r = generator * n + q * m
631 * \param group underlying EC_GROUP object
632 * \param r EC_POINT object for the result
633 * \param n BIGNUM with the multiplier for the group generator (optional)
634 * \param q EC_POINT object with the first factor of the second summand
635 * \param m BIGNUM with the second factor of the second summand
636 * \param ctx BN_CTX object (optional)
637 * \return 1 on success and 0 if an error occured
639 int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *n, const EC_POINT *q, const BIGNUM *m, BN_CTX *ctx);
641 /** Stores multiples of generator for faster point multiplication
642 * \param group EC_GROUP object
643 * \param ctx BN_CTX object (optional)
644 * \return 1 on success and 0 if an error occured
646 int EC_GROUP_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
648 /** Reports whether a precomputation has been done
649 * \param group EC_GROUP object
650 * \return 1 if a pre-computation has been done and 0 otherwise
652 int EC_GROUP_have_precompute_mult(const EC_GROUP *group);
655 /********************************************************************/
657 /********************************************************************/
659 /* EC_GROUP_get_basis_type() returns the NID of the basis type
660 * used to represent the field elements */
661 int EC_GROUP_get_basis_type(const EC_GROUP *);
662 int EC_GROUP_get_trinomial_basis(const EC_GROUP *, unsigned int *k);
663 int EC_GROUP_get_pentanomial_basis(const EC_GROUP *, unsigned int *k1,
664 unsigned int *k2, unsigned int *k3);
666 #define OPENSSL_EC_NAMED_CURVE 0x001
668 typedef struct ecpk_parameters_st ECPKPARAMETERS;
670 EC_GROUP *d2i_ECPKParameters(EC_GROUP **, const unsigned char **in, long len);
671 int i2d_ECPKParameters(const EC_GROUP *, unsigned char **out);
673 #define d2i_ECPKParameters_bio(bp,x) ASN1_d2i_bio_of(EC_GROUP,NULL,d2i_ECPKParameters,bp,x)
674 #define i2d_ECPKParameters_bio(bp,x) ASN1_i2d_bio_of_const(EC_GROUP,i2d_ECPKParameters,bp,x)
675 #define d2i_ECPKParameters_fp(fp,x) (EC_GROUP *)ASN1_d2i_fp(NULL, \
676 (char *(*)())d2i_ECPKParameters,(fp),(unsigned char **)(x))
677 #define i2d_ECPKParameters_fp(fp,x) ASN1_i2d_fp(i2d_ECPKParameters,(fp), \
678 (unsigned char *)(x))
680 #ifndef OPENSSL_NO_BIO
681 int ECPKParameters_print(BIO *bp, const EC_GROUP *x, int off);
683 #ifndef OPENSSL_NO_FP_API
684 int ECPKParameters_print_fp(FILE *fp, const EC_GROUP *x, int off);
688 /********************************************************************/
689 /* EC_KEY functions */
690 /********************************************************************/
692 typedef struct ec_key_st EC_KEY;
694 /* some values for the encoding_flag */
695 #define EC_PKEY_NO_PARAMETERS 0x001
696 #define EC_PKEY_NO_PUBKEY 0x002
698 /** Creates a new EC_KEY object.
699 * \return EC_KEY object or NULL if an error occurred.
701 EC_KEY *EC_KEY_new(void);
703 /** Creates a new EC_KEY object using a named curve as underlying
705 * \param nid NID of the named curve.
706 * \return EC_KEY object or NULL if an error occurred.
708 EC_KEY *EC_KEY_new_by_curve_name(int nid);
710 /** Frees a EC_KEY object.
711 * \param key EC_KEY object to be freed.
713 void EC_KEY_free(EC_KEY *key);
715 /** Copies a EC_KEY object.
716 * \param dst destination EC_KEY object
717 * \param src src EC_KEY object
718 * \return dst or NULL if an error occurred.
720 EC_KEY *EC_KEY_copy(EC_KEY *dst, const EC_KEY *src);
722 /** Creates a new EC_KEY object and copies the content from src to it.
723 * \param src the source EC_KEY object
724 * \return newly created EC_KEY object or NULL if an error occurred.
726 EC_KEY *EC_KEY_dup(const EC_KEY *src);
728 /** Increases the internal reference count of a EC_KEY object.
729 * \param key EC_KEY object
730 * \return 1 on success and 0 if an error occurred.
732 int EC_KEY_up_ref(EC_KEY *key);
734 /** Returns the EC_GROUP object of a EC_KEY object
735 * \param key EC_KEY object
736 * \return the EC_GROUP object (possibly NULL).
738 const EC_GROUP *EC_KEY_get0_group(const EC_KEY *key);
740 /** Sets the EC_GROUP of a EC_KEY object.
741 * \param key EC_KEY object
742 * \param group EC_GROUP to use in the EC_KEY object (note: the EC_KEY
743 * object will use an own copy of the EC_GROUP).
744 * \return 1 on success and 0 if an error occurred.
746 int EC_KEY_set_group(EC_KEY *key, const EC_GROUP *group);
748 /** Returns the private key of a EC_KEY object.
749 * \param key EC_KEY object
750 * \return a BIGNUM with the private key (possibly NULL).
752 const BIGNUM *EC_KEY_get0_private_key(const EC_KEY *key);
754 /** Sets the private key of a EC_KEY object.
755 * \param key EC_KEY object
756 * \param prv BIGNUM with the private key (note: the EC_KEY object
757 * will use an own copy of the BIGNUM).
758 * \return 1 on success and 0 if an error occurred.
760 int EC_KEY_set_private_key(EC_KEY *key, const BIGNUM *prv);
762 /** Returns the public key of a EC_KEY object.
763 * \param key the EC_KEY object
764 * \return a EC_POINT object with the public key (possibly NULL)
766 const EC_POINT *EC_KEY_get0_public_key(const EC_KEY *key);
768 /** Sets the public key of a EC_KEY object.
769 * \param key EC_KEY object
770 * \param pub EC_POINT object with the public key (note: the EC_KEY object
771 * will use an own copy of the EC_POINT object).
772 * \return 1 on success and 0 if an error occurred.
774 int EC_KEY_set_public_key(EC_KEY *key, const EC_POINT *pub);
776 unsigned EC_KEY_get_enc_flags(const EC_KEY *key);
777 void EC_KEY_set_enc_flags(EC_KEY *, unsigned int);
778 point_conversion_form_t EC_KEY_get_conv_form(const EC_KEY *);
779 void EC_KEY_set_conv_form(EC_KEY *, point_conversion_form_t);
780 /* functions to set/get method specific data */
781 void *EC_KEY_get_key_method_data(EC_KEY *,
782 void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
783 void EC_KEY_insert_key_method_data(EC_KEY *, void *data,
784 void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
785 /* wrapper functions for the underlying EC_GROUP object */
786 void EC_KEY_set_asn1_flag(EC_KEY *, int);
788 /** Creates a table of pre-computed multiples of the generator to
789 * accelerate further EC_KEY operations.
790 * \param key EC_KEY object
791 * \param ctx BN_CTX object (optional)
792 * \return 1 on success and 0 if an error occurred.
794 int EC_KEY_precompute_mult(EC_KEY *key, BN_CTX *ctx);
796 /** Creates a new ec private (and optional a new public) key.
797 * \param key EC_KEY object
798 * \return 1 on success and 0 if an error occurred.
800 int EC_KEY_generate_key(EC_KEY *key);
802 /** Verifies that a private and/or public key is valid.
803 * \param key the EC_KEY object
804 * \return 1 on success and 0 otherwise.
806 int EC_KEY_check_key(const EC_KEY *key);
809 /********************************************************************/
810 /* de- and encoding functions for SEC1 ECPrivateKey */
811 /********************************************************************/
813 /** Decodes a private key from a memory buffer.
814 * \param key a pointer to a EC_KEY object which should be used (or NULL)
815 * \param in pointer to memory with the DER encoded private key
816 * \param len length of the DER encoded private key
817 * \return the decoded private key or NULL if an error occurred.
819 EC_KEY *d2i_ECPrivateKey(EC_KEY **key, const unsigned char **in, long len);
821 /** Encodes a private key object and stores the result in a buffer.
822 * \param key the EC_KEY object to encode
823 * \param out the buffer for the result (if NULL the function returns number
825 * \return 1 on success and 0 if an error occurred.
827 int i2d_ECPrivateKey(EC_KEY *key, unsigned char **out);
830 /********************************************************************/
831 /* de- and encoding functions for EC parameters */
832 /********************************************************************/
834 /** Decodes ec parameter from a memory buffer.
835 * \param key a pointer to a EC_KEY object which should be used (or NULL)
836 * \param in pointer to memory with the DER encoded ec parameters
837 * \param len length of the DER encoded ec parameters
838 * \return a EC_KEY object with the decoded parameters or NULL if an error
841 EC_KEY *d2i_ECParameters(EC_KEY **key, const unsigned char **in, long len);
843 /** Encodes ec parameter and stores the result in a buffer.
844 * \param key the EC_KEY object with ec paramters to encode
845 * \param out the buffer for the result (if NULL the function returns number
847 * \return 1 on success and 0 if an error occurred.
849 int i2d_ECParameters(EC_KEY *key, unsigned char **out);
852 /********************************************************************/
853 /* de- and encoding functions for EC public key */
854 /* (octet string, not DER -- hence 'o2i' and 'i2o') */
855 /********************************************************************/
857 /** Decodes a ec public key from a octet string.
858 * \param key a pointer to a EC_KEY object which should be used
859 * \param in memory buffer with the encoded public key
860 * \param len length of the encoded public key
861 * \return EC_KEY object with decoded public key or NULL if an error
864 EC_KEY *o2i_ECPublicKey(EC_KEY **key, const unsigned char **in, long len);
866 /** Encodes a ec public key in an octet string.
867 * \param key the EC_KEY object with the public key
868 * \param out the buffer for the result (if NULL the function returns number
870 * \return 1 on success and 0 if an error occurred
872 int i2o_ECPublicKey(EC_KEY *key, unsigned char **out);
874 #ifndef OPENSSL_NO_BIO
875 /** Prints out the ec parameters on human readable form.
876 * \param bp BIO object to which the information is printed
877 * \param key EC_KEY object
878 * \return 1 on success and 0 if an error occurred
880 int ECParameters_print(BIO *bp, const EC_KEY *key);
882 /** Prints out the contents of a EC_KEY object
883 * \param bp BIO object to which the information is printed
884 * \param key EC_KEY object
885 * \param off line offset
886 * \return 1 on success and 0 if an error occurred
888 int EC_KEY_print(BIO *bp, const EC_KEY *key, int off);
891 #ifndef OPENSSL_NO_FP_API
892 /** Prints out the ec parameters on human readable form.
893 * \param fp file descriptor to which the information is printed
894 * \param key EC_KEY object
895 * \return 1 on success and 0 if an error occurred
897 int ECParameters_print_fp(FILE *fp, const EC_KEY *key);
899 /** Prints out the contents of a EC_KEY object
900 * \param fp file descriptor to which the information is printed
901 * \param key EC_KEY object
902 * \param off line offset
903 * \return 1 on success and 0 if an error occurred
905 int EC_KEY_print_fp(FILE *fp, const EC_KEY *key, int off);
909 #define ECParameters_dup(x) ASN1_dup_of(EC_KEY,i2d_ECParameters,d2i_ECParameters,x)
912 #if defined(__SUNPRO_C)
913 # if __SUNPRO_C >= 0x520
914 # pragma error_messages (default,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE)
919 #define EVP_PKEY_CTX_set_ec_paramgen_curve_nid(ctx, nid) \
920 EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, EVP_PKEY_OP_PARAMGEN, \
921 EVP_PKEY_CTRL_EC_PARAMGEN_CURVE_NID, nid, NULL)
924 #define EVP_PKEY_CTRL_EC_PARAMGEN_CURVE_NID (EVP_PKEY_ALG_CTRL + 1)
926 /* BEGIN ERROR CODES */
927 /* The following lines are auto generated by the script mkerr.pl. Any changes
928 * made after this point may be overwritten when the script is next run.
930 void ERR_load_EC_strings(void);
932 /* Error codes for the EC functions. */
934 /* Function codes. */
935 #define EC_F_BN_TO_FELEM 224
936 #define EC_F_COMPUTE_WNAF 143
937 #define EC_F_D2I_ECPARAMETERS 144
938 #define EC_F_D2I_ECPKPARAMETERS 145
939 #define EC_F_D2I_ECPRIVATEKEY 146
940 #define EC_F_DO_EC_KEY_PRINT 221
941 #define EC_F_ECKEY_PARAM2TYPE 223
942 #define EC_F_ECKEY_PARAM_DECODE 212
943 #define EC_F_ECKEY_PRIV_DECODE 213
944 #define EC_F_ECKEY_PRIV_ENCODE 214
945 #define EC_F_ECKEY_PUB_DECODE 215
946 #define EC_F_ECKEY_PUB_ENCODE 216
947 #define EC_F_ECKEY_TYPE2PARAM 220
948 #define EC_F_ECPARAMETERS_PRINT 147
949 #define EC_F_ECPARAMETERS_PRINT_FP 148
950 #define EC_F_ECPKPARAMETERS_PRINT 149
951 #define EC_F_ECPKPARAMETERS_PRINT_FP 150
952 #define EC_F_ECP_NIST_MOD_192 203
953 #define EC_F_ECP_NIST_MOD_224 204
954 #define EC_F_ECP_NIST_MOD_256 205
955 #define EC_F_ECP_NIST_MOD_521 206
956 #define EC_F_EC_ASN1_GROUP2CURVE 153
957 #define EC_F_EC_ASN1_GROUP2FIELDID 154
958 #define EC_F_EC_ASN1_GROUP2PARAMETERS 155
959 #define EC_F_EC_ASN1_GROUP2PKPARAMETERS 156
960 #define EC_F_EC_ASN1_PARAMETERS2GROUP 157
961 #define EC_F_EC_ASN1_PKPARAMETERS2GROUP 158
962 #define EC_F_EC_EX_DATA_SET_DATA 211
963 #define EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY 208
964 #define EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT 159
965 #define EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE 195
966 #define EC_F_EC_GF2M_SIMPLE_OCT2POINT 160
967 #define EC_F_EC_GF2M_SIMPLE_POINT2OCT 161
968 #define EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES 162
969 #define EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES 163
970 #define EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES 164
971 #define EC_F_EC_GFP_MONT_FIELD_DECODE 133
972 #define EC_F_EC_GFP_MONT_FIELD_ENCODE 134
973 #define EC_F_EC_GFP_MONT_FIELD_MUL 131
974 #define EC_F_EC_GFP_MONT_FIELD_SET_TO_ONE 209
975 #define EC_F_EC_GFP_MONT_FIELD_SQR 132
976 #define EC_F_EC_GFP_MONT_GROUP_SET_CURVE 189
977 #define EC_F_EC_GFP_MONT_GROUP_SET_CURVE_GFP 135
978 #define EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE 225
979 #define EC_F_EC_GFP_NISTP224_POINTS_MUL 228
980 #define EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES 226
981 #define EC_F_EC_GFP_NIST_FIELD_MUL 200
982 #define EC_F_EC_GFP_NIST_FIELD_SQR 201
983 #define EC_F_EC_GFP_NIST_GROUP_SET_CURVE 202
984 #define EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT 165
985 #define EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE 166
986 #define EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE_GFP 100
987 #define EC_F_EC_GFP_SIMPLE_GROUP_SET_GENERATOR 101
988 #define EC_F_EC_GFP_SIMPLE_MAKE_AFFINE 102
989 #define EC_F_EC_GFP_SIMPLE_OCT2POINT 103
990 #define EC_F_EC_GFP_SIMPLE_POINT2OCT 104
991 #define EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE 137
992 #define EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES 167
993 #define EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES_GFP 105
994 #define EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES 168
995 #define EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES_GFP 128
996 #define EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES 169
997 #define EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP 129
998 #define EC_F_EC_GROUP_CHECK 170
999 #define EC_F_EC_GROUP_CHECK_DISCRIMINANT 171
1000 #define EC_F_EC_GROUP_COPY 106
1001 #define EC_F_EC_GROUP_GET0_GENERATOR 139
1002 #define EC_F_EC_GROUP_GET_COFACTOR 140
1003 #define EC_F_EC_GROUP_GET_CURVE_GF2M 172
1004 #define EC_F_EC_GROUP_GET_CURVE_GFP 130
1005 #define EC_F_EC_GROUP_GET_DEGREE 173
1006 #define EC_F_EC_GROUP_GET_ORDER 141
1007 #define EC_F_EC_GROUP_GET_PENTANOMIAL_BASIS 193
1008 #define EC_F_EC_GROUP_GET_TRINOMIAL_BASIS 194
1009 #define EC_F_EC_GROUP_NEW 108
1010 #define EC_F_EC_GROUP_NEW_BY_CURVE_NAME 174
1011 #define EC_F_EC_GROUP_NEW_FROM_DATA 175
1012 #define EC_F_EC_GROUP_PRECOMPUTE_MULT 142
1013 #define EC_F_EC_GROUP_SET_CURVE_GF2M 176
1014 #define EC_F_EC_GROUP_SET_CURVE_GFP 109
1015 #define EC_F_EC_GROUP_SET_EXTRA_DATA 110
1016 #define EC_F_EC_GROUP_SET_GENERATOR 111
1017 #define EC_F_EC_KEY_CHECK_KEY 177
1018 #define EC_F_EC_KEY_COPY 178
1019 #define EC_F_EC_KEY_GENERATE_KEY 179
1020 #define EC_F_EC_KEY_NEW 182
1021 #define EC_F_EC_KEY_PRINT 180
1022 #define EC_F_EC_KEY_PRINT_FP 181
1023 #define EC_F_EC_POINTS_MAKE_AFFINE 136
1024 #define EC_F_EC_POINT_ADD 112
1025 #define EC_F_EC_POINT_CMP 113
1026 #define EC_F_EC_POINT_COPY 114
1027 #define EC_F_EC_POINT_DBL 115
1028 #define EC_F_EC_POINT_GET_AFFINE_COORDINATES_GF2M 183
1029 #define EC_F_EC_POINT_GET_AFFINE_COORDINATES_GFP 116
1030 #define EC_F_EC_POINT_GET_JPROJECTIVE_COORDINATES_GFP 117
1031 #define EC_F_EC_POINT_INVERT 210
1032 #define EC_F_EC_POINT_IS_AT_INFINITY 118
1033 #define EC_F_EC_POINT_IS_ON_CURVE 119
1034 #define EC_F_EC_POINT_MAKE_AFFINE 120
1035 #define EC_F_EC_POINT_MUL 184
1036 #define EC_F_EC_POINT_NEW 121
1037 #define EC_F_EC_POINT_OCT2POINT 122
1038 #define EC_F_EC_POINT_POINT2OCT 123
1039 #define EC_F_EC_POINT_SET_AFFINE_COORDINATES_GF2M 185
1040 #define EC_F_EC_POINT_SET_AFFINE_COORDINATES_GFP 124
1041 #define EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GF2M 186
1042 #define EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GFP 125
1043 #define EC_F_EC_POINT_SET_JPROJECTIVE_COORDINATES_GFP 126
1044 #define EC_F_EC_POINT_SET_TO_INFINITY 127
1045 #define EC_F_EC_PRE_COMP_DUP 207
1046 #define EC_F_EC_PRE_COMP_NEW 196
1047 #define EC_F_EC_WNAF_MUL 187
1048 #define EC_F_EC_WNAF_PRECOMPUTE_MULT 188
1049 #define EC_F_I2D_ECPARAMETERS 190
1050 #define EC_F_I2D_ECPKPARAMETERS 191
1051 #define EC_F_I2D_ECPRIVATEKEY 192
1052 #define EC_F_I2O_ECPUBLICKEY 151
1053 #define EC_F_NISTP224_PRE_COMP_NEW 227
1054 #define EC_F_O2I_ECPUBLICKEY 152
1055 #define EC_F_OLD_EC_PRIV_DECODE 222
1056 #define EC_F_PKEY_EC_CTRL 197
1057 #define EC_F_PKEY_EC_CTRL_STR 198
1058 #define EC_F_PKEY_EC_DERIVE 217
1059 #define EC_F_PKEY_EC_KEYGEN 199
1060 #define EC_F_PKEY_EC_PARAMGEN 219
1061 #define EC_F_PKEY_EC_SIGN 218
1064 #define EC_R_ASN1_ERROR 115
1065 #define EC_R_ASN1_UNKNOWN_FIELD 116
1066 #define EC_R_BIGNUM_OUT_OF_RANGE 144
1067 #define EC_R_BUFFER_TOO_SMALL 100
1068 #define EC_R_D2I_ECPKPARAMETERS_FAILURE 117
1069 #define EC_R_DECODE_ERROR 142
1070 #define EC_R_DISCRIMINANT_IS_ZERO 118
1071 #define EC_R_EC_GROUP_NEW_BY_NAME_FAILURE 119
1072 #define EC_R_FIELD_TOO_LARGE 143
1073 #define EC_R_GROUP2PKPARAMETERS_FAILURE 120
1074 #define EC_R_I2D_ECPKPARAMETERS_FAILURE 121
1075 #define EC_R_INCOMPATIBLE_OBJECTS 101
1076 #define EC_R_INVALID_ARGUMENT 112
1077 #define EC_R_INVALID_COMPRESSED_POINT 110
1078 #define EC_R_INVALID_COMPRESSION_BIT 109
1079 #define EC_R_INVALID_CURVE 141
1080 #define EC_R_INVALID_DIGEST_TYPE 138
1081 #define EC_R_INVALID_ENCODING 102
1082 #define EC_R_INVALID_FIELD 103
1083 #define EC_R_INVALID_FORM 104
1084 #define EC_R_INVALID_GROUP_ORDER 122
1085 #define EC_R_INVALID_PENTANOMIAL_BASIS 132
1086 #define EC_R_INVALID_PRIVATE_KEY 123
1087 #define EC_R_INVALID_TRINOMIAL_BASIS 137
1088 #define EC_R_KEYS_NOT_SET 140
1089 #define EC_R_MISSING_PARAMETERS 124
1090 #define EC_R_MISSING_PRIVATE_KEY 125
1091 #define EC_R_NOT_A_NIST_PRIME 135
1092 #define EC_R_NOT_A_SUPPORTED_NIST_PRIME 136
1093 #define EC_R_NOT_IMPLEMENTED 126
1094 #define EC_R_NOT_INITIALIZED 111
1095 #define EC_R_NO_FIELD_MOD 133
1096 #define EC_R_NO_PARAMETERS_SET 139
1097 #define EC_R_PASSED_NULL_PARAMETER 134
1098 #define EC_R_PKPARAMETERS2GROUP_FAILURE 127
1099 #define EC_R_POINT_AT_INFINITY 106
1100 #define EC_R_POINT_IS_NOT_ON_CURVE 107
1101 #define EC_R_SLOT_FULL 108
1102 #define EC_R_UNDEFINED_GENERATOR 113
1103 #define EC_R_UNDEFINED_ORDER 128
1104 #define EC_R_UNKNOWN_GROUP 129
1105 #define EC_R_UNKNOWN_ORDER 114
1106 #define EC_R_UNSUPPORTED_FIELD 131
1107 #define EC_R_WRONG_CURVE_PARAMETERS 145
1108 #define EC_R_WRONG_ORDER 130