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 #ifndef OPENSSL_SYS_WIN32
159 const EC_METHOD *EC_GFp_nistp224_method(void);
164 /********************************************************************/
165 /* EC_METHOD for curves over GF(2^m) */
166 /********************************************************************/
168 /** Returns the basic GF2m ec method
169 * \return EC_METHOD object
171 const EC_METHOD *EC_GF2m_simple_method(void);
174 /********************************************************************/
175 /* EC_GROUP functions */
176 /********************************************************************/
178 /** Creates a new EC_GROUP object
179 * \param meth EC_METHOD to use
180 * \return newly created EC_GROUP object or NULL in case of an error.
182 EC_GROUP *EC_GROUP_new(const EC_METHOD *meth);
184 /** Frees a EC_GROUP object
185 * \param group EC_GROUP object to be freed.
187 void EC_GROUP_free(EC_GROUP *group);
189 /** Clears and frees a EC_GROUP object
190 * \param group EC_GROUP object to be cleared and freed.
192 void EC_GROUP_clear_free(EC_GROUP *group);
194 /** Copies EC_GROUP objects. Note: both EC_GROUPs must use the same EC_METHOD.
195 * \param dst destination EC_GROUP object
196 * \param src source EC_GROUP object
197 * \return 1 on success and 0 if an error occurred.
199 int EC_GROUP_copy(EC_GROUP *dst, const EC_GROUP *src);
201 /** Creates a new EC_GROUP object and copies the copies the content
202 * form src to the newly created EC_KEY object
203 * \param src source EC_GROUP object
204 * \return newly created EC_GROUP object or NULL in case of an error.
206 EC_GROUP *EC_GROUP_dup(const EC_GROUP *src);
208 /** Returns the EC_METHOD of the EC_GROUP object.
209 * \param group EC_GROUP object
210 * \return EC_METHOD used in this EC_GROUP object.
212 const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group);
214 /** Returns the field type of the EC_METHOD.
215 * \param meth EC_METHOD object
216 * \return NID of the underlying field type OID.
218 int EC_METHOD_get_field_type(const EC_METHOD *meth);
220 /** Sets the generator and it's order/cofactor of a EC_GROUP object.
221 * \param group EC_GROUP object
222 * \param generator EC_POINT object with the generator.
223 * \param order the order of the group generated by the generator.
224 * \param cofactor the index of the sub-group generated by the generator
225 * in the group of all points on the elliptic curve.
226 * \return 1 on success and 0 if an error occured
228 int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator, const BIGNUM *order, const BIGNUM *cofactor);
230 /** Returns the generator of a EC_GROUP object.
231 * \param group EC_GROUP object
232 * \return the currently used generator (possibly NULL).
234 const EC_POINT *EC_GROUP_get0_generator(const EC_GROUP *group);
236 /** Gets the order of a EC_GROUP
237 * \param group EC_GROUP object
238 * \param order BIGNUM to which the order is copied
239 * \param ctx BN_CTX object (optional)
240 * \return 1 on success and 0 if an error occured
242 int EC_GROUP_get_order(const EC_GROUP *group, BIGNUM *order, BN_CTX *ctx);
244 /** Gets the cofactor of a EC_GROUP
245 * \param group EC_GROUP object
246 * \param cofactor BIGNUM to which the cofactor is copied
247 * \param ctx BN_CTX object (optional)
248 * \return 1 on success and 0 if an error occured
250 int EC_GROUP_get_cofactor(const EC_GROUP *group, BIGNUM *cofactor, BN_CTX *ctx);
252 /** Sets the name of a EC_GROUP object
253 * \param group EC_GROUP object
254 * \param nid NID of the curve name OID
256 void EC_GROUP_set_curve_name(EC_GROUP *group, int nid);
258 /** Returns the curve name of a EC_GROUP object
259 * \param group EC_GROUP object
260 * \return NID of the curve name OID or 0 if not set.
262 int EC_GROUP_get_curve_name(const EC_GROUP *group);
264 void EC_GROUP_set_asn1_flag(EC_GROUP *group, int flag);
265 int EC_GROUP_get_asn1_flag(const EC_GROUP *group);
267 void EC_GROUP_set_point_conversion_form(EC_GROUP *, point_conversion_form_t);
268 point_conversion_form_t EC_GROUP_get_point_conversion_form(const EC_GROUP *);
270 unsigned char *EC_GROUP_get0_seed(const EC_GROUP *);
271 size_t EC_GROUP_get_seed_len(const EC_GROUP *);
272 size_t EC_GROUP_set_seed(EC_GROUP *, const unsigned char *, size_t len);
274 /** Sets the parameter of a ec over GFp defined by y^2 = x^3 + a*x + b
275 * \param group EC_GROUP object
276 * \param p BIGNUM with the prime number
277 * \param a BIGNUM with parameter a of the equation
278 * \param b BIGNUM with parameter b of the equation
279 * \param ctx BN_CTX object (optional)
280 * \return 1 on success and 0 if an error occured
282 int EC_GROUP_set_curve_GFp(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
284 /** Gets the parameter of the ec over GFp defined by y^2 = x^3 + a*x + b
285 * \param group EC_GROUP object
286 * \param p BIGNUM for the prime number
287 * \param a BIGNUM for parameter a of the equation
288 * \param b BIGNUM for parameter b of the equation
289 * \param ctx BN_CTX object (optional)
290 * \return 1 on success and 0 if an error occured
292 int EC_GROUP_get_curve_GFp(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
294 /** Sets the parameter of a ec over GF2m defined by y^2 + x*y = x^3 + a*x^2 + b
295 * \param group EC_GROUP object
296 * \param p BIGNUM with the polynomial defining the underlying field
297 * \param a BIGNUM with parameter a of the equation
298 * \param b BIGNUM with parameter b of the equation
299 * \param ctx BN_CTX object (optional)
300 * \return 1 on success and 0 if an error occured
302 int EC_GROUP_set_curve_GF2m(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
304 /** Gets the parameter of the ec over GF2m defined by y^2 + x*y = x^3 + a*x^2 + b
305 * \param group EC_GROUP object
306 * \param p BIGNUM for the polynomial defining the underlying field
307 * \param a BIGNUM for parameter a of the equation
308 * \param b BIGNUM for parameter b of the equation
309 * \param ctx BN_CTX object (optional)
310 * \return 1 on success and 0 if an error occured
312 int EC_GROUP_get_curve_GF2m(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
314 /** Returns the number of bits needed to represent a field element
315 * \param group EC_GROUP object
316 * \return number of bits needed to represent a field element
318 int EC_GROUP_get_degree(const EC_GROUP *group);
320 /** Checks whether the parameter in the EC_GROUP define a valid ec group
321 * \param group EC_GROUP object
322 * \param ctx BN_CTX object (optional)
323 * \return 1 if group is a valid ec group and 0 otherwise
325 int EC_GROUP_check(const EC_GROUP *group, BN_CTX *ctx);
327 /** Checks whether the discriminant of the elliptic curve is zero or not
328 * \param group EC_GROUP object
329 * \param ctx BN_CTX object (optional)
330 * \return 1 if the discriminant is not zero and 0 otherwise
332 int EC_GROUP_check_discriminant(const EC_GROUP *group, BN_CTX *ctx);
334 /** Compares two EC_GROUP objects
335 * \param a first EC_GROUP object
336 * \param b second EC_GROUP object
337 * \param ctx BN_CTX object (optional)
338 * \return 0 if both groups are equal and 1 otherwise
340 int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx);
342 /* EC_GROUP_new_GF*() calls EC_GROUP_new() and EC_GROUP_set_GF*()
343 * after choosing an appropriate EC_METHOD */
345 /** Creates a new EC_GROUP object with the specified parameters defined
346 * over GFp (defined by the equation y^2 = x^3 + a*x + b)
347 * \param p BIGNUM with the prime number
348 * \param a BIGNUM with the parameter a of the equation
349 * \param b BIGNUM with the parameter b of the equation
350 * \param ctx BN_CTX object (optional)
351 * \return newly created EC_GROUP object with the specified parameters
353 EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
355 /** Creates a new EC_GROUP object with the specified parameters defined
356 * over GF2m (defined by the equation y^2 + x*y = x^3 + a*x^2 + b)
357 * \param p BIGNUM with the polynomial defining the underlying field
358 * \param a BIGNUM with the parameter a of the equation
359 * \param b BIGNUM with the parameter b of the equation
360 * \param ctx BN_CTX object (optional)
361 * \return newly created EC_GROUP object with the specified parameters
363 EC_GROUP *EC_GROUP_new_curve_GF2m(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
365 /** Creates a EC_GROUP object with a curve specified by a NID
366 * \param nid NID of the OID of the curve name
367 * \return newly created EC_GROUP object with specified curve or NULL
368 * if an error occurred
370 EC_GROUP *EC_GROUP_new_by_curve_name(int nid);
373 /********************************************************************/
374 /* handling of internal curves */
375 /********************************************************************/
382 /* EC_builtin_curves(EC_builtin_curve *r, size_t size) returns number
383 * of all available curves or zero if a error occurred.
384 * In case r ist not zero nitems EC_builtin_curve structures
385 * are filled with the data of the first nitems internal groups */
386 size_t EC_get_builtin_curves(EC_builtin_curve *r, size_t nitems);
389 /********************************************************************/
390 /* EC_POINT functions */
391 /********************************************************************/
393 /** Creates a new EC_POINT object for the specified EC_GROUP
394 * \param group EC_GROUP the underlying EC_GROUP object
395 * \return newly created EC_POINT object or NULL if an error occurred
397 EC_POINT *EC_POINT_new(const EC_GROUP *group);
399 /** Frees a EC_POINT object
400 * \param point EC_POINT object to be freed
402 void EC_POINT_free(EC_POINT *point);
404 /** Clears and frees a EC_POINT object
405 * \param point EC_POINT object to be cleared and freed
407 void EC_POINT_clear_free(EC_POINT *point);
409 /** Copies EC_POINT object
410 * \param dst destination EC_POINT object
411 * \param src source EC_POINT object
412 * \return 1 on success and 0 if an error occured
414 int EC_POINT_copy(EC_POINT *dst, const EC_POINT *src);
416 /** Creates a new EC_POINT object and copies the content of the supplied
418 * \param src source EC_POINT object
419 * \param group underlying the EC_GROUP object
420 * \return newly created EC_POINT object or NULL if an error occurred
422 EC_POINT *EC_POINT_dup(const EC_POINT *src, const EC_GROUP *group);
424 /** Returns the EC_METHOD used in EC_POINT object
425 * \param point EC_POINT object
426 * \return the EC_METHOD used
428 const EC_METHOD *EC_POINT_method_of(const EC_POINT *point);
430 /** Sets a point to infinity (neutral element)
431 * \param group underlying EC_GROUP object
432 * \param point EC_POINT to set to infinity
433 * \return 1 on success and 0 if an error occured
435 int EC_POINT_set_to_infinity(const EC_GROUP *group, EC_POINT *point);
437 /** Sets the jacobian projective coordinates of a EC_POINT over GFp
438 * \param group underlying EC_GROUP object
439 * \param p EC_POINT object
440 * \param x BIGNUM with the x-coordinate
441 * \param y BIGNUM with the y-coordinate
442 * \param z BIGNUM with the z-coordinate
443 * \param ctx BN_CTX object (optional)
444 * \return 1 on success and 0 if an error occured
446 int EC_POINT_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *p,
447 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx);
449 /** Gets the jacobian projective coordinates of a EC_POINT over GFp
450 * \param group underlying EC_GROUP object
451 * \param p EC_POINT object
452 * \param x BIGNUM for the x-coordinate
453 * \param y BIGNUM for the y-coordinate
454 * \param z BIGNUM for the z-coordinate
455 * \param ctx BN_CTX object (optional)
456 * \return 1 on success and 0 if an error occured
458 int EC_POINT_get_Jprojective_coordinates_GFp(const EC_GROUP *group,
459 const EC_POINT *p, BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx);
461 /** Sets the affine coordinates of a EC_POINT over GFp
462 * \param group underlying EC_GROUP object
463 * \param p EC_POINT object
464 * \param x BIGNUM with the x-coordinate
465 * \param y BIGNUM with the y-coordinate
466 * \param ctx BN_CTX object (optional)
467 * \return 1 on success and 0 if an error occured
469 int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *p,
470 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx);
472 /** Gets the affine coordinates of a EC_POINT over GFp
473 * \param group underlying EC_GROUP object
474 * \param p EC_POINT object
475 * \param x BIGNUM for the x-coordinate
476 * \param y BIGNUM for the y-coordinate
477 * \param ctx BN_CTX object (optional)
478 * \return 1 on success and 0 if an error occured
480 int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group,
481 const EC_POINT *p, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
483 /** Sets the x9.62 compressed coordinates of a EC_POINT over GFp
484 * \param group underlying EC_GROUP object
485 * \param p EC_POINT object
486 * \param x BIGNUM with x-coordinate
487 * \param y_bit integer with the y-Bit (either 0 or 1)
488 * \param ctx BN_CTX object (optional)
489 * \return 1 on success and 0 if an error occured
491 int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *group, EC_POINT *p,
492 const BIGNUM *x, int y_bit, BN_CTX *ctx);
494 /** Sets the affine coordinates of a EC_POINT over GF2m
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 occured
502 int EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP *group, EC_POINT *p,
503 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx);
505 /** Gets the affine coordinates of a EC_POINT over GF2m
506 * \param group underlying EC_GROUP object
507 * \param p EC_POINT object
508 * \param x BIGNUM for the x-coordinate
509 * \param y BIGNUM for the y-coordinate
510 * \param ctx BN_CTX object (optional)
511 * \return 1 on success and 0 if an error occured
513 int EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *group,
514 const EC_POINT *p, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
516 /** Sets the x9.62 compressed coordinates of a EC_POINT over GF2m
517 * \param group underlying EC_GROUP object
518 * \param p EC_POINT object
519 * \param x BIGNUM with x-coordinate
520 * \param y_bit integer with the y-Bit (either 0 or 1)
521 * \param ctx BN_CTX object (optional)
522 * \return 1 on success and 0 if an error occured
524 int EC_POINT_set_compressed_coordinates_GF2m(const EC_GROUP *group, EC_POINT *p,
525 const BIGNUM *x, int y_bit, BN_CTX *ctx);
527 /** Encodes a EC_POINT object to a octet string
528 * \param group underlying EC_GROUP object
529 * \param p EC_POINT object
530 * \param form point conversion form
531 * \param buf memory buffer for the result. If NULL the function returns
532 * required buffer size.
533 * \param len length of the memory buffer
534 * \param ctx BN_CTX object (optional)
535 * \return the length of the encoded octet string or 0 if an error occurred
537 size_t EC_POINT_point2oct(const EC_GROUP *group, const EC_POINT *p,
538 point_conversion_form_t form,
539 unsigned char *buf, size_t len, BN_CTX *ctx);
541 /** Decodes a EC_POINT from a octet string
542 * \param group underlying EC_GROUP object
543 * \param p EC_POINT object
544 * \param buf memory buffer with the encoded ec point
545 * \param len length of the encoded ec point
546 * \param ctx BN_CTX object (optional)
547 * \return 1 on success and 0 if an error occured
549 int EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *p,
550 const unsigned char *buf, size_t len, BN_CTX *ctx);
552 /* other interfaces to point2oct/oct2point: */
553 BIGNUM *EC_POINT_point2bn(const EC_GROUP *, const EC_POINT *,
554 point_conversion_form_t form, BIGNUM *, BN_CTX *);
555 EC_POINT *EC_POINT_bn2point(const EC_GROUP *, const BIGNUM *,
556 EC_POINT *, BN_CTX *);
557 char *EC_POINT_point2hex(const EC_GROUP *, const EC_POINT *,
558 point_conversion_form_t form, BN_CTX *);
559 EC_POINT *EC_POINT_hex2point(const EC_GROUP *, const char *,
560 EC_POINT *, BN_CTX *);
563 /********************************************************************/
564 /* functions for doing EC_POINT arithmetic */
565 /********************************************************************/
567 /** Computes the sum of two EC_POINT
568 * \param group underlying EC_GROUP object
569 * \param r EC_POINT object for the result (r = a + b)
570 * \param a EC_POINT object with the first summand
571 * \param b EC_POINT object with the second summand
572 * \param ctx BN_CTX object (optional)
573 * \return 1 on success and 0 if an error occured
575 int EC_POINT_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx);
577 /** Computes the double of a EC_POINT
578 * \param group underlying EC_GROUP object
579 * \param r EC_POINT object for the result (r = 2 * a)
580 * \param a EC_POINT object
581 * \param ctx BN_CTX object (optional)
582 * \return 1 on success and 0 if an error occured
584 int EC_POINT_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx);
586 /** Computes the inverse of a EC_POINT
587 * \param group underlying EC_GROUP object
588 * \param a EC_POINT object to be inverted (it's used for the result as well)
589 * \param ctx BN_CTX object (optional)
590 * \return 1 on success and 0 if an error occured
592 int EC_POINT_invert(const EC_GROUP *group, EC_POINT *a, BN_CTX *ctx);
594 /** Checks whether the point is the neutral element of the group
595 * \param group the underlying EC_GROUP object
596 * \param p EC_POINT object
597 * \return 1 if the point is the neutral element and 0 otherwise
599 int EC_POINT_is_at_infinity(const EC_GROUP *group, const EC_POINT *p);
601 /** Checks whether the point is on the curve
602 * \param group underlying EC_GROUP object
603 * \param point EC_POINT object to check
604 * \param ctx BN_CTX object (optional)
605 * \return 1 if point if on the curve and 0 otherwise
607 int EC_POINT_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx);
609 /** Compares two EC_POINTs
610 * \param group underlying EC_GROUP object
611 * \param a first EC_POINT object
612 * \param b second EC_POINT object
613 * \param ctx BN_CTX object (optional)
614 * \return 0 if both points are equal and a value != 0 otherwise
616 int EC_POINT_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx);
618 int EC_POINT_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
619 int EC_POINTs_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
621 /** Computes r = generator * n sum_{i=0}^num p[i] * m[i]
622 * \param group underlying EC_GROUP object
623 * \param r EC_POINT object for the result
624 * \param n BIGNUM with the multiplier for the group generator (optional)
625 * \param num number futher summands
626 * \param p array of size num of EC_POINT objects
627 * \param m array of size num of BIGNUM objects
628 * \param ctx BN_CTX object (optional)
629 * \return 1 on success and 0 if an error occured
631 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);
633 /** Computes r = generator * n + q * m
634 * \param group underlying EC_GROUP object
635 * \param r EC_POINT object for the result
636 * \param n BIGNUM with the multiplier for the group generator (optional)
637 * \param q EC_POINT object with the first factor of the second summand
638 * \param m BIGNUM with the second factor of the second summand
639 * \param ctx BN_CTX object (optional)
640 * \return 1 on success and 0 if an error occured
642 int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *n, const EC_POINT *q, const BIGNUM *m, BN_CTX *ctx);
644 /** Stores multiples of generator for faster point multiplication
645 * \param group EC_GROUP object
646 * \param ctx BN_CTX object (optional)
647 * \return 1 on success and 0 if an error occured
649 int EC_GROUP_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
651 /** Reports whether a precomputation has been done
652 * \param group EC_GROUP object
653 * \return 1 if a pre-computation has been done and 0 otherwise
655 int EC_GROUP_have_precompute_mult(const EC_GROUP *group);
658 /********************************************************************/
660 /********************************************************************/
662 /* EC_GROUP_get_basis_type() returns the NID of the basis type
663 * used to represent the field elements */
664 int EC_GROUP_get_basis_type(const EC_GROUP *);
665 int EC_GROUP_get_trinomial_basis(const EC_GROUP *, unsigned int *k);
666 int EC_GROUP_get_pentanomial_basis(const EC_GROUP *, unsigned int *k1,
667 unsigned int *k2, unsigned int *k3);
669 #define OPENSSL_EC_NAMED_CURVE 0x001
671 typedef struct ecpk_parameters_st ECPKPARAMETERS;
673 EC_GROUP *d2i_ECPKParameters(EC_GROUP **, const unsigned char **in, long len);
674 int i2d_ECPKParameters(const EC_GROUP *, unsigned char **out);
676 #define d2i_ECPKParameters_bio(bp,x) ASN1_d2i_bio_of(EC_GROUP,NULL,d2i_ECPKParameters,bp,x)
677 #define i2d_ECPKParameters_bio(bp,x) ASN1_i2d_bio_of_const(EC_GROUP,i2d_ECPKParameters,bp,x)
678 #define d2i_ECPKParameters_fp(fp,x) (EC_GROUP *)ASN1_d2i_fp(NULL, \
679 (char *(*)())d2i_ECPKParameters,(fp),(unsigned char **)(x))
680 #define i2d_ECPKParameters_fp(fp,x) ASN1_i2d_fp(i2d_ECPKParameters,(fp), \
681 (unsigned char *)(x))
683 #ifndef OPENSSL_NO_BIO
684 int ECPKParameters_print(BIO *bp, const EC_GROUP *x, int off);
686 #ifndef OPENSSL_NO_FP_API
687 int ECPKParameters_print_fp(FILE *fp, const EC_GROUP *x, int off);
691 /********************************************************************/
692 /* EC_KEY functions */
693 /********************************************************************/
695 typedef struct ec_key_st EC_KEY;
697 /* some values for the encoding_flag */
698 #define EC_PKEY_NO_PARAMETERS 0x001
699 #define EC_PKEY_NO_PUBKEY 0x002
701 /** Creates a new EC_KEY object.
702 * \return EC_KEY object or NULL if an error occurred.
704 EC_KEY *EC_KEY_new(void);
706 /** Creates a new EC_KEY object using a named curve as underlying
708 * \param nid NID of the named curve.
709 * \return EC_KEY object or NULL if an error occurred.
711 EC_KEY *EC_KEY_new_by_curve_name(int nid);
713 /** Frees a EC_KEY object.
714 * \param key EC_KEY object to be freed.
716 void EC_KEY_free(EC_KEY *key);
718 /** Copies a EC_KEY object.
719 * \param dst destination EC_KEY object
720 * \param src src EC_KEY object
721 * \return dst or NULL if an error occurred.
723 EC_KEY *EC_KEY_copy(EC_KEY *dst, const EC_KEY *src);
725 /** Creates a new EC_KEY object and copies the content from src to it.
726 * \param src the source EC_KEY object
727 * \return newly created EC_KEY object or NULL if an error occurred.
729 EC_KEY *EC_KEY_dup(const EC_KEY *src);
731 /** Increases the internal reference count of a EC_KEY object.
732 * \param key EC_KEY object
733 * \return 1 on success and 0 if an error occurred.
735 int EC_KEY_up_ref(EC_KEY *key);
737 /** Returns the EC_GROUP object of a EC_KEY object
738 * \param key EC_KEY object
739 * \return the EC_GROUP object (possibly NULL).
741 const EC_GROUP *EC_KEY_get0_group(const EC_KEY *key);
743 /** Sets the EC_GROUP of a EC_KEY object.
744 * \param key EC_KEY object
745 * \param group EC_GROUP to use in the EC_KEY object (note: the EC_KEY
746 * object will use an own copy of the EC_GROUP).
747 * \return 1 on success and 0 if an error occurred.
749 int EC_KEY_set_group(EC_KEY *key, const EC_GROUP *group);
751 /** Returns the private key of a EC_KEY object.
752 * \param key EC_KEY object
753 * \return a BIGNUM with the private key (possibly NULL).
755 const BIGNUM *EC_KEY_get0_private_key(const EC_KEY *key);
757 /** Sets the private key of a EC_KEY object.
758 * \param key EC_KEY object
759 * \param prv BIGNUM with the private key (note: the EC_KEY object
760 * will use an own copy of the BIGNUM).
761 * \return 1 on success and 0 if an error occurred.
763 int EC_KEY_set_private_key(EC_KEY *key, const BIGNUM *prv);
765 /** Returns the public key of a EC_KEY object.
766 * \param key the EC_KEY object
767 * \return a EC_POINT object with the public key (possibly NULL)
769 const EC_POINT *EC_KEY_get0_public_key(const EC_KEY *key);
771 /** Sets the public key of a EC_KEY object.
772 * \param key EC_KEY object
773 * \param pub EC_POINT object with the public key (note: the EC_KEY object
774 * will use an own copy of the EC_POINT object).
775 * \return 1 on success and 0 if an error occurred.
777 int EC_KEY_set_public_key(EC_KEY *key, const EC_POINT *pub);
779 unsigned EC_KEY_get_enc_flags(const EC_KEY *key);
780 void EC_KEY_set_enc_flags(EC_KEY *, unsigned int);
781 point_conversion_form_t EC_KEY_get_conv_form(const EC_KEY *);
782 void EC_KEY_set_conv_form(EC_KEY *, point_conversion_form_t);
783 /* functions to set/get method specific data */
784 void *EC_KEY_get_key_method_data(EC_KEY *,
785 void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
786 void EC_KEY_insert_key_method_data(EC_KEY *, void *data,
787 void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
788 /* wrapper functions for the underlying EC_GROUP object */
789 void EC_KEY_set_asn1_flag(EC_KEY *, int);
791 /** Creates a table of pre-computed multiples of the generator to
792 * accelerate further EC_KEY operations.
793 * \param key EC_KEY object
794 * \param ctx BN_CTX object (optional)
795 * \return 1 on success and 0 if an error occurred.
797 int EC_KEY_precompute_mult(EC_KEY *key, BN_CTX *ctx);
799 /** Creates a new ec private (and optional a new public) key.
800 * \param key EC_KEY object
801 * \return 1 on success and 0 if an error occurred.
803 int EC_KEY_generate_key(EC_KEY *key);
805 /** Verifies that a private and/or public key is valid.
806 * \param key the EC_KEY object
807 * \return 1 on success and 0 otherwise.
809 int EC_KEY_check_key(const EC_KEY *key);
811 /** Sets a public key from affine coordindates performing
812 * neccessary NIST PKV tests.
813 * \param key the EC_KEY object
814 * \param x public key x coordinate
815 * \param y public key y coordinate
816 * \return 1 on success and 0 otherwise.
818 int EC_KEY_set_public_key_affine_coordinates(EC_KEY *key, BIGNUM *x, BIGNUM *y);
821 /********************************************************************/
822 /* de- and encoding functions for SEC1 ECPrivateKey */
823 /********************************************************************/
825 /** Decodes a private key from a memory buffer.
826 * \param key a pointer to a EC_KEY object which should be used (or NULL)
827 * \param in pointer to memory with the DER encoded private key
828 * \param len length of the DER encoded private key
829 * \return the decoded private key or NULL if an error occurred.
831 EC_KEY *d2i_ECPrivateKey(EC_KEY **key, const unsigned char **in, long len);
833 /** Encodes a private key object and stores the result in a buffer.
834 * \param key the EC_KEY object to encode
835 * \param out the buffer for the result (if NULL the function returns number
837 * \return 1 on success and 0 if an error occurred.
839 int i2d_ECPrivateKey(EC_KEY *key, unsigned char **out);
842 /********************************************************************/
843 /* de- and encoding functions for EC parameters */
844 /********************************************************************/
846 /** Decodes ec parameter from a memory buffer.
847 * \param key a pointer to a EC_KEY object which should be used (or NULL)
848 * \param in pointer to memory with the DER encoded ec parameters
849 * \param len length of the DER encoded ec parameters
850 * \return a EC_KEY object with the decoded parameters or NULL if an error
853 EC_KEY *d2i_ECParameters(EC_KEY **key, const unsigned char **in, long len);
855 /** Encodes ec parameter and stores the result in a buffer.
856 * \param key the EC_KEY object with ec paramters to encode
857 * \param out the buffer for the result (if NULL the function returns number
859 * \return 1 on success and 0 if an error occurred.
861 int i2d_ECParameters(EC_KEY *key, unsigned char **out);
864 /********************************************************************/
865 /* de- and encoding functions for EC public key */
866 /* (octet string, not DER -- hence 'o2i' and 'i2o') */
867 /********************************************************************/
869 /** Decodes a ec public key from a octet string.
870 * \param key a pointer to a EC_KEY object which should be used
871 * \param in memory buffer with the encoded public key
872 * \param len length of the encoded public key
873 * \return EC_KEY object with decoded public key or NULL if an error
876 EC_KEY *o2i_ECPublicKey(EC_KEY **key, const unsigned char **in, long len);
878 /** Encodes a ec public key in an octet string.
879 * \param key the EC_KEY object with the public key
880 * \param out the buffer for the result (if NULL the function returns number
882 * \return 1 on success and 0 if an error occurred
884 int i2o_ECPublicKey(EC_KEY *key, unsigned char **out);
886 #ifndef OPENSSL_NO_BIO
887 /** Prints out the ec parameters on human readable form.
888 * \param bp BIO object to which the information is printed
889 * \param key EC_KEY object
890 * \return 1 on success and 0 if an error occurred
892 int ECParameters_print(BIO *bp, const EC_KEY *key);
894 /** Prints out the contents of a EC_KEY object
895 * \param bp BIO object to which the information is printed
896 * \param key EC_KEY object
897 * \param off line offset
898 * \return 1 on success and 0 if an error occurred
900 int EC_KEY_print(BIO *bp, const EC_KEY *key, int off);
903 #ifndef OPENSSL_NO_FP_API
904 /** Prints out the ec parameters on human readable form.
905 * \param fp file descriptor to which the information is printed
906 * \param key EC_KEY object
907 * \return 1 on success and 0 if an error occurred
909 int ECParameters_print_fp(FILE *fp, const EC_KEY *key);
911 /** Prints out the contents of a EC_KEY object
912 * \param fp file descriptor to which the information is printed
913 * \param key EC_KEY object
914 * \param off line offset
915 * \return 1 on success and 0 if an error occurred
917 int EC_KEY_print_fp(FILE *fp, const EC_KEY *key, int off);
921 #define ECParameters_dup(x) ASN1_dup_of(EC_KEY,i2d_ECParameters,d2i_ECParameters,x)
924 #if defined(__SUNPRO_C)
925 # if __SUNPRO_C >= 0x520
926 # pragma error_messages (default,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE)
931 #define EVP_PKEY_CTX_set_ec_paramgen_curve_nid(ctx, nid) \
932 EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, EVP_PKEY_OP_PARAMGEN, \
933 EVP_PKEY_CTRL_EC_PARAMGEN_CURVE_NID, nid, NULL)
936 #define EVP_PKEY_CTRL_EC_PARAMGEN_CURVE_NID (EVP_PKEY_ALG_CTRL + 1)
938 /* BEGIN ERROR CODES */
939 /* The following lines are auto generated by the script mkerr.pl. Any changes
940 * made after this point may be overwritten when the script is next run.
942 void ERR_load_EC_strings(void);
944 /* Error codes for the EC functions. */
946 /* Function codes. */
947 #define EC_F_BN_TO_FELEM 224
948 #define EC_F_COMPUTE_WNAF 143
949 #define EC_F_D2I_ECPARAMETERS 144
950 #define EC_F_D2I_ECPKPARAMETERS 145
951 #define EC_F_D2I_ECPRIVATEKEY 146
952 #define EC_F_DO_EC_KEY_PRINT 221
953 #define EC_F_ECKEY_PARAM2TYPE 223
954 #define EC_F_ECKEY_PARAM_DECODE 212
955 #define EC_F_ECKEY_PRIV_DECODE 213
956 #define EC_F_ECKEY_PRIV_ENCODE 214
957 #define EC_F_ECKEY_PUB_DECODE 215
958 #define EC_F_ECKEY_PUB_ENCODE 216
959 #define EC_F_ECKEY_TYPE2PARAM 220
960 #define EC_F_ECPARAMETERS_PRINT 147
961 #define EC_F_ECPARAMETERS_PRINT_FP 148
962 #define EC_F_ECPKPARAMETERS_PRINT 149
963 #define EC_F_ECPKPARAMETERS_PRINT_FP 150
964 #define EC_F_ECP_NIST_MOD_192 203
965 #define EC_F_ECP_NIST_MOD_224 204
966 #define EC_F_ECP_NIST_MOD_256 205
967 #define EC_F_ECP_NIST_MOD_521 206
968 #define EC_F_EC_ASN1_GROUP2CURVE 153
969 #define EC_F_EC_ASN1_GROUP2FIELDID 154
970 #define EC_F_EC_ASN1_GROUP2PARAMETERS 155
971 #define EC_F_EC_ASN1_GROUP2PKPARAMETERS 156
972 #define EC_F_EC_ASN1_PARAMETERS2GROUP 157
973 #define EC_F_EC_ASN1_PKPARAMETERS2GROUP 158
974 #define EC_F_EC_EX_DATA_SET_DATA 211
975 #define EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY 208
976 #define EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT 159
977 #define EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE 195
978 #define EC_F_EC_GF2M_SIMPLE_OCT2POINT 160
979 #define EC_F_EC_GF2M_SIMPLE_POINT2OCT 161
980 #define EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES 162
981 #define EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES 163
982 #define EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES 164
983 #define EC_F_EC_GFP_MONT_FIELD_DECODE 133
984 #define EC_F_EC_GFP_MONT_FIELD_ENCODE 134
985 #define EC_F_EC_GFP_MONT_FIELD_MUL 131
986 #define EC_F_EC_GFP_MONT_FIELD_SET_TO_ONE 209
987 #define EC_F_EC_GFP_MONT_FIELD_SQR 132
988 #define EC_F_EC_GFP_MONT_GROUP_SET_CURVE 189
989 #define EC_F_EC_GFP_MONT_GROUP_SET_CURVE_GFP 135
990 #define EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE 225
991 #define EC_F_EC_GFP_NISTP224_POINTS_MUL 228
992 #define EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES 226
993 #define EC_F_EC_GFP_NIST_FIELD_MUL 200
994 #define EC_F_EC_GFP_NIST_FIELD_SQR 201
995 #define EC_F_EC_GFP_NIST_GROUP_SET_CURVE 202
996 #define EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT 165
997 #define EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE 166
998 #define EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE_GFP 100
999 #define EC_F_EC_GFP_SIMPLE_GROUP_SET_GENERATOR 101
1000 #define EC_F_EC_GFP_SIMPLE_MAKE_AFFINE 102
1001 #define EC_F_EC_GFP_SIMPLE_OCT2POINT 103
1002 #define EC_F_EC_GFP_SIMPLE_POINT2OCT 104
1003 #define EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE 137
1004 #define EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES 167
1005 #define EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES_GFP 105
1006 #define EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES 168
1007 #define EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES_GFP 128
1008 #define EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES 169
1009 #define EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP 129
1010 #define EC_F_EC_GROUP_CHECK 170
1011 #define EC_F_EC_GROUP_CHECK_DISCRIMINANT 171
1012 #define EC_F_EC_GROUP_COPY 106
1013 #define EC_F_EC_GROUP_GET0_GENERATOR 139
1014 #define EC_F_EC_GROUP_GET_COFACTOR 140
1015 #define EC_F_EC_GROUP_GET_CURVE_GF2M 172
1016 #define EC_F_EC_GROUP_GET_CURVE_GFP 130
1017 #define EC_F_EC_GROUP_GET_DEGREE 173
1018 #define EC_F_EC_GROUP_GET_ORDER 141
1019 #define EC_F_EC_GROUP_GET_PENTANOMIAL_BASIS 193
1020 #define EC_F_EC_GROUP_GET_TRINOMIAL_BASIS 194
1021 #define EC_F_EC_GROUP_NEW 108
1022 #define EC_F_EC_GROUP_NEW_BY_CURVE_NAME 174
1023 #define EC_F_EC_GROUP_NEW_FROM_DATA 175
1024 #define EC_F_EC_GROUP_PRECOMPUTE_MULT 142
1025 #define EC_F_EC_GROUP_SET_CURVE_GF2M 176
1026 #define EC_F_EC_GROUP_SET_CURVE_GFP 109
1027 #define EC_F_EC_GROUP_SET_EXTRA_DATA 110
1028 #define EC_F_EC_GROUP_SET_GENERATOR 111
1029 #define EC_F_EC_KEY_CHECK_KEY 177
1030 #define EC_F_EC_KEY_COPY 178
1031 #define EC_F_EC_KEY_GENERATE_KEY 179
1032 #define EC_F_EC_KEY_NEW 182
1033 #define EC_F_EC_KEY_PRINT 180
1034 #define EC_F_EC_KEY_PRINT_FP 181
1035 #define EC_F_EC_KEY_SET_PUBLIC_KEY_AFFINE_COORDINATES 229
1036 #define EC_F_EC_POINTS_MAKE_AFFINE 136
1037 #define EC_F_EC_POINT_ADD 112
1038 #define EC_F_EC_POINT_CMP 113
1039 #define EC_F_EC_POINT_COPY 114
1040 #define EC_F_EC_POINT_DBL 115
1041 #define EC_F_EC_POINT_GET_AFFINE_COORDINATES_GF2M 183
1042 #define EC_F_EC_POINT_GET_AFFINE_COORDINATES_GFP 116
1043 #define EC_F_EC_POINT_GET_JPROJECTIVE_COORDINATES_GFP 117
1044 #define EC_F_EC_POINT_INVERT 210
1045 #define EC_F_EC_POINT_IS_AT_INFINITY 118
1046 #define EC_F_EC_POINT_IS_ON_CURVE 119
1047 #define EC_F_EC_POINT_MAKE_AFFINE 120
1048 #define EC_F_EC_POINT_MUL 184
1049 #define EC_F_EC_POINT_NEW 121
1050 #define EC_F_EC_POINT_OCT2POINT 122
1051 #define EC_F_EC_POINT_POINT2OCT 123
1052 #define EC_F_EC_POINT_SET_AFFINE_COORDINATES_GF2M 185
1053 #define EC_F_EC_POINT_SET_AFFINE_COORDINATES_GFP 124
1054 #define EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GF2M 186
1055 #define EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GFP 125
1056 #define EC_F_EC_POINT_SET_JPROJECTIVE_COORDINATES_GFP 126
1057 #define EC_F_EC_POINT_SET_TO_INFINITY 127
1058 #define EC_F_EC_PRE_COMP_DUP 207
1059 #define EC_F_EC_PRE_COMP_NEW 196
1060 #define EC_F_EC_WNAF_MUL 187
1061 #define EC_F_EC_WNAF_PRECOMPUTE_MULT 188
1062 #define EC_F_I2D_ECPARAMETERS 190
1063 #define EC_F_I2D_ECPKPARAMETERS 191
1064 #define EC_F_I2D_ECPRIVATEKEY 192
1065 #define EC_F_I2O_ECPUBLICKEY 151
1066 #define EC_F_NISTP224_PRE_COMP_NEW 227
1067 #define EC_F_O2I_ECPUBLICKEY 152
1068 #define EC_F_OLD_EC_PRIV_DECODE 222
1069 #define EC_F_PKEY_EC_CTRL 197
1070 #define EC_F_PKEY_EC_CTRL_STR 198
1071 #define EC_F_PKEY_EC_DERIVE 217
1072 #define EC_F_PKEY_EC_KEYGEN 199
1073 #define EC_F_PKEY_EC_PARAMGEN 219
1074 #define EC_F_PKEY_EC_SIGN 218
1077 #define EC_R_ASN1_ERROR 115
1078 #define EC_R_ASN1_UNKNOWN_FIELD 116
1079 #define EC_R_BIGNUM_OUT_OF_RANGE 144
1080 #define EC_R_BUFFER_TOO_SMALL 100
1081 #define EC_R_COORDINATES_OUT_OF_RANGE 146
1082 #define EC_R_D2I_ECPKPARAMETERS_FAILURE 117
1083 #define EC_R_DECODE_ERROR 142
1084 #define EC_R_DISCRIMINANT_IS_ZERO 118
1085 #define EC_R_EC_GROUP_NEW_BY_NAME_FAILURE 119
1086 #define EC_R_FIELD_TOO_LARGE 143
1087 #define EC_R_GROUP2PKPARAMETERS_FAILURE 120
1088 #define EC_R_I2D_ECPKPARAMETERS_FAILURE 121
1089 #define EC_R_INCOMPATIBLE_OBJECTS 101
1090 #define EC_R_INVALID_ARGUMENT 112
1091 #define EC_R_INVALID_COMPRESSED_POINT 110
1092 #define EC_R_INVALID_COMPRESSION_BIT 109
1093 #define EC_R_INVALID_CURVE 141
1094 #define EC_R_INVALID_DIGEST_TYPE 138
1095 #define EC_R_INVALID_ENCODING 102
1096 #define EC_R_INVALID_FIELD 103
1097 #define EC_R_INVALID_FORM 104
1098 #define EC_R_INVALID_GROUP_ORDER 122
1099 #define EC_R_INVALID_PENTANOMIAL_BASIS 132
1100 #define EC_R_INVALID_PRIVATE_KEY 123
1101 #define EC_R_INVALID_TRINOMIAL_BASIS 137
1102 #define EC_R_KEYS_NOT_SET 140
1103 #define EC_R_MISSING_PARAMETERS 124
1104 #define EC_R_MISSING_PRIVATE_KEY 125
1105 #define EC_R_NOT_A_NIST_PRIME 135
1106 #define EC_R_NOT_A_SUPPORTED_NIST_PRIME 136
1107 #define EC_R_NOT_IMPLEMENTED 126
1108 #define EC_R_NOT_INITIALIZED 111
1109 #define EC_R_NO_FIELD_MOD 133
1110 #define EC_R_NO_PARAMETERS_SET 139
1111 #define EC_R_PASSED_NULL_PARAMETER 134
1112 #define EC_R_PKPARAMETERS2GROUP_FAILURE 127
1113 #define EC_R_POINT_AT_INFINITY 106
1114 #define EC_R_POINT_IS_NOT_ON_CURVE 107
1115 #define EC_R_SLOT_FULL 108
1116 #define EC_R_UNDEFINED_GENERATOR 113
1117 #define EC_R_UNDEFINED_ORDER 128
1118 #define EC_R_UNKNOWN_GROUP 129
1119 #define EC_R_UNKNOWN_ORDER 114
1120 #define EC_R_UNSUPPORTED_FIELD 131
1121 #define EC_R_WRONG_CURVE_PARAMETERS 145
1122 #define EC_R_WRONG_ORDER 130