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 #ifndef OPENSSL_NO_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);
163 #ifndef OPENSSL_NO_EC2M
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);
176 /********************************************************************/
177 /* EC_GROUP functions */
178 /********************************************************************/
180 /** Creates a new EC_GROUP object
181 * \param meth EC_METHOD to use
182 * \return newly created EC_GROUP object or NULL in case of an error.
184 EC_GROUP *EC_GROUP_new(const EC_METHOD *meth);
186 /** Frees a EC_GROUP object
187 * \param group EC_GROUP object to be freed.
189 void EC_GROUP_free(EC_GROUP *group);
191 /** Clears and frees a EC_GROUP object
192 * \param group EC_GROUP object to be cleared and freed.
194 void EC_GROUP_clear_free(EC_GROUP *group);
196 /** Copies EC_GROUP objects. Note: both EC_GROUPs must use the same EC_METHOD.
197 * \param dst destination EC_GROUP object
198 * \param src source EC_GROUP object
199 * \return 1 on success and 0 if an error occurred.
201 int EC_GROUP_copy(EC_GROUP *dst, const EC_GROUP *src);
203 /** Creates a new EC_GROUP object and copies the copies the content
204 * form src to the newly created EC_KEY object
205 * \param src source EC_GROUP object
206 * \return newly created EC_GROUP object or NULL in case of an error.
208 EC_GROUP *EC_GROUP_dup(const EC_GROUP *src);
210 /** Returns the EC_METHOD of the EC_GROUP object.
211 * \param group EC_GROUP object
212 * \return EC_METHOD used in this EC_GROUP object.
214 const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group);
216 /** Returns the field type of the EC_METHOD.
217 * \param meth EC_METHOD object
218 * \return NID of the underlying field type OID.
220 int EC_METHOD_get_field_type(const EC_METHOD *meth);
222 /** Sets the generator and it's order/cofactor of a EC_GROUP object.
223 * \param group EC_GROUP object
224 * \param generator EC_POINT object with the generator.
225 * \param order the order of the group generated by the generator.
226 * \param cofactor the index of the sub-group generated by the generator
227 * in the group of all points on the elliptic curve.
228 * \return 1 on success and 0 if an error occured
230 int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator, const BIGNUM *order, const BIGNUM *cofactor);
232 /** Returns the generator of a EC_GROUP object.
233 * \param group EC_GROUP object
234 * \return the currently used generator (possibly NULL).
236 const EC_POINT *EC_GROUP_get0_generator(const EC_GROUP *group);
238 /** Gets the order of a EC_GROUP
239 * \param group EC_GROUP object
240 * \param order BIGNUM to which the order is copied
241 * \param ctx BN_CTX object (optional)
242 * \return 1 on success and 0 if an error occured
244 int EC_GROUP_get_order(const EC_GROUP *group, BIGNUM *order, BN_CTX *ctx);
246 /** Gets the cofactor of a EC_GROUP
247 * \param group EC_GROUP object
248 * \param cofactor BIGNUM to which the cofactor is copied
249 * \param ctx BN_CTX object (optional)
250 * \return 1 on success and 0 if an error occured
252 int EC_GROUP_get_cofactor(const EC_GROUP *group, BIGNUM *cofactor, BN_CTX *ctx);
254 /** Sets the name of a EC_GROUP object
255 * \param group EC_GROUP object
256 * \param nid NID of the curve name OID
258 void EC_GROUP_set_curve_name(EC_GROUP *group, int nid);
260 /** Returns the curve name of a EC_GROUP object
261 * \param group EC_GROUP object
262 * \return NID of the curve name OID or 0 if not set.
264 int EC_GROUP_get_curve_name(const EC_GROUP *group);
266 void EC_GROUP_set_asn1_flag(EC_GROUP *group, int flag);
267 int EC_GROUP_get_asn1_flag(const EC_GROUP *group);
269 void EC_GROUP_set_point_conversion_form(EC_GROUP *group, point_conversion_form_t form);
270 point_conversion_form_t EC_GROUP_get_point_conversion_form(const EC_GROUP *);
272 unsigned char *EC_GROUP_get0_seed(const EC_GROUP *x);
273 size_t EC_GROUP_get_seed_len(const EC_GROUP *);
274 size_t EC_GROUP_set_seed(EC_GROUP *, const unsigned char *, size_t len);
276 /** Sets the parameter of a ec over GFp defined by y^2 = x^3 + a*x + b
277 * \param group EC_GROUP object
278 * \param p BIGNUM with the prime number
279 * \param a BIGNUM with parameter a of the equation
280 * \param b BIGNUM with parameter b of the equation
281 * \param ctx BN_CTX object (optional)
282 * \return 1 on success and 0 if an error occured
284 int EC_GROUP_set_curve_GFp(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
286 /** Gets the parameter of the ec over GFp defined by y^2 = x^3 + a*x + b
287 * \param group EC_GROUP object
288 * \param p BIGNUM for the prime number
289 * \param a BIGNUM for parameter a of the equation
290 * \param b BIGNUM for parameter b of the equation
291 * \param ctx BN_CTX object (optional)
292 * \return 1 on success and 0 if an error occured
294 int EC_GROUP_get_curve_GFp(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
296 #ifndef OPENSSL_NO_EC2M
297 /** Sets the parameter of a ec over GF2m defined by y^2 + x*y = x^3 + a*x^2 + b
298 * \param group EC_GROUP object
299 * \param p BIGNUM with the polynomial defining the underlying field
300 * \param a BIGNUM with parameter a of the equation
301 * \param b BIGNUM with parameter b of the equation
302 * \param ctx BN_CTX object (optional)
303 * \return 1 on success and 0 if an error occured
305 int EC_GROUP_set_curve_GF2m(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
307 /** Gets the parameter of the ec over GF2m defined by y^2 + x*y = x^3 + a*x^2 + b
308 * \param group EC_GROUP object
309 * \param p BIGNUM for the polynomial defining the underlying field
310 * \param a BIGNUM for parameter a of the equation
311 * \param b BIGNUM for parameter b of the equation
312 * \param ctx BN_CTX object (optional)
313 * \return 1 on success and 0 if an error occured
315 int EC_GROUP_get_curve_GF2m(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
317 /** Returns the number of bits needed to represent a field element
318 * \param group EC_GROUP object
319 * \return number of bits needed to represent a field element
321 int EC_GROUP_get_degree(const EC_GROUP *group);
323 /** Checks whether the parameter in the EC_GROUP define a valid ec group
324 * \param group EC_GROUP object
325 * \param ctx BN_CTX object (optional)
326 * \return 1 if group is a valid ec group and 0 otherwise
328 int EC_GROUP_check(const EC_GROUP *group, BN_CTX *ctx);
330 /** Checks whether the discriminant of the elliptic curve is zero or not
331 * \param group EC_GROUP object
332 * \param ctx BN_CTX object (optional)
333 * \return 1 if the discriminant is not zero and 0 otherwise
335 int EC_GROUP_check_discriminant(const EC_GROUP *group, BN_CTX *ctx);
337 /** Compares two EC_GROUP objects
338 * \param a first EC_GROUP object
339 * \param b second EC_GROUP object
340 * \param ctx BN_CTX object (optional)
341 * \return 0 if both groups are equal and 1 otherwise
343 int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx);
345 /* EC_GROUP_new_GF*() calls EC_GROUP_new() and EC_GROUP_set_GF*()
346 * after choosing an appropriate EC_METHOD */
348 /** Creates a new EC_GROUP object with the specified parameters defined
349 * over GFp (defined by the equation y^2 = x^3 + a*x + b)
350 * \param p BIGNUM with the prime number
351 * \param a BIGNUM with the parameter a of the equation
352 * \param b BIGNUM with the parameter b of the equation
353 * \param ctx BN_CTX object (optional)
354 * \return newly created EC_GROUP object with the specified parameters
356 EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
357 #ifndef OPENSSL_NO_EC2M
358 /** Creates a new EC_GROUP object with the specified parameters defined
359 * over GF2m (defined by the equation y^2 + x*y = x^3 + a*x^2 + b)
360 * \param p BIGNUM with the polynomial defining the underlying field
361 * \param a BIGNUM with the parameter a of the equation
362 * \param b BIGNUM with the parameter b of the equation
363 * \param ctx BN_CTX object (optional)
364 * \return newly created EC_GROUP object with the specified parameters
366 EC_GROUP *EC_GROUP_new_curve_GF2m(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
368 /** Creates a EC_GROUP object with a curve specified by a NID
369 * \param nid NID of the OID of the curve name
370 * \return newly created EC_GROUP object with specified curve or NULL
371 * if an error occurred
373 EC_GROUP *EC_GROUP_new_by_curve_name(int nid);
376 /********************************************************************/
377 /* handling of internal curves */
378 /********************************************************************/
385 /* EC_builtin_curves(EC_builtin_curve *r, size_t size) returns number
386 * of all available curves or zero if a error occurred.
387 * In case r ist not zero nitems EC_builtin_curve structures
388 * are filled with the data of the first nitems internal groups */
389 size_t EC_get_builtin_curves(EC_builtin_curve *r, size_t nitems);
392 /********************************************************************/
393 /* EC_POINT functions */
394 /********************************************************************/
396 /** Creates a new EC_POINT object for the specified EC_GROUP
397 * \param group EC_GROUP the underlying EC_GROUP object
398 * \return newly created EC_POINT object or NULL if an error occurred
400 EC_POINT *EC_POINT_new(const EC_GROUP *group);
402 /** Frees a EC_POINT object
403 * \param point EC_POINT object to be freed
405 void EC_POINT_free(EC_POINT *point);
407 /** Clears and frees a EC_POINT object
408 * \param point EC_POINT object to be cleared and freed
410 void EC_POINT_clear_free(EC_POINT *point);
412 /** Copies EC_POINT object
413 * \param dst destination EC_POINT object
414 * \param src source EC_POINT object
415 * \return 1 on success and 0 if an error occured
417 int EC_POINT_copy(EC_POINT *dst, const EC_POINT *src);
419 /** Creates a new EC_POINT object and copies the content of the supplied
421 * \param src source EC_POINT object
422 * \param group underlying the EC_GROUP object
423 * \return newly created EC_POINT object or NULL if an error occurred
425 EC_POINT *EC_POINT_dup(const EC_POINT *src, const EC_GROUP *group);
427 /** Returns the EC_METHOD used in EC_POINT object
428 * \param point EC_POINT object
429 * \return the EC_METHOD used
431 const EC_METHOD *EC_POINT_method_of(const EC_POINT *point);
433 /** Sets a point to infinity (neutral element)
434 * \param group underlying EC_GROUP object
435 * \param point EC_POINT to set to infinity
436 * \return 1 on success and 0 if an error occured
438 int EC_POINT_set_to_infinity(const EC_GROUP *group, EC_POINT *point);
440 /** Sets the jacobian projective coordinates of a EC_POINT over GFp
441 * \param group underlying EC_GROUP object
442 * \param p EC_POINT object
443 * \param x BIGNUM with the x-coordinate
444 * \param y BIGNUM with the y-coordinate
445 * \param z BIGNUM with the z-coordinate
446 * \param ctx BN_CTX object (optional)
447 * \return 1 on success and 0 if an error occured
449 int EC_POINT_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *p,
450 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx);
452 /** Gets the jacobian projective coordinates of a EC_POINT over GFp
453 * \param group underlying EC_GROUP object
454 * \param p EC_POINT object
455 * \param x BIGNUM for the x-coordinate
456 * \param y BIGNUM for the y-coordinate
457 * \param z BIGNUM for the z-coordinate
458 * \param ctx BN_CTX object (optional)
459 * \return 1 on success and 0 if an error occured
461 int EC_POINT_get_Jprojective_coordinates_GFp(const EC_GROUP *group,
462 const EC_POINT *p, BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx);
464 /** Sets the affine coordinates of a EC_POINT over GFp
465 * \param group underlying EC_GROUP object
466 * \param p EC_POINT object
467 * \param x BIGNUM with the x-coordinate
468 * \param y BIGNUM with the y-coordinate
469 * \param ctx BN_CTX object (optional)
470 * \return 1 on success and 0 if an error occured
472 int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *p,
473 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx);
475 /** Gets the affine coordinates of a EC_POINT over GFp
476 * \param group underlying EC_GROUP object
477 * \param p EC_POINT object
478 * \param x BIGNUM for the x-coordinate
479 * \param y BIGNUM for the y-coordinate
480 * \param ctx BN_CTX object (optional)
481 * \return 1 on success and 0 if an error occured
483 int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group,
484 const EC_POINT *p, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
486 /** Sets the x9.62 compressed coordinates of a EC_POINT over GFp
487 * \param group underlying EC_GROUP object
488 * \param p EC_POINT object
489 * \param x BIGNUM with x-coordinate
490 * \param y_bit integer with the y-Bit (either 0 or 1)
491 * \param ctx BN_CTX object (optional)
492 * \return 1 on success and 0 if an error occured
494 int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *group, EC_POINT *p,
495 const BIGNUM *x, int y_bit, BN_CTX *ctx);
496 #ifndef OPENSSL_NO_EC2M
497 /** Sets the affine coordinates of a EC_POINT over GF2m
498 * \param group underlying EC_GROUP object
499 * \param p EC_POINT object
500 * \param x BIGNUM with the x-coordinate
501 * \param y BIGNUM with the y-coordinate
502 * \param ctx BN_CTX object (optional)
503 * \return 1 on success and 0 if an error occured
505 int EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP *group, EC_POINT *p,
506 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx);
508 /** Gets the affine coordinates of a EC_POINT over GF2m
509 * \param group underlying EC_GROUP object
510 * \param p EC_POINT object
511 * \param x BIGNUM for the x-coordinate
512 * \param y BIGNUM for the y-coordinate
513 * \param ctx BN_CTX object (optional)
514 * \return 1 on success and 0 if an error occured
516 int EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *group,
517 const EC_POINT *p, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
519 /** Sets the x9.62 compressed coordinates of a EC_POINT over GF2m
520 * \param group underlying EC_GROUP object
521 * \param p EC_POINT object
522 * \param x BIGNUM with x-coordinate
523 * \param y_bit integer with the y-Bit (either 0 or 1)
524 * \param ctx BN_CTX object (optional)
525 * \return 1 on success and 0 if an error occured
527 int EC_POINT_set_compressed_coordinates_GF2m(const EC_GROUP *group, EC_POINT *p,
528 const BIGNUM *x, int y_bit, BN_CTX *ctx);
530 /** Encodes a EC_POINT object to a octet string
531 * \param group underlying EC_GROUP object
532 * \param p EC_POINT object
533 * \param form point conversion form
534 * \param buf memory buffer for the result. If NULL the function returns
535 * required buffer size.
536 * \param len length of the memory buffer
537 * \param ctx BN_CTX object (optional)
538 * \return the length of the encoded octet string or 0 if an error occurred
540 size_t EC_POINT_point2oct(const EC_GROUP *group, const EC_POINT *p,
541 point_conversion_form_t form,
542 unsigned char *buf, size_t len, BN_CTX *ctx);
544 /** Decodes a EC_POINT from a octet string
545 * \param group underlying EC_GROUP object
546 * \param p EC_POINT object
547 * \param buf memory buffer with the encoded ec point
548 * \param len length of the encoded ec point
549 * \param ctx BN_CTX object (optional)
550 * \return 1 on success and 0 if an error occured
552 int EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *p,
553 const unsigned char *buf, size_t len, BN_CTX *ctx);
555 /* other interfaces to point2oct/oct2point: */
556 BIGNUM *EC_POINT_point2bn(const EC_GROUP *, const EC_POINT *,
557 point_conversion_form_t form, BIGNUM *, BN_CTX *);
558 EC_POINT *EC_POINT_bn2point(const EC_GROUP *, const BIGNUM *,
559 EC_POINT *, BN_CTX *);
560 char *EC_POINT_point2hex(const EC_GROUP *, const EC_POINT *,
561 point_conversion_form_t form, BN_CTX *);
562 EC_POINT *EC_POINT_hex2point(const EC_GROUP *, const char *,
563 EC_POINT *, BN_CTX *);
566 /********************************************************************/
567 /* functions for doing EC_POINT arithmetic */
568 /********************************************************************/
570 /** Computes the sum of two EC_POINT
571 * \param group underlying EC_GROUP object
572 * \param r EC_POINT object for the result (r = a + b)
573 * \param a EC_POINT object with the first summand
574 * \param b EC_POINT object with the second summand
575 * \param ctx BN_CTX object (optional)
576 * \return 1 on success and 0 if an error occured
578 int EC_POINT_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx);
580 /** Computes the double of a EC_POINT
581 * \param group underlying EC_GROUP object
582 * \param r EC_POINT object for the result (r = 2 * a)
583 * \param a EC_POINT object
584 * \param ctx BN_CTX object (optional)
585 * \return 1 on success and 0 if an error occured
587 int EC_POINT_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx);
589 /** Computes the inverse of a EC_POINT
590 * \param group underlying EC_GROUP object
591 * \param a EC_POINT object to be inverted (it's used for the result as well)
592 * \param ctx BN_CTX object (optional)
593 * \return 1 on success and 0 if an error occured
595 int EC_POINT_invert(const EC_GROUP *group, EC_POINT *a, BN_CTX *ctx);
597 /** Checks whether the point is the neutral element of the group
598 * \param group the underlying EC_GROUP object
599 * \param p EC_POINT object
600 * \return 1 if the point is the neutral element and 0 otherwise
602 int EC_POINT_is_at_infinity(const EC_GROUP *group, const EC_POINT *p);
604 /** Checks whether the point is on the curve
605 * \param group underlying EC_GROUP object
606 * \param point EC_POINT object to check
607 * \param ctx BN_CTX object (optional)
608 * \return 1 if point if on the curve and 0 otherwise
610 int EC_POINT_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx);
612 /** Compares two EC_POINTs
613 * \param group underlying EC_GROUP object
614 * \param a first EC_POINT object
615 * \param b second EC_POINT object
616 * \param ctx BN_CTX object (optional)
617 * \return 0 if both points are equal and a value != 0 otherwise
619 int EC_POINT_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx);
621 int EC_POINT_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx);
622 int EC_POINTs_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx);
624 /** Computes r = generator * n sum_{i=0}^num p[i] * m[i]
625 * \param group underlying EC_GROUP object
626 * \param r EC_POINT object for the result
627 * \param n BIGNUM with the multiplier for the group generator (optional)
628 * \param num number futher summands
629 * \param p array of size num of EC_POINT objects
630 * \param m array of size num of BIGNUM objects
631 * \param ctx BN_CTX object (optional)
632 * \return 1 on success and 0 if an error occured
634 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);
636 /** Computes r = generator * n + q * m
637 * \param group underlying EC_GROUP object
638 * \param r EC_POINT object for the result
639 * \param n BIGNUM with the multiplier for the group generator (optional)
640 * \param q EC_POINT object with the first factor of the second summand
641 * \param m BIGNUM with the second factor of the second summand
642 * \param ctx BN_CTX object (optional)
643 * \return 1 on success and 0 if an error occured
645 int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *n, const EC_POINT *q, const BIGNUM *m, BN_CTX *ctx);
647 /** Stores multiples of generator for faster point multiplication
648 * \param group EC_GROUP object
649 * \param ctx BN_CTX object (optional)
650 * \return 1 on success and 0 if an error occured
652 int EC_GROUP_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
654 /** Reports whether a precomputation has been done
655 * \param group EC_GROUP object
656 * \return 1 if a pre-computation has been done and 0 otherwise
658 int EC_GROUP_have_precompute_mult(const EC_GROUP *group);
661 /********************************************************************/
663 /********************************************************************/
665 /* EC_GROUP_get_basis_type() returns the NID of the basis type
666 * used to represent the field elements */
667 int EC_GROUP_get_basis_type(const EC_GROUP *);
668 #ifndef OPENSSL_NO_EC2M
669 int EC_GROUP_get_trinomial_basis(const EC_GROUP *, unsigned int *k);
670 int EC_GROUP_get_pentanomial_basis(const EC_GROUP *, unsigned int *k1,
671 unsigned int *k2, unsigned int *k3);
674 #define OPENSSL_EC_NAMED_CURVE 0x001
676 typedef struct ecpk_parameters_st ECPKPARAMETERS;
678 EC_GROUP *d2i_ECPKParameters(EC_GROUP **, const unsigned char **in, long len);
679 int i2d_ECPKParameters(const EC_GROUP *, unsigned char **out);
681 #define d2i_ECPKParameters_bio(bp,x) ASN1_d2i_bio_of(EC_GROUP,NULL,d2i_ECPKParameters,bp,x)
682 #define i2d_ECPKParameters_bio(bp,x) ASN1_i2d_bio_of_const(EC_GROUP,i2d_ECPKParameters,bp,x)
683 #define d2i_ECPKParameters_fp(fp,x) (EC_GROUP *)ASN1_d2i_fp(NULL, \
684 (char *(*)())d2i_ECPKParameters,(fp),(unsigned char **)(x))
685 #define i2d_ECPKParameters_fp(fp,x) ASN1_i2d_fp(i2d_ECPKParameters,(fp), \
686 (unsigned char *)(x))
688 #ifndef OPENSSL_NO_BIO
689 int ECPKParameters_print(BIO *bp, const EC_GROUP *x, int off);
691 #ifndef OPENSSL_NO_FP_API
692 int ECPKParameters_print_fp(FILE *fp, const EC_GROUP *x, int off);
696 /********************************************************************/
697 /* EC_KEY functions */
698 /********************************************************************/
700 typedef struct ec_key_st EC_KEY;
702 /* some values for the encoding_flag */
703 #define EC_PKEY_NO_PARAMETERS 0x001
704 #define EC_PKEY_NO_PUBKEY 0x002
706 /* some values for the flags field */
707 #define EC_FLAG_NON_FIPS_ALLOW 0x1
708 #define EC_FLAG_FIPS_CHECKED 0x2
710 /** Creates a new EC_KEY object.
711 * \return EC_KEY object or NULL if an error occurred.
713 EC_KEY *EC_KEY_new(void);
715 int EC_KEY_get_flags(const EC_KEY *key);
717 void EC_KEY_set_flags(EC_KEY *key, int flags);
719 void EC_KEY_clear_flags(EC_KEY *key, int flags);
721 /** Creates a new EC_KEY object using a named curve as underlying
723 * \param nid NID of the named curve.
724 * \return EC_KEY object or NULL if an error occurred.
726 EC_KEY *EC_KEY_new_by_curve_name(int nid);
728 /** Frees a EC_KEY object.
729 * \param key EC_KEY object to be freed.
731 void EC_KEY_free(EC_KEY *key);
733 /** Copies a EC_KEY object.
734 * \param dst destination EC_KEY object
735 * \param src src EC_KEY object
736 * \return dst or NULL if an error occurred.
738 EC_KEY *EC_KEY_copy(EC_KEY *dst, const EC_KEY *src);
740 /** Creates a new EC_KEY object and copies the content from src to it.
741 * \param src the source EC_KEY object
742 * \return newly created EC_KEY object or NULL if an error occurred.
744 EC_KEY *EC_KEY_dup(const EC_KEY *src);
746 /** Increases the internal reference count of a EC_KEY object.
747 * \param key EC_KEY object
748 * \return 1 on success and 0 if an error occurred.
750 int EC_KEY_up_ref(EC_KEY *key);
752 /** Returns the EC_GROUP object of a EC_KEY object
753 * \param key EC_KEY object
754 * \return the EC_GROUP object (possibly NULL).
756 const EC_GROUP *EC_KEY_get0_group(const EC_KEY *key);
758 /** Sets the EC_GROUP of a EC_KEY object.
759 * \param key EC_KEY object
760 * \param group EC_GROUP to use in the EC_KEY object (note: the EC_KEY
761 * object will use an own copy of the EC_GROUP).
762 * \return 1 on success and 0 if an error occurred.
764 int EC_KEY_set_group(EC_KEY *key, const EC_GROUP *group);
766 /** Returns the private key of a EC_KEY object.
767 * \param key EC_KEY object
768 * \return a BIGNUM with the private key (possibly NULL).
770 const BIGNUM *EC_KEY_get0_private_key(const EC_KEY *key);
772 /** Sets the private key of a EC_KEY object.
773 * \param key EC_KEY object
774 * \param prv BIGNUM with the private key (note: the EC_KEY object
775 * will use an own copy of the BIGNUM).
776 * \return 1 on success and 0 if an error occurred.
778 int EC_KEY_set_private_key(EC_KEY *key, const BIGNUM *prv);
780 /** Returns the public key of a EC_KEY object.
781 * \param key the EC_KEY object
782 * \return a EC_POINT object with the public key (possibly NULL)
784 const EC_POINT *EC_KEY_get0_public_key(const EC_KEY *key);
786 /** Sets the public key of a EC_KEY object.
787 * \param key EC_KEY object
788 * \param pub EC_POINT object with the public key (note: the EC_KEY object
789 * will use an own copy of the EC_POINT object).
790 * \return 1 on success and 0 if an error occurred.
792 int EC_KEY_set_public_key(EC_KEY *key, const EC_POINT *pub);
794 unsigned EC_KEY_get_enc_flags(const EC_KEY *key);
795 void EC_KEY_set_enc_flags(EC_KEY *eckey, unsigned int flags);
796 point_conversion_form_t EC_KEY_get_conv_form(const EC_KEY *key);
797 void EC_KEY_set_conv_form(EC_KEY *eckey, point_conversion_form_t cform);
798 /* functions to set/get method specific data */
799 void *EC_KEY_get_key_method_data(EC_KEY *key,
800 void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
801 void EC_KEY_insert_key_method_data(EC_KEY *key, void *data,
802 void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
803 /* wrapper functions for the underlying EC_GROUP object */
804 void EC_KEY_set_asn1_flag(EC_KEY *eckey, int asn1_flag);
806 /** Creates a table of pre-computed multiples of the generator to
807 * accelerate further EC_KEY operations.
808 * \param key EC_KEY object
809 * \param ctx BN_CTX object (optional)
810 * \return 1 on success and 0 if an error occurred.
812 int EC_KEY_precompute_mult(EC_KEY *key, BN_CTX *ctx);
814 /** Creates a new ec private (and optional a new public) key.
815 * \param key EC_KEY object
816 * \return 1 on success and 0 if an error occurred.
818 int EC_KEY_generate_key(EC_KEY *key);
820 /** Verifies that a private and/or public key is valid.
821 * \param key the EC_KEY object
822 * \return 1 on success and 0 otherwise.
824 int EC_KEY_check_key(const EC_KEY *key);
826 /** Sets a public key from affine coordindates performing
827 * neccessary NIST PKV tests.
828 * \param key the EC_KEY object
829 * \param x public key x coordinate
830 * \param y public key y coordinate
831 * \return 1 on success and 0 otherwise.
833 int EC_KEY_set_public_key_affine_coordinates(EC_KEY *key, BIGNUM *x, BIGNUM *y);
836 /********************************************************************/
837 /* de- and encoding functions for SEC1 ECPrivateKey */
838 /********************************************************************/
840 /** Decodes a private key from a memory buffer.
841 * \param key a pointer to a EC_KEY object which should be used (or NULL)
842 * \param in pointer to memory with the DER encoded private key
843 * \param len length of the DER encoded private key
844 * \return the decoded private key or NULL if an error occurred.
846 EC_KEY *d2i_ECPrivateKey(EC_KEY **key, const unsigned char **in, long len);
848 /** Encodes a private key object and stores the result in a buffer.
849 * \param key the EC_KEY object to encode
850 * \param out the buffer for the result (if NULL the function returns number
852 * \return 1 on success and 0 if an error occurred.
854 int i2d_ECPrivateKey(EC_KEY *key, unsigned char **out);
857 /********************************************************************/
858 /* de- and encoding functions for EC parameters */
859 /********************************************************************/
861 /** Decodes ec parameter from a memory buffer.
862 * \param key a pointer to a EC_KEY object which should be used (or NULL)
863 * \param in pointer to memory with the DER encoded ec parameters
864 * \param len length of the DER encoded ec parameters
865 * \return a EC_KEY object with the decoded parameters or NULL if an error
868 EC_KEY *d2i_ECParameters(EC_KEY **key, const unsigned char **in, long len);
870 /** Encodes ec parameter and stores the result in a buffer.
871 * \param key the EC_KEY object with ec paramters to encode
872 * \param out the buffer for the result (if NULL the function returns number
874 * \return 1 on success and 0 if an error occurred.
876 int i2d_ECParameters(EC_KEY *key, unsigned char **out);
879 /********************************************************************/
880 /* de- and encoding functions for EC public key */
881 /* (octet string, not DER -- hence 'o2i' and 'i2o') */
882 /********************************************************************/
884 /** Decodes a ec public key from a octet string.
885 * \param key a pointer to a EC_KEY object which should be used
886 * \param in memory buffer with the encoded public key
887 * \param len length of the encoded public key
888 * \return EC_KEY object with decoded public key or NULL if an error
891 EC_KEY *o2i_ECPublicKey(EC_KEY **key, const unsigned char **in, long len);
893 /** Encodes a ec public key in an octet string.
894 * \param key the EC_KEY object with the public key
895 * \param out the buffer for the result (if NULL the function returns number
897 * \return 1 on success and 0 if an error occurred
899 int i2o_ECPublicKey(EC_KEY *key, unsigned char **out);
901 #ifndef OPENSSL_NO_BIO
902 /** Prints out the ec parameters on human readable form.
903 * \param bp BIO object to which the information is printed
904 * \param key EC_KEY object
905 * \return 1 on success and 0 if an error occurred
907 int ECParameters_print(BIO *bp, const EC_KEY *key);
909 /** Prints out the contents of a EC_KEY object
910 * \param bp BIO object to which the information is printed
911 * \param key EC_KEY object
912 * \param off line offset
913 * \return 1 on success and 0 if an error occurred
915 int EC_KEY_print(BIO *bp, const EC_KEY *key, int off);
918 #ifndef OPENSSL_NO_FP_API
919 /** Prints out the ec parameters on human readable form.
920 * \param fp file descriptor to which the information is printed
921 * \param key EC_KEY object
922 * \return 1 on success and 0 if an error occurred
924 int ECParameters_print_fp(FILE *fp, const EC_KEY *key);
926 /** Prints out the contents of a EC_KEY object
927 * \param fp file descriptor to which the information is printed
928 * \param key EC_KEY object
929 * \param off line offset
930 * \return 1 on success and 0 if an error occurred
932 int EC_KEY_print_fp(FILE *fp, const EC_KEY *key, int off);
936 #define ECParameters_dup(x) ASN1_dup_of(EC_KEY,i2d_ECParameters,d2i_ECParameters,x)
939 #if defined(__SUNPRO_C)
940 # if __SUNPRO_C >= 0x520
941 # pragma error_messages (default,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE)
946 #define EVP_PKEY_CTX_set_ec_paramgen_curve_nid(ctx, nid) \
947 EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, EVP_PKEY_OP_PARAMGEN, \
948 EVP_PKEY_CTRL_EC_PARAMGEN_CURVE_NID, nid, NULL)
951 #define EVP_PKEY_CTRL_EC_PARAMGEN_CURVE_NID (EVP_PKEY_ALG_CTRL + 1)
953 /* BEGIN ERROR CODES */
954 /* The following lines are auto generated by the script mkerr.pl. Any changes
955 * made after this point may be overwritten when the script is next run.
957 void ERR_load_EC_strings(void);
959 /* Error codes for the EC functions. */
961 /* Function codes. */
962 #define EC_F_BN_TO_FELEM 224
963 #define EC_F_COMPUTE_WNAF 143
964 #define EC_F_D2I_ECPARAMETERS 144
965 #define EC_F_D2I_ECPKPARAMETERS 145
966 #define EC_F_D2I_ECPRIVATEKEY 146
967 #define EC_F_DO_EC_KEY_PRINT 221
968 #define EC_F_ECKEY_PARAM2TYPE 223
969 #define EC_F_ECKEY_PARAM_DECODE 212
970 #define EC_F_ECKEY_PRIV_DECODE 213
971 #define EC_F_ECKEY_PRIV_ENCODE 214
972 #define EC_F_ECKEY_PUB_DECODE 215
973 #define EC_F_ECKEY_PUB_ENCODE 216
974 #define EC_F_ECKEY_TYPE2PARAM 220
975 #define EC_F_ECPARAMETERS_PRINT 147
976 #define EC_F_ECPARAMETERS_PRINT_FP 148
977 #define EC_F_ECPKPARAMETERS_PRINT 149
978 #define EC_F_ECPKPARAMETERS_PRINT_FP 150
979 #define EC_F_ECP_NIST_MOD_192 203
980 #define EC_F_ECP_NIST_MOD_224 204
981 #define EC_F_ECP_NIST_MOD_256 205
982 #define EC_F_ECP_NIST_MOD_521 206
983 #define EC_F_EC_ASN1_GROUP2CURVE 153
984 #define EC_F_EC_ASN1_GROUP2FIELDID 154
985 #define EC_F_EC_ASN1_GROUP2PARAMETERS 155
986 #define EC_F_EC_ASN1_GROUP2PKPARAMETERS 156
987 #define EC_F_EC_ASN1_PARAMETERS2GROUP 157
988 #define EC_F_EC_ASN1_PKPARAMETERS2GROUP 158
989 #define EC_F_EC_EX_DATA_SET_DATA 211
990 #define EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY 208
991 #define EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT 159
992 #define EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE 195
993 #define EC_F_EC_GF2M_SIMPLE_OCT2POINT 160
994 #define EC_F_EC_GF2M_SIMPLE_POINT2OCT 161
995 #define EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES 162
996 #define EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES 163
997 #define EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES 164
998 #define EC_F_EC_GFP_MONT_FIELD_DECODE 133
999 #define EC_F_EC_GFP_MONT_FIELD_ENCODE 134
1000 #define EC_F_EC_GFP_MONT_FIELD_MUL 131
1001 #define EC_F_EC_GFP_MONT_FIELD_SET_TO_ONE 209
1002 #define EC_F_EC_GFP_MONT_FIELD_SQR 132
1003 #define EC_F_EC_GFP_MONT_GROUP_SET_CURVE 189
1004 #define EC_F_EC_GFP_MONT_GROUP_SET_CURVE_GFP 135
1005 #define EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE 225
1006 #define EC_F_EC_GFP_NISTP224_POINTS_MUL 228
1007 #define EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES 226
1008 #define EC_F_EC_GFP_NIST_FIELD_MUL 200
1009 #define EC_F_EC_GFP_NIST_FIELD_SQR 201
1010 #define EC_F_EC_GFP_NIST_GROUP_SET_CURVE 202
1011 #define EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT 165
1012 #define EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE 166
1013 #define EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE_GFP 100
1014 #define EC_F_EC_GFP_SIMPLE_GROUP_SET_GENERATOR 101
1015 #define EC_F_EC_GFP_SIMPLE_MAKE_AFFINE 102
1016 #define EC_F_EC_GFP_SIMPLE_OCT2POINT 103
1017 #define EC_F_EC_GFP_SIMPLE_POINT2OCT 104
1018 #define EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE 137
1019 #define EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES 167
1020 #define EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES_GFP 105
1021 #define EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES 168
1022 #define EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES_GFP 128
1023 #define EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES 169
1024 #define EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP 129
1025 #define EC_F_EC_GROUP_CHECK 170
1026 #define EC_F_EC_GROUP_CHECK_DISCRIMINANT 171
1027 #define EC_F_EC_GROUP_COPY 106
1028 #define EC_F_EC_GROUP_GET0_GENERATOR 139
1029 #define EC_F_EC_GROUP_GET_COFACTOR 140
1030 #define EC_F_EC_GROUP_GET_CURVE_GF2M 172
1031 #define EC_F_EC_GROUP_GET_CURVE_GFP 130
1032 #define EC_F_EC_GROUP_GET_DEGREE 173
1033 #define EC_F_EC_GROUP_GET_ORDER 141
1034 #define EC_F_EC_GROUP_GET_PENTANOMIAL_BASIS 193
1035 #define EC_F_EC_GROUP_GET_TRINOMIAL_BASIS 194
1036 #define EC_F_EC_GROUP_NEW 108
1037 #define EC_F_EC_GROUP_NEW_BY_CURVE_NAME 174
1038 #define EC_F_EC_GROUP_NEW_FROM_DATA 175
1039 #define EC_F_EC_GROUP_PRECOMPUTE_MULT 142
1040 #define EC_F_EC_GROUP_SET_CURVE_GF2M 176
1041 #define EC_F_EC_GROUP_SET_CURVE_GFP 109
1042 #define EC_F_EC_GROUP_SET_EXTRA_DATA 110
1043 #define EC_F_EC_GROUP_SET_GENERATOR 111
1044 #define EC_F_EC_KEY_CHECK_KEY 177
1045 #define EC_F_EC_KEY_COPY 178
1046 #define EC_F_EC_KEY_GENERATE_KEY 179
1047 #define EC_F_EC_KEY_NEW 182
1048 #define EC_F_EC_KEY_PRINT 180
1049 #define EC_F_EC_KEY_PRINT_FP 181
1050 #define EC_F_EC_KEY_SET_PUBLIC_KEY_AFFINE_COORDINATES 229
1051 #define EC_F_EC_POINTS_MAKE_AFFINE 136
1052 #define EC_F_EC_POINT_ADD 112
1053 #define EC_F_EC_POINT_CMP 113
1054 #define EC_F_EC_POINT_COPY 114
1055 #define EC_F_EC_POINT_DBL 115
1056 #define EC_F_EC_POINT_GET_AFFINE_COORDINATES_GF2M 183
1057 #define EC_F_EC_POINT_GET_AFFINE_COORDINATES_GFP 116
1058 #define EC_F_EC_POINT_GET_JPROJECTIVE_COORDINATES_GFP 117
1059 #define EC_F_EC_POINT_INVERT 210
1060 #define EC_F_EC_POINT_IS_AT_INFINITY 118
1061 #define EC_F_EC_POINT_IS_ON_CURVE 119
1062 #define EC_F_EC_POINT_MAKE_AFFINE 120
1063 #define EC_F_EC_POINT_MUL 184
1064 #define EC_F_EC_POINT_NEW 121
1065 #define EC_F_EC_POINT_OCT2POINT 122
1066 #define EC_F_EC_POINT_POINT2OCT 123
1067 #define EC_F_EC_POINT_SET_AFFINE_COORDINATES_GF2M 185
1068 #define EC_F_EC_POINT_SET_AFFINE_COORDINATES_GFP 124
1069 #define EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GF2M 186
1070 #define EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GFP 125
1071 #define EC_F_EC_POINT_SET_JPROJECTIVE_COORDINATES_GFP 126
1072 #define EC_F_EC_POINT_SET_TO_INFINITY 127
1073 #define EC_F_EC_PRE_COMP_DUP 207
1074 #define EC_F_EC_PRE_COMP_NEW 196
1075 #define EC_F_EC_WNAF_MUL 187
1076 #define EC_F_EC_WNAF_PRECOMPUTE_MULT 188
1077 #define EC_F_I2D_ECPARAMETERS 190
1078 #define EC_F_I2D_ECPKPARAMETERS 191
1079 #define EC_F_I2D_ECPRIVATEKEY 192
1080 #define EC_F_I2O_ECPUBLICKEY 151
1081 #define EC_F_NISTP224_PRE_COMP_NEW 227
1082 #define EC_F_O2I_ECPUBLICKEY 152
1083 #define EC_F_OLD_EC_PRIV_DECODE 222
1084 #define EC_F_PKEY_EC_CTRL 197
1085 #define EC_F_PKEY_EC_CTRL_STR 198
1086 #define EC_F_PKEY_EC_DERIVE 217
1087 #define EC_F_PKEY_EC_KEYGEN 199
1088 #define EC_F_PKEY_EC_PARAMGEN 219
1089 #define EC_F_PKEY_EC_SIGN 218
1092 #define EC_R_ASN1_ERROR 115
1093 #define EC_R_ASN1_UNKNOWN_FIELD 116
1094 #define EC_R_BIGNUM_OUT_OF_RANGE 144
1095 #define EC_R_BUFFER_TOO_SMALL 100
1096 #define EC_R_COORDINATES_OUT_OF_RANGE 146
1097 #define EC_R_D2I_ECPKPARAMETERS_FAILURE 117
1098 #define EC_R_DECODE_ERROR 142
1099 #define EC_R_DISCRIMINANT_IS_ZERO 118
1100 #define EC_R_EC_GROUP_NEW_BY_NAME_FAILURE 119
1101 #define EC_R_FIELD_TOO_LARGE 143
1102 #define EC_R_GF2M_NOT_SUPPORTED 147
1103 #define EC_R_GROUP2PKPARAMETERS_FAILURE 120
1104 #define EC_R_I2D_ECPKPARAMETERS_FAILURE 121
1105 #define EC_R_INCOMPATIBLE_OBJECTS 101
1106 #define EC_R_INVALID_ARGUMENT 112
1107 #define EC_R_INVALID_COMPRESSED_POINT 110
1108 #define EC_R_INVALID_COMPRESSION_BIT 109
1109 #define EC_R_INVALID_CURVE 141
1110 #define EC_R_INVALID_DIGEST_TYPE 138
1111 #define EC_R_INVALID_ENCODING 102
1112 #define EC_R_INVALID_FIELD 103
1113 #define EC_R_INVALID_FORM 104
1114 #define EC_R_INVALID_GROUP_ORDER 122
1115 #define EC_R_INVALID_PENTANOMIAL_BASIS 132
1116 #define EC_R_INVALID_PRIVATE_KEY 123
1117 #define EC_R_INVALID_TRINOMIAL_BASIS 137
1118 #define EC_R_KEYS_NOT_SET 140
1119 #define EC_R_MISSING_PARAMETERS 124
1120 #define EC_R_MISSING_PRIVATE_KEY 125
1121 #define EC_R_NOT_A_NIST_PRIME 135
1122 #define EC_R_NOT_A_SUPPORTED_NIST_PRIME 136
1123 #define EC_R_NOT_IMPLEMENTED 126
1124 #define EC_R_NOT_INITIALIZED 111
1125 #define EC_R_NO_FIELD_MOD 133
1126 #define EC_R_NO_PARAMETERS_SET 139
1127 #define EC_R_PASSED_NULL_PARAMETER 134
1128 #define EC_R_PKPARAMETERS2GROUP_FAILURE 127
1129 #define EC_R_POINT_AT_INFINITY 106
1130 #define EC_R_POINT_IS_NOT_ON_CURVE 107
1131 #define EC_R_SLOT_FULL 108
1132 #define EC_R_UNDEFINED_GENERATOR 113
1133 #define EC_R_UNDEFINED_ORDER 128
1134 #define EC_R_UNKNOWN_GROUP 129
1135 #define EC_R_UNKNOWN_ORDER 114
1136 #define EC_R_UNSUPPORTED_FIELD 131
1137 #define EC_R_WRONG_CURVE_PARAMETERS 145
1138 #define EC_R_WRONG_ORDER 130