EC_GROUP_get_cofactor(3ossl)

1EC_GROUP_COPY(3ossl)                OpenSSL               EC_GROUP_COPY(3ossl)
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NAME

6       EC_GROUP_get0_order, EC_GROUP_order_bits, EC_GROUP_get0_cofactor,
7       EC_GROUP_copy, EC_GROUP_dup, EC_GROUP_method_of,
8       EC_GROUP_set_generator, EC_GROUP_get0_generator, EC_GROUP_get_order,
9       EC_GROUP_get_cofactor, EC_GROUP_set_curve_name,
10       EC_GROUP_get_curve_name, EC_GROUP_set_asn1_flag,
11       EC_GROUP_get_asn1_flag, EC_GROUP_set_point_conversion_form,
12       EC_GROUP_get_point_conversion_form, EC_GROUP_get0_seed,
13       EC_GROUP_get_seed_len, EC_GROUP_set_seed, EC_GROUP_get_degree,
14       EC_GROUP_check, EC_GROUP_check_named_curve,
15       EC_GROUP_check_discriminant, EC_GROUP_cmp, EC_GROUP_get_basis_type,
16       EC_GROUP_get_trinomial_basis, EC_GROUP_get_pentanomial_basis,
17       EC_GROUP_get0_field, EC_GROUP_get_field_type - Functions for
18       manipulating EC_GROUP objects
19

SYNOPSIS

21        #include <openssl/ec.h>
22
23        int EC_GROUP_copy(EC_GROUP *dst, const EC_GROUP *src);
24        EC_GROUP *EC_GROUP_dup(const EC_GROUP *src);
25
26        int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator,
27                                   const BIGNUM *order, const BIGNUM *cofactor);
28        const EC_POINT *EC_GROUP_get0_generator(const EC_GROUP *group);
29
30        int EC_GROUP_get_order(const EC_GROUP *group, BIGNUM *order, BN_CTX *ctx);
31        const BIGNUM *EC_GROUP_get0_order(const EC_GROUP *group);
32        int EC_GROUP_order_bits(const EC_GROUP *group);
33        int EC_GROUP_get_cofactor(const EC_GROUP *group, BIGNUM *cofactor, BN_CTX *ctx);
34        const BIGNUM *EC_GROUP_get0_cofactor(const EC_GROUP *group);
35        const BIGNUM *EC_GROUP_get0_field(const EC_GROUP *group);
36
37        void EC_GROUP_set_curve_name(EC_GROUP *group, int nid);
38        int EC_GROUP_get_curve_name(const EC_GROUP *group);
39
40        void EC_GROUP_set_asn1_flag(EC_GROUP *group, int flag);
41        int EC_GROUP_get_asn1_flag(const EC_GROUP *group);
42
43        void EC_GROUP_set_point_conversion_form(EC_GROUP *group, point_conversion_form_t form);
44        point_conversion_form_t EC_GROUP_get_point_conversion_form(const EC_GROUP *group);
45
46        unsigned char *EC_GROUP_get0_seed(const EC_GROUP *group);
47        size_t EC_GROUP_get_seed_len(const EC_GROUP *group);
48        size_t EC_GROUP_set_seed(EC_GROUP *group, const unsigned char *, size_t len);
49
50        int EC_GROUP_get_degree(const EC_GROUP *group);
51
52        int EC_GROUP_check(const EC_GROUP *group, BN_CTX *ctx);
53        int EC_GROUP_check_named_curve(const EC_GROUP *group, int nist_only,
54                                       BN_CTX *ctx);
55
56        int EC_GROUP_check_discriminant(const EC_GROUP *group, BN_CTX *ctx);
57
58        int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx);
59
60        int EC_GROUP_get_basis_type(const EC_GROUP *group);
61        int EC_GROUP_get_trinomial_basis(const EC_GROUP *group, unsigned int *k);
62        int EC_GROUP_get_pentanomial_basis(const EC_GROUP *group, unsigned int *k1,
63                                           unsigned int *k2, unsigned int *k3);
64
65        int EC_GROUP_get_field_type(const EC_GROUP *group);
66
67       The following function has been deprecated since OpenSSL 3.0, and can
68       be hidden entirely by defining OPENSSL_API_COMPAT with a suitable
69       version value, see openssl_user_macros(7):
70
71        const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group);
72

DESCRIPTION

74       EC_GROUP_copy() copies the curve src into dst. Both src and dst must
75       use the same EC_METHOD.
76
77       EC_GROUP_dup() creates a new EC_GROUP object and copies the content
78       from src to the newly created EC_GROUP object.
79
80       EC_GROUP_method_of() obtains the EC_METHOD of group.  This function was
81       deprecated in OpenSSL 3.0, since EC_METHOD is no longer a public
82       concept.
83
84       EC_GROUP_set_generator() sets curve parameters that must be agreed by
85       all participants using the curve. These parameters include the
86       generator, the order and the cofactor. The generator is a well defined
87       point on the curve chosen for cryptographic operations. Integers used
88       for point multiplications will be between 0 and n-1 where n is the
89       order. The order multiplied by the cofactor gives the number of points
90       on the curve.
91
92       EC_GROUP_get0_generator() returns the generator for the identified
93       group.
94
95       EC_GROUP_get_order() retrieves the order of group and copies its value
96       into order.  It fails in case group is not fully initialized (i.e., its
97       order is not set or set to zero).
98
99       EC_GROUP_get_cofactor() retrieves the cofactor of group and copies its
100       value into cofactor. It fails in case  group is not fully initialized
101       or if the cofactor is not set (or set to zero).
102
103       The functions EC_GROUP_set_curve_name() and EC_GROUP_get_curve_name(),
104       set and get the NID for the curve respectively (see EC_GROUP_new(3)).
105       If a curve does not have a NID associated with it, then
106       EC_GROUP_get_curve_name will return NID_undef.
107
108       The asn1_flag value is used to determine whether the curve encoding
109       uses explicit parameters or a named curve using an ASN1 OID: many
110       applications only support the latter form. If asn1_flag is
111       OPENSSL_EC_NAMED_CURVE then the named curve form is used and the
112       parameters must have a corresponding named curve NID set. If asn1_flags
113       is OPENSSL_EC_EXPLICIT_CURVE the parameters are explicitly encoded. The
114       functions EC_GROUP_get_asn1_flag() and EC_GROUP_set_asn1_flag() get and
115       set the status of the asn1_flag for the curve.  Note:
116       OPENSSL_EC_EXPLICIT_CURVE was added in OpenSSL 1.1.0, for previous
117       versions of OpenSSL the value 0 must be used instead. Before OpenSSL
118       1.1.0 the default form was to use explicit parameters (meaning that
119       applications would have to explicitly set the named curve form) in
120       OpenSSL 1.1.0 and later the named curve form is the default.
121
122       The point_conversion_form for a curve controls how EC_POINT data is
123       encoded as ASN1 as defined in X9.62 (ECDSA).  point_conversion_form_t
124       is an enum defined as follows:
125
126        typedef enum {
127               /** the point is encoded as z||x, where the octet z specifies
128                *   which solution of the quadratic equation y is  */
129               POINT_CONVERSION_COMPRESSED = 2,
130               /** the point is encoded as z||x||y, where z is the octet 0x04  */
131               POINT_CONVERSION_UNCOMPRESSED = 4,
132               /** the point is encoded as z||x||y, where the octet z specifies
133                *  which solution of the quadratic equation y is  */
134               POINT_CONVERSION_HYBRID = 6
135        } point_conversion_form_t;
136
137       For POINT_CONVERSION_UNCOMPRESSED the point is encoded as an octet
138       signifying the UNCOMPRESSED form has been used followed by the octets
139       for x, followed by the octets for y.
140
141       For any given x coordinate for a point on a curve it is possible to
142       derive two possible y values. For POINT_CONVERSION_COMPRESSED the point
143       is encoded as an octet signifying that the COMPRESSED form has been
144       used AND which of the two possible solutions for y has been used,
145       followed by the octets for x.
146
147       For POINT_CONVERSION_HYBRID the point is encoded as an octet signifying
148       the HYBRID form has been used AND which of the two possible solutions
149       for y has been used, followed by the octets for x, followed by the
150       octets for y.
151
152       The functions EC_GROUP_set_point_conversion_form() and
153       EC_GROUP_get_point_conversion_form(), set and get the
154       point_conversion_form for the curve respectively.
155
156       ANSI X9.62 (ECDSA standard) defines a method of generating the curve
157       parameter b from a random number. This provides advantages in that a
158       parameter obtained in this way is highly unlikely to be susceptible to
159       special purpose attacks, or have any trapdoors in it.  If the seed is
160       present for a curve then the b parameter was generated in a verifiable
161       fashion using that seed. The OpenSSL EC library does not use this seed
162       value but does enable you to inspect it using EC_GROUP_get0_seed().
163       This returns a pointer to a memory block containing the seed that was
164       used. The length of the memory block can be obtained using
165       EC_GROUP_get_seed_len(). A number of the built-in curves within the
166       library provide seed values that can be obtained. It is also possible
167       to set a custom seed using EC_GROUP_set_seed() and passing a pointer to
168       a memory block, along with the length of the seed. Again, the EC
169       library will not use this seed value, although it will be preserved in
170       any ASN1 based communications.
171
172       EC_GROUP_get_degree() gets the degree of the field.  For Fp fields this
173       will be the number of bits in p.  For F2^m fields this will be the
174       value m.
175
176       EC_GROUP_get_field_type() identifies what type of field the EC_GROUP
177       structure supports, which will be either F2^m or Fp.
178
179       The function EC_GROUP_check_discriminant() calculates the discriminant
180       for the curve and verifies that it is valid.  For a curve defined over
181       Fp the discriminant is given by the formula 4*a^3 + 27*b^2 whilst for
182       F2^m curves the discriminant is simply b. In either case for the curve
183       to be valid the discriminant must be non zero.
184
185       The function EC_GROUP_check() behaves in the following way: For the
186       OpenSSL default provider it performs a number of checks on a curve to
187       verify that it is valid. Checks performed include verifying that the
188       discriminant is non zero; that a generator has been defined; that the
189       generator is on the curve and has the correct order. For the OpenSSL
190       FIPS provider it uses EC_GROUP_check_named_curve() to conform to
191       SP800-56Ar3.
192
193       The function EC_GROUP_check_named_curve() determines if the group's
194       domain parameters match one of the built-in curves supported by the
195       library.  The curve name is returned as a NID if it matches. If the
196       group's domain parameters have been modified then no match will be
197       found.  If the curve name of the given group is NID_undef (e.g. it has
198       been created by using explicit parameters with no curve name), then
199       this method can be used to lookup the name of the curve that matches
200       the group domain parameters. The built-in curves contain aliases, so
201       that multiple NID's can map to the same domain parameters. For such
202       curves it is unspecified which of the aliases will be returned if the
203       curve name of the given group is NID_undef.  If nist_only is 1 it will
204       only look for NIST approved curves, otherwise it searches all built-in
205       curves.  This function may be passed a BN_CTX object in the ctx
206       parameter.  The ctx parameter may be NULL.
207
208       EC_GROUP_cmp() compares a and b to determine whether they represent the
209       same curve or not.
210
211       The functions EC_GROUP_get_basis_type(), EC_GROUP_get_trinomial_basis()
212       and EC_GROUP_get_pentanomial_basis() should only be called for curves
213       defined over an F2^m field. Addition and multiplication operations
214       within an F2^m field are performed using an irreducible polynomial
215       function f(x). This function is either a trinomial of the form:
216
217       f(x) = x^m + x^k + 1 with m > k >= 1
218
219       or a pentanomial of the form:
220
221       f(x) = x^m + x^k3 + x^k2 + x^k1 + 1 with m > k3 > k2 > k1 >= 1
222
223       The function EC_GROUP_get_basis_type() returns a NID identifying
224       whether a trinomial or pentanomial is in use for the field. The
225       function EC_GROUP_get_trinomial_basis() must only be called where f(x)
226       is of the trinomial form, and returns the value of k. Similarly the
227       function EC_GROUP_get_pentanomial_basis() must only be called where
228       f(x) is of the pentanomial form, and returns the values of k1, k2 and
229       k3 respectively.
230

RETURN VALUES

232       The following functions return 1 on success or 0 on error:
233       EC_GROUP_copy(), EC_GROUP_set_generator(), EC_GROUP_check(),
234       EC_GROUP_check_discriminant(), EC_GROUP_get_trinomial_basis() and
235       EC_GROUP_get_pentanomial_basis().
236
237       EC_GROUP_dup() returns a pointer to the duplicated curve, or NULL on
238       error.
239
240       EC_GROUP_method_of() returns the EC_METHOD implementation in use for
241       the given curve or NULL on error.
242
243       EC_GROUP_get0_generator() returns the generator for the given curve or
244       NULL on error.
245
246       EC_GROUP_get_order() returns 0 if the order is not set (or set to zero)
247       for group or if copying into order fails, 1 otherwise.
248
249       EC_GROUP_get_cofactor() returns 0 if the cofactor is not set (or is set
250       to zero) for group or if copying into cofactor fails, 1 otherwise.
251
252       EC_GROUP_get_curve_name() returns the curve name (NID) for group or
253       will return NID_undef if no curve name is associated.
254
255       EC_GROUP_get_asn1_flag() returns the ASN1 flag for the specified group
256       .
257
258       EC_GROUP_get_point_conversion_form() returns the point_conversion_form
259       for group.
260
261       EC_GROUP_get_degree() returns the degree for group or 0 if the
262       operation is not supported by the underlying group implementation.
263
264       EC_GROUP_get_field_type() returns either NID_X9_62_prime_field for
265       prime curves or NID_X9_62_characteristic_two_field for binary curves;
266       these values are defined in the <openssl/obj_mac.h> header file.
267
268       EC_GROUP_check_named_curve() returns the nid of the matching named
269       curve, otherwise it returns 0 for no match, or -1 on error.
270
271       EC_GROUP_get0_order() returns an internal pointer to the group order.
272       EC_GROUP_order_bits() returns the number of bits in the group order.
273       EC_GROUP_get0_cofactor() returns an internal pointer to the group
274       cofactor.  EC_GROUP_get0_field() returns an internal pointer to the
275       group field. For curves over GF(p), this is the modulus; for curves
276       over GF(2^m), this is the irreducible polynomial defining the field.
277
278       EC_GROUP_get0_seed() returns a pointer to the seed that was used to
279       generate the parameter b, or NULL if the seed is not specified.
280       EC_GROUP_get_seed_len() returns the length of the seed or 0 if the seed
281       is not specified.
282
283       EC_GROUP_set_seed() returns the length of the seed that has been set.
284       If the supplied seed is NULL, or the supplied seed length is 0, the
285       return value will be 1. On error 0 is returned.
286
287       EC_GROUP_cmp() returns 0 if the curves are equal, 1 if they are not
288       equal, or -1 on error.
289
290       EC_GROUP_get_basis_type() returns the values NID_X9_62_tpBasis or
291       NID_X9_62_ppBasis (as defined in <openssl/obj_mac.h>) for a trinomial
292       or pentanomial respectively. Alternatively in the event of an error a 0
293       is returned.
294

HISTORY

300       EC_GROUP_method_of() was deprecated in OpenSSL 3.0.
301       EC_GROUP_get0_field(), EC_GROUP_check_named_curve() and
302       EC_GROUP_get_field_type() were added in OpenSSL 3.0.
303       EC_GROUP_get0_order(), EC_GROUP_order_bits() and
304       EC_GROUP_get0_cofactor() were added in OpenSSL 1.1.0.
305

COPYRIGHT

307       Copyright 2013-2023 The OpenSSL Project Authors. All Rights Reserved.
308
309       Licensed under the Apache License 2.0 (the "License").  You may not use
310       this file except in compliance with the License.  You can obtain a copy
311       in the file LICENSE in the source distribution or at
312       <https://www.openssl.org/source/license.html>.
313
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315
3163.0.9                             2023-07-27              EC_GROUP_COPY(3ossl)

NAME

SYNOPSIS

DESCRIPTION

RETURN VALUES

SEE ALSO

HISTORY

COPYRIGHT