1EC_GROUP_COPY(3)                    OpenSSL                   EC_GROUP_COPY(3)
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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_discriminant, EC_GROUP_cmp,
15       EC_GROUP_get_basis_type, EC_GROUP_get_trinomial_basis,
16       EC_GROUP_get_pentanomial_basis - Functions for manipulating EC_GROUP
17       objects
18

SYNOPSIS

20        #include <openssl/ec.h>
21
22        int EC_GROUP_copy(EC_GROUP *dst, const EC_GROUP *src);
23        EC_GROUP *EC_GROUP_dup(const EC_GROUP *src);
24
25        const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group);
26
27        int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator,
28                                   const BIGNUM *order, const BIGNUM *cofactor);
29        const EC_POINT *EC_GROUP_get0_generator(const EC_GROUP *group);
30
31        int EC_GROUP_get_order(const EC_GROUP *group, BIGNUM *order, BN_CTX *ctx);
32        const BIGNUM *EC_GROUP_get0_order(const EC_GROUP *group);
33        int EC_GROUP_order_bits(const EC_GROUP *group);
34        int EC_GROUP_get_cofactor(const EC_GROUP *group, BIGNUM *cofactor, BN_CTX *ctx);
35        const BIGNUM *EC_GROUP_get0_cofactor(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 *);
45
46        unsigned char *EC_GROUP_get0_seed(const EC_GROUP *x);
47        size_t EC_GROUP_get_seed_len(const EC_GROUP *);
48        size_t EC_GROUP_set_seed(EC_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
54        int EC_GROUP_check_discriminant(const EC_GROUP *group, BN_CTX *ctx);
55
56        int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx);
57
58        int EC_GROUP_get_basis_type(const EC_GROUP *);
59        int EC_GROUP_get_trinomial_basis(const EC_GROUP *, unsigned int *k);
60        int EC_GROUP_get_pentanomial_basis(const EC_GROUP *, unsigned int *k1,
61                                           unsigned int *k2, unsigned int *k3);
62

DESCRIPTION

64       EC_GROUP_copy copies the curve src into dst. Both src and dst must use
65       the same EC_METHOD.
66
67       EC_GROUP_dup creates a new EC_GROUP object and copies the content from
68       src to the newly created EC_GROUP object.
69
70       EC_GROUP_method_of obtains the EC_METHOD of group.
71
72       EC_GROUP_set_generator sets curve parameters that must be agreed by all
73       participants using the curve. These parameters include the generator,
74       the order and the cofactor. The generator is a well defined point on
75       the curve chosen for cryptographic operations. Integers used for point
76       multiplications will be between 0 and n-1 where n is the order. The
77       order multiplied by the cofactor gives the number of points on the
78       curve.
79
80       EC_GROUP_get0_generator returns the generator for the identified group.
81
82       The functions EC_GROUP_get_order and EC_GROUP_get_cofactor populate the
83       provided order and cofactor parameters with the respective order and
84       cofactors for the group.
85
86       The functions EC_GROUP_set_curve_name and EC_GROUP_get_curve_name, set
87       and get the NID for the curve respectively (see EC_GROUP_new(3)). If a
88       curve does not have a NID associated with it, then
89       EC_GROUP_get_curve_name will return 0.
90
91       The asn1_flag value is used to determine whether the curve encoding
92       uses explicit parameters or a named curve using an ASN1 OID: many
93       applications only support the latter form. If asn1_flag is
94       OPENSSL_EC_NAMED_CURVE then the named curve form is used and the
95       parameters must have a corresponding named curve NID set. If asn1_flags
96       is OPENSSL_EC_EXPLICIT_CURVE the parameters are explicitly encoded. The
97       functions EC_GROUP_get_asn1_flag and EC_GROUP_set_asn1_flag get and set
98       the status of the asn1_flag for the curve.  Note:
99       OPENSSL_EC_EXPLICIT_CURVE was added in OpenSSL 1.1.0, for previous
100       versions of OpenSSL the value 0 must be used instead. Before OpenSSL
101       1.1.0 the default form was to use explicit parameters (meaning that
102       applications would have to explicitly set the named curve form) in
103       OpenSSL 1.1.0 and later the named curve form is the default.
104
105       The point_conversion_form for a curve controls how EC_POINT data is
106       encoded as ASN1 as defined in X9.62 (ECDSA).  point_conversion_form_t
107       is an enum defined as follows:
108
109        typedef enum {
110               /** the point is encoded as z||x, where the octet z specifies
111                *   which solution of the quadratic equation y is  */
112               POINT_CONVERSION_COMPRESSED = 2,
113               /** the point is encoded as z||x||y, where z is the octet 0x04  */
114               POINT_CONVERSION_UNCOMPRESSED = 4,
115               /** the point is encoded as z||x||y, where the octet z specifies
116                *  which solution of the quadratic equation y is  */
117               POINT_CONVERSION_HYBRID = 6
118        } point_conversion_form_t;
119
120       For POINT_CONVERSION_UNCOMPRESSED the point is encoded as an octet
121       signifying the UNCOMPRESSED form has been used followed by the octets
122       for x, followed by the octets for y.
123
124       For any given x co-ordinate for a point on a curve it is possible to
125       derive two possible y values. For POINT_CONVERSION_COMPRESSED the point
126       is encoded as an octet signifying that the COMPRESSED form has been
127       used AND which of the two possible solutions for y has been used,
128       followed by the octets for x.
129
130       For POINT_CONVERSION_HYBRID the point is encoded as an octet signifying
131       the HYBRID form has been used AND which of the two possible solutions
132       for y has been used, followed by the octets for x, followed by the
133       octets for y.
134
135       The functions EC_GROUP_set_point_conversion_form and
136       EC_GROUP_get_point_conversion_form set and get the
137       point_conversion_form for the curve respectively.
138
139       ANSI X9.62 (ECDSA standard) defines a method of generating the curve
140       parameter b from a random number. This provides advantages in that a
141       parameter obtained in this way is highly unlikely to be susceptible to
142       special purpose attacks, or have any trapdoors in it.  If the seed is
143       present for a curve then the b parameter was generated in a verifiable
144       fashion using that seed. The OpenSSL EC library does not use this seed
145       value but does enable you to inspect it using EC_GROUP_get0_seed. This
146       returns a pointer to a memory block containing the seed that was used.
147       The length of the memory block can be obtained using
148       EC_GROUP_get_seed_len. A number of the builtin curves within the
149       library provide seed values that can be obtained. It is also possible
150       to set a custom seed using EC_GROUP_set_seed and passing a pointer to a
151       memory block, along with the length of the seed. Again, the EC library
152       will not use this seed value, although it will be preserved in any ASN1
153       based communications.
154
155       EC_GROUP_get_degree gets the degree of the field. For Fp fields this
156       will be the number of bits in p.  For F2^m fields this will be the
157       value m.
158
159       The function EC_GROUP_check_discriminant calculates the discriminant
160       for the curve and verifies that it is valid.  For a curve defined over
161       Fp the discriminant is given by the formula 4*a^3 + 27*b^2 whilst for
162       F2^m curves the discriminant is simply b. In either case for the curve
163       to be valid the discriminant must be non zero.
164
165       The function EC_GROUP_check performs a number of checks on a curve to
166       verify that it is valid. Checks performed include verifying that the
167       discriminant is non zero; that a generator has been defined; that the
168       generator is on the curve and has the correct order.
169
170       EC_GROUP_cmp compares a and b to determine whether they represent the
171       same curve or not.
172
173       The functions EC_GROUP_get_basis_type, EC_GROUP_get_trinomial_basis and
174       EC_GROUP_get_pentanomial_basis should only be called for curves defined
175       over an F2^m field. Addition and multiplication operations within an
176       F2^m field are performed using an irreducible polynomial function f(x).
177       This function is either a trinomial of the form:
178
179       f(x) = x^m + x^k + 1 with m > k >= 1
180
181       or a pentanomial of the form:
182
183       f(x) = x^m + x^k3 + x^k2 + x^k1 + 1 with m > k3 > k2 > k1 >= 1
184
185       The function EC_GROUP_get_basis_type returns a NID identifying whether
186       a trinomial or pentanomial is in use for the field. The function
187       EC_GROUP_get_trinomial_basis must only be called where f(x) is of the
188       trinomial form, and returns the value of k. Similarly the function
189       EC_GROUP_get_pentanomial_basis must only be called where f(x) is of the
190       pentanomial form, and returns the values of k1, k2 and k3 respectively.
191

RETURN VALUES

193       The following functions return 1 on success or 0 on error:
194       EC_GROUP_copy, EC_GROUP_set_generator, EC_GROUP_check,
195       EC_GROUP_check_discriminant, EC_GROUP_get_trinomial_basis and
196       EC_GROUP_get_pentanomial_basis.
197
198       EC_GROUP_dup returns a pointer to the duplicated curve, or NULL on
199       error.
200
201       EC_GROUP_method_of returns the EC_METHOD implementation in use for the
202       given curve or NULL on error.
203
204       EC_GROUP_get0_generator returns the generator for the given curve or
205       NULL on error.
206
207       EC_GROUP_get_order, EC_GROUP_get_cofactor, EC_GROUP_get_curve_name,
208       EC_GROUP_get_asn1_flag, EC_GROUP_get_point_conversion_form and
209       EC_GROUP_get_degree return the order, cofactor, curve name (NID), ASN1
210       flag, point_conversion_form and degree for the specified curve
211       respectively. If there is no curve name associated with a curve then
212       EC_GROUP_get_curve_name will return 0.
213
214       EC_GROUP_get0_order() returns an internal pointer to the group order.
215       EC_GROUP_order_bits() returns the number of bits in the group order.
216       EC_GROUP_get0_cofactor() returns an internal pointer to the group
217       cofactor.
218
219       EC_GROUP_get0_seed returns a pointer to the seed that was used to
220       generate the parameter b, or NULL if the seed is not specified.
221       EC_GROUP_get_seed_len returns the length of the seed or 0 if the seed
222       is not specified.
223
224       EC_GROUP_set_seed returns the length of the seed that has been set. If
225       the supplied seed is NULL, or the supplied seed length is 0, the return
226       value will be 1. On error 0 is returned.
227
228       EC_GROUP_cmp returns 0 if the curves are equal, 1 if they are not
229       equal, or -1 on error.
230
231       EC_GROUP_get_basis_type returns the values NID_X9_62_tpBasis or
232       NID_X9_62_ppBasis (as defined in <openssl/obj_mac.h>) for a trinomial
233       or pentanomial respectively. Alternatively in the event of an error a 0
234       is returned.
235

SEE ALSO

237       crypto(7), EC_GROUP_new(3), EC_POINT_new(3), EC_POINT_add(3),
238       EC_KEY_new(3), EC_GFp_simple_method(3), d2i_ECPKParameters(3)
239
241       Copyright 2013-2017 The OpenSSL Project Authors. All Rights Reserved.
242
243       Licensed under the OpenSSL license (the "License").  You may not use
244       this file except in compliance with the License.  You can obtain a copy
245       in the file LICENSE in the source distribution or at
246       <https://www.openssl.org/source/license.html>.
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2501.1.1d                            2019-10-03                  EC_GROUP_COPY(3)
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