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 *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
65       use the same EC_METHOD.
66
67       EC_GROUP_dup() creates a new EC_GROUP object and copies the content
68       from 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
73       all participants using the curve. These parameters include the
74       generator, the order and the cofactor. The generator is a well defined
75       point on the curve chosen for cryptographic operations. Integers used
76       for point multiplications will be between 0 and n-1 where n is the
77       order. The order multiplied by the cofactor gives the number of points
78       on the curve.
79
80       EC_GROUP_get0_generator() returns the generator for the identified
81       group.
82
83       EC_GROUP_get_order() retrieves the order of group and copies its value
84       into order.  It fails in case group is not fully initialized (i.e., its
85       order is not set or set to zero).
86
87       EC_GROUP_get_cofactor() retrieves the cofactor of group and copies its
88       value into cofactor. It fails in case  group is not fully initialized
89       or if the cofactor is not set (or set to zero).
90
91       The functions EC_GROUP_set_curve_name() and EC_GROUP_get_curve_name(),
92       set and get the NID for the curve respectively (see EC_GROUP_new(3)).
93       If a curve does not have a NID associated with it, then
94       EC_GROUP_get_curve_name will return NID_undef.
95
96       The asn1_flag value is used to determine whether the curve encoding
97       uses explicit parameters or a named curve using an ASN1 OID: many
98       applications only support the latter form. If asn1_flag is
99       OPENSSL_EC_NAMED_CURVE then the named curve form is used and the
100       parameters must have a corresponding named curve NID set. If asn1_flags
101       is OPENSSL_EC_EXPLICIT_CURVE the parameters are explicitly encoded. The
102       functions EC_GROUP_get_asn1_flag() and EC_GROUP_set_asn1_flag() get and
103       set the status of the asn1_flag for the curve.  Note:
104       OPENSSL_EC_EXPLICIT_CURVE was added in OpenSSL 1.1.0, for previous
105       versions of OpenSSL the value 0 must be used instead. Before OpenSSL
106       1.1.0 the default form was to use explicit parameters (meaning that
107       applications would have to explicitly set the named curve form) in
108       OpenSSL 1.1.0 and later the named curve form is the default.
109
110       The point_conversion_form for a curve controls how EC_POINT data is
111       encoded as ASN1 as defined in X9.62 (ECDSA).  point_conversion_form_t
112       is an enum defined as follows:
113
114        typedef enum {
115               /** the point is encoded as z||x, where the octet z specifies
116                *   which solution of the quadratic equation y is  */
117               POINT_CONVERSION_COMPRESSED = 2,
118               /** the point is encoded as z||x||y, where z is the octet 0x04  */
119               POINT_CONVERSION_UNCOMPRESSED = 4,
120               /** the point is encoded as z||x||y, where the octet z specifies
121                *  which solution of the quadratic equation y is  */
122               POINT_CONVERSION_HYBRID = 6
123        } point_conversion_form_t;
124
125       For POINT_CONVERSION_UNCOMPRESSED the point is encoded as an octet
126       signifying the UNCOMPRESSED form has been used followed by the octets
127       for x, followed by the octets for y.
128
129       For any given x co-ordinate for a point on a curve it is possible to
130       derive two possible y values. For POINT_CONVERSION_COMPRESSED the point
131       is encoded as an octet signifying that the COMPRESSED form has been
132       used AND which of the two possible solutions for y has been used,
133       followed by the octets for x.
134
135       For POINT_CONVERSION_HYBRID the point is encoded as an octet signifying
136       the HYBRID form has been used AND which of the two possible solutions
137       for y has been used, followed by the octets for x, followed by the
138       octets for y.
139
140       The functions EC_GROUP_set_point_conversion_form() and
141       EC_GROUP_get_point_conversion_form(), set and get the
142       point_conversion_form for the curve respectively.
143
144       ANSI X9.62 (ECDSA standard) defines a method of generating the curve
145       parameter b from a random number. This provides advantages in that a
146       parameter obtained in this way is highly unlikely to be susceptible to
147       special purpose attacks, or have any trapdoors in it.  If the seed is
148       present for a curve then the b parameter was generated in a verifiable
149       fashion using that seed. The OpenSSL EC library does not use this seed
150       value but does enable you to inspect it using EC_GROUP_get0_seed().
151       This returns a pointer to a memory block containing the seed that was
152       used. The length of the memory block can be obtained using
153       EC_GROUP_get_seed_len(). A number of the built-in curves within the
154       library provide seed values that can be obtained. It is also possible
155       to set a custom seed using EC_GROUP_set_seed() and passing a pointer to
156       a memory block, along with the length of the seed. Again, the EC
157       library will not use this seed value, although it will be preserved in
158       any ASN1 based communications.
159
160       EC_GROUP_get_degree() gets the degree of the field. For Fp fields this
161       will be the number of bits in p.  For F2^m fields this will be the
162       value m.
163
164       The function EC_GROUP_check_discriminant() calculates the discriminant
165       for the curve and verifies that it is valid.  For a curve defined over
166       Fp the discriminant is given by the formula 4*a^3 + 27*b^2 whilst for
167       F2^m curves the discriminant is simply b. In either case for the curve
168       to be valid the discriminant must be non zero.
169
170       The function EC_GROUP_check() performs a number of checks on a curve to
171       verify that it is valid. Checks performed include verifying that the
172       discriminant is non zero; that a generator has been defined; that the
173       generator is on the curve and has the correct order.
174
175       EC_GROUP_cmp() compares a and b to determine whether they represent the
176       same curve or not.
177
178       The functions EC_GROUP_get_basis_type(), EC_GROUP_get_trinomial_basis()
179       and EC_GROUP_get_pentanomial_basis() should only be called for curves
180       defined over an F2^m field. Addition and multiplication operations
181       within an F2^m field are performed using an irreducible polynomial
182       function f(x). This function is either a trinomial of the form:
183
184       f(x) = x^m + x^k + 1 with m > k >= 1
185
186       or a pentanomial of the form:
187
188       f(x) = x^m + x^k3 + x^k2 + x^k1 + 1 with m > k3 > k2 > k1 >= 1
189
190       The function EC_GROUP_get_basis_type() returns a NID identifying
191       whether a trinomial or pentanomial is in use for the field. The
192       function EC_GROUP_get_trinomial_basis() must only be called where f(x)
193       is of the trinomial form, and returns the value of k. Similarly the
194       function EC_GROUP_get_pentanomial_basis() must only be called where
195       f(x) is of the pentanomial form, and returns the values of k1, k2 and
196       k3 respectively.
197

RETURN VALUES

199       The following functions return 1 on success or 0 on error:
200       EC_GROUP_copy(), EC_GROUP_set_generator(), EC_GROUP_check(),
201       EC_GROUP_check_discriminant(), EC_GROUP_get_trinomial_basis() and
202       EC_GROUP_get_pentanomial_basis().
203
204       EC_GROUP_dup() returns a pointer to the duplicated curve, or NULL on
205       error.
206
207       EC_GROUP_method_of() returns the EC_METHOD implementation in use for
208       the given curve or NULL on error.
209
210       EC_GROUP_get0_generator() returns the generator for the given curve or
211       NULL on error.
212
213       EC_GROUP_get_order() returns 0 if the order is not set (or set to zero)
214       for group or if copying into order fails, 1 otherwise.
215
216       EC_GROUP_get_cofactor() returns 0 if the cofactor is not set (or is set
217       to zero) for group or if copying into cofactor fails, 1 otherwise.
218
219       EC_GROUP_get_curve_name() returns the curve name (NID) for group or
220       will return NID_undef if no curve name is associated.
221
222       EC_GROUP_get_asn1_flag() returns the ASN1 flag for the specified group
223       .
224
225       EC_GROUP_get_point_conversion_form() returns the point_conversion_form
226       for group.
227
228       EC_GROUP_get_degree() returns the degree for group or 0 if the
229       operation is not supported by the underlying group implementation.
230
231       EC_GROUP_get0_order() returns an internal pointer to the group order.
232       EC_GROUP_order_bits() returns the number of bits in the group order.
233       EC_GROUP_get0_cofactor() returns an internal pointer to the group
234       cofactor.
235
236       EC_GROUP_get0_seed() returns a pointer to the seed that was used to
237       generate the parameter b, or NULL if the seed is not specified.
238       EC_GROUP_get_seed_len() returns the length of the seed or 0 if the seed
239       is not specified.
240
241       EC_GROUP_set_seed() returns the length of the seed that has been set.
242       If the supplied seed is NULL, or the supplied seed length is 0, the
243       return value will be 1. On error 0 is returned.
244
245       EC_GROUP_cmp() returns 0 if the curves are equal, 1 if they are not
246       equal, or -1 on error.
247
248       EC_GROUP_get_basis_type() returns the values NID_X9_62_tpBasis or
249       NID_X9_62_ppBasis (as defined in <openssl/obj_mac.h>) for a trinomial
250       or pentanomial respectively. Alternatively in the event of an error a 0
251       is returned.
252

SEE ALSO

254       crypto(7), EC_GROUP_new(3), EC_POINT_new(3), EC_POINT_add(3),
255       EC_KEY_new(3), EC_GFp_simple_method(3), d2i_ECPKParameters(3)
256
258       Copyright 2013-2017 The OpenSSL Project Authors. All Rights Reserved.
259
260       Licensed under the OpenSSL license (the "License").  You may not use
261       this file except in compliance with the License.  You can obtain a copy
262       in the file LICENSE in the source distribution or at
263       <https://www.openssl.org/source/license.html>.
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2671.1.1k                            2021-03-26                  EC_GROUP_COPY(3)
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