1=pod
2
3=head1 NAME
4
5EC_GROUP_get0_order, EC_GROUP_order_bits, EC_GROUP_get0_cofactor,
6EC_GROUP_copy, EC_GROUP_dup, EC_GROUP_method_of, EC_GROUP_set_generator,
7EC_GROUP_get0_generator, EC_GROUP_get_order, EC_GROUP_get_cofactor,
8EC_GROUP_set_curve_name, EC_GROUP_get_curve_name, EC_GROUP_set_asn1_flag,
9EC_GROUP_get_asn1_flag, EC_GROUP_set_point_conversion_form,
10EC_GROUP_get_point_conversion_form, EC_GROUP_get0_seed,
11EC_GROUP_get_seed_len, EC_GROUP_set_seed, EC_GROUP_get_degree,
12EC_GROUP_check, EC_GROUP_check_named_curve,
13EC_GROUP_check_discriminant, EC_GROUP_cmp,
14EC_GROUP_get_basis_type, EC_GROUP_get_trinomial_basis,
15EC_GROUP_get_pentanomial_basis, EC_GROUP_get0_field,
16EC_GROUP_get_field_type
17- Functions for manipulating EC_GROUP objects
18
19=head1 SYNOPSIS
20
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
67Deprecated since OpenSSL 3.0:
68
69 const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group);
70
71=head1 DESCRIPTION
72
73EC_GROUP_copy() copies the curve B<src> into B<dst>. Both B<src> and B<dst> must use the same EC_METHOD.
74
75EC_GROUP_dup() creates a new EC_GROUP object and copies the content from B<src> to the newly created
76EC_GROUP object.
77
78EC_GROUP_method_of() obtains the EC_METHOD of B<group>.
79This function was deprecated in OpenSSL 3.0, since EC_METHOD is no longer a public concept.
80
81EC_GROUP_set_generator() sets curve parameters that must be agreed by all participants using the curve. These
82parameters include the B<generator>, the B<order> and the B<cofactor>. The B<generator> is a well defined point on the
83curve chosen for cryptographic operations. Integers used for point multiplications will be between 0 and
84n-1 where n is the B<order>. The B<order> multiplied by the B<cofactor> gives the number of points on the curve.
85
86EC_GROUP_get0_generator() returns the generator for the identified B<group>.
87
88EC_GROUP_get_order() retrieves the order of B<group> and copies its value into
89B<order>.  It fails in case B<group> is not fully initialized (i.e., its order
90is not set or set to zero).
91
92EC_GROUP_get_cofactor() retrieves the cofactor of B<group> and copies its value
93into B<cofactor>. It fails in case  B<group> is not fully initialized or if the
94cofactor is not set (or set to zero).
95
96The functions EC_GROUP_set_curve_name() and EC_GROUP_get_curve_name(), set and get the NID for the curve respectively
97(see L<EC_GROUP_new(3)>). If a curve does not have a NID associated with it, then EC_GROUP_get_curve_name
98will return NID_undef.
99
100The asn1_flag value is used to determine whether the curve encoding uses
101explicit parameters or a named curve using an ASN1 OID: many applications only
102support the latter form. If asn1_flag is B<OPENSSL_EC_NAMED_CURVE> then the
103named curve form is used and the parameters must have a corresponding
104named curve NID set. If asn1_flags is B<OPENSSL_EC_EXPLICIT_CURVE> the
105parameters are explicitly encoded. The functions EC_GROUP_get_asn1_flag() and
106EC_GROUP_set_asn1_flag() get and set the status of the asn1_flag for the curve.
107Note: B<OPENSSL_EC_EXPLICIT_CURVE> was added in OpenSSL 1.1.0, for
108previous versions of OpenSSL the value 0 must be used instead. Before OpenSSL
1091.1.0 the default form was to use explicit parameters (meaning that
110applications would have to explicitly set the named curve form) in OpenSSL
1111.1.0 and later the named curve form is the default.
112
113The point_conversion_form for a curve controls how EC_POINT data is encoded as ASN1 as defined in X9.62 (ECDSA).
114point_conversion_form_t is an enum defined as follows:
115
116 typedef enum {
117        /** the point is encoded as z||x, where the octet z specifies
118         *   which solution of the quadratic equation y is  */
119        POINT_CONVERSION_COMPRESSED = 2,
120        /** the point is encoded as z||x||y, where z is the octet 0x04  */
121        POINT_CONVERSION_UNCOMPRESSED = 4,
122        /** the point is encoded as z||x||y, where the octet z specifies
123         *  which solution of the quadratic equation y is  */
124        POINT_CONVERSION_HYBRID = 6
125 } point_conversion_form_t;
126
127For POINT_CONVERSION_UNCOMPRESSED the point is encoded as an octet signifying the UNCOMPRESSED form has been used followed by
128the octets for x, followed by the octets for y.
129
130For any given x co-ordinate for a point on a curve it is possible to derive two possible y values. For
131POINT_CONVERSION_COMPRESSED the point is encoded as an octet signifying that the COMPRESSED form has been used AND which of
132the two possible solutions for y has been used, followed by the octets for x.
133
134For POINT_CONVERSION_HYBRID the point is encoded as an octet signifying the HYBRID form has been used AND which of the two
135possible solutions for y has been used, followed by the octets for x, followed by the octets for y.
136
137The functions EC_GROUP_set_point_conversion_form() and EC_GROUP_get_point_conversion_form(), set and get the point_conversion_form
138for the curve respectively.
139
140ANSI X9.62 (ECDSA standard) defines a method of generating the curve parameter b from a random number. This provides advantages
141in that a parameter obtained in this way is highly unlikely to be susceptible to special purpose attacks, or have any trapdoors in it.
142If the seed is present for a curve then the b parameter was generated in a verifiable fashion using that seed. The OpenSSL EC library
143does not use this seed value but does enable you to inspect it using EC_GROUP_get0_seed(). This returns a pointer to a memory block
144containing the seed that was used. The length of the memory block can be obtained using EC_GROUP_get_seed_len(). A number of the
145built-in curves within the library provide seed values that can be obtained. It is also possible to set a custom seed using
146EC_GROUP_set_seed() and passing a pointer to a memory block, along with the length of the seed. Again, the EC library will not use
147this seed value, although it will be preserved in any ASN1 based communications.
148
149EC_GROUP_get_degree() gets the degree of the field.
150For Fp fields this will be the number of bits in p.
151For F2^m fields this will be the value m.
152
153EC_GROUP_get_field_type() identifies what type of field the EC_GROUP structure supports,
154which will be either F2^m or Fp.
155
156The function EC_GROUP_check_discriminant() calculates the discriminant for the curve and verifies that it is valid.
157For a curve defined over Fp the discriminant is given by the formula 4*a^3 + 27*b^2 whilst for F2^m curves the discriminant is
158simply b. In either case for the curve to be valid the discriminant must be non zero.
159
160The function EC_GROUP_check() performs a number of checks on a curve to verify that it is valid. Checks performed include
161verifying that the discriminant is non zero; that a generator has been defined; that the generator is on the curve and has
162the correct order.
163
164The function EC_GROUP_check_named_curve() determines if the group's domain parameters match one of the built-in curves supported by the library.
165The curve name is returned as a B<NID> if it matches. If the group's domain parameters have been modified then no match will be found.
166If the curve name of the given group is B<NID_undef> (e.g. it has been created by using explicit parameters with no curve name),
167then this method can be used to lookup the name of the curve that matches the group domain parameters. The built-in curves contain
168aliases, so that multiple NID's can map to the same domain parameters. For such curves it is unspecified which of the aliases will be
169returned if the curve name of the given group is NID_undef.
170If B<nist_only> is 1 it will only look for NIST approved curves, otherwise it searches all built-in curves.
171This function may be passed a BN_CTX object in the B<ctx> parameter.
172The B<ctx> parameter may be NULL.
173
174EC_GROUP_cmp() compares B<a> and B<b> to determine whether they represent the same curve or not.
175
176The functions EC_GROUP_get_basis_type(), EC_GROUP_get_trinomial_basis() and EC_GROUP_get_pentanomial_basis() should only be called for curves
177defined over an F2^m field. Addition and multiplication operations within an F2^m field are performed using an irreducible polynomial
178function f(x). This function is either a trinomial of the form:
179
180f(x) = x^m + x^k + 1 with m > k >= 1
181
182or a pentanomial of the form:
183
184f(x) = x^m + x^k3 + x^k2 + x^k1 + 1 with m > k3 > k2 > k1 >= 1
185
186The function EC_GROUP_get_basis_type() returns a NID identifying whether a trinomial or pentanomial is in use for the field. The
187function EC_GROUP_get_trinomial_basis() must only be called where f(x) is of the trinomial form, and returns the value of B<k>. Similarly
188the function EC_GROUP_get_pentanomial_basis() must only be called where f(x) is of the pentanomial form, and returns the values of B<k1>,
189B<k2> and B<k3> respectively.
190
191=head1 RETURN VALUES
192
193The following functions return 1 on success or 0 on error: EC_GROUP_copy(), EC_GROUP_set_generator(), EC_GROUP_check(),
194EC_GROUP_check_discriminant(), EC_GROUP_get_trinomial_basis() and EC_GROUP_get_pentanomial_basis().
195
196EC_GROUP_dup() returns a pointer to the duplicated curve, or NULL on error.
197
198EC_GROUP_method_of() returns the EC_METHOD implementation in use for the given curve or NULL on error.
199
200EC_GROUP_get0_generator() returns the generator for the given curve or NULL on error.
201
202EC_GROUP_get_order() returns 0 if the order is not set (or set to zero) for
203B<group> or if copying into B<order> fails, 1 otherwise.
204
205EC_GROUP_get_cofactor() returns 0 if the cofactor is not set (or is set to zero) for B<group> or if copying into B<cofactor> fails, 1 otherwise.
206
207EC_GROUP_get_curve_name() returns the curve name (NID) for B<group> or will return NID_undef if no curve name is associated.
208
209EC_GROUP_get_asn1_flag() returns the ASN1 flag for the specified B<group> .
210
211EC_GROUP_get_point_conversion_form() returns the point_conversion_form for B<group>.
212
213EC_GROUP_get_degree() returns the degree for B<group> or 0 if the operation is not supported by the underlying group implementation.
214
215EC_GROUP_get_field_type() returns either B<NID_X9_62_prime_field> for prime curves
216or B<NID_X9_62_characteristic_two_field> for binary curves;
217these values are defined in the F<< <openssl/obj_mac.h> >> header file.
218
219EC_GROUP_check_named_curve() returns the nid of the matching named curve, otherwise it returns 0 for no match, or -1 on error.
220
221EC_GROUP_get0_order() returns an internal pointer to the group order.
222EC_GROUP_order_bits() returns the number of bits in the group order.
223EC_GROUP_get0_cofactor() returns an internal pointer to the group cofactor.
224EC_GROUP_get0_field() returns an internal pointer to the group field. For curves over GF(p), this is the modulus; for curves
225over GF(2^m), this is the irreducible polynomial defining the field.
226
227EC_GROUP_get0_seed() returns a pointer to the seed that was used to generate the parameter b, or NULL if the seed is not
228specified. EC_GROUP_get_seed_len() returns the length of the seed or 0 if the seed is not specified.
229
230EC_GROUP_set_seed() returns the length of the seed that has been set. If the supplied seed is NULL, or the supplied seed length is
2310, the return value will be 1. On error 0 is returned.
232
233EC_GROUP_cmp() returns 0 if the curves are equal, 1 if they are not equal, or -1 on error.
234
235EC_GROUP_get_basis_type() returns the values NID_X9_62_tpBasis or NID_X9_62_ppBasis (as defined in F<< <openssl/obj_mac.h> >>) for a
236trinomial or pentanomial respectively. Alternatively in the event of an error a 0 is returned.
237
238=head1 SEE ALSO
239
240L<crypto(7)>, L<EC_GROUP_new(3)>,
241L<EC_POINT_new(3)>, L<EC_POINT_add(3)>, L<EC_KEY_new(3)>,
242L<EC_GFp_simple_method(3)>, L<d2i_ECPKParameters(3)>
243
244=head1 HISTORY
245
246EC_GROUP_method_of() was deprecated in OpenSSL 3.0.
247
248EC_GROUP_check_named_curve() and EC_GROUP_get_field_type() were added in OpenSSL 3.0.
249
250=head1 COPYRIGHT
251
252Copyright 2013-2021 The OpenSSL Project Authors. All Rights Reserved.
253
254Licensed under the Apache License 2.0 (the "License").  You may not use
255this file except in compliance with the License.  You can obtain a copy
256in the file LICENSE in the source distribution or at
257L<https://www.openssl.org/source/license.html>.
258
259=cut
260