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1=pod
2
3=head1 NAME
4
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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_discriminant, EC_GROUP_cmp,
13EC_GROUP_get_basis_type, EC_GROUP_get_trinomial_basis,
14EC_GROUP_get_pentanomial_basis
15- Functions for manipulating EC_GROUP objects
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16
17=head1 SYNOPSIS
18
19 #include <openssl/ec.h>
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20
21 int EC_GROUP_copy(EC_GROUP *dst, const EC_GROUP *src);
22 EC_GROUP *EC_GROUP_dup(const EC_GROUP *src);
23
24 const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group);
25
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26 int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator,
27 const BIGNUM *order, const BIGNUM *cofactor);
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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);
be2e334f 31 const BIGNUM *EC_GROUP_get0_order(const EC_GROUP *group);
14f46560 32 int EC_GROUP_order_bits(const EC_GROUP *group);
aafbe1cc 33 int EC_GROUP_get_cofactor(const EC_GROUP *group, BIGNUM *cofactor, BN_CTX *ctx);
be2e334f 34 const BIGNUM *EC_GROUP_get0_cofactor(const EC_GROUP *group);
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35
36 void EC_GROUP_set_curve_name(EC_GROUP *group, int nid);
37 int EC_GROUP_get_curve_name(const EC_GROUP *group);
38
39 void EC_GROUP_set_asn1_flag(EC_GROUP *group, int flag);
40 int EC_GROUP_get_asn1_flag(const EC_GROUP *group);
41
42 void EC_GROUP_set_point_conversion_form(EC_GROUP *group, point_conversion_form_t form);
43 point_conversion_form_t EC_GROUP_get_point_conversion_form(const EC_GROUP *);
44
45 unsigned char *EC_GROUP_get0_seed(const EC_GROUP *x);
46 size_t EC_GROUP_get_seed_len(const EC_GROUP *);
47 size_t EC_GROUP_set_seed(EC_GROUP *, const unsigned char *, size_t len);
48
49 int EC_GROUP_get_degree(const EC_GROUP *group);
50
51 int EC_GROUP_check(const EC_GROUP *group, BN_CTX *ctx);
52
53 int EC_GROUP_check_discriminant(const EC_GROUP *group, BN_CTX *ctx);
54
55 int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx);
56
57 int EC_GROUP_get_basis_type(const EC_GROUP *);
58 int EC_GROUP_get_trinomial_basis(const EC_GROUP *, unsigned int *k);
1bc74519 59 int EC_GROUP_get_pentanomial_basis(const EC_GROUP *, unsigned int *k1,
e9b77246 60 unsigned int *k2, unsigned int *k3);
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61
62=head1 DESCRIPTION
63
64EC_GROUP_copy copies the curve B<src> into B<dst>. Both B<src> and B<dst> must use the same EC_METHOD.
65
66EC_GROUP_dup creates a new EC_GROUP object and copies the content from B<src> to the newly created
67EC_GROUP object.
68
69EC_GROUP_method_of obtains the EC_METHOD of B<group>.
70
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71EC_GROUP_set_generator sets curve parameters that must be agreed by all participants using the curve. These
72parameters include the B<generator>, the B<order> and the B<cofactor>. The B<generator> is a well defined point on the
aafbe1cc 73curve chosen for cryptographic operations. Integers used for point multiplications will be between 0 and
186bb907 74n-1 where n is the B<order>. The B<order> multiplied by the B<cofactor> gives the number of points on the curve.
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75
76EC_GROUP_get0_generator returns the generator for the identified B<group>.
77
78The functions EC_GROUP_get_order and EC_GROUP_get_cofactor populate the provided B<order> and B<cofactor> parameters
79with the respective order and cofactors for the B<group>.
80
81The functions EC_GROUP_set_curve_name and EC_GROUP_get_curve_name, set and get the NID for the curve respectively
9b86974e 82(see L<EC_GROUP_new(3)>). If a curve does not have a NID associated with it, then EC_GROUP_get_curve_name
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83will return 0.
84
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85The asn1_flag value is used to determine whether the curve encoding uses
86explicit parameters or a named curve using an ASN1 OID: many applications only
87support the latter form. If asn1_flag is B<OPENSSL_EC_NAMED_CURVE> then the
88named curve form is used and the parameters must have a corresponding
89named curve NID set. If asn1_flags is B<OPENSSL_EC_EXPLICIT_CURVE> the
90parameters are explicitly encoded. The functions EC_GROUP_get_asn1_flag and
91EC_GROUP_set_asn1_flag get and set the status of the asn1_flag for the curve.
92Note: B<OPENSSL_EC_EXPLICIT_CURVE> was first added to OpenSSL 1.1.0, for
93previous versions of OpenSSL the value 0 must be used instead. Before OpenSSL
941.1.0 the default form was to use explicit parameters (meaning that
95applications would have to explicitly set the named curve form) in OpenSSL
961.1.0 and later the named curve form is the default.
aafbe1cc 97
186bb907 98The point_conversion_form for a curve controls how EC_POINT data is encoded as ASN1 as defined in X9.62 (ECDSA).
1bc74519 99point_conversion_form_t is an enum defined as follows:
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100
101 typedef enum {
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102 /** the point is encoded as z||x, where the octet z specifies
103 * which solution of the quadratic equation y is */
104 POINT_CONVERSION_COMPRESSED = 2,
14f46560 105 /** the point is encoded as z||x||y, where z is the octet 0x04 */
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106 POINT_CONVERSION_UNCOMPRESSED = 4,
107 /** the point is encoded as z||x||y, where the octet z specifies
aafbe1cc 108 * which solution of the quadratic equation y is */
1bc74519 109 POINT_CONVERSION_HYBRID = 6
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110 } point_conversion_form_t;
111
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112For POINT_CONVERSION_UNCOMPRESSED the point is encoded as an octet signifying the UNCOMPRESSED form has been used followed by
113the octets for x, followed by the octets for y.
114
115For any given x co-ordinate for a point on a curve it is possible to derive two possible y values. For
116POINT_CONVERSION_COMPRESSED the point is encoded as an octet signifying that the COMPRESSED form has been used AND which of
1bc74519 117the two possible solutions for y has been used, followed by the octets for x.
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118
119For POINT_CONVERSION_HYBRID the point is encoded as an octet signifying the HYBRID form has been used AND which of the two
120possible solutions for y has been used, followed by the octets for x, followed by the octets for y.
121
122The functions EC_GROUP_set_point_conversion_form and EC_GROUP_get_point_conversion_form set and get the point_conversion_form
123for the curve respectively.
124
125ANSI X9.62 (ECDSA standard) defines a method of generating the curve parameter b from a random number. This provides advantages
126in that a parameter obtained in this way is highly unlikely to be susceptible to special purpose attacks, or have any trapdoors in it.
127If the seed is present for a curve then the b parameter was generated in a verifiable fashion using that seed. The OpenSSL EC library
128does 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
129containing the seed that was used. The length of the memory block can be obtained using EC_GROUP_get_seed_len. A number of the
130builtin curves within the library provide seed values that can be obtained. It is also possible to set a custom seed using
131EC_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
132this seed value, although it will be preserved in any ASN1 based communications.
133
134EC_GROUP_get_degree gets the degree of the field. For Fp fields this will be the number of bits in p. For F2^m fields this will be
135the value m.
136
137The function EC_GROUP_check_discriminant calculates the discriminant for the curve and verifies that it is valid.
138For 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
139simply b. In either case for the curve to be valid the discriminant must be non zero.
140
141The function EC_GROUP_check performs a number of checks on a curve to verify that it is valid. Checks performed include
142verifying that the discriminant is non zero; that a generator has been defined; that the generator is on the curve and has
143the correct order.
144
145EC_GROUP_cmp compares B<a> and B<b> to determine whether they represent the same curve or not.
146
147The functions EC_GROUP_get_basis_type, EC_GROUP_get_trinomial_basis and EC_GROUP_get_pentanomial_basis should only be called for curves
148defined over an F2^m field. Addition and multiplication operations within an F2^m field are performed using an irreducible polynomial
149function f(x). This function is either a trinomial of the form:
150
151f(x) = x^m + x^k + 1 with m > k >= 1
152
153or a pentanomial of the form:
154
155f(x) = x^m + x^k3 + x^k2 + x^k1 + 1 with m > k3 > k2 > k1 >= 1
156
157The function EC_GROUP_get_basis_type returns a NID identifying whether a trinomial or pentanomial is in use for the field. The
186bb907 158function 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
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159the 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>,
160B<k2> and B<k3> respectively.
161
162=head1 RETURN VALUES
163
164The following functions return 1 on success or 0 on error: EC_GROUP_copy, EC_GROUP_set_generator, EC_GROUP_check,
165EC_GROUP_check_discriminant, EC_GROUP_get_trinomial_basis and EC_GROUP_get_pentanomial_basis.
166
167EC_GROUP_dup returns a pointer to the duplicated curve, or NULL on error.
168
169EC_GROUP_method_of returns the EC_METHOD implementation in use for the given curve or NULL on error.
170
171EC_GROUP_get0_generator returns the generator for the given curve or NULL on error.
172
173EC_GROUP_get_order, EC_GROUP_get_cofactor, EC_GROUP_get_curve_name, EC_GROUP_get_asn1_flag, EC_GROUP_get_point_conversion_form
174and EC_GROUP_get_degree return the order, cofactor, curve name (NID), ASN1 flag, point_conversion_form and degree for the
175specified curve respectively. If there is no curve name associated with a curve then EC_GROUP_get_curve_name will return 0.
176
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177EC_GROUP_get0_order() returns an internal pointer to the group order.
178EC_GROUP_get_order_bits() returns the number of bits in the group order.
179EC_GROUP_get0_cofactor() returns an internal pointer to the group cofactor.
180
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181EC_GROUP_get0_seed returns a pointer to the seed that was used to generate the parameter b, or NULL if the seed is not
182specified. EC_GROUP_get_seed_len returns the length of the seed or 0 if the seed is not specified.
183
184EC_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
d900a015 1850, the return value will be 1. On error 0 is returned.
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186
187EC_GROUP_cmp returns 0 if the curves are equal, 1 if they are not equal, or -1 on error.
188
189EC_GROUP_get_basis_type returns the values NID_X9_62_tpBasis or NID_X9_62_ppBasis (as defined in <openssl/obj_mac.h>) for a
190trinomial or pentanomial respectively. Alternatively in the event of an error a 0 is returned.
191
192=head1 SEE ALSO
193
9e183d22 194L<crypto(7)>, L<EC_GROUP_new(3)>,
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195L<EC_POINT_new(3)>, L<EC_POINT_add(3)>, L<EC_KEY_new(3)>,
196L<EC_GFp_simple_method(3)>, L<d2i_ECPKParameters(3)>
aafbe1cc 197
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198=head1 COPYRIGHT
199
9e183d22 200Copyright 2013-2017 The OpenSSL Project Authors. All Rights Reserved.
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201
202Licensed under the OpenSSL license (the "License"). You may not use
203this file except in compliance with the License. You can obtain a copy
204in the file LICENSE in the source distribution or at
205L<https://www.openssl.org/source/license.html>.
206
207=cut