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_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 16 17=head1 SYNOPSIS 18 19 #include <openssl/ec.h> 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 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 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); 59 int EC_GROUP_get_pentanomial_basis(const EC_GROUP *, unsigned int *k1, 60 unsigned int *k2, unsigned int *k3); 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 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 73curve chosen for cryptographic operations. Integers used for point multiplications will be between 0 and 74n-1 where n is the B<order>. The B<order> multiplied by the B<cofactor> gives the number of points on the curve. 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 82(see L<EC_GROUP_new(3)>). If a curve does not have a NID associated with it, then EC_GROUP_get_curve_name 83will return 0. 84 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 added in 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. 97 98The point_conversion_form for a curve controls how EC_POINT data is encoded as ASN1 as defined in X9.62 (ECDSA). 99point_conversion_form_t is an enum defined as follows: 100 101 typedef enum { 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, 105 /** the point is encoded as z||x||y, where z is the octet 0x04 */ 106 POINT_CONVERSION_UNCOMPRESSED = 4, 107 /** the point is encoded as z||x||y, where the octet z specifies 108 * which solution of the quadratic equation y is */ 109 POINT_CONVERSION_HYBRID = 6 110 } point_conversion_form_t; 111 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 117the two possible solutions for y has been used, followed by the octets for x. 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 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 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 177EC_GROUP_get0_order() returns an internal pointer to the group order. 178EC_GROUP_order_bits() returns the number of bits in the group order. 179EC_GROUP_get0_cofactor() returns an internal pointer to the group cofactor. 180 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 1850, the return value will be 1. On error 0 is returned. 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 194L<crypto(7)>, L<EC_GROUP_new(3)>, 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)> 197 198=head1 COPYRIGHT 199 200Copyright 2013-2017 The OpenSSL Project Authors. All Rights Reserved. 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 208