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 *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 78EC_GROUP_get_order() retrieves the order of B<group> and copies its value into 79B<order>. It fails in case B<group> is not fully initialized (i.e., its order 80is not set or set to zero). 81 82EC_GROUP_get_cofactor() retrieves the cofactor of B<group> and copies its value 83into B<cofactor>. It fails in case B<group> is not fully initialized or if the 84cofactor is not set (or set to zero). 85 86The functions EC_GROUP_set_curve_name() and EC_GROUP_get_curve_name(), set and get the NID for the curve respectively 87(see L<EC_GROUP_new(3)>). If a curve does not have a NID associated with it, then EC_GROUP_get_curve_name 88will return NID_undef. 89 90The asn1_flag value is used to determine whether the curve encoding uses 91explicit parameters or a named curve using an ASN1 OID: many applications only 92support the latter form. If asn1_flag is B<OPENSSL_EC_NAMED_CURVE> then the 93named curve form is used and the parameters must have a corresponding 94named curve NID set. If asn1_flags is B<OPENSSL_EC_EXPLICIT_CURVE> the 95parameters are explicitly encoded. The functions EC_GROUP_get_asn1_flag() and 96EC_GROUP_set_asn1_flag() get and set the status of the asn1_flag for the curve. 97Note: B<OPENSSL_EC_EXPLICIT_CURVE> was added in OpenSSL 1.1.0, for 98previous versions of OpenSSL the value 0 must be used instead. Before OpenSSL 991.1.0 the default form was to use explicit parameters (meaning that 100applications would have to explicitly set the named curve form) in OpenSSL 1011.1.0 and later the named curve form is the default. 102 103The point_conversion_form for a curve controls how EC_POINT data is encoded as ASN1 as defined in X9.62 (ECDSA). 104point_conversion_form_t is an enum defined as follows: 105 106 typedef enum { 107 /** the point is encoded as z||x, where the octet z specifies 108 * which solution of the quadratic equation y is */ 109 POINT_CONVERSION_COMPRESSED = 2, 110 /** the point is encoded as z||x||y, where z is the octet 0x04 */ 111 POINT_CONVERSION_UNCOMPRESSED = 4, 112 /** the point is encoded as z||x||y, where the octet z specifies 113 * which solution of the quadratic equation y is */ 114 POINT_CONVERSION_HYBRID = 6 115 } point_conversion_form_t; 116 117For POINT_CONVERSION_UNCOMPRESSED the point is encoded as an octet signifying the UNCOMPRESSED form has been used followed by 118the octets for x, followed by the octets for y. 119 120For any given x co-ordinate for a point on a curve it is possible to derive two possible y values. For 121POINT_CONVERSION_COMPRESSED the point is encoded as an octet signifying that the COMPRESSED form has been used AND which of 122the two possible solutions for y has been used, followed by the octets for x. 123 124For POINT_CONVERSION_HYBRID the point is encoded as an octet signifying the HYBRID form has been used AND which of the two 125possible solutions for y has been used, followed by the octets for x, followed by the octets for y. 126 127The functions EC_GROUP_set_point_conversion_form() and EC_GROUP_get_point_conversion_form(), set and get the point_conversion_form 128for the curve respectively. 129 130ANSI X9.62 (ECDSA standard) defines a method of generating the curve parameter b from a random number. This provides advantages 131in that a parameter obtained in this way is highly unlikely to be susceptible to special purpose attacks, or have any trapdoors in it. 132If the seed is present for a curve then the b parameter was generated in a verifiable fashion using that seed. The OpenSSL EC library 133does 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 134containing the seed that was used. The length of the memory block can be obtained using EC_GROUP_get_seed_len(). A number of the 135built-in curves within the library provide seed values that can be obtained. It is also possible to set a custom seed using 136EC_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 137this seed value, although it will be preserved in any ASN1 based communications. 138 139EC_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 140the value m. 141 142The function EC_GROUP_check_discriminant() calculates the discriminant for the curve and verifies that it is valid. 143For 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 144simply b. In either case for the curve to be valid the discriminant must be non zero. 145 146The function EC_GROUP_check() performs a number of checks on a curve to verify that it is valid. Checks performed include 147verifying that the discriminant is non zero; that a generator has been defined; that the generator is on the curve and has 148the correct order. 149 150EC_GROUP_cmp() compares B<a> and B<b> to determine whether they represent the same curve or not. 151 152The functions EC_GROUP_get_basis_type(), EC_GROUP_get_trinomial_basis() and EC_GROUP_get_pentanomial_basis() should only be called for curves 153defined over an F2^m field. Addition and multiplication operations within an F2^m field are performed using an irreducible polynomial 154function f(x). This function is either a trinomial of the form: 155 156f(x) = x^m + x^k + 1 with m > k >= 1 157 158or a pentanomial of the form: 159 160f(x) = x^m + x^k3 + x^k2 + x^k1 + 1 with m > k3 > k2 > k1 >= 1 161 162The function EC_GROUP_get_basis_type() returns a NID identifying whether a trinomial or pentanomial is in use for the field. The 163function 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 164the 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>, 165B<k2> and B<k3> respectively. 166 167=head1 RETURN VALUES 168 169The following functions return 1 on success or 0 on error: EC_GROUP_copy(), EC_GROUP_set_generator(), EC_GROUP_check(), 170EC_GROUP_check_discriminant(), EC_GROUP_get_trinomial_basis() and EC_GROUP_get_pentanomial_basis(). 171 172EC_GROUP_dup() returns a pointer to the duplicated curve, or NULL on error. 173 174EC_GROUP_method_of() returns the EC_METHOD implementation in use for the given curve or NULL on error. 175 176EC_GROUP_get0_generator() returns the generator for the given curve or NULL on error. 177 178EC_GROUP_get_order() returns 0 if the order is not set (or set to zero) for 179B<group> or if copying into B<order> fails, 1 otherwise. 180 181EC_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. 182 183EC_GROUP_get_curve_name() returns the curve name (NID) for B<group> or will return NID_undef if no curve name is associated. 184 185EC_GROUP_get_asn1_flag() returns the ASN1 flag for the specified B<group> . 186 187EC_GROUP_get_point_conversion_form() returns the point_conversion_form for B<group>. 188 189EC_GROUP_get_degree() returns the degree for B<group> or 0 if the operation is not supported by the underlying group implementation. 190 191EC_GROUP_get0_order() returns an internal pointer to the group order. 192EC_GROUP_order_bits() returns the number of bits in the group order. 193EC_GROUP_get0_cofactor() returns an internal pointer to the group cofactor. 194 195EC_GROUP_get0_seed() returns a pointer to the seed that was used to generate the parameter b, or NULL if the seed is not 196specified. EC_GROUP_get_seed_len() returns the length of the seed or 0 if the seed is not specified. 197 198EC_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 1990, the return value will be 1. On error 0 is returned. 200 201EC_GROUP_cmp() returns 0 if the curves are equal, 1 if they are not equal, or -1 on error. 202 203EC_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 204trinomial or pentanomial respectively. Alternatively in the event of an error a 0 is returned. 205 206=head1 SEE ALSO 207 208L<crypto(7)>, L<EC_GROUP_new(3)>, 209L<EC_POINT_new(3)>, L<EC_POINT_add(3)>, L<EC_KEY_new(3)>, 210L<EC_GFp_simple_method(3)>, L<d2i_ECPKParameters(3)> 211 212=head1 COPYRIGHT 213 214Copyright 2013-2017 The OpenSSL Project Authors. All Rights Reserved. 215 216Licensed under the OpenSSL license (the "License"). You may not use 217this file except in compliance with the License. You can obtain a copy 218in the file LICENSE in the source distribution or at 219L<https://www.openssl.org/source/license.html>. 220 221=cut 222