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 67The following function has been deprecated since OpenSSL 3.0, and can be 68hidden entirely by defining B<OPENSSL_API_COMPAT> with a suitable version value, 69see L<openssl_user_macros(7)>: 70 71 const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group); 72 73=head1 DESCRIPTION 74 75EC_GROUP_copy() copies the curve B<src> into B<dst>. Both B<src> and B<dst> must use the same EC_METHOD. 76 77EC_GROUP_dup() creates a new EC_GROUP object and copies the content from B<src> to the newly created 78EC_GROUP object. 79 80EC_GROUP_method_of() obtains the EC_METHOD of B<group>. 81This function was deprecated in OpenSSL 3.0, since EC_METHOD is no longer a public concept. 82 83EC_GROUP_set_generator() sets curve parameters that must be agreed by all participants using the curve. These 84parameters include the B<generator>, the B<order> and the B<cofactor>. The B<generator> is a well defined point on the 85curve chosen for cryptographic operations. Integers used for point multiplications will be between 0 and 86n-1 where n is the B<order>. The B<order> multiplied by the B<cofactor> gives the number of points on the curve. 87 88EC_GROUP_get0_generator() returns the generator for the identified B<group>. 89 90EC_GROUP_get_order() retrieves the order of B<group> and copies its value into 91B<order>. It fails in case B<group> is not fully initialized (i.e., its order 92is not set or set to zero). 93 94EC_GROUP_get_cofactor() retrieves the cofactor of B<group> and copies its value 95into B<cofactor>. It fails in case B<group> is not fully initialized or if the 96cofactor is not set (or set to zero). 97 98The functions EC_GROUP_set_curve_name() and EC_GROUP_get_curve_name(), set and get the NID for the curve respectively 99(see L<EC_GROUP_new(3)>). If a curve does not have a NID associated with it, then EC_GROUP_get_curve_name 100will return NID_undef. 101 102The asn1_flag value is used to determine whether the curve encoding uses 103explicit parameters or a named curve using an ASN1 OID: many applications only 104support the latter form. If asn1_flag is B<OPENSSL_EC_NAMED_CURVE> then the 105named curve form is used and the parameters must have a corresponding 106named curve NID set. If asn1_flags is B<OPENSSL_EC_EXPLICIT_CURVE> the 107parameters are explicitly encoded. The functions EC_GROUP_get_asn1_flag() and 108EC_GROUP_set_asn1_flag() get and set the status of the asn1_flag for the curve. 109Note: B<OPENSSL_EC_EXPLICIT_CURVE> was added in OpenSSL 1.1.0, for 110previous versions of OpenSSL the value 0 must be used instead. Before OpenSSL 1111.1.0 the default form was to use explicit parameters (meaning that 112applications would have to explicitly set the named curve form) in OpenSSL 1131.1.0 and later the named curve form is the default. 114 115The point_conversion_form for a curve controls how EC_POINT data is encoded as ASN1 as defined in X9.62 (ECDSA). 116point_conversion_form_t is an enum defined as follows: 117 118 typedef enum { 119 /** the point is encoded as z||x, where the octet z specifies 120 * which solution of the quadratic equation y is */ 121 POINT_CONVERSION_COMPRESSED = 2, 122 /** the point is encoded as z||x||y, where z is the octet 0x04 */ 123 POINT_CONVERSION_UNCOMPRESSED = 4, 124 /** the point is encoded as z||x||y, where the octet z specifies 125 * which solution of the quadratic equation y is */ 126 POINT_CONVERSION_HYBRID = 6 127 } point_conversion_form_t; 128 129For POINT_CONVERSION_UNCOMPRESSED the point is encoded as an octet signifying the UNCOMPRESSED form has been used followed by 130the octets for x, followed by the octets for y. 131 132For any given x coordinate for a point on a curve it is possible to derive two possible y values. For 133POINT_CONVERSION_COMPRESSED the point is encoded as an octet signifying that the COMPRESSED form has been used AND which of 134the two possible solutions for y has been used, followed by the octets for x. 135 136For POINT_CONVERSION_HYBRID the point is encoded as an octet signifying the HYBRID form has been used AND which of the two 137possible solutions for y has been used, followed by the octets for x, followed by the octets for y. 138 139The functions EC_GROUP_set_point_conversion_form() and EC_GROUP_get_point_conversion_form(), set and get the point_conversion_form 140for the curve respectively. 141 142ANSI X9.62 (ECDSA standard) defines a method of generating the curve parameter b from a random number. This provides advantages 143in that a parameter obtained in this way is highly unlikely to be susceptible to special purpose attacks, or have any trapdoors in it. 144If the seed is present for a curve then the b parameter was generated in a verifiable fashion using that seed. The OpenSSL EC library 145does 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 146containing the seed that was used. The length of the memory block can be obtained using EC_GROUP_get_seed_len(). A number of the 147built-in curves within the library provide seed values that can be obtained. It is also possible to set a custom seed using 148EC_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 149this seed value, although it will be preserved in any ASN1 based communications. 150 151EC_GROUP_get_degree() gets the degree of the field. 152For Fp fields this will be the number of bits in p. 153For F2^m fields this will be the value m. 154 155EC_GROUP_get_field_type() identifies what type of field the EC_GROUP structure supports, 156which will be either F2^m or Fp. 157 158The function EC_GROUP_check_discriminant() calculates the discriminant for the curve and verifies that it is valid. 159For 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 160simply b. In either case for the curve to be valid the discriminant must be non zero. 161 162The function EC_GROUP_check() behaves in the following way: 163For the OpenSSL default provider it performs a number of checks on a curve to verify that it is valid. Checks performed include 164verifying that the discriminant is non zero; that a generator has been defined; that the generator is on the curve and has 165the correct order. For the OpenSSL FIPS provider it uses EC_GROUP_check_named_curve() to conform to SP800-56Ar3. 166 167The function EC_GROUP_check_named_curve() determines if the group's domain parameters match one of the built-in curves supported by the library. 168The 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. 169If 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), 170then this method can be used to lookup the name of the curve that matches the group domain parameters. The built-in curves contain 171aliases, so that multiple NID's can map to the same domain parameters. For such curves it is unspecified which of the aliases will be 172returned if the curve name of the given group is NID_undef. 173If B<nist_only> is 1 it will only look for NIST approved curves, otherwise it searches all built-in curves. 174This function may be passed a BN_CTX object in the B<ctx> parameter. 175The B<ctx> parameter may be NULL. 176 177EC_GROUP_cmp() compares B<a> and B<b> to determine whether they represent the same curve or not. 178 179The functions EC_GROUP_get_basis_type(), EC_GROUP_get_trinomial_basis() and EC_GROUP_get_pentanomial_basis() should only be called for curves 180defined over an F2^m field. Addition and multiplication operations within an F2^m field are performed using an irreducible polynomial 181function f(x). This function is either a trinomial of the form: 182 183f(x) = x^m + x^k + 1 with m > k >= 1 184 185or a pentanomial of the form: 186 187f(x) = x^m + x^k3 + x^k2 + x^k1 + 1 with m > k3 > k2 > k1 >= 1 188 189The function EC_GROUP_get_basis_type() returns a NID identifying whether a trinomial or pentanomial is in use for the field. The 190function 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 191the 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>, 192B<k2> and B<k3> respectively. 193 194=head1 RETURN VALUES 195 196The following functions return 1 on success or 0 on error: EC_GROUP_copy(), EC_GROUP_set_generator(), EC_GROUP_check(), 197EC_GROUP_check_discriminant(), EC_GROUP_get_trinomial_basis() and EC_GROUP_get_pentanomial_basis(). 198 199EC_GROUP_dup() returns a pointer to the duplicated curve, or NULL on error. 200 201EC_GROUP_method_of() returns the EC_METHOD implementation in use for the given curve or NULL on error. 202 203EC_GROUP_get0_generator() returns the generator for the given curve or NULL on error. 204 205EC_GROUP_get_order() returns 0 if the order is not set (or set to zero) for 206B<group> or if copying into B<order> fails, 1 otherwise. 207 208EC_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. 209 210EC_GROUP_get_curve_name() returns the curve name (NID) for B<group> or will return NID_undef if no curve name is associated. 211 212EC_GROUP_get_asn1_flag() returns the ASN1 flag for the specified B<group> . 213 214EC_GROUP_get_point_conversion_form() returns the point_conversion_form for B<group>. 215 216EC_GROUP_get_degree() returns the degree for B<group> or 0 if the operation is not supported by the underlying group implementation. 217 218EC_GROUP_get_field_type() returns either B<NID_X9_62_prime_field> for prime curves 219or B<NID_X9_62_characteristic_two_field> for binary curves; 220these values are defined in the F<< <openssl/obj_mac.h> >> header file. 221 222EC_GROUP_check_named_curve() returns the nid of the matching named curve, otherwise it returns 0 for no match, or -1 on error. 223 224EC_GROUP_get0_order() returns an internal pointer to the group order. 225EC_GROUP_order_bits() returns the number of bits in the group order. 226EC_GROUP_get0_cofactor() returns an internal pointer to the group cofactor. 227EC_GROUP_get0_field() returns an internal pointer to the group field. For curves over GF(p), this is the modulus; for curves 228over GF(2^m), this is the irreducible polynomial defining the field. 229 230EC_GROUP_get0_seed() returns a pointer to the seed that was used to generate the parameter b, or NULL if the seed is not 231specified. EC_GROUP_get_seed_len() returns the length of the seed or 0 if the seed is not specified. 232 233EC_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 2340, the return value will be 1. On error 0 is returned. 235 236EC_GROUP_cmp() returns 0 if the curves are equal, 1 if they are not equal, or -1 on error. 237 238EC_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 239trinomial or pentanomial respectively. Alternatively in the event of an error a 0 is returned. 240 241=head1 SEE ALSO 242 243L<crypto(7)>, L<EC_GROUP_new(3)>, 244L<EC_POINT_new(3)>, L<EC_POINT_add(3)>, L<EC_KEY_new(3)>, 245L<EC_GFp_simple_method(3)>, L<d2i_ECPKParameters(3)> 246 247=head1 HISTORY 248 249EC_GROUP_method_of() was deprecated in OpenSSL 3.0. 250EC_GROUP_get0_field(), EC_GROUP_check_named_curve() and EC_GROUP_get_field_type() were added in OpenSSL 3.0. 251EC_GROUP_get0_order(), EC_GROUP_order_bits() and EC_GROUP_get0_cofactor() were added in OpenSSL 1.1.0. 252 253=head1 COPYRIGHT 254 255Copyright 2013-2023 The OpenSSL Project Authors. All Rights Reserved. 256 257Licensed under the Apache License 2.0 (the "License"). You may not use 258this file except in compliance with the License. You can obtain a copy 259in the file LICENSE in the source distribution or at 260L<https://www.openssl.org/source/license.html>. 261 262=cut 263