1=pod 2 3=head1 NAME 4 5EC_GROUP_copy, EC_GROUP_dup, EC_GROUP_method_of, EC_GROUP_set_generator, EC_GROUP_get0_generator, EC_GROUP_get_order, EC_GROUP_get_cofactor, EC_GROUP_set_curve_name, EC_GROUP_get_curve_name, EC_GROUP_set_asn1_flag, EC_GROUP_get_asn1_flag, EC_GROUP_set_point_conversion_form, EC_GROUP_get_point_conversion_form, EC_GROUP_get0_seed, EC_GROUP_get_seed_len, EC_GROUP_set_seed, EC_GROUP_get_degree, EC_GROUP_check, EC_GROUP_check_discriminant, EC_GROUP_cmp, EC_GROUP_get_basis_type, EC_GROUP_get_trinomial_basis, EC_GROUP_get_pentanomial_basis - Functions for manipulating B<EC_GROUP> objects. 6 7=head1 SYNOPSIS 8 9 #include <openssl/ec.h> 10 #include <openssl/bn.h> 11 12 int EC_GROUP_copy(EC_GROUP *dst, const EC_GROUP *src); 13 EC_GROUP *EC_GROUP_dup(const EC_GROUP *src); 14 15 const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group); 16 17 int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator, const BIGNUM *order, const BIGNUM *cofactor); 18 const EC_POINT *EC_GROUP_get0_generator(const EC_GROUP *group); 19 20 int EC_GROUP_get_order(const EC_GROUP *group, BIGNUM *order, BN_CTX *ctx); 21 int EC_GROUP_get_cofactor(const EC_GROUP *group, BIGNUM *cofactor, BN_CTX *ctx); 22 23 void EC_GROUP_set_curve_name(EC_GROUP *group, int nid); 24 int EC_GROUP_get_curve_name(const EC_GROUP *group); 25 26 void EC_GROUP_set_asn1_flag(EC_GROUP *group, int flag); 27 int EC_GROUP_get_asn1_flag(const EC_GROUP *group); 28 29 void EC_GROUP_set_point_conversion_form(EC_GROUP *group, point_conversion_form_t form); 30 point_conversion_form_t EC_GROUP_get_point_conversion_form(const EC_GROUP *); 31 32 unsigned char *EC_GROUP_get0_seed(const EC_GROUP *x); 33 size_t EC_GROUP_get_seed_len(const EC_GROUP *); 34 size_t EC_GROUP_set_seed(EC_GROUP *, const unsigned char *, size_t len); 35 36 int EC_GROUP_get_degree(const EC_GROUP *group); 37 38 int EC_GROUP_check(const EC_GROUP *group, BN_CTX *ctx); 39 40 int EC_GROUP_check_discriminant(const EC_GROUP *group, BN_CTX *ctx); 41 42 int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx); 43 44 int EC_GROUP_get_basis_type(const EC_GROUP *); 45 int EC_GROUP_get_trinomial_basis(const EC_GROUP *, unsigned int *k); 46 int EC_GROUP_get_pentanomial_basis(const EC_GROUP *, unsigned int *k1, 47 unsigned int *k2, unsigned int *k3); 48 49=head1 DESCRIPTION 50 51EC_GROUP_copy copies the curve B<src> into B<dst>. Both B<src> and B<dst> must use the same EC_METHOD. 52 53EC_GROUP_dup creates a new EC_GROUP object and copies the content from B<src> to the newly created 54EC_GROUP object. 55 56EC_GROUP_method_of obtains the EC_METHOD of B<group>. 57 58EC_GROUP_set_generator sets curve paramaters that must be agreed by all participants using the curve. These 59paramaters include the B<generator>, the B<order> and the B<cofactor>. The B<generator> is a well defined point on the 60curve chosen for cryptographic operations. Integers used for point multiplications will be between 0 and 61n-1 where n is the B<order>. The B<order> multipied by the B<cofactor> gives the number of points on the curve. 62 63EC_GROUP_get0_generator returns the generator for the identified B<group>. 64 65The functions EC_GROUP_get_order and EC_GROUP_get_cofactor populate the provided B<order> and B<cofactor> parameters 66with the respective order and cofactors for the B<group>. 67 68The functions EC_GROUP_set_curve_name and EC_GROUP_get_curve_name, set and get the NID for the curve respectively 69(see L<EC_GROUP_new(3)|EC_GROUP_new(3)>). If a curve does not have a NID associated with it, then EC_GROUP_get_curve_name 70will return 0. 71 72The asn1_flag value on a curve is used to determine whether there is a specific ASN1 OID to describe the curve or not. 73If the asn1_flag is 1 then this is a named curve with an associated ASN1 OID. If not then asn1_flag is 0. The functions 74EC_GROUP_get_asn1_flag and EC_GROUP_set_asn1_flag get and set the status of the asn1_flag for the curve. If set then 75the curve_name must also be set. 76 77The point_coversion_form for a curve controls how EC_POINT data is encoded as ASN1 as defined in X9.62 (ECDSA). 78point_conversion_form_t is an enum defined as follows: 79 80 typedef enum { 81 /** the point is encoded as z||x, where the octet z specifies 82 * which solution of the quadratic equation y is */ 83 POINT_CONVERSION_COMPRESSED = 2, 84 /** the point is encoded as z||x||y, where z is the octet 0x02 */ 85 POINT_CONVERSION_UNCOMPRESSED = 4, 86 /** the point is encoded as z||x||y, where the octet z specifies 87 * which solution of the quadratic equation y is */ 88 POINT_CONVERSION_HYBRID = 6 89 } point_conversion_form_t; 90 91 92For POINT_CONVERSION_UNCOMPRESSED the point is encoded as an octet signifying the UNCOMPRESSED form has been used followed by 93the octets for x, followed by the octets for y. 94 95For any given x co-ordinate for a point on a curve it is possible to derive two possible y values. For 96POINT_CONVERSION_COMPRESSED the point is encoded as an octet signifying that the COMPRESSED form has been used AND which of 97the two possible solutions for y has been used, followed by the octets for x. 98 99For POINT_CONVERSION_HYBRID the point is encoded as an octet signifying the HYBRID form has been used AND which of the two 100possible solutions for y has been used, followed by the octets for x, followed by the octets for y. 101 102The functions EC_GROUP_set_point_conversion_form and EC_GROUP_get_point_conversion_form set and get the point_conversion_form 103for the curve respectively. 104 105ANSI X9.62 (ECDSA standard) defines a method of generating the curve parameter b from a random number. This provides advantages 106in that a parameter obtained in this way is highly unlikely to be susceptible to special purpose attacks, or have any trapdoors in it. 107If the seed is present for a curve then the b parameter was generated in a verifiable fashion using that seed. The OpenSSL EC library 108does 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 109containing the seed that was used. The length of the memory block can be obtained using EC_GROUP_get_seed_len. A number of the 110builtin curves within the library provide seed values that can be obtained. It is also possible to set a custom seed using 111EC_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 112this seed value, although it will be preserved in any ASN1 based communications. 113 114EC_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 115the value m. 116 117The function EC_GROUP_check_discriminant calculates the discriminant for the curve and verifies that it is valid. 118For 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 119simply b. In either case for the curve to be valid the discriminant must be non zero. 120 121The function EC_GROUP_check performs a number of checks on a curve to verify that it is valid. Checks performed include 122verifying that the discriminant is non zero; that a generator has been defined; that the generator is on the curve and has 123the correct order. 124 125EC_GROUP_cmp compares B<a> and B<b> to determine whether they represent the same curve or not. 126 127The functions EC_GROUP_get_basis_type, EC_GROUP_get_trinomial_basis and EC_GROUP_get_pentanomial_basis should only be called for curves 128defined over an F2^m field. Addition and multiplication operations within an F2^m field are performed using an irreducible polynomial 129function f(x). This function is either a trinomial of the form: 130 131f(x) = x^m + x^k + 1 with m > k >= 1 132 133or a pentanomial of the form: 134 135f(x) = x^m + x^k3 + x^k2 + x^k1 + 1 with m > k3 > k2 > k1 >= 1 136 137The function EC_GROUP_get_basis_type returns a NID identifying whether a trinomial or pentanomial is in use for the field. The 138function EC_GROUP_get_trinomial_basis must only be called where f(x) is of the trinomial form, and returns the value of B<k>. Similary 139the 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>, 140B<k2> and B<k3> respectively. 141 142=head1 RETURN VALUES 143 144The following functions return 1 on success or 0 on error: EC_GROUP_copy, EC_GROUP_set_generator, EC_GROUP_check, 145EC_GROUP_check_discriminant, EC_GROUP_get_trinomial_basis and EC_GROUP_get_pentanomial_basis. 146 147EC_GROUP_dup returns a pointer to the duplicated curve, or NULL on error. 148 149EC_GROUP_method_of returns the EC_METHOD implementation in use for the given curve or NULL on error. 150 151EC_GROUP_get0_generator returns the generator for the given curve or NULL on error. 152 153EC_GROUP_get_order, EC_GROUP_get_cofactor, EC_GROUP_get_curve_name, EC_GROUP_get_asn1_flag, EC_GROUP_get_point_conversion_form 154and EC_GROUP_get_degree return the order, cofactor, curve name (NID), ASN1 flag, point_conversion_form and degree for the 155specified curve respectively. If there is no curve name associated with a curve then EC_GROUP_get_curve_name will return 0. 156 157EC_GROUP_get0_seed returns a pointer to the seed that was used to generate the parameter b, or NULL if the seed is not 158specified. EC_GROUP_get_seed_len returns the length of the seed or 0 if the seed is not specified. 159 160EC_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 1610, the return value will be 1. On error 0 is returned. 162 163EC_GROUP_cmp returns 0 if the curves are equal, 1 if they are not equal, or -1 on error. 164 165EC_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 166trinomial or pentanomial respectively. Alternatively in the event of an error a 0 is returned. 167 168=head1 SEE ALSO 169 170L<crypto(3)|crypto(3)>, L<ec(3)|ec(3)>, L<EC_GROUP_new(3)|EC_GROUP_new(3)>, 171L<EC_POINT_new(3)|EC_POINT_new(3)>, L<EC_POINT_add(3)|EC_POINT_add(3)>, L<EC_KEY_new(3)|EC_KEY_new(3)>, 172L<EC_GFp_simple_method(3)|EC_GFp_simple_method(3)>, L<d2i_ECPKParameters(3)|d2i_ECPKParameters(3)> 173 174=cut 175