EC_GROUP_copy, EC_GROUP_dup, EC_GROUP_method_of, EC_GROUP_set_genera-
       tor, EC_GROUP_get0_generator, EC_GROUP_get_order, EC_GROUP_get_cofac-
       tor, EC_GROUP_set_curve_name, EC_GROUP_get_curve_name,
       EC_GROUP_set_asn1_flag, EC_GROUP_get_asn1_flag, EC_GROUP_set_point_con-
       version_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 EC_GROUP


        #include <openssl/ec.h>
        #include <openssl/bn.h>

        int EC_GROUP_copy(EC_GROUP *dst, const EC_GROUP *src);
        EC_GROUP *EC_GROUP_dup(const EC_GROUP *src);

        const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group);

        int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator, const BIGNUM *order, const BIGNUM *cofactor);
        const EC_POINT *EC_GROUP_get0_generator(const EC_GROUP *group);

        int EC_GROUP_get_order(const EC_GROUP *group, BIGNUM *order, BN_CTX *ctx);
        int EC_GROUP_get_cofactor(const EC_GROUP *group, BIGNUM *cofactor, BN_CTX *ctx);

        void EC_GROUP_set_curve_name(EC_GROUP *group, int nid);
        int EC_GROUP_get_curve_name(const EC_GROUP *group);

        void EC_GROUP_set_asn1_flag(EC_GROUP *group, int flag);
        int EC_GROUP_get_asn1_flag(const EC_GROUP *group);

        void EC_GROUP_set_point_conversion_form(EC_GROUP *group, point_conversion_form_t form);
        point_conversion_form_t EC_GROUP_get_point_conversion_form(const EC_GROUP *);

        unsigned char *EC_GROUP_get0_seed(const EC_GROUP *x);
        size_t EC_GROUP_get_seed_len(const EC_GROUP *);
        size_t EC_GROUP_set_seed(EC_GROUP *, const unsigned char *, size_t len);

        int EC_GROUP_get_degree(const EC_GROUP *group);

        int EC_GROUP_check(const EC_GROUP *group, BN_CTX *ctx);

        int EC_GROUP_check_discriminant(const EC_GROUP *group, BN_CTX *ctx);

        int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx);

        int EC_GROUP_get_basis_type(const EC_GROUP *);
        int EC_GROUP_get_trinomial_basis(const EC_GROUP *, unsigned int *k);
        int EC_GROUP_get_pentanomial_basis(const EC_GROUP *, unsigned int *k1,
               unsigned int *k2, unsigned int *k3);


       EC_GROUP_copy copies the curve src into dst. Both src and dst must use
       the same EC_METHOD.

       EC_GROUP_dup creates a new EC_GROUP object and copies the content from
       src to the newly created EC_GROUP object.

       EC_GROUP_method_of obtains the EC_METHOD of group.

       EC_GROUP_set_generator sets curve paramaters that must be agreed by all
       participants using the curve. These paramaters include the generator,
       the order and the cofactor. The generator is a well defined point on
       the curve chosen for cryptographic operations. Integers used for point
       multiplications will be between 0 and n-1 where n is the order. The
       order multipied by the cofactor gives the number of points on the

       EC_GROUP_get0_generator returns the generator for the identified group.

       The functions EC_GROUP_get_order and EC_GROUP_get_cofactor populate the
       provided order and cofactor parameters with the respective order and
       cofactors for the group.

       The functions EC_GROUP_set_curve_name and EC_GROUP_get_curve_name, set
       and get the NID for the curve respectively (see EC_GROUP_new(3)). If a
       curve does not have a NID associated with it, then
       EC_GROUP_get_curve_name will return 0.

       The asn1_flag value on a curve is used to determine whether there is a
       specific ASN1 OID to describe the curve or not.  If 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 EC_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 the curve_name must also be set.

       The point_coversion_form for a curve controls how EC_POINT data is
       encoded as ASN1 as defined in X9.62 (ECDSA).  point_conversion_form_t
       is an enum defined as follows:

        typedef enum {
               /** the point is encoded as z||x, where the octet z specifies
                *   which solution of the quadratic equation y is  */
               /** the point is encoded as z||x||y, where z is the octet 0x02  */
               /** the point is encoded as z||x||y, where the octet z specifies
                *  which solution of the quadratic equation y is  */
               POINT_CONVERSION_HYBRID = 6
        } point_conversion_form_t;

       For POINT_CONVERSION_UNCOMPRESSED the point is encoded as an octet sig-
       nifying the UNCOMPRESSED form has been used followed by the octets for
       x, followed by the octets for y.

       For any given x co-ordinate for a point on a curve it is possible to
       derive two possible y values. For POINT_CONVERSION_COMPRESSED the point
       is encoded as an octet signifying that the COMPRESSED form has been
       used AND which of the two possible solutions for y has been used, fol-
       lowed by the octets for x.

       For POINT_CONVERSION_HYBRID the point is encoded as an octet signifying
       the HYBRID form has been used AND which of the two possible solutions
       for y has been used, followed by the octets for x, followed by the
       octets for y.

       The functions EC_GROUP_set_point_conversion_form and
       EC_GROUP_get_point_conversion_form set and get the point_conver-
       sion_form for the curve respectively.

       ANSI X9.62 (ECDSA standard) defines a method of generating the curve
       parameter b from a random number. This provides advantages in that a
       parameter obtained in this way is highly unlikely to be susceptible to
       special purpose attacks, or have any trapdoors in it.  If the seed is
       present for a curve then the b parameter was generated in a verifiable
       fashion using that seed. The OpenSSL EC library does 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 containing the seed that was used.
       The length of the memory block can be obtained using
       EC_GROUP_get_seed_len. A number of the builtin curves within the
       library provide seed values that can be obtained. It is also possible
       to set a custom seed using EC_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 this seed value, although it will be preserved in any ASN1
       based communications.

       EC_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 the
       value m.

       The function EC_GROUP_check_discriminant calculates the discriminant
       for the curve and verifies that it is valid.  For 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 simply b. In either case for the curve
       to be valid the discriminant must be non zero.

       The function EC_GROUP_check performs a number of checks on a curve to
       verify that it is valid. Checks performed include verifying that the
       discriminant is non zero; that a generator has been defined; that the
       generator is on the curve and has the correct order.

       EC_GROUP_cmp compares a and b to determine whether they represent the
       same curve or not.

       The functions EC_GROUP_get_basis_type, EC_GROUP_get_trinomial_basis and
       EC_GROUP_get_pentanomial_basis should only be called for curves defined
       over an F2^m field. Addition and multiplication operations within an
       F2^m field are performed using an irreducible polynomial function f(x).
       This function is either a trinomial of the form:

       f(x) = x^m + x^k + 1 with m > k >= 1

       or a pentanomial of the form:

       f(x) = x^m + x^k3 + x^k2 + x^k1 + 1 with m > k3 > k2 > k1 >= 1

       The function EC_GROUP_get_basis_type returns a NID identifying whether
       a trinomial or pentanomial is in use for the field. The function
       EC_GROUP_get_trinomial_basis must only be called where f(x) is of the
       trinomial form, and returns the value of k. Similary the function
       EC_GROUP_get_pentanomial_basis must only be called where f(x) is of the
       pentanomial form, and returns the values of k1, k2 and k3 respectively.


       The following functions return 1 on success or 0 on error:
       EC_GROUP_copy, EC_GROUP_set_generator, EC_GROUP_check,
       EC_GROUP_check_discriminant, EC_GROUP_get_trinomial_basis and

       EC_GROUP_dup returns a pointer to the duplicated curve, or NULL on

       EC_GROUP_method_of returns the EC_METHOD implementation in use for the
       given curve or NULL on error.

       EC_GROUP_get0_generator returns the generator for the given curve or
       NULL on error.

       EC_GROUP_get_order, EC_GROUP_get_cofactor, EC_GROUP_get_curve_name,
       EC_GROUP_get_asn1_flag, EC_GROUP_get_point_conversion_form and
       EC_GROUP_get_degree return the order, cofactor, curve name (NID), ASN1
       flag, point_conversion_form and degree for the specified curve respec-
       tively. If there is no curve name associated with a curve then
       EC_GROUP_get_curve_name will return 0.

       EC_GROUP_get0_seed returns a pointer to the seed that was used to gen-
       erate the parameter b, or NULL if the seed is not specified.
       EC_GROUP_get_seed_len returns the length of the seed or 0 if the seed
       is not specified.

       EC_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 0, the return
       value will be 1. On error 0 is returned.

       EC_GROUP_cmp returns 0 if the curves are equal, 1 if they are not
       equal, or -1 on error.

       EC_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 trinomial
       or pentanomial respectively. Alternatively in the event of an error a 0
       is returned.


       crypto(3), ec(3), EC_GROUP_new(3), EC_POINT_new(3), EC_POINT_add(3),
       EC_KEY_new(3), EC_GFp_simple_method(3), d2i_ECPKParameters(3)

1.0.2t                            2019-09-10                  EC_GROUP_copy(3)

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