EC_GROUP_copy(3)             OpenSSL             EC_GROUP_copy(3)


     EC_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_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 objects.


      #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);

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EC_GROUP_copy(3)             OpenSSL             EC_GROUP_copy(3)

      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 curve.

     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:

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EC_GROUP_copy(3)             OpenSSL             EC_GROUP_copy(3)

      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_form_t;

     For POINT_CONVERSION_UNCOMPRESSED the point is encoded as an
     octet signifying 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, followed
     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_conversion_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

     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

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EC_GROUP_copy(3)             OpenSSL             EC_GROUP_copy(3)

     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 >=

     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_get_pentanomial_basis.

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

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EC_GROUP_copy(3)             OpenSSL             EC_GROUP_copy(3)

     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
     respectively. 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 generate 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

     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),

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