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+=head1 NAME
+EC_GROUP_get0_order, EC_GROUP_order_bits, EC_GROUP_get0_cofactor,
+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_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,
+- Functions for manipulating EC_GROUP objects
+=head1 SYNOPSIS
+ #include <openssl/ec.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);
+ const BIGNUM *EC_GROUP_get0_order(const EC_GROUP *group);
+ int EC_GROUP_order_bits(const EC_GROUP *group);
+ int EC_GROUP_get_cofactor(const EC_GROUP *group, BIGNUM *cofactor, BN_CTX *ctx);
+ const BIGNUM *EC_GROUP_get0_cofactor(const EC_GROUP *group);
+ 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 B<src> into B<dst>. Both B<src> and B<dst> must use the same EC_METHOD.
+EC_GROUP_dup creates a new EC_GROUP object and copies the content from B<src> to the newly created
+EC_GROUP object.
+EC_GROUP_method_of obtains the EC_METHOD of B<group>.
+EC_GROUP_set_generator sets curve parameters that must be agreed by all participants using the curve. These
+parameters include the B<generator>, the B<order> and the B<cofactor>. The B<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 B<order>. The B<order> multiplied by the B<cofactor> gives the number of points on the curve.
+EC_GROUP_get0_generator returns the generator for the identified B<group>.
+The functions EC_GROUP_get_order and EC_GROUP_get_cofactor populate the provided B<order> and B<cofactor> parameters
+with the respective order and cofactors for the B<group>.
+The functions EC_GROUP_set_curve_name and EC_GROUP_get_curve_name, set and get the NID for the curve respectively
+(see L<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 is used to determine whether the curve encoding uses
+explicit parameters or a named curve using an ASN1 OID: many applications only
+support the latter form. If asn1_flag is B<OPENSSL_EC_NAMED_CURVE> then the
+named curve form is used and the parameters must have a corresponding
+named curve NID set. If asn1_flags is B<OPENSSL_EC_EXPLICIT_CURVE> the
+parameters are explicitly encoded. 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.
+Note: B<OPENSSL_EC_EXPLICIT_CURVE> was first added to OpenSSL 1.1.0, for
+previous versions of OpenSSL the value 0 must be used instead. Before OpenSSL
+1.1.0 the default form was to use explicit parameters (meaning that
+applications would have to explicitly set the named curve form) in OpenSSL
+1.1.0 and later the named curve form is the default.
+The point_conversion_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 0x04 */
+ /** 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 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 B<a> and B<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 B<k>. Similarly
+the 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>,
+B<k2> and B<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.
+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_order() returns an internal pointer to the group order.
+EC_GROUP_get_order_bits() returns the number of bits in the group order.
+EC_GROUP_get0_cofactor() returns an internal pointer to the group cofactor.
+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 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.
+=head1 SEE ALSO
+L<crypto(7)>, L<EC_GROUP_new(3)>,
+L<EC_POINT_new(3)>, L<EC_POINT_add(3)>, L<EC_KEY_new(3)>,
+L<EC_GFp_simple_method(3)>, L<d2i_ECPKParameters(3)>
+Copyright 2013-2017 The OpenSSL Project Authors. All Rights Reserved.
+Licensed under the OpenSSL license (the "License"). You may not use
+this file except in compliance with the License. You can obtain a copy
+in the file LICENSE in the source distribution or at