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EC_GROUP_COPY(3ossl)                 OpenSSL                EC_GROUP_COPY(3ossl)





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_named_curve, EC_GROUP_check_discriminant,
       EC_GROUP_cmp, EC_GROUP_get_basis_type, EC_GROUP_get_trinomial_basis,
       EC_GROUP_get_pentanomial_basis, EC_GROUP_get0_field,
       EC_GROUP_get_field_type - Functions for manipulating EC_GROUP objects


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);

        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);
        const BIGNUM *EC_GROUP_get0_field(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 *group);

        unsigned char *EC_GROUP_get0_seed(const EC_GROUP *group);
        size_t EC_GROUP_get_seed_len(const EC_GROUP *group);
        size_t EC_GROUP_set_seed(EC_GROUP *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_named_curve(const EC_GROUP *group, int nist_only,
                                       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 *group);
        int EC_GROUP_get_trinomial_basis(const EC_GROUP *group, unsigned int *k);
        int EC_GROUP_get_pentanomial_basis(const EC_GROUP *group, unsigned int *k1,
                                           unsigned int *k2, unsigned int *k3);

        int EC_GROUP_get_field_type(const EC_GROUP *group);

       The following function has been deprecated since OpenSSL 3.0, and can be
       hidden entirely by defining OPENSSL_API_COMPAT with a suitable version
       value, see openssl_user_macros(7):

        const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group);


DESCRIPTION

       EC_GROUP_copy(3) 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.  This function was
       deprecated in OpenSSL 3.0, since EC_METHOD is no longer a public concept.

       EC_GROUP_set_generator() sets curve parameters that must be agreed by all
       participants using the curve. These parameters 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
       multiplied by the cofactor gives the number of points on the curve.

       EC_GROUP_get0_generator() returns the generator for the identified group.

       EC_GROUP_get_order() retrieves the order of group and copies its value
       into order.  It fails in case group is not fully initialized (i.e., its
       order is not set or set to zero).

       EC_GROUP_get_cofactor() retrieves the cofactor of group and copies its
       value into cofactor. It fails in case  group is not fully initialized or
       if the cofactor is not set (or set to zero).

       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 NID_undef.

       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 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 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: OPENSSL_EC_EXPLICIT_CURVE was added in 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  */
               POINT_CONVERSION_COMPRESSED = 2,
               /** the point is encoded as z||x||y, where z is the octet 0x04  */
               POINT_CONVERSION_UNCOMPRESSED = 4,
               /** 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
       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 built-in 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.

       EC_GROUP_get_field_type() identifies what type of field the EC_GROUP
       structure supports, which will be either F2^m or Fp.

       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() behaves in the following way: For the
       OpenSSL default provider it 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. For the OpenSSL FIPS
       provider it uses EC_GROUP_check_named_curve() to conform to SP800-56Ar3.

       The function EC_GROUP_check_named_curve() determines if the group's
       domain parameters match one of the built-in curves supported by the
       library.  The curve name is returned as a NID if it matches. If the
       group's domain parameters have been modified then no match will be found.
       If the curve name of the given group is NID_undef (e.g. it has been
       created by using explicit parameters with no curve name), then this
       method can be used to lookup the name of the curve that matches the group
       domain parameters. The built-in curves contain aliases, so that multiple
       NID's can map to the same domain parameters. For such curves it is
       unspecified which of the aliases will be returned if the curve name of
       the given group is NID_undef.  If nist_only is 1 it will only look for
       NIST approved curves, otherwise it searches all built-in curves.  This
       function may be passed a BN_CTX object in the ctx parameter.  The ctx
       parameter may be NULL.

       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. 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 k1, k2 and k3 respectively.


RETURN VALUES

       The following functions return 1 on success or 0 on error:
       EC_GROUP_copy(3), 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() returns 0 if the order is not set (or set to zero)
       for group or if copying into order fails, 1 otherwise.

       EC_GROUP_get_cofactor() returns 0 if the cofactor is not set (or is set
       to zero) for group or if copying into cofactor fails, 1 otherwise.

       EC_GROUP_get_curve_name() returns the curve name (NID) for group or will
       return NID_undef if no curve name is associated.

       EC_GROUP_get_asn1_flag() returns the ASN1 flag for the specified group .

       EC_GROUP_get_point_conversion_form() returns the point_conversion_form
       for group.

       EC_GROUP_get_degree() returns the degree for group or 0 if the operation
       is not supported by the underlying group implementation.

       EC_GROUP_get_field_type() returns either NID_X9_62_prime_field for prime
       curves or NID_X9_62_characteristic_two_field for binary curves; these
       values are defined in the <openssl/obj_mac.h> header file.

       EC_GROUP_check_named_curve() returns the nid of the matching named curve,
       otherwise it returns 0 for no match, or -1 on error.

       EC_GROUP_get0_order() returns an internal pointer to the group order.
       EC_GROUP_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_field() returns an internal pointer to the group
       field. For curves over GF(p), this is the modulus; for curves over
       GF(2^m), this is the irreducible polynomial defining the field.

       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.


SEE ALSO

       crypto(7), EC_GROUP_new(3), EC_POINT_new(3), EC_POINT_add(3),
       EC_KEY_new(3), EC_GFp_simple_method(3), d2i_ECPKParameters(3)


HISTORY

       EC_GROUP_method_of() was deprecated in OpenSSL 3.0.
       EC_GROUP_get0_field(), EC_GROUP_check_named_curve() and
       EC_GROUP_get_field_type() were added in OpenSSL 3.0.
       EC_GROUP_get0_order(), EC_GROUP_order_bits() and EC_GROUP_get0_cofactor()
       were added in OpenSSL 1.1.0.


COPYRIGHT

       Copyright 2013-2023 The OpenSSL Project Authors. All Rights Reserved.

       Licensed under the Apache License 2.0 (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
       <https://www.openssl.org/source/license.html>.



3.0.8                              2023-02-07               EC_GROUP_COPY(3ossl)

openssl 3.0.8 - Generated Wed Feb 8 19:16:36 CST 2023
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