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.\" ========================================================================
.\"
.IX Title "EC_GROUP_copy 3"
.TH EC_GROUP_copy 3 "2019-12-20" "1.0.2u" "OpenSSL"
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.nh
.SH "NAME"
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, EC_GROUP_get_pentanomial_basis \- Functions for manipulating EC_GROUP objects.
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 2
\& #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);
.Ve
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
EC_GROUP_copy copies the curve \fBsrc\fR into \fBdst\fR. Both \fBsrc\fR and \fBdst\fR must use the same \s-1EC_METHOD.\s0
.PP
EC_GROUP_dup creates a new \s-1EC_GROUP\s0 object and copies the content from \fBsrc\fR to the newly created
\&\s-1EC_GROUP\s0 object.
.PP
EC_GROUP_method_of obtains the \s-1EC_METHOD\s0 of \fBgroup\fR.
.PP
EC_GROUP_set_generator sets curve paramaters that must be agreed by all participants using the curve. These
paramaters include the \fBgenerator\fR, the \fBorder\fR and the \fBcofactor\fR. The \fBgenerator\fR 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 \fBorder\fR. The \fBorder\fR multipied by the \fBcofactor\fR gives the number of points on the curve.
.PP
EC_GROUP_get0_generator returns the generator for the identified \fBgroup\fR.
.PP
The functions EC_GROUP_get_order and EC_GROUP_get_cofactor populate the provided \fBorder\fR and \fBcofactor\fR parameters
with the respective order and cofactors for the \fBgroup\fR.
.PP
The functions EC_GROUP_set_curve_name and EC_GROUP_get_curve_name, set and get the \s-1NID\s0 for the curve respectively
(see \fBEC_GROUP_new\fR\|(3)). If a curve does not have a \s-1NID\s0 associated with it, then EC_GROUP_get_curve_name
will return 0.
.PP
The asn1_flag value on a curve is used to determine whether there is a specific \s-1ASN1 OID\s0 to describe the curve or not.
If the asn1_flag is 1 then this is a named curve with an associated \s-1ASN1 OID.\s0 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.
.PP
The point_coversion_form for a curve controls how \s-1EC_POINT\s0 data is encoded as \s-1ASN1\s0 as defined in X9.62 (\s-1ECDSA\s0).
point_conversion_form_t is an enum defined as follows:
.PP
.Vb 10
\& 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 0x02 */
\& 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;
.Ve
.PP
For \s-1POINT_CONVERSION_UNCOMPRESSED\s0 the point is encoded as an octet signifying the \s-1UNCOMPRESSED\s0 form has been used followed by
the octets for x, followed by the octets for y.
.PP
For any given x co-ordinate for a point on a curve it is possible to derive two possible y values. For
\&\s-1POINT_CONVERSION_COMPRESSED\s0 the point is encoded as an octet signifying that the \s-1COMPRESSED\s0 form has been used \s-1AND\s0 which of
the two possible solutions for y has been used, followed by the octets for x.
.PP
For \s-1POINT_CONVERSION_HYBRID\s0 the point is encoded as an octet signifying the \s-1HYBRID\s0 form has been used \s-1AND\s0 which of the two
possible solutions for y has been used, followed by the octets for x, followed by the octets for y.
.PP
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.
.PP
\&\s-1ANSI X9.62\s0 (\s-1ECDSA\s0 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 \s-1EC\s0 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 \s-1EC\s0 library will not use
this seed value, although it will be preserved in any \s-1ASN1\s0 based communications.
.PP
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.
.PP
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.
.PP
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.
.PP
EC_GROUP_cmp compares \fBa\fR and \fBb\fR to determine whether they represent the same curve or not.
.PP
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:
.PP
f(x) = x^m + x^k + 1 with m > k >= 1
.PP
or a pentanomial of the form:
.PP
f(x) = x^m + x^k3 + x^k2 + x^k1 + 1 with m > k3 > k2 > k1 >= 1
.PP
The function EC_GROUP_get_basis_type returns a \s-1NID\s0 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 \fBk\fR. 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 \fBk1\fR,
\&\fBk2\fR and \fBk3\fR respectively.
.SH "RETURN VALUES"
.IX Header "RETURN VALUES"
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.
.PP
EC_GROUP_dup returns a pointer to the duplicated curve, or \s-1NULL\s0 on error.
.PP
EC_GROUP_method_of returns the \s-1EC_METHOD\s0 implementation in use for the given curve or \s-1NULL\s0 on error.
.PP
EC_GROUP_get0_generator returns the generator for the given curve or \s-1NULL\s0 on error.
.PP
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 (\s-1NID\s0), \s-1ASN1\s0 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.
.PP
EC_GROUP_get0_seed returns a pointer to the seed that was used to generate the parameter b, or \s-1NULL\s0 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.
.PP
EC_GROUP_set_seed returns the length of the seed that has been set. If the supplied seed is \s-1NULL,\s0 or the supplied seed length is
0, the return value will be 1. On error 0 is returned.
.PP
EC_GROUP_cmp returns 0 if the curves are equal, 1 if they are not equal, or \-1 on error.
.PP
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.
.SH "SEE ALSO"
.IX Header "SEE ALSO"
\&\fBcrypto\fR\|(3), \fBec\fR\|(3), \fBEC_GROUP_new\fR\|(3),
\&\fBEC_POINT_new\fR\|(3), \fBEC_POINT_add\fR\|(3), \fBEC_KEY_new\fR\|(3),
\&\fBEC_GFp_simple_method\fR\|(3), \fBd2i_ECPKParameters\fR\|(3)
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