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EC_GROUP_COPY(3) Library Functions Manual 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_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 — manipulate 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);

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);

These functions operate on EC_GROUP objects created by the functions described in EC_GROUP_new(3).

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

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

() obtains the EC_METHOD of group.

() 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 order - 1. The order multiplied by the cofactor gives the number of points on the curve.

() returns the generator for the identified group.

The functions () and () populate the provided order and cofactor parameters with the respective order and cofactors for the group.

The functions () and () 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 ASN.1 OID to describe the curve or not. If the asn1_flag is 1 then this is a named curve with an associated ASN.1 OID. If not then asn1_flag is 0. The functions () and () get and set the status of the asn1_flag for the curve. If set, then the curve_name must also be set.

The point_conversion_form for a curve controls how EC_POINT data is encoded as ASN.1 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 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;

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 coordinate 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 () and () 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 (). This returns a pointer to a memory block containing the seed that was used. The length of the memory block can be obtained using (). 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 () 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 ASN.1 based communications.

() 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 () 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 () 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.

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

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

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), ASN.1 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() returns 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 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.

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

EC_GROUP_copy(), EC_GROUP_method_of(), EC_GROUP_set_generator(), EC_GROUP_get0_generator(), EC_GROUP_get_order(), and EC_GROUP_get_cofactor() first appeared in OpenSSL 0.9.7 and have been available since OpenBSD 3.2.

EC_GROUP_dup(), 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(), and EC_GROUP_get_pentanomial_basis() first appeared in OpenSSL 0.9.8 and has been available since OpenBSD 4.5.

March 23, 2018 OpenBSD-6.6