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.

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.

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(), 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_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

COPYRIGHT

Copyright 2013-2019 The OpenSSL Project Authors. All Rights Reserved.