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Title "EC_GROUP_COPY 3"
way too many mistakes in technical documents.
\fBEC_GROUP_dup() creates a new \s-1EC_GROUP\s0 object and copies the content from src to the newly created \s-1EC_GROUP\s0 object.
\fBEC_GROUP_method_of() obtains the \s-1EC_METHOD\s0 of group.
\fBEC_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.
\fBEC_GROUP_get0_generator() returns the generator for the identified group.
\fBEC_GROUP_get_order() retrieves the order of group and copies its value into \fBorder. It fails in case group is not fully initialized (i.e., its order is not set or set to zero).
\fBEC_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 \s-1NID\s0 for the curve respectively (see EC_GROUP_new\|(3)). If a curve does not have a \s-1NID\s0 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 \s-1ASN1 OID:\s0 many applications only support the latter form. If asn1_flag is \s-1OPENSSL_EC_NAMED_CURVE\s0 then the named curve form is used and the parameters must have a corresponding named curve \s-1NID\s0 set. If asn1_flags is \s-1OPENSSL_EC_EXPLICIT_CURVE\s0 the parameters are explicitly encoded. The functions EC_GROUP_get_asn1_flag() and \fBEC_GROUP_set_asn1_flag() get and set the status of the asn1_flag for the curve. Note: \s-1OPENSSL_EC_EXPLICIT_CURVE\s0 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 \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:
.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 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; .Ve
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.
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.
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.
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.
\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 built-in curves within the library provide seed values that can be obtained. It is also possible to set a custom seed using \fBEC_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.
\fBEC_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.
\fBEC_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 \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 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, \fBk2 and k3 respectively.
\fBEC_GROUP_dup() returns a pointer to the duplicated curve, or \s-1NULL\s0 on error.
\fBEC_GROUP_method_of() returns the \s-1EC_METHOD\s0 implementation in use for the given curve or \s-1NULL\s0 on error.
\fBEC_GROUP_get0_generator() returns the generator for the given curve or \s-1NULL\s0 on error.
\fBEC_GROUP_get_order() returns 0 if the order is not set (or set to zero) for \fBgroup or if copying into order fails, 1 otherwise.
\fBEC_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.
\fBEC_GROUP_get_curve_name() returns the curve name (\s-1NID\s0) for group or will return NID_undef if no curve name is associated.
\fBEC_GROUP_get_asn1_flag() returns the \s-1ASN1\s0 flag for the specified group .
\fBEC_GROUP_get_point_conversion_form() returns the point_conversion_form for group.
\fBEC_GROUP_get_degree() returns the degree for group or 0 if the operation is not supported by the underlying group implementation.
\fBEC_GROUP_get0_order() returns an internal pointer to the group order. \fBEC_GROUP_order_bits() returns the number of bits in the group order. \fBEC_GROUP_get0_cofactor() returns an internal pointer to the group cofactor.
\fBEC_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.
\fBEC_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.
\fBEC_GROUP_cmp() returns 0 if the curves are equal, 1 if they are not equal, or -1 on error.
\fBEC_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.
Licensed under the OpenSSL license (the \*(L"License\*(R"). You may not use this file except in compliance with the License. You can obtain a copy in the file \s-1LICENSE\s0 in the source distribution or at <https://www.openssl.org/source/license.html>.