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Title "EC_GROUP_copy 3"
way too many mistakes in technical documents.
EC_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.
EC_GROUP_method_of obtains the \s-1EC_METHOD\s0 of group.
EC_GROUP_set_generator sets curve paramaters that must be agreed by all participants using the curve. These paramaters 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 multipied by the cofactor gives the number of points on the curve.
EC_GROUP_get0_generator returns the generator for the identified group.
The functions EC_GROUP_get_order and EC_GROUP_get_cofactor populate the provided order and cofactor parameters with the respective order and cofactors for the group.
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 0.
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.
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:
.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
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 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.
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.
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 \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. 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 k1, \fBk2 and k3 respectively.
EC_GROUP_dup returns a pointer to the duplicated curve, or \s-1NULL\s0 on error.
EC_GROUP_method_of returns the \s-1EC_METHOD\s0 implementation in use for the given curve or \s-1NULL\s0 on error.
EC_GROUP_get0_generator returns the generator for the given curve or \s-1NULL\s0 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 (\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.
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.
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.
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.