OpenSSL/EC GFp simple method
The Elliptic Curve library provides a number of different implementations through a single common interface. When constructing a curve using EC_GROUP_new (see EC_GROUP_new) an implementation method must be provided. The functions described here all return a const pointer to an EC_METHOD structure that can be passed to EC_GROUP_NEW. It is important that the correct implementation type for the form of curve selected is used.
For F2^m curves there is only one implementation choice, i.e. EC_GF2_simple_method.
For Fp curves the lowest common denominator implementation is the EC_GFp_simple_method implementation. All other implementations are based on this one. EC_GFp_mont_method builds on EC_GFp_simple_method but adds the use of montgomery multiplication (refer to Bignum). EC_GFp_nist_method offers an implementation optimised for use with NIST recommended curves (NIST curves are available through EC_GROUP_new_by_curve_name as described in EC_GROUP_new).
The functions EC_GFp_nistp224_method, EC_GFp_nistp256_method and EC_GFp_nistp521_method offer 64 bit optimised implementations for the NIST P224, P256 and P521 curves respectively. Note, however, that these implementations are not available on all platforms.
EC_METHOD_get_field_type identifies what type of field the EC_METHOD structure supports, which will be either F2^m or Fp. If the field type is Fp then the value NID_X9_62_prime_field is returned. If the field type is F2^m then the value NID_X9_62_characteristic_two_field is returned. These values are defined in the obj_mac.h header file.
Return Values 
All EC_GFp* functions and EC_GF2m_simple_method always return a const pointer to an EC_METHOD structure.
EC_METHOD_get_field_type returns an integer that identifies the type of field the EC_METHOD structure supports.