Cryptology relies on the difficulty of solving mathematical problems, such as the factor of large integers composed of two large prime numbers and the discrete logarithm of a random eliptic curve. This module provides low-level features of the latter. Elliptic Curve protocols can provide the same security with smaller keys.
There are 2 forms of elliptic curves,
F2^m. These curves use irreducible
trinomial or pentanomial . Being a generic interface to a wide range of algorithms,
the cuves are generally referenced by
EcGroup. There are many built in groups
OpenSSL Wiki explains the fields and curves in detail at Eliptic Curve Cryptography.