Mapping an Arbritrary Message to an Elliptic Curve When Defined over GF(2^n)

The use of elliptic curve cryptography (ECC) when used as a public-key cryptosystem for encryption is such that if one has a message to encrypt, then they attempt to map it to some point in the prime subgroup of the elliptic curve by systematically modifying the message in a deterministic manner. The applications typically used for ECC are the key-exchange, digital signature or a hybrid encryption systems (ECIES) all of which avoid this problem. In this paper we provide a deterministic method that guarantees that the map of a message to an elliptic curve point can be made without any modification. This paper provides a solution to the open problem posed in [7] concerning the creation of a deterministic method to map arbitrary message to an elliptic curve.