The implementation of Elliptic Curve binary finite field (F2m) for the global smart card

At this moment, main problems of global smart card are created with Rivest-Shamir-Adleman (RSA) public key algorithm because long key length and slow decryption time. Alternative public key encryption can solve these two problems such as Elliptic Curve Cryptography (ECC). Mathematic background of ECC is based on coordinate systems that two main arithmetic operations are explained and RSA encryption and ECC encryption key lengths have compared with diagram. Essentially, this paper is mentioned ECC over binary field F₂^m for global smart card systems with four applications. Main contribution of this paper is to propose ECC public key encryption in global smart card which is explained four applications of global smart card.