Performance of Finite Field Arithmetic in an Elliptic Curve Cryptosystem

Performance of Finite Field Arithmetic in an Elliptic Curve Cryptosystem Zhi Li, John Higgins, Mark Clement 3361 TMCB Brigham Young University Provo, UT 84602 {zli,higgins,clement}@cs.byu.edu Abstract As the Internet commerce becomes a more important part of the economy, network security is receiving more emphasis. Time spent in data encryption can be a significant performance bottleneck for many applications. Elliptic Curve Cryptography (ECC) has been shown to provide stronger encryption than conventional integer factorization schemes such as RSA or discrete logarithmbased systems such as Diffie -Hellman. This research explores the efficiency advantages of ECC by implementing and evaluating the underlying finite field arithmetic of the ElGamal encryption protocol using both polynomial basis (PB) and normal basis (NB) representations. The Normal basis implementation performs more than two times as fast as the polynomial basis representation and more than 50 times faster than traditional encryption schemes.