—Finite field or Galois field plays an important role in efficient architecture design and implementation of Elliptic curve cryptosystem. A lot of research work is going on in this area since it is suitable for cryptography as well as error correcting codes useful for digital communication, compact disks etc. In this paper we discuss the basic concepts of finite field and its application to elliptic curve cryptography (ECC). A detailed study and analysis of various implementation options available in finite field has been explored and highlighted for effective system design. In section IX we discuss a few efficient hardware design approaches adopted by many researchers useful for ECC.
—Finite field, elliptic curve, multiplier, architecture.
Manuscript received May 02, 2009. Bimal Kumar Meher is with Information Technology Department of Silicon Institute of Technology, Bhubaneswar, India.(phone+919937156042)
Cite: Bimal Kumar Meher, "A Study of Suitability and Effectiveness of Various Implementation Options Of Finite Field Arithmetic on Elliptic Curve Crypto System," International Journal of Computer Theory and Engineering
vol. 1, no. 4, pp. 389-393, 2009.