Elliptic Curve Cryptography: an Overview

Implementing Elliptic Curve Cryptography in Smart Cards using Galois Field

Abstract

Elliptic curvecryptography is one of the emerging techniques that stand as an alternative forconventional public key cryptography. Elliptic curve cryptography has severalapplications of which smart cards are also one among them.  A smart card is nothing but a single chipthat contains microprocessor components. Smart cards are mainly used forsecured sign-on in big organizations. The security feature of smart card isprovided by elliptic curve cryptography. Elliptic curve cryptography for smart cards can be implemented throughseveral ways. Of them implementation using Galois Field is one of the veryfamous techniques. This essay discusses in detail how elliptic curvecryptography is implemented in smart cards using a concept called Galois finitefield.