An Evolutionary Approach to the Design of Cellular Automata Architecture for Multiplication in Elliptic Curve Cryptography over Finite Fields

Abstract

Cellular Automata (CA) has been used in evolutionary computation for over a decade and Elliptic Curve Cryptography (ECC) has recently received a lot of attention due to their important and practical applications in public key cryptographys. The two elliptic curve operations are the Add and Double, which are computed by field arithmetic operations, such as additions, modular multiplications, modular squarings and divisions. The addition operation for field elements is trivial and squaring is so much faster than regular multiplication. Divisions which are the important contributors for the run time also can be implemented by repeating multiplications. Thus we propose an special and efficient multiplication architecture based on CA in ECC over GF(2 n ). The proposed evolutionary computation architectures can be used in the effectual hardware design of coprocessor for ECC since they have high regularity and a reduced latency.