New Hardware Architecture for Multiplication over GF (2^m) and Comparisons with Normal and Polynomial Basis Multipliers for Elliptic Curve Cryptography

Abstract

We propose a new linear array for multiplication in GF (2^m) which outperforms most of the existing linear multipliers in terms of the area and time complexity. Moreover we will give a very detailed comparison of our array with other existing architectures for the five binary fields GF (2^m), m=163,233,283,409,571, recommended by NIST for elliptic curve cryptography.