EFFICIENT BIT SERIAL MULTIPLIERS OF BERLEKAMP TYPE IN ${\mathbb{F}}_2^m$

Using good properties of an optimal normal basis of type I in a finite field ${\mathbb{F}}_{2^m}$, we present a design of a bit serial multiplier of Berlekamp type, which is very effective in computing $xy^2$. It is shown that our multiplier does not need a basis conversion process and a squaring operation is a simple permutation in our basis. Therefore our multiplier provides a fast and an efficient hardware architecture for a bit serial multiplication of two elements in ${\mathbb{F}}_{2^m}$.