EFFICIENT PARALLEL GAUSSIAN NORMAL BASES MULTIPLIERS OVER FINITE FIELDS

The normal basis has the advantage that the result of squaring an element is simply the right cyclic shift of its coordinates in hardware implementation over finite fields. In particular, the optimal normal basis is the most efficient to hardware implementation over finite fields. In this paper, we propose an efficient parallel architecture which transforms the Gaussian normal basis multiplication in GF( $2^m$ ) into the type-I optimal normal basis multiplication in GF( $2^{mk}$ ), which is based on the palindromic representation of polynomials.