Efficient multiplication algorithm over the finite fields GF(qm) where q=3, 5

Abstract

Galois field multiplication is central to coding theory. In many applications of finite fields, there is need for a multiplication algorithm which can be realised easily on VLSI chips. In the paper, what is called the Babylonian multiplication algorithm for using tables of squares is applied to the Galois fields GF(qm). It is shown that this multiplication method for certain Galois fields eliminates the need for the division operation of dividing by four in the original Babylonian algorithm. Also, it is found that this multiplier can be used to compute complex multiplications defined on the direct sum of two identical copies of these Galois fields.