EFFICIENT MULTIPLICATION ALGORITHM OVER THE FINITE-FIELDS GF(Q(M)) WHERE Q = 3, 5

Galois field multiplication is central to coding theory. In many appli cations of finite fields, there is need for a multiplication algorithm which can be realised easily on VLSI chips. In the paper, what is cal led the Babylonian multiplication algorithm for using tables of square s is applied to the Galois fields GF(q(m)). It is shown that this mult iplication method for certain Galois fields eliminates the need for th e division operation of dividing by four in the original Babylonian al gorithm. Also, it is found that this multiplier can be used to compute complex multiplications defined on the direct sum of two identical co pies of these Galois fields.