Low complexity bit serial systolic multipliers over GF(2m) for three classes of finite fields

By using a standard polynomial basis, we present a low complexity bit serial systolic multiplier over GF(2(m)) when there exist the following types of irreducible polynomials, x(m)+x(m-1) + 1, x(m)+Sigma(i=0)(m-2) x(i) and Sigma(i=0)(m) x(i), an all one polynomial. When compared with most of other bit serial systolic multipliers, our multiplier needs two latches fewer in each basic cell. Therefore, the hardware complexity of our systolic array is approximately 20 percent reduced from other existing multipliers.