New bit-parallel systolic multipliers for a class of GF(2^m)

The operations of the cyclic shifting and the inner proadct are defined based on the properties of irreducible all one polynomials. With the two operations, an effective algorithm for computing multiplications over a class of GF(2^m) was developed in this paper. The low-complexity bit-parallel systolic multiplier is presented. The multiplier is the latency of m/2+2 clock cycles. The multiplier has very low latency, which makes them very fast. Moreover the architectures of the multiplier can also be applied to compute multiplications over the class of GF(2^m) in which the elements are represented with the root of an irreducible equally spaced polynomial of degree m.