Novel algorithms and VLSI design for division over GF(2^m)

In this paper, we present the division algorithm (DA) for the computation of b = c/a over GF(2^m) in two aspects. First, we derive a new formulation for the discrete-time Wiener-Hopf equation (DTWHE) Ab = c in GF(2) over any basis. Symmetry of the matrix A is observed on some special bases and a three-step procedure is developed to solve the symmetric DTWHE. Secondly, we extend a variant of Stein's binary algorithm and propose a novel iterative division algorithm EB*. Owing to its structural simplicity, this algorithm can be mapped onto a systolic array with high speed and low area complexity.