Novel Algorithms and VLSI Design for Division over GF(2m)

Chien-Hsing WU  Chien-Ming WU  Ming-Der SHIEH  Yin-Tsung HWANG  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E85-A   No.5   pp.1129-1139
Publication Date: 2002/05/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: VLSI Design Technology and CAD
division algorithm,  basis matrix,  Stein's algorithm,  high speed,  finite field,  

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In this paper, we present the division algorithm (DA) for the computation of b=c/a over GF(2m) 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.