Efficient Construction of Gate Circuit for Computing Multiplicative Inverses over GF (2m)

Masakatu MORII  Masao KASAHARA  

IEICE TRANSACTIONS (1976-1990)   Vol.E72   No.1   pp.37-42
Publication Date: 1989/01/25
Online ISSN: 
Print ISSN: 0000-0000
Type of Manuscript: PAPER
Category: Information Theory and Coding Theory

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The theory of finite fields has been successfully applied to the constructing of the various algebraic codes, digital signal processing, and techniques of cryptography. Especially the theories on four operations are very important, because it is strongly related to the size and the throughput of the gate circuits for the various encoders and decoders. In this paper we shall give a new method for constructing the gate circuit that yields the multiplicative inverses over GF (2m). The method is based on a new algorithm for computing multiplicative inverses in GF (2m). The operations needed for our algorithm are rarely performed on GF (2m), but primarily on the subfields of GF (2m). When performing the multiplication and division over finite fields, the idea of using the subfield has been given wide attention. However the conventional algorithms taking advantage of this idea are not necessarily efficient from the practical point of view. We see that our algorithm proved superior to the conventional methods when GF (2m) has the subfield GF (22).