[show abstract][hide abstract] ABSTRACT: Finite field arithmetic logic is central in the implementation of Reed-Solomon coders and in some cryptographic algorithms. There is a need for good multiplication and inversion algorithms that can be easily realized on VLSI chips. Massey and Omura  recently developed a new multiplication algorithm for Galois fields based on a normal basis representation. In this paper, a pipeline structure is developed to realize the Massey-Omura multiplier in the finite field GF(2m). With the simple squaring property of the normal basis representation used together with this multiplier, a pipeline architecture is also developed for computing inverse elements in GF(2m). The designs developed for the Massey-Omura multiplier and the computation of inverse elements are regular, simple, expandable, and therefore, naturally suitable for VLSI implementation.
IEEE Transactions on Computers 07/1985; 34:709-717. · 1.38 Impact Factor
[show abstract][hide abstract] ABSTRACT: Report presents mathematical principles of Berlekamp bit serial multiplier algorithm and its application to design of very-large-scale integrated (VLSI) encoders for Reed-Solomon error-correcting codes. Structure made readily on single chip of negatively doped channel metal oxide semiconductor.