VLSI array synthesis for polynomial GCD computation and application to finite field division

Abstract

Many practical algorithms have dynamic (or datadependent) dependency structure in their computation, which is not desirable for VLSI hardware implementation. Polynomial GCD computation by Euclid's algorithm is a typical example of dynamic dependency. In this paper, we use an algorithmic transformation technique to derive static (or data-independent) dependencies for Euclid's GCD algorithm. The resulting algorithm is mapped to a linear systolic array which is area-efficient and achieves maximum throughput with pipeliing. It has mo + no + 1 processing elements, where mo and no are degrees of two polynomials. We have applied the technique to the extended GCD algorithm and developed a systolic finite field divider, which can be efficiently used in decoding a variety of error correcting codes. a time (7') index. For example, in the two-dimensional case,