Vlsi Array Synthesis for Polynomial Gcd Computation and Application to Finite Field Division

Abstract

Many practical algorithms have dynamic (or data-dependent) 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 pipelining. It has mo + no + 1 processing elements, where m0 and n0 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. © 1994 IEEE