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

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 m₀+n ₀+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