PARALLEL POLYNOMIAL ARITHMETIC OVER FINITE RINGS

Convolution algorithms for polynomial multiplication are well known, as is the use of Residue Number Systems and the Chinese Remainder Theorem. This paper discusses how these techniques may be used to perform polynomial arithmetic over very large rings or finite fields. The algorithm is practical and structured so that it can be implemented very efficiently on either a shared memory or a message passing parallel computer. We discuss the mathematical basis of the algorithm and contrast its performance on an Alliant FX/8 and a Symult S2010. These are, respectively, shared memory and message passing parallel computers. © 1990.