On Bivariate Hensel Lifting and its Parallelization - Abstract

Laurent Bernardin, ETH Zürich

We present a new parallel algorithm for performing linear Hensel lifting of bivariate polynomials over a finite field. The sequential version of our algorithm has a running time of O(m n^4) for lifting m univariate polynomials of degree n with respect to a bivariate polynomial of degree n in both variables, assuming that we use classical polynomial multiplication.

Our parallel algorithm further reduces this complexity to O(m n/s n^3) on s processing nodes, assuming that s

We also present an asymptotically faster algorithm, which has a complexity of O((ln m) n^2 ln n) operations in the coefficient field, using fast polynomial multiplication and O(n ln m) processors.

Experimental results on a massively parallel, distributed memory machine confirm that our algorithm scales well on high numbers of processing nodes.