Paper 2012/110

Finding Optimal Formulae for Bilinear Maps

Razvan Barbulescu and Jérémie Detrey and Nicolas Estibals and Paul Zimmermann

Abstract

We describe a unified framework to search for optimal formulae evaluating bilinear --- or quadratic --- maps. This framework applies to polynomial multiplication and squaring, finite field arithmetic, matrix multiplication, etc. We then propose a new algorithm to solve problems in this unified framework. With an implementation of this algorithm, we prove the optimality of various published upper bounds, and find improved upper bounds.