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Springer, Lecture Notes in Computer Science, p. 168-186, 2012

DOI: 10.1007/978-3-642-31662-3_12

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Finding Optimal Formulae for Bilinear Maps

Proceedings article published in 2012 by Razvan Barbulescu, Jérémie Detrey, Nicolas Estibals, Paul Zimmermann ORCID
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This paper is available in a repository.

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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.