Finding Optimal Formulae for Bilinear Maps

Razvan Barbulescu 1 Jérémie Detrey 1 Nicolas Estibals 1 Paul Zimmermann 1
1 CARAMEL - Cryptology, Arithmetic: Hardware and Software
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
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.
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Submitted on : Tuesday, February 28, 2012 - 8:03:00 AM
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Razvan Barbulescu, Jérémie Detrey, Nicolas Estibals, Paul Zimmermann. Finding Optimal Formulae for Bilinear Maps. International Workshop of the Arithmetics of Finite Fields, Ruhr Universitat Bochum, Jul 2012, Bochum, Germany. ⟨10.1007/978-3-642-31662-3_12⟩. ⟨hal-00640165v2⟩

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