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Preprints, Working Papers, ... Year : 2018

Improved method for finding optimal formulae for bilinear maps in a finite field

Abstract

In 2012, Barbulescu, Detrey, Estibals and Zimmermann proposed a new framework to exhaustively search for optimal formulae for evaluating bilinear maps, such as Strassen or Karatsuba formulae. The main contribution of this work is a new criterion to aggressively prune useless branches in the exhaustive search, thus leading to the computation of new optimal formulae, in particular for the short product modulo X 5 and the circulant product modulo (X 5 − 1). Moreover , we are able to prove that there is essentially only one optimal decomposition of the product of 3 x 2 by 2 x 3 matrices up to the action of some group of automorphisms.
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Dates and versions

hal-01519408 , version 1 (07-05-2017)
hal-01519408 , version 2 (28-11-2017)
hal-01519408 , version 3 (30-11-2018)

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Svyatoslav Covanov. Improved method for finding optimal formulae for bilinear maps in a finite field. 2018. ⟨hal-01519408v3⟩
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