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

Svyatoslav Covanov 1
1 CARAMBA - Cryptology, arithmetic : algebraic methods for better algorithms
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
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 × 2 by 2 × 3 matrices up to the action of some group of automorphisms.
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Submitted on : Tuesday, November 28, 2017 - 11:15:20 AM
Last modification on : Tuesday, December 18, 2018 - 4:18:26 PM

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  • HAL Id : hal-01519408, version 2
  • ARXIV : 1705.07728

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Svyatoslav Covanov. Improved method for finding optimal formulae for bilinear maps in a finite field. 2017. ⟨hal-01519408v2⟩

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