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

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.

Mots clés: bilinear map; finite field arithmetic; bilinear rank; automorphisms; optimal formulae; matrix multiplication; polynomial multiplication

Domaines: Complexité [cs.CC]; Calcul formel [cs.SC]; Mathématique discrète [cs.DM]

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