Graph-Theoretic Algorithms for the “Isomorphism of Polynomials” Problem - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2013

Graph-Theoretic Algorithms for the “Isomorphism of Polynomials” Problem


We give three new algorithms to solve the "isomorphism of polynomial" problem, which was underlying the hardness of recovering the secret-key in some multivariate trapdoor one-way functions. In this problem, the adversary is given two quadratic functions, with the promise that they are equal up to linear changes of coordinates. Her objective is to compute these changes of coordinates, a task which is known to be harder than Graph-Isomorphism. Our new algorithm build on previous work in a novel way. Exploiting the birthday paradox, we break instances of the problem in time q 2n/3 (rigorously) and q n/2 (heuristically), where q n is the time needed to invert the quadratic trapdoor function by exhaustive search. These results are obtained by turning the algebraic problem into a combinatorial one, namely that of recovering partial information on an isomorphism between two exponentially large graphs. These graphs, derived from the quadratic functions, are new tools in multivariate crypt-analysis.
Fichier principal
Vignette du fichier
BFV13.pdf (1.96 Mo) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-00825503 , version 1 (23-05-2013)
hal-00825503 , version 2 (12-12-2014)



Charles Bouillaguet, Pierre-Alain Fouque, Amandine Véber. Graph-Theoretic Algorithms for the “Isomorphism of Polynomials” Problem. Advances in Cryptology - {EUROCRYPT} 2013, May 2013, Athenes, Greece. pp.17, ⟨10.1007/978-3-642-38348-9_13⟩. ⟨hal-00825503v2⟩
669 View
284 Download



Gmail Facebook Twitter LinkedIn More