Polynomial equivalence problems and applications to multivariate cryptosystems - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Reports (Research Report) Year : 2004

Polynomial equivalence problems and applications to multivariate cryptosystems

Abstract

At Eurocrypt'96, J.Patarin proposed a signature and authentication scheme whose security relies on the difficulty of the Isomorphism of Polynomials problem . In this paper, we study a variant of this problem, namely the Isomorphism of Polynomials with one secret problem and we propose new algorithms to solve it, which improve on all the previously known algorithms. As a consequence, we prove that, when the number of polynomials (u) is close to the number of variables (n), the instances considered in and can be broken. We point out that the case n-u small is the most relevant one for cryptographic applications. Besides, we show that a large class of instances that have been presumed difficult in and can be solved in deterministic polynomial time. We also give numerical results to illustrate our methods.
Fichier principal
Vignette du fichier
RR-5119.pdf (337.09 Ko) Télécharger le fichier

Dates and versions

inria-00071464 , version 1 (23-05-2006)

Identifiers

  • HAL Id : inria-00071464 , version 1

Cite

Françoise Levy-Dit-Vehel, Ludovic Perret. Polynomial equivalence problems and applications to multivariate cryptosystems. [Research Report] RR-5119, INRIA. 2004. ⟨inria-00071464⟩
64 View
407 Download

Share

Gmail Facebook Twitter LinkedIn More