A Fast Cryptanalysis of the Isomorphism of Polynomials with One Secret Problem

Abstract

At Eurocrypt’96, Patarin proposed [9] new cryptographic schemes based on the Isomorphism of Polynomials with one Secret problem (IP1S) [9]. We study in this paper a restriction of IP1S called Polynomial Linear Equivalence problem (PLE) [7]. We show that PLE is in fact not a restriction of IP1S, in the sense that any algorithm solving PLE can be efficiently transformed into an algorithm for solving IP1S. Motivated by the cryptanalysis of schemes based on IP1S, we present a new efficient algorithm for solving PLE. This algorithm is mainly based on a differential property of PLE. The main advantage of this approach is to translate PLE into a simple linear algebra problem. The performances of our algorithm evidence that, with the parameters proposed in [9], schemes based on IP1S are far from achieving the security level required for cryptographic applications.