Generalisation of Kipnis and Shamir Cryptanalysis of the HFE public key cryptosystem

Authors: Omessaad Hamdi, Ammar Bouallegue, Sami Harari

Abstract:

In [4], Kipnis and Shamir have cryptanalised a version of HFE of degree 2. In this paper, we describe the generalization of this attack of HFE of degree more than 2. We are based on Fourier Transformation to acheive partially this attack.

Keywords: Public, cryptosystem, cryptanalisis, HFE.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1330021

References:

[1] Nicolas Courtois, Louis Goubin, Jacques Patarin: Quartz, 128-bit long digital signatures: in cryptographers- Track Rsa Confrence 2001, LNCS 2020, pp 282-297, Springer-Verlag.
[2] Nicolas Courtois:The security of Hidden Field Equations (HFE), Cryptographers Track Rsa Conference 2001,LNCS 2020, pp. 266-281, Springer-Verlag.
[3] PATARIN Jacques:"Hidden Fields Equations (HFE) and Isomorphisms of Polynomials (IP): two new families of Asymmetric Algorithms"; Eurocrypt-96, Springer Verlag, pp. 33-48.
[4] SHAMIR Adi, KIPNIS Aviad:"Cryptanalysis of the HFE public key cryptosystem"; Crypto-99. www.minrank.org hfe.