Skip to Main content Skip to Navigation
Journal articles

On enumeration of polynomial equivalence classes and their application to MPKC

Abstract : The Isomorphism of Polynomials (IP) is one of the most fundamental problems in multivariate public key cryptography (MPKC). In this paper, we introduce a new framework to study the counting problem associated to IP. Namely, we present tools of finite geometry allowing to investigate the counting problem associated to IP. Precisely, we focus on enumerating or estimating the number of isomorphism equivalence classes of homogeneous quadratic polynomial systems. These problems are equivalent to finding the scale of the key space of a multivariate cryptosystem and the total number of different multivariate cryptographic schemes respectively, which might impact the security and the potential capability of MPKC. We also consider their applications in the analysis of a specific multivariate public key cryptosystem. Our results not only answer how many cryptographic schemes can be derived from monomials and how big the key space is for a fixed scheme, but also show that quite many HFE cryptosystems are equivalent to a Matsumoto-Imai scheme.
Document type :
Journal articles
Complete list of metadata

Cited literature [25 references]  Display  Hide  Download
Contributor : Ludovic Perret <>
Submitted on : Tuesday, January 15, 2013 - 3:30:08 PM
Last modification on : Friday, January 8, 2021 - 5:42:02 PM
Long-term archiving on: : Tuesday, April 16, 2013 - 3:52:42 AM


Files produced by the author(s)



Dongdai Lin, Jean-Charles Faugère, Ludovic Perret, Tianze Wang. On enumeration of polynomial equivalence classes and their application to MPKC. Finite Fields and Their Applications, Elsevier, 2012, 18 (2), pp.283-302. ⟨10.1016/j.ffa.2011.09.001⟩. ⟨hal-00776073⟩



Record views


Files downloads