on enumeration of polynomial equivalence classes and their application to mpkc

	on enumeration of polynomial equivalence classes and their application to mpkc
	Lin Dongdai ; Faug&# ; re Jean-Charles ; Perret Ludovic ; Wang Tianze
	2011
会议名称	on enumeration of polynomial equivalence classes and their application to mpkc
会议日期	2010
会议地点	北京
关键词	Polynomials Public key cryptography Set theory
页码	-
英文摘要	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. © 2011 Elsevier Inc. All rights reserved.
收录类别	EI
会议录	Finite Fields and their Applications
ISSN号	10715797
WOS记录号	WOS:000325594100004
内容类型	会议论文
源URL	[http://124.16.136.157/handle/311060/14259]
专题	软件研究所_信息安全国家重点实验室_会议论文
推荐引用方式 GB/T 7714	Lin Dongdai,Faug&#,re Jean-Charles,et al. on enumeration of polynomial equivalence classes and their application to mpkc[C]. 见:on enumeration of polynomial equivalence classes and their application to mpkc. 北京. 2010.