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on enumeration of polynomial equivalence classes and their application to mpkc
作者: Lin Dongdai ; Faug&# ; re Jean-Charles ; Perret Ludovic ; Wang Tianze
会议文集: Finite Fields and their Applications
会议名称: on enumeration of polynomial equivalence classes and their application to mpkc
会议日期: 2010
出版日期: 2011
会议地点: 北京
关键词: Polynomials ; Public key cryptography ; Set theory
收录类别: EI
ISSN: 10715797
部门归属: (1) SKLOIS, Institute of Software, Chinese Academy of Sciences, Haidian District, Beijing 100190, China; (2) Paris-Rocquencourt Center, SALSA Project, UPMC Univ Paris 06, UMR 7606, LIP6, F-75005, Paris, France; (3) CNRS, UMR 7606, LIP6, F-75005, Paris, France; (4) Graduate University of Chinese Academy of Sciences, Beijing 100149, China
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.
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内容类型: 会议论文
URI标识: http://ir.iscas.ac.cn/handle/311060/14259
Appears in Collections:信息安全国家重点实验室_会议论文

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Recommended Citation:
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.
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