| 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 |
| 会议录名称 | Finite Fields and their Applications |
| 页码 | - |
| 会议日期 | 2010 |
| 会议地点 | 北京 |
| 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 |
| 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. |
| 关键词 | Polynomials Public Key Cryptography Set Theory |
| WOS记录号 | WOS:000325594100004 |
| 引用统计 | |
| 内容类型 | 会议论文 |
| URI标识 | http://ir.iscas.ac.cn/handle/311060/14259 |
| 专题 | 信息安全国家重点实验室 |
| 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],2011:-. |
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