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| on enumeration of polynomial equivalence classes and their application to mpkc | |
| Lin Dongdai; Faug&#; re Jean-Charles; Perret Ludovic; Wang Tianze | |
| 2011 | |
| Conference Name | on enumeration of polynomial equivalence classes and their application to mpkc |
| Source | Finite Fields and their Applications |
| Pages | - |
| Conference Date | 2010 |
| Conference Place | 北京 |
| Indexed Type | EI |
| ISSN | 10715797 |
| Department | (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 |
| English 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. © 2011 Elsevier Inc. All rights reserved. |
| Keyword | Polynomials Public Key Cryptography Set Theory |
| WOS ID | WOS:000325594100004 |
| Citation statistics | |
| Content Type | 会议论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/14259 |
| Collection | 信息安全国家重点实验室 |
| Recommended Citation GB/T 7714 | Lin Dongdai,Faug&#,re Jean-Charles,et al. on enumeration of polynomial equivalence classes and their application to mpkc[C],2011:-. |
| Files in This Item: | ||||||
| File Name/Size | DocType | Version | Access | License | ||
| on enumeration of po（690KB） | 开放获取 | -- | Application Full Text | |||
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