on enumeration of polynomial equivalence classes

ISCAS OpenIR

	on enumeration of polynomial equivalence classes
	Wang TianZe; Lin DongDai
	2012
会议名称	SCIENCE CHINA Mathematics
页码	1137-1152
收录类别	SPRINGER ; SCI
ISSN	1674-7283
部门归属	State Key Laboratory of Information Security Institute of Software Chinese Academy of Sciences Beijing 100190 China
摘要	The isomorphism of polynomials (IP), one of the hard problems in multivariate public key cryptography induces an equivalence relation on a set of systems of polynomials. Then the enumeration problem of IP consists of counting the numbers of different classes and counting the cardinality of each class that is highly related to the scale of key space for a multivariate public key cryptosystem. In this paper we show the enumeration of the equivalence classes containing when char = 2, which implies that these polynomials are all weak IP instances. Moreover, we study the cardinality of an equivalence class containing the binomial over without the restriction that char() = 2, which gives us a deeper understanding of finite geometry as a tool to investigate the enumeration problem of IP.; The isomorphism of polynomials (IP), one of the hard problems in multivariate public key cryptography induces an equivalence relation on a set of systems of polynomials. Then the enumeration problem of IP consists of counting the numbers of different classes and counting the cardinality of each class that is highly related to the scale of key space for a multivariate public key cryptosystem. In this paper we show the enumeration of the equivalence classes containing when char = 2, which implies that these polynomials are all weak IP instances. Moreover, we study the cardinality of an equivalence class containing the binomial over without the restriction that char() = 2, which gives us a deeper understanding of finite geometry as a tool to investigate the enumeration problem of IP.
关键词	Enumerative Problem &#8211 Isomorphism Of Polynomials &#8211 Finite Geometry
学科领域	Mathematics
语种	英语
WOS记录号	WOS:000304616900003
引用统计
内容类型	会议论文
URI标识	http://ir.iscas.ac.cn/handle/311060/15736
专题	中国科学院软件研究所
推荐引用方式 GB/T 7714	Wang TianZe,Lin DongDai. on enumeration of polynomial equivalence classes[C],2012:1137-1152.