| Subject: | Mathematics
|
| Title: | on enumeration of polynomial equivalence classes |
| Author: | Wang TianZe
; Lin DongDai
|
| Conference Name: | SCIENCE CHINA Mathematics
|
| Issued Date: | 2012
|
| Keyword: | enumerative problem –
; isomorphism of polynomials –
; finite geometry
|
| Indexed Type: | SPRINGER
; SCI
|
| ISSN: | 1674-7283
|
| Department: | State Key Laboratory of Information Security Institute of Software Chinese Academy of Sciences Beijing 100190 China
|
| Abstract: | 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. |
| English Abstract: | 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. |
| Language: | 英语
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| Citation statistics: |
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| Content Type: | 会议论文
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| URI: | http://ir.iscas.ac.cn/handle/311060/15736
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| Appears in Collections: | 软件所图书馆_会议论文
|
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| Recommended Citation: | |
Wang TianZe,Lin DongDai. on enumeration of polynomial equivalence classes[C]. 见:SCIENCE CHINA Mathematics.
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