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A FRAMEWORK FOR REAL-VALUED CIPHER SYSTEMS

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Journal of Systems Science & Complexity 2007年第4期20卷 486-491页

作者： Zhaozhi ZHANG Nan JIANG Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China College of Computer Science and Technology Beijing University of Technology Beijing 100022 China

Most cipher systems designed thus far are binary-valued or integer-valued cipher systems. Their security relies on the assumption that one-way functions exist. Though the existence of one-way functions has not been proved yet, most cryptographic researchers believe that one-way functions exist. In addition, many candidates for one-way functions have been proposed. Therefore, the key step for developing real-valued cipher systems is to define real one-way functions and to propose candidates for them. In this paper, based on computational complexity theory over the real field, we give two definitions of real one-way functions; one is for digital one-way functions and the other is for general one-way functions. Candidates for these two classes of one-way functions are also proposed. Moreover, we present two examples to demonstrate that the candidates for both digital one-way functions and general one-way functions can be applied to construct secure real-valued cipher systems.

关键词： Computational complexity theory digital one-way function general one-way function real-valued cipher system.

Constructions for Anonymous Secret Sharing Schemes Using Combinatorial Designs

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Acta Mathematicae Applicatae Sinica 2007年第1期23卷 67-78页

作者： Ying-pu Deng Li-feng Guo Mu-lan Liu Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China State Key Laboratory of Information Security Graduate School of Chinese Academy of Sciences Beijing 100049China

In an anonymous secret sharing scheme the secret can be reconstructed without knowledge of which participants hold which shares. In this paper some constructions of anonymous secret sharing schemes with 2 thresholds by using combinatorial designs are given. Let v（t, w, q） denote the minimum size of the set of shares of a perfect anonymous （t, w） threshold secret sharing scheme with q secrets. In this paper we prove that v（t, w, q） - Θ（q） if t and w are fixed and that the lower bound of the size of the set of shares in [4] is not optimal under certain condition.

关键词： Anonymous secret sharing schemes Steiner systems group divisible designs difference families,relative difference sets

Linear multi-secret sharing schemes

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Science in China(Series F) 2005年第1期48卷 125-136页

作者： XlAOLiangliang LIUMulan AcademyofMathematicsandSystemSciencesandKeyLaboratoryofMathematicsMechanization ChineseAcademyofSciencesBeijing100080China

In this paper the linear multi-secret sharing schemes are studied by using monotone span programs. A relation between computing monotone Boolean functions by using monotone span programs and realizing multi-access structures by using linear multi-secret sharing schemes is shown. Furthermore, the concept of optimal linear multi-secret sharing scheme is presented and the several schemes are proved to be optimal.

关键词： multi-secret sharing scheme linear multi-secret sharing scheme monotone span program optimal linear multi-secret sharing scheme.

Isomorphism classes of hyperelliptic curves of genus 2 over finite fields with characteristic 2

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Science China Mathematics 2006年第2期49卷 173-184页

作者： DENG Yingpu LIU Mulan Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100080 China Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100080 China

In this paper we study the computation of the number of isomorphism classes of hyperelliptic curves of genus 2 over finite fields Fq with q even. We show the formula of the number of isomorphism classes, that is, for q = 2m, if 4 (|) m, then the formula is 2q3 + q2 - q;if 4 | m, then the formula is 2q3 + q2 - q + 8. These results can be used in the classification problems and the hyperelliptic curve cryptosystems.

关键词： hyperelliptic curves hyperelliptic curve cryptosystems Jacobian groups isomorphism classes.

THRESHOLD SCHEMES WITH WEIGHTS

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Journal of Systems Science & Complexity 2004年第4期17卷 578-581页

作者： XIAOLiangliang LIUMulan AcademyofMathematicsandSystemsScience ChineseAcademyofSciencesBeijing100080China

In this paper, we present the model of threshold schemes with weights as a natural generalization of Shamir's threshold scheme and show how to apply the model to construct secret sharing schemes by two examples.

关键词： secrete sharing schemes threshold scheme weight

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两个指定验证人签名方案的安全性分析

软件学报 2008年第7期19卷 1753-1757页

作者：曹正军刘丽华上海大学数学系上海200444 上海海事大学信息与计算科学系上海200135

2005年,王晓明等人把多重指定验证人签名与门限代理签名结合起来,提出了一个门限代理多重指定验证人签名(Wang-Fu).同年,陈伟东等人也提出了一个指定验证人的数字签名方案(Chen-Feng-Tan).证明Wang-Fu方案中指定验证人集合的管理者可以... 详细信息

2005年,王晓明等人把多重指定验证人签名与门限代理签名结合起来,提出了一个门限代理多重指定验证人签名(Wang-Fu).同年,陈伟东等人也提出了一个指定验证人的数字签名方案(Chen-Feng-Tan).证明Wang-Fu方案中指定验证人集合的管理者可以直接伪造签名.为此,每个验证人对在验证阶段使用私钥产生的部分数据必须进行零知识证明.CFT方案不满足非传递性,即指定验证人可以向第三方证明其拥有的签名是由签名人签署的.其原因在于,该方案直接利用了Schnorr签名技巧,指定验证人很客易把拥有的签名转化为关于原始签名人公钥参数的一个普通签名.

关键词：指定验证人签名门限代理签名非传递性提名人签名 Schnorr签名