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Secure Multi-Party Proof and its Applications

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Journal of Software Engineering and Applications 2010年第7期3卷 709-717页

作者： chunming tang Shuhong Gao 不详

We define a new type cryptographical model called secure multi-party proof that allows any players and a verifier to securely compute a function : each of the players learns nothing about other players’ input and about the value of , and the verifier obtains the value of and it’s validity but learns nothing about the input of any of the players. It is implemented by a protocol using oblivious transfer and Yao’s scrambled circuit. We prove that our protocol is secure if the players and the verifier are semi-honest (i.e. they follow the protocol) and polynomial time bounded. The main applications of our protocol are for electronic voting and electronic bidding.

关键词： Multi-Party Proof Multi-Party Computation Electronic Voting Electronic Bidding

SEVERAL CRYPTOGRAPHIC APPLICATIONS OF ∑-PROTOCOL

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Journal of Systems Science & Complexity 2009年第2期22卷 260-279页

作者： chunming tang Zheng-an YAO School of Mathematics and Information Science Guangzhou University Guangzhou 510006 China State KeyLaboratory of Information Security Institute of Software Science Beijing 100190~ China. School of Mathematics and Computational Sciences Sun Yat-Sen University Guangzhou 510275 China.

Σ-protocol 被证明了是一个很强大的密码的工具并且广泛地在众多的重要密码的应用使用。在这篇论文，作者作为一个主要工具使用 Σ-protocol 解决下列困难的问题 1 3 并且构造三个有效密码的协议 4 6：1 ) 怎么为证明一个秘密整数，是... 详细信息

Σ-protocol 被证明了是一个很强大的密码的工具并且广泛地在众多的重要密码的应用使用。在这篇论文，作者作为一个主要工具使用 Σ-protocol 解决下列困难的问题 1 3 并且构造三个有效密码的协议 4 6：1 ) 怎么为证明一个秘密整数，是有形式 PQ 的一个 Blum 整数构造一个协议 P， Q 是二个不同素数和两 ≡3 (现代派 4 ) ；2 ) 怎么为与准确的度 t − 证明一个秘密多项式构造一个协议1 在里面一(t， n ) 阀值秘密分享计划；3 ) 怎么不从零知识的证明构造难区分的证人和证人躲协议；4 ) 有信息理论上的安全的一个公开可证实的秘密分享计划；5 ) 一个代表在单程的排列的存在下面的有能力的签名计划；6 ) 不相关的通用指明的验证器签名计划。

关键词：加密协议加密工具应用程序零知识证明秘密共享方案公开可验证后冲签名方案

THE OPTIMAL LINEAR SECRET SHARING SCHEME FOR ANY GIVEN ACCESS STRUCTURE

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Journal of Systems Science & Complexity 2013年第4期26卷 634-649页

作者： tang chunming GAO Shuhong ZHANG Chengli School of Mathematics and Information Science Guangzhou University Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes Guangzhou University Department of Mathematical Sciences Clemson University29634U.S.A

Any linear code can be used to construct a linear secret sharing scheme.In this paper,it is shown how to decide optimal linear codes(i.e.,with the biggest information rate)realizing a given access structure over finite fields.It amounts to solving a system of quadratic equations constructed from the given access structure and the corresponding adversary structure.The system becomes a linear system for binary codes.An algorithm is also given for finding the adversary structure for any given access structure.

关键词：秘密共享方案访问结构线性代码线性系统二次方程式二进制代码信息速率接入结构

Monotone Span Program vs. Linear Code

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Chinese Journal of Electronics 2016年第6期25卷 991-998页

作者： tang chunming CHEN Yuenai GAO Xuhong School of Mathematics and Information Sciences Guangzhou University Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes Guangzhou University Department of Mathematical Sciences Clemson University

Monotone span program(MSP) and Linear code(LC) are efficient tools to construct Linear secret sharing scheme(LSSS) for a given access structure. Since the size of an MSP or the length of an LC corresponds to the communicational complexity of an LSSS, one main motivation to study MSPs or LCs is the lower bound for their sizes or lengths. Therefore, it is one of the most important open problems how to efficiently construct an MSP or LC for a given access structure Γ with the smallest sizes or shortest length. Our contributions are: We extend tang et al.’s result, showing that, for any given access structureΓ, there exists an MSP or an LC to realize Γ if and only if a system of quadratic equations has solutions; We utilize the relationship between LCs and MSPs to obtain the greatest lower bound on the row size and the column size of MSPs realizing a given Γ, as well as an upper bound on the column size of MSPs; We give an algorithm to construct an MSP with the smallest sizes.

关键词： Cryptography Secret sharing scheme Monotone span program Linear code Size

Cryptography on twisted Edwards curves over local fields

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Science China(Information Sciences) 2015年第1期58卷 150-164页

作者： tang chunming XU MaoZhi QI YanFeng School of Mathematics and Information China West Normal University Laboratory of Mathematics and Applied Mathematics School of Mathematical SciencesPeking University School of Science Hangzhou Dianzi University

Twisted Edwards curves over finite fields have attracted great interest for their efficient and unified addition formula. In this paper, we consider twisted Edwards curves over local fields and introduce a cryptosystem based on quotient groups of twisted Edwards curves over local fields. From the study of formal groups of twisted Edwards curves and twisted Edwards curves over local fields, we give the choice of cryptographic groups.An element in these groups can be uniformly represented by two n digit p-adic numbers, whereas an element in the elliptic curves in Weierstrass form over local fields is represented by a 3n-2 digit p-adic number and a4n-3 digit p-adic number. In the cryptography on elliptic curves in Weierstrass form over local fields, five cases for different input point pairs in computing points addition have to be considered and sometimes points have to be lifted. In the cryptography on twisted Edwards curves over local fields, the addition formula is simple,unified, and complete, which is efficient, does not need lifting points, and is against the side channel analysis.Finally, a speedy point multiplication algorithm and some concrete instances are given.

关键词： local fields formal groups elliptic curve cryptography twisted Edwards curves addition law

A strongly secure identity-based authenticated group key exchange protocol

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Science China(Information Sciences) 2015年第9期58卷 98-109页

作者： TENG JiKai WU ChuanKun tang chunming TIAN YouLiang State Key Laboratory of Information Security Institute of Information Engineering Chinese Academy of Sciences School of Mathematics and Information Science Guangzhou University

In group key exchange(GKE) protocols, a shared secret key is established among a group of members for cryptographic use over a public network. An identity-based protocol is preferred to that under the employment of traditional public key infrastructure(PKI), since identity-based cryptosystem can simplify public key management procedure. In ASIACCS 2011, a security model for GKE protocol called EGBG model was proposed. The EGBG model takes ephemeral secret key leakage attack into consideration. Until now, there is no ID-based GKE protocol secure in the EGBG model. In this paper, we propose an identity-based GKE protocol. Its AKE-security with KCIR and full forward secrecy, MA-security with KCIR and its contributiveness are proven in the EGBG model. The proposed protocol does not involve NAXOS trick, which does not resist side channel attack and thus it provides stronger security guarantee. It achieves mutual authentication without applying signature, which makes the protocol more practical.

关键词： identity-based cryptography group key exchange provable security insider security

An Improved Identity-Based Society Oriented Signature Scheme with Anonymous Signers

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Wuhan University Journal of Natural Sciences 2007年第1期12卷 121-125页

作者： tang chunming School of Mathematics and Information Sciences/ Guangdong Province Key Laboratory Institute of Information Security Guangzhou University Guangzhou 510006 Guangdong China

In this paper, we present an improved identity-based society oriented signature scheme with anonymous signers, which satisfies：（1） when members leave or join an organization, the public verification key and the signature verification procedure are unchanged; （2） a user participates in several organizations at the same time, her secret key is only related with her identity. However, no previous schemes have these two properties.

关键词： signature identity-based society oriented signature

Delegateable signatures based on non-interactive witness indistinguishable and non-interactive witness hiding proofs

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Science in China(Series F) 2008年第2期51卷 128-144页

作者： tang chunming PEI DingYi WANG XiaoFeng LIU ZhuoJun Province Key Laboratory Institute of Information Security of Guangzhou University Guangzhou 510006 China State Key Laboratory of Information Security Chinese Academy of Sciences Beijing 100080China School of Mathematics and Computational Mathematics of Shenzhen University Shenzhen 518060 China Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China

A delegateable signature scheme （DSS） which was first introduced by Barak is mainly based on the non-interactive zero-knowledge proof （NIZK） for preventing the signing verifier from telling which witness （i.e., restricted subset） is being used. However, the scheme is not significantly efficient due to the difficulty of constructing NIZK. We first show that a non-interactive witness indistinguishable （NlWl） proof system and a non-interactive witness hiding （NIWH） proof system are easier and more efficient proof models than NIZK in some cases. Furthermore, the witnesses em- ployed in these two protocols （NlWl and NIWT） cannot also be distinguished by the verifiers. Combined with the E-protocol, we then construct NlWl and NIWH proofs for any NP statement under the existence of one-way functions and show that each proof is different from those under the existence of trapdoor permutations, Finally, based on our NlWl and NIWH proofs, we construct delegateable signature schemes under the existence of one-way functions, which are more efficient than Barak＇s scheme under the existence of trapdoor permutations.

关键词： delegateable signature non-interactive zero-knowledge non-interactive witness indistinguishable non-interactive witness hiding,∑-protocol

Implementing optimized pairings with elliptic nets

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Science China(Information Sciences) 2014年第5期57卷 137-146页

作者： tang chunming NI DongMei XU MaoZhi GUO BaoAn QI YanFeng School of Mathematics and Information China West Normal University LMAM Chinese Ministry of Education Peking University School of Mathematical Sciences Peking University

In this paper,we use elliptic nets to implement the optimized Ate pairings and optimal pairings on the Barreto-Naehrig curves with embedding degree 12.In order to do the arithmetic of elliptic curves over finite fields with elliptic nets,we first give some basic properties of elliptic nets associated to elliptic curves over finite fields and the expression of Miller function in terms of elliptic nets.Then we give formulae to compute some optimized pairings with elliptic nets,which is a new method to implement pairings.This method with elliptic nets has time complexity comparable to Miller’s algorithm and it can be optimized.

关键词： elliptic curves elliptic nets pairings Miller’s algorithm pairing-based cryptography