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| zero-knowledge argument for simultaneous discrete logarithms | |
| Chow Sherman S.M.; Ma Changshe; Weng Jian | |
| 2011 | |
| Source | Algorithmica (New York)
 |
| ISSN | 0178-4617 |
| Volume | 64Issue:2Pages:1-21 |
| English Abstract | In Crypto 1992, Chaum and Pedersen introduced a protocol (CP protocol for short) for proving the equality of two discrete logarithms (EQDL) with unconditional soundness, which is widely used nowadays and plays a central role in DL-based cryptography. Somewhat surprisingly, the CP protocol has never been improved for nearly two decades since its advent. We note that the CP protocol is usually used as a non-interactive proof by using the Fiat-Shamir heuristic, which inevitably relies on the random oracle model (ROM) and assumes that the adversary is computationally bounded. In this paper, we present an EQDL protocol in the ROM which saves approximately 40% of the computational cost and approximately 33% of the prover's outgoing message size when instantiated with the same security parameter. The catch is that our security guarantee only holds for computationally bounded adversaries. Our idea can be naturally extended for simultaneously showing the equality of n discrete logarithms with O(1)-size commitment, in contrast to the n-element adaption of the CP protocol which requires O(n)-size. This improvement benefits a variety of interesting cryptosystems, ranging from signatures and anonymous credential systems, to verifiable secret sharing and threshold cryptosystems. As an example, we present a signature scheme that only takes one (offline) exponentiation to sign, without utilizing pairing, relying on the standard decisional Diffie-Hellman assumption. © 2011 Springer Science+Business Media, LLC.; In Crypto 1992, Chaum and Pedersen introduced a protocol (CP protocol for short) for proving the equality of two discrete logarithms (EQDL) with unconditional soundness, which is widely used nowadays and plays a central role in DL-based cryptography. Somewhat surprisingly, the CP protocol has never been improved for nearly two decades since its advent. We note that the CP protocol is usually used as a non-interactive proof by using the Fiat-Shamir heuristic, which inevitably relies on the random oracle model (ROM) and assumes that the adversary is computationally bounded. In this paper, we present an EQDL protocol in the ROM which saves approximately 40% of the computational cost and approximately 33% of the prover's outgoing message size when instantiated with the same security parameter. The catch is that our security guarantee only holds for computationally bounded adversaries. Our idea can be naturally extended for simultaneously showing the equality of n discrete logarithms with O(1)-size commitment, in contrast to the n-element adaption of the CP protocol which requires O(n)-size. This improvement benefits a variety of interesting cryptosystems, ranging from signatures and anonymous credential systems, to verifiable secret sharing and threshold cryptosystems. As an example, we present a signature scheme that only takes one (offline) exponentiation to sign, without utilizing pairing, relying on the standard decisional Diffie-Hellman assumption. © 2011 Springer Science+Business Media, LLC. |
| Indexed Type | EI ; SCI |
| Keyword | Network Security |
| Department | (1) Department of Combinatorics and Optimization and Centre for Applied Cryptographic Research University of Waterloo Waterloo N2L3G1 Canada; (2) School of Computer South China Normal University Guangzhou 510631 China; (3) Department of Computer Science Jinan University Guangzhou 510632 China; (4) State Key Laboratory of Information Security Institute of Software Chinese Academy of Sciences Beijing 100080 China; (5) State Key Laboratory of Networking and Switching Technology Beijing University of Posts and Telecommunications Beijing 100876 China; (6) Emergency Technology Research Center of Risk Evaluation and Prewarning on Public Network Security Guangdong 510632 China |
| Subject | Computer Science ; Mathematics |
| Sponsorship | Office of Research, Singapore Management University; National Science Foundation of China 60903178, 61070217, 61005049, 61133014; Fundamental Research Funds for the Central Universities 21610204; Guangdong Provincial Science and Technology Project 2010A032000002 |
| Language | 英语 |
| Content Type | 期刊论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/16068 |
| Collection | 中国科学院软件研究所 |
| Recommended Citation GB/T 7714 | Chow Sherman S.M.,Ma Changshe,Weng Jian. zero-knowledge argument for simultaneous discrete logarithms[J]. Algorithmica (New York),2011,64(2):1-21. |
| APA | Chow Sherman S.M.,Ma Changshe,&Weng Jian.(2011).zero-knowledge argument for simultaneous discrete logarithms.Algorithmica (New York),64(2),1-21. |
| MLA | Chow Sherman S.M.,et al."zero-knowledge argument for simultaneous discrete logarithms".Algorithmica (New York) 64.2(2011):1-21. |
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