A Framework for Practical Universally Composable Zero-Knowledge Protocols

J. Camenisch, S. Krenn, V. Shoup, in:, D. Lee, X. Wang (Eds.), Springer, 2011, pp. 449–467.

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Abstract
Zero-knowledge proofs of knowledge (ZK-PoK) for discrete logarithms and related problems are indispensable for practical cryptographic protocols. Recently, Camenisch, Kiayias, and Yung provided a specification language (the CKY-language) for such protocols which allows for a modular design and protocol analysis: for every zero-knowledge proof specified in this language, protocol designers are ensured that there exists an efficient protocol which indeed proves the specified statement. However, the protocols resulting from their compilation techniques only satisfy the classical notion of ZK-PoK, which is not retained are when they used as building blocks for higher-level applications or composed with other protocols. This problem can be tackled by moving to the Universal Composability (UC) framework, which guarantees retention of security when composing protocols in arbitrary ways. While there exist generic transformations from $\Sigma$-protocols to UC-secure protocols, these transformation are often too inefficient for practice. In this paper we introduce a specification language akin to the CKY-language and a compiler such that the resulting protocols are UC-secure and efficient. To this end, we propose an extension of the UC-framework addressing the issue that UC-secure zero-knowledge proofs are by definition proofs of knowledge, and state a special composition theorem which allows one to use the weaker -- but more efficient and often sufficient -- notion of proofs of membership in the UC-framework. We believe that our contributions enable the design of practically efficient protocols that are UC-secure and thus themselves can be used as building blocks.
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Date Published
2011-11-21
Acknowledgement
This work was in part funded by the Swiss Hasler Foundation, and the EU FP7 grants 216483 and 216499, as well as by the NSF grant CNS-0716690.
Volume
7073
Page
449 - 467
Conference
ASIACRYPT: Theory and Application of Cryptology and Information Security
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Camenisch J, Krenn S, Shoup V. A Framework for Practical Universally Composable Zero-Knowledge Protocols. In: Lee D, Wang X, eds. Vol 7073. Springer; 2011:449-467. doi:10.1007/978-3-642-25385-0
Camenisch, J., Krenn, S., & Shoup, V. (2011). A Framework for Practical Universally Composable Zero-Knowledge Protocols. In D. Lee & X. Wang (Eds.) (Vol. 7073, pp. 449–467). Presented at the ASIACRYPT: Theory and Application of Cryptology and Information Security, Springer. https://doi.org/10.1007/978-3-642-25385-0
Camenisch, Jan, Stephan Krenn, and Victor Shoup. “A Framework for Practical Universally Composable Zero-Knowledge Protocols.” edited by Dong Lee and Xiaoyun Wang, 7073:449–67. Springer, 2011. https://doi.org/10.1007/978-3-642-25385-0.
J. Camenisch, S. Krenn, and V. Shoup, “A Framework for Practical Universally Composable Zero-Knowledge Protocols,” presented at the ASIACRYPT: Theory and Application of Cryptology and Information Security, 2011, vol. 7073, pp. 449–467.
Camenisch J, Krenn S, Shoup V. 2011. A Framework for Practical Universally Composable Zero-Knowledge Protocols. ASIACRYPT: Theory and Application of Cryptology and Information Security, LNCS, vol. 7073. 449–467.
Camenisch, Jan, et al. A Framework for Practical Universally Composable Zero-Knowledge Protocols. Edited by Dong Lee and Xiaoyun Wang, vol. 7073, Springer, 2011, pp. 449–67, doi:10.1007/978-3-642-25385-0.

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