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International Conference on Information Theoretic Security

ICITS 2015: Information Theoretic Security pp 51–68Cite as

On Zero-Knowledge with Strict Polynomial-Time Simulation and Extraction from Differing-Input Obfuscation for Circuits

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9063))

Abstract

This paper investigates the exact round complexity of zero-knowledge arguments of knowledge (ZKAOK) with strict-polynomial-time simulation and extraction. Previously, Barak and Lindell [STOC 02] presented a constant-round such ZKAOK. With the parallel technique by Ostrovsky and Visconti [ECCC 12] for implementing Barak’s zero-knowledge [FOCS 01] in 6 rounds, the Barak-Lindell ZKAOK can be implemented in, we believe, 7 rounds, which achieves the best exact round complexity for such ZKAOK from reasonable assumptions.

Recently, Pandey et al. [ePrint 13] proposed a 4-round (concurrent) ZK with strict-polynomial-time simulation based on differing-input obfuscation for machines. Based on their construction, Ding [ISC 14] presented a 4-round ZKAOK with strict-polynomial-time simulation and extraction. However, the known construction of differing-input obfuscation for machines uses knowledge assumptions which are too strong. So an interesting question is whether we can reduce the round complexity of such ZKAOK without using differing-input obfuscation for machines.

In this paper we show that based on differing-input obfuscation for some circuit samplers and other reasonable assumptions, there exists a 6-round ZKAOK for NP with strict-polynomial-time simulation and extraction. Importantly, the assumption of differing-input obfuscation for circuits does not use any knowledge assumption and thus is mild. Moreover, we note that the auxiliary inputs output by the circuit samplers in our construction are public coins and perfectly-hiding commitments, which is quite natural. So this assumption, in our view, could be considered reasonable.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, China

    Ning Ding

  2. NTT Secure Platform Laboratories, chiyoda-ku, Japan

    Ning Ding

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  1. Ning Ding
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Correspondence to Ning Ding .

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Editors and Affiliations

  1. IBM Research Zurich, Rüschlikon, Switzerland

    Anja Lehmann

  2. Università della Svizzera italiana (USI), Lugano, Switzerland

    Stefan Wolf

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Ding, N. (2015). On Zero-Knowledge with Strict Polynomial-Time Simulation and Extraction from Differing-Input Obfuscation for Circuits. In: Lehmann, A., Wolf, S. (eds) Information Theoretic Security. ICITS 2015. Lecture Notes in Computer Science(), vol 9063. Springer, Cham. https://doi.org/10.1007/978-3-319-17470-9_4

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  • DOI: https://doi.org/10.1007/978-3-319-17470-9_4

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-17469-3

  • Online ISBN: 978-3-319-17470-9

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