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Concurrently Non-malleable Black-Box Zero Knowledge in the Bare Public-Key Model

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Computer Science - Theory and Applications (CSR 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5675))

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Abstract

In this paper we study the possibility of reducing the setup assumptions under which concurrent non-malleable zero knowledge protocol can be realized. A natural model choice is the bare public-key (BPK) model of [6], a model with very minimal setup assumptions. Our main contribution is to show in this model the following about constant-round concurrent non-malleable black-box zero-knowledge arguments.

  • They can be constructed from any one-way function for any language in \(\mathcal{NP}\). Here, our construction takes 5 rounds, and we can reduce it to a 4-round (round-optimal) argument under existence of one-way permutations.

  • Under number-theoretic assumptions, they admit a time-efficient instantiation for some specific \(\mathcal{NP}\) languages (e.g., all languages having efficient Σ protocols, for which we can implement our construction using only \(\mathcal{O}(1)\) modular exponentiations).

Compared to the non-black-box construction in a concurrent work of [OPV, ICALP 2008] in this model, our protocol (even the construction from one-way function) is significantly more time- and round-efficient and can be based on more general assumptions.

This work was supported in part by the National Natural Science Foundation of China Under Grant NO.60803128, and the 973 Program of China (2007CB311202), and the National Natural Science Foundation of China Under Grant NO. 60673069.

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Authors and Affiliations

  1. State Key Laboratory of Information Security, Institute of Software, Chinese Academy of sciences, Beijing, 100190, China

    Yi Deng, Dongdai Lin & Dengguo Feng

  2. Telcordia Technologies, Piscataway, NJ, USA

    Giovanni Di Crescenzo

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  1. Yi Deng
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  2. Giovanni Di Crescenzo
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  3. Dongdai Lin
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  4. Dengguo Feng
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Editor information

Editors and Affiliations

  1. Sobolev Institute of Mathematics SB RAS, 4 Koptyug av, 630090, Novosibirsk, Russia

    Anna Frid

  2. Sobolev Institute of Mathematics SB RAS, Koptyug av. 4, 630090, Novosibirsk, Russia

    Andrey Morozov

  3. Max Planck Institute for Software Systems, Campus E1 4, 66123, Saarbrücken, Germany

    Andrey Rybalchenko

  4. Lehrstuhl für Theoretische Informatik, Institut für Informatik, Julius-Maximilians-Universität Würzburg, Am Hubland, 97974, Würzburg, Germany

    Klaus W. Wagner

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Deng, Y., Di Crescenzo, G., Lin, D., Feng, D. (2009). Concurrently Non-malleable Black-Box Zero Knowledge in the Bare Public-Key Model. In: Frid, A., Morozov, A., Rybalchenko, A., Wagner, K.W. (eds) Computer Science - Theory and Applications. CSR 2009. Lecture Notes in Computer Science, vol 5675. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03351-3_10

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  • DOI: https://doi.org/10.1007/978-3-642-03351-3_10

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