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Improving of Non-Interactive Zero-Knowledge Arguments Using Oblivious Transfer

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New Results in Dependability and Computer Systems

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 224))

Abstract

We study non-interactive zero-knowledge (NIZK) arguments using oblivious transfer (OT) that correspond to interactive proof protocols but assuming that the prover is computationally bounded. As opposed to the single theorem NIZK proof protocols using common random string, NIZK argument protocols using OT are «multilingual» that is language L or the one-way function can be chosen and declared by prover in non-interactive mode. These protocols use m-out-of-n OT with public keys given by verifier to prover in the initialization phase and common element with unknown to prover and verifier pre-image. It is shown that due to usage of different verifier’s secret encryption keys the implementation of NIZK argument protocols can be simplified using a single randomizer for p successive elementary transactions. For systems using 1-out-of-2 OT, proposal allows increase the information rate approximately to 5p/(3p+1) times or reduce the soundness probability of NIZK arguments to the same degree. The above factor for single use NIZK is about two that corresponds to almost quadratic decreasing of soundness probability. For NIZK argument using t+1-out-of-2t OT (t>1), it is shown that its soundness probability for small t is essentially lower in comparison with soundness probability of NIZK arguments using 1-out-of-2 OT.

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Authors and Affiliations

  1. National Research University Moscow Power Engineering Institute, 111250, Moscow, Krasnokazarmennaya, Russian Federation

    Alexander Frolov

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  1. Alexander Frolov
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Correspondence to Alexander Frolov .

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Editors and Affiliations

  1. , Institute of Computer Engineering, Wrocław University of Technology, ul. Janiszewskiego 11/17, Wrocław, 50-372, Poland

    Wojciech Zamojski

  2. , Institute of Computer Engineering, Wrocław University of Technology, ul. Janiszewskiego 11/17, Wrocław, 50-372, Poland

    Jacek Mazurkiewicz

  3. , Institute of Computer Engineering, Wrocław University of Technology, ul. Janiszewskiego 11/17, Wrocław, 50-372, Poland

    Jarosław Sugier

  4. , Institute of Computer Engineering, Wrocław University of Technology, ul. Janiszewskiego 11/17, Wrocław, 50-372, Poland

    Tomasz Walkowiak

  5. , Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, Warszawa, 01-447, Poland

    Janusz Kacprzyk

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Frolov, A. (2013). Improving of Non-Interactive Zero-Knowledge Arguments Using Oblivious Transfer. In: Zamojski, W., Mazurkiewicz, J., Sugier, J., Walkowiak, T., Kacprzyk, J. (eds) New Results in Dependability and Computer Systems. Advances in Intelligent Systems and Computing, vol 224. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00945-2_14

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