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A New Approach to Efficient Non-Malleable Zero-Knowledge

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Book cover Advances in Cryptology – CRYPTO 2022 (CRYPTO 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13510))

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Abstract

Non-malleable zero-knowledge, originally introduced in the context of man-in-the-middle attacks, serves as an important building block to protect against concurrent attacks where different protocols may coexist and interleave. While this primitive admits almost optimal constructions in the plain model, they are several orders of magnitude slower in practice than standalone zero-knowledge. This is in sharp contrast to non-malleable commitments where practical constructions (under the DDH assumption) have been known for a while.

We present a new approach for constructing efficient non-malleable zero-knowledge for all languages in \(\mathcal{N}\mathcal{P}\), based on a new primitive called instance-based non-malleable commitment (\(\textsf{IB}\text {-}\textsf{NMC}\)). We show how to construct practical \(\textsf{IB}\text {-}\textsf{NMC}\) by leveraging the fact that simulators of sub-linear zero-knowledge protocols can be much faster than the honest prover algorithm. With an efficient implementation of \(\textsf{IB}\text {-}\textsf{NMC}\), our approach yields the first general-purpose non-malleable zero-knowledge protocol that achieves practical efficiency in the plain model.

All of our protocols can be instantiated from symmetric primitives such as block-ciphers and collision-resistant hash functions, have reasonable efficiency in practice, and are general-purpose. Our techniques also yield the first efficient non-malleable commitment scheme without public-key assumptions.

This material is based upon work supported in part by DARPA SIEVE Award HR00112020026, NSF CAREER Award 2144303, NSF grants 1907908, 2028920, 2106263, and 2128187. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the United States Government, DARPA, or NSF.

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Notes

  1. 1.

    Although details may vary, known protocols in this paradigm generally require some form of non-algebraic consistency proof over a non-malleable commitment supporting large identities and message spaces.

  2. 2.

    We remark that for non-malleable commitments based on non-malleable codes such as [43], it is hard to estimate the overall complexity; the asymptotic analysis of underlying codes such as [1] has astronomically large constants, making them unsuitable in practice.

  3. 3.

    The analysis in [68] does not separate identity lengths from security levels; it further provides only asymptotic analysis which hides multiplicative constants and does not specify the exact negligible and super-logarithmic functions. This makes it difficult to assess the security level supported by their protocol. If the analysis is performed to support \(\lambda \)-bit security and k-bit identities, the overhead is at least \(20k\lambda \log \lambda \) group exponentiations.

  4. 4.

    We remark that statement \(\widetilde{x}\) may be chosen either adaptively depending on the left execution, or statically by announcing it before the left execution begins.

  5. 5.

    We remark that [2] also presented another approach—applying Fiat-Shamir transformation to their ZKIPCP will give a (fully) ZK protocol directly; moreover, the resulting protocol will be non-interactive. But this approach is irrelevant in the current paper as we are interested in constructions in the plain model (without random oracles).

  6. 6.

    Recall that the language \(L^\rho _{\textsf{consis}}\) is defined toward the end of \(\mathrm {\Pi } ^\textsf{Mini}_\textsc {bgrrv} \) (Protocol 1).

  7. 7.

    Note that \((h_1, b_1, \widetilde{b}_1)\) and \((h_2, b_2, \widetilde{b}_2)\) will be known to V when the protocol reaches the final \(\textsf{sWIAoK}\) stage.

  8. 8.

    We warn that this version cannot be used in our \(\textsf{NMZK}\) protocol yet. See Sect. 5.4.

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Authors and Affiliations

  1. Stony Brook University, Stony Brook, USA

    Allen Kim, Xiao Liang & Omkant Pandey

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  1. Allen Kim
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  2. Xiao Liang
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  3. Omkant Pandey
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Correspondence to Xiao Liang .

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  1. New York University, New York, NY, USA

    Yevgeniy Dodis

  2. University of Florida, Gainesville, FL, USA

    Thomas Shrimpton

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© 2022 International Association for Cryptologic Research

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Kim, A., Liang, X., Pandey, O. (2022). A New Approach to Efficient Non-Malleable Zero-Knowledge. In: Dodis, Y., Shrimpton, T. (eds) Advances in Cryptology – CRYPTO 2022. CRYPTO 2022. Lecture Notes in Computer Science, vol 13510. Springer, Cham. https://doi.org/10.1007/978-3-031-15985-5_14

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  • DOI: https://doi.org/10.1007/978-3-031-15985-5_14

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  • Print ISBN: 978-3-031-15984-8

  • Online ISBN: 978-3-031-15985-5

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