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Four-Round Black-Box Non-malleable Schemes from One-Way Permutations

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Theory of Cryptography (TCC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13748))

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Abstract

We construct the first four-round non-malleable commitment scheme based solely on the black-box use of one-to-one one-way functions. Prior to our work, all non-malleable commitment schemes based on black-box use of polynomial-time cryptographic primitives require more than 16 rounds of interaction.

A key tool for our construction is a proof system that satisfies a new definition of security that we call non-malleable zero-knowledge with respect to commitments. In a nutshell, such a proof system can be safely run in parallel with any (potentially interactive) commitment scheme. We provide an instantiation of this tool using the MPC-in-the-Head approach in combination with BMR.

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Notes

  1. 1.

    In this paper we will consider only NM commitments w.r.t. commitments. For the case of NM w.r.t. decommitments see [4, 14, 21, 35, 39, 41].

  2. 2.

    Our BB 4-round non-malleable commitment scheme satisfies the notion of standalone (or one-one) non-malleability. Obtaining a concurrent (or many-many) BB non-malleable commitment scheme in just 4 rounds, or less, still remains an open question.

  3. 3.

    In Sect. 8 we propose a comparison between the approach based on rewind-secure primitives of [24] and the one we propose in this work. In particular, we explain why and how we can rely on a simpler underlying weak-non-malleable commitment scheme compared to the one used in [24].

  4. 4.

    This sketch protocol gives a noticeable probability of cheating to the prover, typically the soundness of the protocol can be easily amplified via parallel repetition.

  5. 5.

    Such commitments are sometimes called equivocal or trapdoor commitments.

  6. 6.

    \(\varPi _\textsf{AI}\) works for any type of secret sharing scheme, and in our case \(\varPi _\textsf{AI}\) is parametrized by the reconstruction algorithm of the verifiable secret sharing \(\varPi ^\textsf{vss}\) (i.e., the prover of \(\varPi _\textsf{AI}\) expects to receive n views generated using the sharing algorithm of \(\varPi ^\textsf{vss}\)). We note that given that \(\varPi ^\textsf{vss}\) is information-theoretic, then \(\varPi _\textsf{AI}\) still makes black-box use of the underlying cryptographic primitives.

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Acknowledgements

We thank Carmit Hazay and Muthuramakrishnan Venkitasubramaniam for insightful discussions on the MPC-in-the-head approach. Emmanuela Orsini was supported by the Defense Advanced Research Projects Agency (DARPA) under contract No. HR001120C0085, and by CyberSecurity Research Flanders with reference number VR20192203. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the DARPA, the US Government or Cyber Security Research Flanders. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright annotation therein.

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Authors and Affiliations

  1. The University of Edinburgh, Edinburgh, UK

    Michele Ciampi

  2. imec-COSIC, KU Leuven, Leuven, Belgium

    Emmanuela Orsini

  3. Department Computer Science, Aarhus University, Aarhus, Denmark

    Luisa Siniscalchi

  4. Concordium Blockchain Research Center, Aarhus, Denmark

    Luisa Siniscalchi

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  1. Michele Ciampi
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Correspondence to Michele Ciampi .

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Editors and Affiliations

  1. Ruhr University Bochum, Bochum, Germany

    Eike Kiltz

  2. Massachusetts Institute of Technology, Cambridge, MA, USA

    Vinod Vaikuntanathan

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Ciampi, M., Orsini, E., Siniscalchi, L. (2022). Four-Round Black-Box Non-malleable Schemes from One-Way Permutations. In: Kiltz, E., Vaikuntanathan, V. (eds) Theory of Cryptography. TCC 2022. Lecture Notes in Computer Science, vol 13748. Springer, Cham. https://doi.org/10.1007/978-3-031-22365-5_11

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