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Single-to-Multi-theorem Transformations for Non-interactive Statistical Zero-Knowledge

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Public-Key Cryptography – PKC 2021 (PKC 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12711))

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Abstract

Non-interactive zero-knowledge proofs or arguments allow a prover to show validity of a statement without further interaction. For non-trivial statements such protocols require a setup assumption in form of a common random or reference string (CRS). Generally, the CRS can only be used for one statement (single-theorem zero-knowledge) such that a fresh CRS would need to be generated for each proof. Fortunately, Feige, Lapidot and Shamir (FOCS 1990) presented a transformation for any non-interactive zero-knowledge proof system that allows the CRS to be reused any polynomial number of times (multi-theorem zero-knowledge). This FLS transformation, however, is only known to work for either computational zero-knowledge or requires a structured, non-uniform common reference string.

In this paper we present FLS-like transformations that work for non-interactive statistical zero-knowledge arguments in the common random string model. They allow to go from single-theorem to multi-theorem zero-knowledge and also preserve soundness, for both properties in the adaptive and non-adaptive case. Our first transformation is based on the general assumption that one-way permutations exist, while our second transformation uses lattice-based assumptions. Additionally, we define different possible soundness notions for non-interactive arguments and discuss their relationships.

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Notes

  1. 1.

    We use here the terminology from [4] for the comparable scenario of admissible decryption queries in chosen-ciphertext security.

  2. 2.

    Note that we define one-way permutations as one-way functions that are 1-1 and length-preserving, not as a family of such functions.

  3. 3.

    Strictly speaking, their notion of exclusiveness allows for a negligible error which could be integrated in our notion as well.

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Acknowledgments

We thank the anonymous reviewers for valuable comments. Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – SFB 1119 – 236615297.

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Authors and Affiliations

  1. Cryptoplexity, Technische Universität Darmstadt, Darmstadt, Germany

    Marc Fischlin & Felix Rohrbach

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  1. Marc Fischlin
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Correspondence to Marc Fischlin .

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  1. Texas A&M University, College Station, TX, USA

    Juan A. Garay

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Fischlin, M., Rohrbach, F. (2021). Single-to-Multi-theorem Transformations for Non-interactive Statistical Zero-Knowledge. In: Garay, J.A. (eds) Public-Key Cryptography – PKC 2021. PKC 2021. Lecture Notes in Computer Science(), vol 12711. Springer, Cham. https://doi.org/10.1007/978-3-030-75248-4_8

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  • DOI: https://doi.org/10.1007/978-3-030-75248-4_8

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