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Paper: Single-to-Multi-Theorem Transformations for Non-Interactive Statistical Zero-Knowledge

Authors:
Marc Fischlin
Felix Rohrbach
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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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BibTeX
@article{pkc-2021-30958,
  title={Single-to-Multi-Theorem Transformations for Non-Interactive Statistical Zero-Knowledge},
  booktitle={Public-Key Cryptography - PKC 2021},
  publisher={Springer},
  author={Marc Fischlin and Felix Rohrbach},
  year=2021
}