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On Adaptive Security of Delayed-Input Sigma Protocols and Fiat-Shamir NIZKs

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12238)

Abstract

We study adaptive security of delayed-input Sigma protocols and non-interactive zero-knowledge (NIZK) proof systems in the common reference string (CRS) model. Our contributions are threefold:
  • We exhibit a generic compiler taking any delayed-input Sigma protocol and returning a delayed-input Sigma protocol satisfying adaptive-input special honest-verifier zero knowledge (SHVZK). In case the initial Sigma protocol also satisfies adaptive-input special soundness, our compiler preserves this property.

  • We revisit the recent paradigm by Canetti et al. (STOC 2019) for obtaining NIZK proof systems in the CRS model via the Fiat-Shamir transform applied to so-called trapdoor Sigma protocols, in the context of adaptive security. In particular, assuming correlation-intractable hash functions for all sparse relations, we prove that Fiat-Shamir NIZKs satisfy either:
    1. (i)

      Adaptive soundness (and non-adaptive zero knowledge), so long as the challenge is obtained by hashing both the prover’s first round and the instance being proven;

       
    2. (ii)

      Adaptive zero knowledge (and non-adaptive soundness), so long as the challenge is obtained by hashing only the prover’s first round, and further assuming that the initial trapdoor Sigma protocol satisfies adaptive-input SHVZK.

       
  • We exhibit a generic compiler taking any Sigma protocol and returning a trapdoor Sigma protocol. Unfortunately, this transform does not preserve the delayed-input property of the initial Sigma protocol (if any). To complement this result, we also give yet another compiler taking any delayed-input trapdoor Sigma protocol and returning a delayed-input trapdoor Sigma protocol with adaptive-input SHVZK.

An attractive feature of our first two compilers is that they allow obtaining efficient delayed-input Sigma protocols with adaptive security, and efficient Fiat-Shamir NIZKs with adaptive soundness (and non-adaptive zero knowledge) in the CRS model. Prior to our work, the latter was only possible using generic NP reductions.

Keywords

Sigma protocols Non-interactive zero knowledge Adaptive security 

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.The University of EdinburghEdinburghUK
  2. 2.Simula UiBBergenNorway
  3. 3.Sapienza University of RomeRomeItaly

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