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## 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:

- (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;

- (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.

- 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:

- (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;

- (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.

Original language | English |
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Title of host publication | Security and Cryptography for Networks. SCN 2020 |

Editors | Clemente Galdi, Vladimir Kolesnikov |

Publisher | Springer-Verlag |

Pages | 670-690 |

Number of pages | 21 |

ISBN (Electronic) | 978-3-030-57990-6 |

ISBN (Print) | 978-3-030-57989-0 |

DOIs | |

Publication status | Published - 7 Sep 2020 |

Event | 12th Conference on Security and Cryptography for Networks - Virtual Conference Duration: 14 Sep 2020 → 16 Sep 2020 https://scn.unisa.it/ |

### Publication series

Name | Lecture Notes in Computer Science |
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Publisher | Springer |

Volume | 12238 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 12th Conference on Security and Cryptography for Networks |
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Abbreviated title | SCN 2020 |

City | Virtual Conference |

Period | 14/09/20 → 16/09/20 |

Internet address |

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## Projects

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