### Abstract

We consider the problem of Non-Interactive Two-Party Secure Computation (NISC), where Rachel wishes to publish an encryption of her input x, in such a way that any other party, who holds an input y, can send her a single message which conveys to her the value f(x, y), and nothing more. We demand security against malicious parties. While such protocols are easy to construct using garbled circuits and general non-interactive zero-knowledge proofs, this approach inherently makes a non-black-box use of the underlying cryptographic primitives and is infeasible in practice. Ishai et al. (Eurocrypt 2011) showed how to construct NISC protocols that only use parallel calls to an ideal oblivious transfer (OT) oracle, and additionally make only a black-box use of any pseudorandom generator. Combined with the efficient 2-message OT protocol of Peikert et al. (Crypto 2008), this leads to a practical approach to NISC that has been implemented in subsequent works. However, a major limitation of all known OT-based NISC protocols is that they are subject to selective failure attacks that allows a malicious sender to entirely compromise the security of the protocol when the receiver’s first message is reused. Motivated by the failure of the OT-based approach, we consider the problem of basing reusable NISC on parallel invocations of a standard arithmetic generalization of OT known as oblivious linear-function evaluation (OLE). We obtain the following results: We construct an information-theoretically secure reusable NISC protocol for arithmetic branching programs and general zero-knowledge functionalities in the OLE-hybrid model. Our zero-knowledge protocol only makes an absolute constant number of OLE calls per gate in an arithmetic circuit whose satisfiability is being proved. We also get reusable NISC in the OLE-hybrid model for general Boolean circuits using any one-way function.We complement this by a negative result, showing that reusable NISC is impossible to achieve in the OT-hybrid model. This provides a formal justification for the need to replace OT by OLE.We build a universally composable 2-message reusable OLE protocol in the CRS model that can be based on the security of Paillier encryption and requires only a constant number of modular exponentiations. This provides the first arithmetic analogue of the 2-message OT protocols of Peikert et al. (Crypto 2008).By combining our NISC protocol in the OLE-hybrid model and the 2-message OLE protocol, we get protocols with new attractive asymptotic and concrete efficiency features. In particular, we get the first (designated-verifier) NIZK protocols for NP where following a statement-independent preprocessing, both proving and verifying are entirely “non-cryptographic” and involve only a constant computational overhead. Furthermore, we get the first statistical designated-verifier NIZK argument for NP under an assumption related to factoring.

Original language | English (US) |
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Title of host publication | Advances in Cryptology – CRYPTO 2019 - 39th Annual International Cryptology Conference, Proceedings |

Editors | Daniele Micciancio, Alexandra Boldyreva |

Publisher | Springer Verlag |

Pages | 462-488 |

Number of pages | 27 |

ISBN (Print) | 9783030269531 |

DOIs | |

State | Published - Jan 1 2019 |

Event | 39th Annual International Cryptology Conference, CRYPTO 2019 - Santa Barbara, United States Duration: Aug 18 2019 → Aug 22 2019 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11694 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 39th Annual International Cryptology Conference, CRYPTO 2019 |
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Country | United States |

City | Santa Barbara |

Period | 8/18/19 → 8/22/19 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Advances in Cryptology – CRYPTO 2019 - 39th Annual International Cryptology Conference, Proceedings*(pp. 462-488). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11694 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-26954-8_15