## Abstract

We initiate a study of garbled circuits that contain both Boolean and arithmetic gates in secure multiparty computation. In particular, we incorporate the garbling gadgets for arithmetic circuits recently presented by Ball, Malkin, and Rosulek (ACM CCS 2016) into the multiparty garbling paradigm initially introduced by Beaver, Micali, and Rogaway (STOC ’90). This is the first work that studies arithmetic garbled circuits in the multiparty setting. Using mixed Boolean-arithmetic circuits allows more efficient secure computation of functions that naturally combine Boolean and arithmetic computations. Our garbled circuits are secure in the semi-honest model, under the same hardness assumptions as Ball et al., and can be efficiently and securely computed in constant rounds assuming an honest majority. We first extend free addition and multiplication by a constant to the multiparty setting. We then extend to the multiparty setting efficient garbled multiplication gates. The garbled multiplication gate construction we show was previously achieved only in the two-party setting and assuming a random oracle. We further present a new garbling technique, and show how this technique can improve efficiency in garbling selector gates. Selector gates compute a simple “if statement” in the arithmetic setting: the gate selects the output value from two input integer values, according to a Boolean selector bit; if the bit is 0 the output equals the first value, and if the bit is 1 the output equals the second value. Using our new technique, we show a new and designated garbled selector gate that reduces by approximately 33% the evaluation time, for any number of parties, from the best previously known constructions that use existing techniques and are secure based on the same hardness assumptions. On the downside, we find that testing equality and computing exponentiation by a constant are significantly more complex to garble in the multiparty setting than in the two-party setting.

Original language | English |
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Title of host publication | Advances in Cryptology – ASIACRYPT 2018 - 24th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings |

Editors | Thomas Peyrin, Steven Galbraith |

Publisher | Springer Verlag |

Pages | 3-33 |

Number of pages | 31 |

ISBN (Print) | 9783030033316 |

DOIs | |

State | Published - 1 Jan 2018 |

Event | 24th Annual International Conference on Theory and Application of Cryptology and Information Security, ASIACRYPT 2018 - Brisbane, Australia Duration: 2 Dec 2018 → 6 Dec 2018 |

### 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 | 11274 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 24th Annual International Conference on Theory and Application of Cryptology and Information Security, ASIACRYPT 2018 |
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Country/Territory | Australia |

City | Brisbane |

Period | 2/12/18 → 6/12/18 |

## Keywords

- Arithmetic garbled circuits
- Constant round MPC
- Multiparty garbling

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science