## Abstract

We study the complexity of securely evaluating an arithmetic circuit over a finite field ð�”½ in the setting of secure two-party computation with semi-honest adversaries. In all existing protocols, the number of arithmetic operations per multiplication gate grows either linearly with log |ð�”½| or polylogarithmically with the security parameter. We present the first protocol that only makes a constant (amortized) number of field operations per gate. The protocol uses the underlying field ð�”½ as a black box, and its security is based on arithmetic analogues of well-studied cryptographic assumptions. Our protocol is particularly appealing in the special case of securely evaluating a “vector-OLE” function of the form ax+b, where x ∈ ð�”½ is the input of one party and a, b ∈ ð�”½^{w} are the inputs of the other party. In this case, which is motivated by natural applications, our protocol can achieve an asymptotic rate of 1/3 (i.e., the communication is dominated by sending roughly 3w elements of ð�”½). Our implementation of this protocol suggests that it outperforms competing approaches even for relatively small fields ð�”½ and over fast networks. Our technical approach employs two new ingredients that may be of independent interest. First, we present a general way to combine any linear code that has a fast encoder and a cryptographic (“LPN-style”) pseudorandomness property with another linear code that supports fast encoding and erasure-decoding, obtaining a code that inherits both the pseudorandomness feature of the former code and the efficiency features of the latter code. Second, we employ local arithmetic pseudo-random generators, proposing arithmetic generalizations of boolean candidates that resist all known attacks.

Original language | English |
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Title of host publication | Advances in Cryptology – CRYPTO 2017 - 37th Annual International Cryptology Conference, Proceedings |

Editors | Hovav Shacham, Jonathan Katz |

Publisher | Springer Verlag |

Pages | 223-254 |

Number of pages | 32 |

ISBN (Print) | 9783319636870 |

DOIs | |

State | Published - 2017 |

Event | 37th Annual International Cryptology Conference, CRYPTO 2017 - Santa Barbara, United States Duration: 20 Aug 2017 → 24 Aug 2017 |

### 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 | 10401 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 37th Annual International Cryptology Conference, CRYPTO 2017 |
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Country/Territory | United States |

City | Santa Barbara |

Period | 20/08/17 → 24/08/17 |

### Funding

Funders | Funder number |
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Horizon 2020 Framework Programme | 669255, 639813 |