### Samenvatting

In 1994, Feige, Kilian, and Naor proposed a simple protocol for secure 3-way comparison of integers a and b from the range [0,Â 2]. Their observation is that for (Formula Presented), the Legendre symbol (Formula Presented) coincides with the sign of x for (Formula Presented), thus reducing secure comparison to secure evaluation of the Legendre symbol. More recently, in 2011, Yu generalized this idea to handle secure comparisons for integers from substantially larger ranges [0,Â d], essentially by searching for primes for which the Legendre symbol coincides with the sign function on (Formula Presented). In this paper, we present new comparison protocols based on the Legendre symbol that additionally employ some form of error correction. We relax the prime search by requiring that the Legendre symbol encodes the sign function in a noisy fashion only. Practically, we use the majority vote over a window of (Formula Presented) adjacent Legendre symbols, for small positive integers k. Our technique significantly increases the comparison range: e.g., for a modulus of 60 bits, d increases by a factor of 2.8 (for (Formula Presented)) and 3.8 (for (Formula Presented)) respectively. We give a practical method to find primes with suitable noisy encodings. We demonstrate the practical relevance of our comparison protocol by applying it in a secure neural network classifier for the MNIST dataset. Concretely, we discuss a secure multiparty computation based on the binarized multi-layer perceptron of Hubara et al., using our comparison for the second and third layers.

Originele taal-2 | Engels |
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Titel | Topics in Cryptology – CT-RSA 2019 - The Cryptographers’ Track at the RSA Conference 2019, Proceedings |

Redacteuren | Mitsuru Matsui |

Plaats van productie | Cham |

Uitgeverij | Springer |

Pagina's | 453-472 |

Aantal pagina's | 20 |

ISBN van elektronische versie | 978-3-030-12612-4 |

ISBN van geprinte versie | 978-3-030-12611-7 |

DOI's | |

Status | Gepubliceerd - 1 jan 2019 |

Evenement | Cryptographers Track at the RSA Conference 2019, CT-RSA 2019 - San Francisco, Verenigde Staten van Amerika Duur: 4 mrt 2019 → 8 mrt 2019 |

### Publicatie series

Naam | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11405 LNCS |

ISSN van geprinte versie | 0302-9743 |

ISSN van elektronische versie | 1611-3349 |

### Congres

Congres | Cryptographers Track at the RSA Conference 2019, CT-RSA 2019 |
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Land | Verenigde Staten van Amerika |

Stad | San Francisco |

Periode | 4/03/19 → 8/03/19 |

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## Citeer dit

*Topics in Cryptology – CT-RSA 2019 - The Cryptographers’ Track at the RSA Conference 2019, Proceedings*(blz. 453-472). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11405 LNCS). Springer. https://doi.org/10.1007/978-3-030-12612-4_23