Fast secure comparison for medium-sized integers and its application in binarized neural networks

Mark Abspoel, Niek J. Bouman, Berry Schoenmakers, Niels de Vreede

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

4 Citations (Scopus)


In 1994, Feige, Kilian, and Naor proposed a simple protocol for secure 3-way comparison of integers a and b from the range [0, 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, 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.

Original languageEnglish
Title of host publicationTopics in Cryptology – CT-RSA 2019 - The Cryptographers’ Track at the RSA Conference 2019, Proceedings
EditorsMitsuru Matsui
Place of PublicationCham
Number of pages20
ISBN (Electronic)978-3-030-12612-4
ISBN (Print)978-3-030-12611-7
Publication statusPublished - 1 Jan 2019
EventCryptographers Track at the RSA Conference 2019, CT-RSA 2019 - San Francisco, United States
Duration: 4 Mar 20198 Mar 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11405 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


ConferenceCryptographers Track at the RSA Conference 2019, CT-RSA 2019
Country/TerritoryUnited States
CitySan Francisco


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