TY - GEN

T1 - Fast secure comparison for medium-sized integers and its application in binarized neural networks

AU - Abspoel, Mark

AU - Bouman, Niek J.

AU - Schoenmakers, Berry

AU - de Vreede, Niels

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85062778029&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-12612-4_23

DO - 10.1007/978-3-030-12612-4_23

M3 - Conference contribution

AN - SCOPUS:85062778029

SN - 978-3-030-12611-7

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 453

EP - 472

BT - Topics in Cryptology – CT-RSA 2019 - The Cryptographers’ Track at the RSA Conference 2019, Proceedings

A2 - Matsui, Mitsuru

PB - Springer

CY - Cham

T2 - Cryptographers Track at the RSA Conference 2019, CT-RSA 2019

Y2 - 4 March 2019 through 8 March 2019

ER -