Improving BDD Enumeration for LWE Problem Using GPU

Mohamed S Esseissah,Hatem M Bahig,Ashraf Bhery

doi:10.1109/access.2019.2961091

Mohamed S Esseissah, Hatem M Bahig + Show 1 more

Open Access

https://doi.org/10.1109/access.2019.2961091

Copy DOI

Abstract

In this paper, we present a GPU-based parallel algorithm for the Learning With Errors (LWE) problem using a lattice-based Bounded Distance Decoding (BDD) approach. To the best of our knowledge, this is the first GPU-based implementation for the LWE problem. Compared to the sequential BDD implementation of Lindner-Peikert and pruned-enumeration strategies by Kirshanova [1], our GPU-based implementation is almost faster by a factor 6 and 9 respectively. The used GPU is NVIDIA GeForce GTX 1060 6G. We also provided a parallel implementation using two GPUs. The results showed that our algorithm is scalable and faster than the sequential version (Lindner-Peikert and pruned-enumeration) by a factor of almost 13 and 16 respectively. Moreover, the results showed that our parallel implementation using two GPUs is more efficient than Kirshanova et al.'s parallel implementation using 20 CPU-cores.

Highlights

For the last few decades, the public-key cryptosystems based on the integer factorization problem, the discrete logarithm problem and the elliptic curve problem have been considered among the most secure public key cryptosystems
EXPERIMENTAL RESULTS This section presents the results obtained by using Algorithm 5 for the parallel implementation and Algorithm 2 for the sequential implementation
In Subsection VI-B, we show the execution times of Algorithms 5 on a single GPU and two GPUs as well as the execution time of Algorithm 2 using the sequential implementation provided by Kirshanova et al on a our CPU

Summary

Introduction

For the last few decades, the public-key cryptosystems based on the integer factorization problem, the discrete logarithm problem and the elliptic curve problem have been considered among the most secure public key cryptosystems. The emergence of the quantum computing has posed a major threat to these types of cryptosystems. The wide evolution of the technology increases the feeling that the emerging of the quantum computers is not far off. The most promising cryptosystems are those based on lattice problems such as GGH [2], NTRU [3] and recently LWE-based cryptosystems [4], [5]. The lattice problems are known to be post-quantum problems [6]. There is no quantum algorithm that can solve the lattice problems in polynomial time

Objectives

Results

Conclusion