Efficient Implementations of Sieving and Enumeration Algorithms for Lattice-Based Cryptography

Hami Satılmış,Sedat Akleylek,Cheng-Chi Lee

doi:10.3390/math9141618

Hami Satılmış, Sedat Akleylek + Show 1 more

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https://doi.org/10.3390/math9141618

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Abstract

The security of lattice-based cryptosystems is based on solving hard lattice problems such as the shortest vector problem (SVP) and the closest vector problem (CVP). Various cryptanalysis algorithms such as (Pro)GaussSieve, HashSieve, ENUM, and BKZ have been proposed to solve these hard problems. Several implementations of these algorithms have been developed. On the other hand, the implementations of these algorithms are expected to be efficient in terms of run time and memory space. In this paper, a modular software package/library containing efficient implementations of GaussSieve, ProGaussSieve, HashSieve, and BKZ algorithms is developed. These implementations are considered efficient in terms of run time. While constructing this software library, some modifications to the algorithms are made to increase the performance. Then, the run times of these implementations are compared with the others. According to the experimental results, the proposed GaussSieve, ProGaussSieve, and HashSieve implementations are at least 70%, 75%, and 49% more efficient than previous ones, respectively.

Highlights

Traditional public key cryptosystems such as RSA and (EC)DSA are based on the hardness of the integer factorization and the discrete logarithm problem [1]
The basis of the difficulty of lattice-based cryptography consists of lattice problems such as shortest vector problem (SVP) and closest vector problem (CVP), for which the solution is unknown in polynomialtime, even in the quantum computer era
A modular software infrastructure library was developed to provide an infrastructure for efficient implementations of the sieving, enumeration, and reduction algorithms

Summary

Introduction

Traditional public key cryptosystems such as RSA and (EC)DSA are based on the hardness of the integer factorization and the discrete logarithm problem [1]. Due to the Shor algorithm in [2], they are insecure in the quantum era. For this reason, new cryptosystems are needed to avoid vulnerability in communication networks after the widespread use of quantum computers. The family of lattice-based cryptosystems is one of the candidates in the quantum era due to the efficiency and security reasons [1]. The basis of the difficulty of lattice-based cryptography consists of lattice problems such as SVP and CVP, for which the solution is unknown in polynomialtime, even in the quantum computer era. To solve hard problems such as SVP and CVP, i.e., to break the lattice-based cryptography, many sieving-based and enumeration-based algorithms and their implementations of these algorithms are proposed in [5,6,7,8,9,10]

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