On the Properties of Reduced Basis Related to Lattice-Reduced Algorithm

Abstract

The concept of the Shortest Vector Problem (SVP) has surprisingly been used widely in many applications of lattice-based cryptography, notably in public-key cryptanalysis. One of the applications is to develop a well-known algorithm of lattice reduction, namely the LLL (Lenstra-Lenstra-Lovasz) algorithm. The LLL algorithm is known to be able to reduce the basis of a lattice to a minimum set of vectors, which is called the LLL-reduced basis. In this paper, we investigate the properties of the LLL-reduced basis for some different factor δ values. By changing and adjusting the value of factor δ, the proposed value of factor δ in the LLL-reduced basis produces some interesting properties. We also looked into the relationship between the initial vector and the factor δ in the LLL-reduced basis and developed some related properties.