Security Analysis of Public Key Encryption via Lattice Reduction Algorithms

Abstract

In this paper, we show how “lattices” have been used in cryptography. In particular, we explain the definition, the notion of the (approximate) shortest vector problem, and lattice reduction algorithms. Then, we recall one of the applications, i.e., lattice-based Coppersmithʼs methods to solve integer/modular equations with applications to RSA cryptanalyses.