Lattice-based cryptanalysis — How to estimate the security parameter of lattice-based cryptosystem

The usual cryptosystem behind debit card is RSA cryptosystem, which would be broken immediately by quantum computer. Thus, post-quantum cryptography rises and aims to develop cryptosystems which resist the quantum attack. Lattice-based cryptography is one on post-quantum cryptography, and is used to construct various cryptosystems. The central problem behind the lattice-based cryptosystem is Shortest Vector Problem (SVP), finding the shortest vector in the given lattice. Based on the previous results, we re-design the implementation method to improve the performance on GPU. Moreover, we implement and compare the enumeration and sieve algorithm to solve SVP on GPU. Thus, we can estimate the security parameter of lattice-based cryptosystem in reasonable way.