Comparison of the quality of sampling algorithms from discrete normal distribution on NTRU lattices

Abstract

Post-quantum cryptography is a field of research that studies cryptographic transformations protected against attacks using quantum computers. For many years, lattice-based cryptography has become one of the most promising solutions to protect against the threat of quantum computing. An important feature of the post-quantum period in cryptography is the significant uncertainty about the source data for cryptanalysis and countermeasures in the capabilities of quantum computers, their mathematical support and software, as well as the application of quantum cryptanalysis to existing cryptocurrencies and cryptoprotocol. The main methods are mathematical methods of electronic signature, which have undergone significant analysis and justification in the process of extensive research by cryptologists and mathematicians at the highest level. The security of signature schemes depends strongly on the standard deviation of the discrete Gaussian distribution, which has a sampling algorithm. In this paper, the most common variants of sampling algorithms were considered and analyzed, because the quality of all algorithms depends significantly on the structure of the lattice for which sampling takes place. A comparison of the quality of lattice sampling algorithms is highlighted. In particular, the paper considers Klein's algorithms (its modification is the Thomas Prest and Dukas algorithm), Peikert's algorithm and the floating-point sampling algorithm. Klein's sampling algorithm, in particular its modification, namely, the Dukas-Prest algorithm, gives the smallest vectors. Theoretically, it is much better than Klein's algorithm on NTRU lattices, but it requires the use of floating-point arithmetic, which complicates greatly the analysis of its security and tocreation of software or hardware implementation.