Lattice Gaussian Sampling by Markov Chain Monte Carlo: Bounded Distance Decoding and Trapdoor Sampling

Zheng Wang; Cong Ling

Paper 2019/660 Original: eprint.iacr.org/2019/660 ↗

Lattice Gaussian Sampling by Markov Chain Monte Carlo: Bounded Distance Decoding and Trapdoor Sampling

Zheng Wang

Cong Ling

Abstract

Sampling from the lattice Gaussian distribution plays an important role in various research fields. In this paper, the Markov chain Monte Carlo (MCMC)-based sampling technique is advanced in several fronts. Firstly, the spectral gap for the independent Metropolis-Hastings-Klein (MHK) algorithm is derived, which is then extended to Peikert's algorithm and rejection sampling; we show that independent MHK exhibits faster convergence. Then, the performance of bounded distance decoding using MCMC is analyzed, revealing a flexible trade-off between the decoding radius and complexity. MCMC is further applied to trapdoor sampling, again offering a trade-off between security and complexity. Finally, the independent multiple-try Metropolis-Klein (MTMK) algorithm is proposed to enhance the convergence rate. The proposed algorithms allow parallel implementation, which is beneficial for practical applications.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
History: 2019-06-05: last updated; 2019-06-04: published
Short URL: https://ia.cr/2019/660
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2019/660,
      author = {Zheng Wang and Cong Ling},
      title = {Lattice Gaussian Sampling by Markov Chain Monte Carlo: Bounded Distance Decoding and Trapdoor Sampling},
      howpublished = {Cryptology {ePrint} Archive, Paper 2019/660},
      year = {2019},
      url = {https://eprint.iacr.org/2019/660}
}