Polar sampler: A novel Bernoulli sampler using polar codes with application to integer Gaussian sampling

Abstract

Cryptographic constructions based on hard lattice problems have emerged as a front runner for the standardization of post-quantum public-key cryptography. As the standardization process takes place, optimizing specific parts of proposed schemes, e.g., Bernoulli sampling and integer Gaussian sampling, becomes a worthwhile endeavor. In this work, we propose a novel Bernoulli sampler based on polar codes, dubbed “polar sampler”. The polar sampler is information theoretically optimum in the sense that the number of uniformly random bits it consumes approaches the entropy bound asymptotically. It also features quasi-linear complexity and constant-time implementation. An integer Gaussian sampler is developed using multilevel polar samplers. Our algorithm becomes effective when sufficiently many samples are required at each query to the sampler. Security analysis is given based on Kullback–Leibler divergence and Rényi divergence. Experimental and asymptotic comparisons between our integer Gaussian sampler and state-of-the-art samplers verify its efficiency in terms of entropy consumption, running time and memory cost. We envisage that the proposed Bernoulli sampler can find other applications in cryptography in addition to Gaussian sampling.

Hybrid Billiards Archimedes optimization of Multi-kernel polar codesfor 5G communications

“…These positions are influenced by the shot's accuracy. The inaccuracy decreases as the search proceeds in an effort to improve exploitation potential.The new placements of the regular balls are determined by the equations (21,22)…”

“…2023 Wang J et al[21] had proposed the polar sampler is a brand-new Bernoulli sampler that applies polar coding to integer Gaussian sampling. An integer Gaussian sampler was made using multi-level polar samples.…”