Binary Discrete Gaussian Samplers based on Boolean Vector Operations

Tsun-ming Chan

doi:10.1109/tc.2026.3741374

Binary Discrete Gaussian Samplers based on Boolean Vector Operations

2026-10-08

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DOI：10.1109/tc.2026.3741374

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Discrete Gaussian sampling over the integers is one of the fundamental building blocks in lattice-based cryptography. The binary discrete Gaussian distribution is a special discrete Gaussian distribution over the set of non-negative integers. It can be used as the base sampler distribution in a generic Gaussian sampling algorithm based on rejection sampling. In this article, we propose a constant-time sampling algorithm based on Boolean vector operations for the binary Gaussian distribution. It is more efficient than the algorithm based on a full-table access CDT, and is friendly for FPGA hardware implementation. We also present a Bernoulli sampling algorithm based on Boolean vector operations, which helps us to sample efficiently from discrete Gaussian distributions of larger parameters based on the binary Gaussian sampling. The experimental results from both software and FPGA hardware implementations validate the effectiveness of our proposed sampling algorithms.

Keywords:

lattice-based cryptography

discrete Gaussian sampling

Bernoulli distribution

timing attack

Boolean vector

Binary Discrete Gaussian Samplers based on Boolean Vector Operations

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