Vectorized Discrete Gaussian Sampling with SIMD Support

Abstract

Discrete Gaussian sampling is a fundamental building block of lattice-based cryptography. Sampling from a Gaussian distribution ℤ, , over the integers ℤ is an important sub-problem of discrete Gaussian sampling, where parameter σ > 0 and center c ∈ ℝ. In this paper, we show that two common sampling algorithms for discrete Gaussian distribution over the integers can be implemented more efficiently by using vectorization with SIMD (Single Instruction Multiple Data) support. Specifically, we use the VCL (C++ vector class library) by Agner Fog, which offers optimized vector operations for integers and floating-point numbers with the support of SIMD. The VCL is also a simple tool for constant-time implementations, which helps prevent the information leakage caused by the timing attacks on sampling operations.