Discrete Gaussian is a cornerstone of many lattice-based cryptographic constructions. Aiming at the orthogonal lattice of a vector, we propose a discrete Gaussian rejection sampling algorithm, by modifying the dynamic programming process for subset sum problems. Within O(nq2) time, our algorithm generates a distribution statistically indistinguishable from discrete Gaussian at width s>ω(log n). Moreover, we apply our sampling algorithm to general high-dimensional dense lattices, and orthogonal lattices of matrices $\matA\in\Z_q^{O(1)\times n}$. Compared with previous polynomial-time discrete Gaussian samplers, our algorithm does not rely on the short basis.

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Cryptanalysis of Widely-used Hash Function Standards and Beyond
Cryptology

Xiao, D, Yu, Y, & Bi, J. (2018). A new discrete gaussian sampler over orthogonal lattices. IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences, (11), 1880–1887.