Paper 2019/1011
Compact and Scalable Arbitrary-centered Discrete Gaussian Sampling over Integers
Raymond K. Zhao and Ron Steinfeld and Amin Sakzad
Abstract
The arbitrary-centered discrete Gaussian sampler is a fundamental subroutine in implementing lattice trapdoor sampling algorithms. However, existing approaches typically rely on either a fast implementation of another discrete Gaussian sampler or pre-computations with regards to some specific discrete Gaussian distributions with fixed centers and standard deviations. These approaches may only support sampling from standard deviations within a limited range, or cannot efficiently sample from arbitrary standard deviations determined on-the-fly at run-time. In this paper, we propose a compact and scalable rejection sampling algorithm by sampling from a continuous normal distribution and performing rejection sampling on rounded samples. Our scheme does not require pre-computations related to any specific discrete Gaussian distributions. Our scheme can sample from both arbitrary centers and arbitrary standard deviations determined on-the-fly at run-time. In addition, we show that our scheme only requires a low number of trials close to 2 per sample on average, and our scheme maintains good performance when scaling up the standard deviation. We also provide a concrete error analysis of our scheme based on the Renyi divergence.
Metadata
- Available format(s)
- Category
- Implementation
- Publication info
- Preprint. MINOR revision.
- Keywords
- Lattice-based cryptodiscrete Gaussian samplingimplementationefficiency
- Contact author(s)
- raymond zhao @ monash edu
- History
- 2020-09-25: last of 4 revisions
- 2019-09-09: received
- See all versions
- Short URL
- https://ia.cr/2019/1011
- License
-
CC BY