An Efficient and Parallel Gaussian Sampler for Lattices

At the heart of many recent lattice-based cryptographic schemes is a polynomial-time algorithm that, given a ‘high-quality’ basis, generates a lattice point according to a Gaussian-like distribution. Unlike most other operations in lattice-based cryptography, however, the known algorithm for this task (due to Gentry, Peikert, and Vaikuntanathan; STOC 2008) is rather inefficient, and is inherently sequential. We present a new Gaussian sampling algorithm for lattices that is efficient and highly parallelizable. We also show that in most cryptographic applications, the algorithm’s efficiency comes at almost no cost in asymptotic security. At a high level, our algorithm resembles the “perturbation” heuristic proposed as part of NTRUSign (Hoffstein et al., CT-RSA 2003), though the details are quite different. To our knowledge, this is the first algorithm and rigorous analysis demonstrating the security of a perturbation-like technique.