Gaussian Sampling Precision and Information Leakage in Lattice Cryptography

Security parameters and attack countermeasures for Lattice-based cryptosystems have not yet matured to the level that we now expect from RSA and Elliptic Curve implementations. Many modern Ring-LWE and other lattice-based public key algorithms require high precision random sampling from the Discrete Gaussian distribution. The sampling procedure often represents the biggest implementation bottleneck due to its memory and computational requirements. We examine the stated requirements of precision for Gaussian samplers, where statistical distance to the theoretical distribution is typically expected to be below 2−90 or 2−128 for 90 or 128 “bit” security level. We argue that such precision is excessive and give precise theoretical arguments why half of the precision of the security parameter is almost always sufficient. This leads to faster and more compact implementations; almost halving implementation size in both hardware and software. We observe that many of the proposed algorithms for discrete Gaussian sampling may leak significant amounts of secret information in easily mounted timing attacks. We further offer new recommendations for practical samplers.