Learn about improved discrete Gaussian and subgaussian analysis techniques for lattice-based cryptography in this conference talk presented at PKC 2020. Explore a modular approach to discrete Gaussian analysis, covering lattice background, spherical and non-spherical discrete Gaussian sampling, smoothness properties, and applications to the Learning with Errors (LWE) problem. Gain insights into subgaussian random variables and matrices, addressing previous issues with unknown constants. Discover how these advancements contribute to the development of more efficient and secure lattice-based cryptographic systems.