"Much currently deployed cryptography is designed using more “art'” than “science,” and most of the schemes used in practice lack rigorous justification for their security. While theoretically sound designs do exist, they tend to be quite a bit slower to run and hence are not realistic from a practical point of view. This gap is especially evident in “low-level” cryptographic primitives, which are the building blocks that ultimately process the largest quantities of data.Recent years have witnessed dramatic progress in the understanding of highly-parallelizable (local) cryptography, and in the construction of schemes based on the mathematics of geometric objects called lattices. Besides being based on firm theoretical foundations, these schemes also allow for very efficient implementations, especially on modern microprocessors. Yet despite all this recent progress, there has not yet been a major effort specifically focused on bringing the efficiency of such constructions as close as possible to practicality; this project will do exactly that.The main goal of the Fast and Sound Cryptography project is to develop new tools and techniques that would lead to practical and theoretically sound implementations of cryptographic primitives. We plan to draw ideas from both theory and practice, and expect their combination to generate new questions, conjectures, and insights. A considerable fraction of our efforts will be devoted to demonstrating the efficiency of our constructions. This will be achieved by a concrete setting of parameters, allowing for cryptanalysis and direct performance comparison to popular designs.While our initial focus will be on low-level primitives, we expect our research to also have direct impact on the practical efficiency of higher-level cryptographic tasks. Indeed, many of the recent improvements in the efficiency of lattice-based public-key cryptography can be traced back to research on the efficiency of lattice-based hash functions."