Special session paper: efficient arithmetic for lattice-based cryptography

Lattice-based cryptography is a promising family of post quantum algorithms. Contrary to other approaches, lattice-based primitives are extremely versatile and allow the realisation of several essential cryptographic primitives, such as encryption and digital signatures. In addition, they enable more sophisicated schemes to be constructed, such as Identity-based and Attribute-based Encryption, and even Fully Homomorphic Encryption. However, lattice-based cryptography requires novel implementations of several computationally intensive building blocks, for example discrete sampling (often from a Gaussian distribution) and Number Theoretic Transforms. This paper reviews the state-of-the-art in efficient designs for these core components in hardware and software.