Practical post-quantum lattice-based non-interactive key exchange

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The Diffe-Hellman non-interactive key exchange is critical to many protocols and applications, such as the Signal protocol and Noise protocol framework. The non-interactive property importantly allows asynchronous communication, valuable privacy properties and other practical benefits such as energy savings in wireless and sensor networks.The emergence of quantum computers threatens the security of modern cryptosystems (including those utilising Diffe-Hellman) through their ability to solve the underlying hard problems. The need for quantum-resistant alternatives is therefore paramount. This project will be primarily building on the work of SWOOSH - a proposed post-quantum lattice-based non-interactive key exchange, with a focus on practicality, security and privacy preserving properties. I will be addressing several open problems in SWOOSH. For example, investigating attacks on the construction, the non-interactive zero knowledge proof required for active security, resulting complete instantiations, estimating the hardness of the inhomogeneous 1-dimensional short integer solution problem, theoretical results on SWOOSH's feasibility, and analysis of its privacy properties.