Cryptography is a core building block of our secure internet infrastructure and enables performing data analysis in a privacy-friendly way. One such method is fully homormorphic encryption (FHE) which allows to perform arbitrary computation on encrypted data without the evaluator learning any information about the data. Essentially all FHE schemes are currently built over lattices, a mathematical structure over which noisy linear equations are hard to solve. Lattices enable further advanced applications of cryptography and, importantly, are also amongst the winners in a recent competition for post-quantum secure cryptography, organized by the National Institute of Standards and Technology (NIST). This project explores the power and limitations of lattice-based cryptography in light of a recent trend of hardness assumptions which have more hints and structure than random noisy linear equations and which led to more advanced applications.

2024

2026