Today’s encryption will crumble once a sufficiently powerful quantum computer arrives, and this project aims to build the next generation of cryptographic tools that can resist that attack. The problem is stark: standardisation bodies are finalising basic post-quantum encryption and signatures, but many advanced cryptographic functions already in use—such as credentials that remain secure even if a server is hacked, or privacy-preserving contact tracing—have no efficient post-quantum equivalents. This project tackles that gap by asking three concrete questions: how hard are the underlying lattice problems for a quantum computer; what new mathematical assumptions are needed to match the features of today’s cryptography; and how to safely combine post-quantum schemes with existing ones in hybrid systems. If successful, the research will provide the cryptographic infrastructure for a smooth, secure transition to the post-quantum era. This matters for systems people rarely think about—secure messaging, digital signatures on software updates, encrypted financial transactions, and authentication for critical infrastructure like energy grids and water treatment plants. The work is applied and practical: it aims to produce deployable solutions, not just theoretical insights.
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Standardisation efforts for post-quantum public-key encryption and signatures are close to completion. At the same time the most recent decade has seen the deployment, at scale, of more advanced cryptographic algorithms where no efficient post-quantum candidates exist. These algorithms e.g. permit to give strong guarantees even after some parties were compromised, privacy-preserving contact lookups, credentials and e-cash. This project will tackle the challenge of "lifting" such constructions to the post-quantum era by pursuing three guiding questions: - What is the cost of solving lattice problems with and without hints on a quantum computer? Answers to this question will provide confidence in the entire stack of lattice-based cryptography from "basic" to "advanced". Studying the presence of hints tackles side-channel attacks and advanced constructions. - What are the lattice assumptions that establish feature- and (near) performance-parity with pre-quantum cryptography? Standard lattice assumptions do not seem to establish feature parity with pairing-based or even some Diffie-Hellman-based pre-quantum constructions, how can we achieve efficient and secure advanced practical post-quantum solutions? - How efficient is a careful composition of lattice-base cryptography with other assumptions? If we want to deploy our post-quantum solutions in practice, we will need to design hybrid schemes that are secure if either of their pre- or post-quantum part is secure and to deploy many advanced lattice-based primitives in practice we need to carefully compose them with zero-knowledge proofs to rule out some attacks. Lattice-based cryptography has established itself as a key technology to realise both efficient basic primitives like post-quantum encryption and advanced solutions such as computation with encrypted data and programs. It is thus well positioned to tackle the middle ground of advanced yet practical primitives for phase 2 of the post-quantum transition.
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