Post-quantum Group-based Cryptography in the AI Era in Europe

Our EMS Tropical Activity Group aims to promote European collaboration in the field of Post-Quantum Group-Based Cryptography. In particular, our team focuses on the mathematical foundations of post-quantum cryptography, aiming to develop cryptographic systems secure against quantum attacks while fostering collaboration between mathematics and cryptography. Since classical schemes based on factoring or discrete logarithms are broken by quantum algorithms such as Shor’s and Grover’s, we aim to explore alternative hardness assumptions grounded in rich algebraic, combinatorial, and geometric structures.

Particular attention is given to the Learning With Errors (LWE) problem and its variants over different algebraic settings, which underpin many modern post-quantum constructions, as well as to group-based cryptography, where security relies on the difficulty of algorithmic problems in non-commutative groups. We also aim to cover advanced cryptographic functionalities, including fully homomorphic and functional encryption, which enable secure computation and fine-grained access control on encrypted data.

A key research direction is the mathematical modelling of quantum adversaries, providing provable post-quantum security guarantees. While we emphasize mathematically inspired frameworks, we will actively connect with other post-quantum paradigms (lattice-based, code-based, and isogeny-based cryptography) to promote integration and comparison of approaches. Through this broad perspective, our goal is to strengthen Europe’s leadership in the theoretical and applied development of secure cryptography for the quantum and AI era.