Cryptology is a pillar of information security in the digital world. Today's digital infrastructure is mostly protected by a form of cryptography based on complexity theoretic hardness assumptions. As a consequence, testing these hardness assumptions is crucial to ensuring the security of the digital world. The main ambition of Algorithmic Cryptology research group is to study and challenge these assumptions by proposing and analysing new and advanced algorithms designed to solve the underlying hard problems as efficiently as currently feasible. In particular, the group has a specific focus on number theoretic algorithms.