With the rapid advancements in quantum computing, cryptography faces both a profound disruption and a remarkable opportunity. Quantum algorithms expose the fragility of classical public-key infrastructures, rendering many long-trusted systems insecure. Yet this pivotal moment calls for a return to the mathematical foundations of cryptography, to uncover structures that not only withstand quantum attacks but also give rise to intrinsically quantum protocols harnessing the full capabilities of quantum computation.

This talk explores how fundamental properties of quantum computing can encode deep structures from number theory, leading to new frameworks for quantum cryptography. After a brief overview of her research, she will present recent work on group actions, isogeny graphs, and quantum walks, showing how algebraic constructions connect with quantum computation, yielding novel schemes such as our Quantum Onion Routing.

Dr. Eleni Agathocleous is a Postdoctoral Research Fellow at The Cyprus Institute. She received her PhD in Mathematics (Algebraic and Algorithmic Number Theory) from the University of Maryland, College Park. Her research is interdisciplinary, focusing on the interactions between number theory, cryptography, and quantum computing. Before joining The Cyprus Institute, she held research positions at research institutes in Germany.

She worked on the ALMACRYPT (Algorithmic and Mathematical Cryptology) project at the CISPA Helmholtz Center for Information Security, on cryptography and quantum computing at the Deutsches Elektronen-Synchrotron (DESY), and received a research grant from the Max Planck Institute for Mathematics in Bonn, where she continued her work on the mathematical foundations of isogeny-based cryptography.