Post-quantum cryptography

Public-key cryptosystems, including the well-known RSA, are ubiquitous. The security of most of our day-to-day communications is ensured by those cryptosystems, and indeed RSA is robust against attacks from classical computing. However, quantum computing can in theory factor integers in polynomial time, as such it could break RSA.
Quantum computing has been but a promise for a long time, but has recently known significant progress. Therefore, there is a need for post-quantum cryptosystems (PQCs), i.e. cryptosystems that are robust against quantum attacks and efficient in practice. The two major kinds of PQCs are lattice-based cryptosystems and code-based cryptosystems.
This project uses algebraic techniques from ring theory, group theory, and algebraic geometry, in order to obtain theoretical properties of PQCs. These results can then be translated into security metrics and performance criteria, and based on those, we will be able to: provide guidelines on how to use existing cryptosystems; adapt, modify, or fine-tune those cryptosystems; or even design new alternatives.