Description of the thesis topic

A common method for online scams is to create convincing replicas of, for example, online banking websites and to convince users of entering their data there. If it was possible to securely verify that the website's server is in the guarded server room of the bank, however, it would foil the scammers' scheme. This example illustrates the idea underlying position-based cryptography (PBC). Instead of using a secret key, the position of a party is used as credential. Secure position verification is therefore an important primitive for PBC. The setup for secure position verification is that a group of verifiers send questions to a prover which has to answer correctly. Since signals cannot travel faster than light, the response time of the prover allows the verifiers to bound their distance to the prover. Unfortunately, with classical computing alone, secure position verification is impossible. The reason is that classical information can be perfectly copied. Hence, a group of colluding attackers can copy the verifiers' questions and impersonate the honest prover.

Quantum information, however, cannot be copied perfectly due to the no-cloning theorem. Therefore, different protocols for quantum position verification (QPV) were developed. In these QPV protocols, the verifiers do not only send classical questions, but also quantum states to the prover. However, quantum attackers are also more powerful than classical attackers. It was shown that there exist attacks based on quantum teleportation which allow to break any QPV protocol, provided sufficiently many entangled pairs are available. While unconditional security is impossible, work has focused on proving security against bounded attackers and QPV has recently become a very active field. A team including one of the supervisors for this PhD project has proven that there are very simple QPV protocols involving only a single qubit and 2n classical bits for the honest parties which can only be attacked if the attackers have Ω(n) qubits at their disposal. The verifiers in these protocols can thus spend classical resources to increase the quantum resources the attackers need to break the protocol, which makes it practically secure if the number n of classical bits is chosen large enough since quantum resources are harder to manipulate. The measuring protocol is thus a good candidate for experimental implementation. It is inspired by the BB84 protocol for quantum key distribution (QKD) and another QPV protocol. While it is not secure against arbitrary amounts of photon loss which is needed for an implementation with fiber optics, one of the supervisors for this PhD project and coauthors have recently shown that adding a commitment step to the measuring protocol makes it secure against arbitrary photon loss while retaining all other desirable properties. The PhD projects will contribute to making secure quantum positionverification a reality. This project will be financed by the ANR JCJC project PraQPV (project number ANR-24-CE47-3023).

Work Context

The work will be carried out in the CAPP team at LIG.

The position is located in a sector under the protection of scientific and technical potential (PPST), and therefore requires, in accordance with the regulations, that your arrival is authorized by the competent authority of the MESR.

Constraints and risks

We are looking for a PhD candidate who is highly motivated to work on problems at
the intersection of mathematics, physics, and computer science. The candidate must have a master degree in either mathematics, physics, or computer science. They should be familiar with the mathematical formalism of quantum mechanics. Some familiarity with quantum information theory would be highly welcome. Moreover, the candidate should have a good working knowledge of linear algebra, be able to write rigorous mathematical proofs, and be motivated to acquire any mathematical skills they might need during the course of the project.