PhD thesis - Advanced Post-Quantum Signatures F/M

about the role

Your role is to carry out a thesis work on the design of advanced post-quantum signatures.

Context.

Authentication in the digital world relies on electronic signatures that has proved both efficient and secure but that are often criticized for their lack of privacy. Indeed, a signature often leaks unnecessary information and enables to trace its owner.

This led to the introduction of advanced signatures, addressing these privacy concerns by design, which are now standardized and deployed in billions of chips. In the meantime, new features, such as the ability to compactly aggregate signatures, were identified as very suitable for practical use-cases.

Unfortunately, all these mechanisms are vulnerable to quantum computing and thus require to be replaced by so-called “post-quantum” counterparts. In this area, some recent works, part of which led by Orange, have shown that it was possible to design post-quantum solutions with rather good efficiency, but some obstacles remain to overcome. 

Scientific Objective.

The objective of this thesis is overcome all or part of the following scientific obstacles:

• Improvements of Lattice-based Advanced Signatures. The recent advances in this area are still insufficient to envision real-world deployments. The first goal of this thesis will be to improve the most recent constructions from the state-of-the-art, potentially by adding new features.
• SNARK-based Constructions. Advanced signatures suffer from their reliance on zero-knowledge (ZK) proofs whose complexity is high and hard to improve. A second goal of this thesis will be to investigate alternatives based on SNARKs whose potential in this area has been demonstrated by several recent works.
• Interoperability with standards. The imminent deployment of post-quantum standards calls for compatible mechanisms, including ZK proofs. Unfortunately, the latter are usually hard to combine with standards and thus require adaptations whose design constitutes the third goal of this thesis.
• Constructions without lattices. Lattices have proved suitable for post-quantum cryptography but yet suffer from inherent limitations that reverberate throughout advanced signatures. A last goal of this thesis will be to investigate symmetric-based constructions, such as those following the MPC-in-the-head paradigm, to circumvent these limitations.