Improving lattice-based signature schemes and applications to advanced cryptographic functionalities – AMIRAL

Cryptography applications inevitably come into play when a communication between several entities must be secured.
We see their expressions in everyday financial transactions, military or government communications, or between individuals when consulting medical data or even simple exchanges in a social circle.

From a cryptographic point of view, our digital security is largely based on so-called "public key" constructions, such as (EC)DSA digital signatures based on elliptic curves or RSA encryption. Even if there does not exist a quantum computer sufficiently developed to attack the currently deployed cryptographic constructions yet, it is important to prepare for this eventuality and for a migration to post-quantum solutions as quickly as possible.

Among all the possibilities of post-quantum constructions, lattice-based cryptography seems to be one of the most promising, as we can see in the ongoing NIST competition to find new standards on post-quantum cryptographic constructions.
Indeed, five of the seven finalists are based on hard problems on lattices. The schemes submitted to NIST have allowed an important advance towards secure and efficient cryptosystems. However, many questions remain open in order to ensure a transition to post-quantum cryptography in all its existing and emerging applications, both in theory and in concrete realizations.

Our project proposal is in this context ,and our main objective is to propose several constructionss or improvements for signature schemes whose security relies on lattices. As well as on more advanced, potentially efficient constructions, which are fundamentally based on signatures. In this objective, we propose three lines of research: The concrete improvement and the extension of the possibilities of the two signature schemes finalists in the NIST competition, Dilithium and Falcon. The design and study of efficient signatures allowing more advanced functionalities, focusing on blind, aggregated and threshold signatures, for which we believe that we can improve the state of the art significantly. And finally, applications that can benefit from improvements in signature construction techniques, such as identity-based and attribute-based encryption.