Description
Date depot: 12 avril 2019
Titre: Algebraic Structures in Code-based Cryptography
Directeur de thèse:
Jean-Pierre TILLICH (Inria-Paris (ED-130))
Domaine scientifique: Sciences et technologies de l'information et de la communication
Thématique CNRS : Non defini
Resumé:
The aim of this project is to obtain a better understanding of the impact of the underlying algebraic structure on the
security of the code-based schemes submitted to the NIST competition for
post-quantum cryptography. For instance the following issues could be considered:
- algebraic attacks on Goppa codes. This involves in particular
studying the algorithm proposed in
cite{FGOPT13} that is able to distinguish a high rate Goppa code from a
random linear code of the same
length and dimension. For instance, it should be studied whether this
distinguisher could be turned into an attack on such Goppa codes
similarly to what has been obtained in cite{COT14a}.
- studying the ring structure of the NIST submissions in code-based
cryptography. In particular the security of most of those systems relies
on decision problems for codes using this kind of ring structure whereas
the parameters of those systems are chosen according to search
problems for the same codes. It would highly desirable to have a
reduction from search to decision in this case. This search to decision
reduction is
readily obtained for unstructured linear codes. What makes the problem
more complicated is the additional ring structure. There has been some
progress in lattice-based cryptography for proving such kind of
reductions. It would be interesting to see whether some of these
techniques carry
over to the code-based setting.
Doctorant.e: Mora Rocco