Generic constructions of PoRs from codes and instantiations

Julien Lavauzelle (1, 2) , Françoise Levy-Dit-Vehel (1, 2, 3)

1 GRACE - Geometry, arithmetic, algorithms, codes and encryption
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
3 ENSTA Paris - École Nationale Supérieure de Techniques Avancées

In this paper, we show how to construct, from any linear code, a Proof of Retrievability (PoR) which features very low computation complexity on both the client (Verifier) and server (Prover) side, as well as small client storage (typically 512 bits). We adapt the security model initiated by Juels and Kaliski [JK07] to fit into the framework of Paterson et al. [PSU13], from which our construction evolves. We thus provide a rigorous treatment of the security of our generic design; more precisely, we sharply bound the extraction failure of our protocol according to this security model. Next, we instantiate our formal construction with codes built from tensor-products as well as with Reed-Muller codes and lifted codes [GKS13], yielding PoRs with moderate communication complexity and (server) storage overhead, in addition to the aforementioned features.

Mots clés: Proofs of retrievability; Error correcting codes; Cloud storage

Domaines: Cryptographie et sécurité [cs.CR]

Julien Lavauzelle, Françoise Levy-Dit-Vehel. Generic constructions of PoRs from codes and instantiations. Journal of Mathematical Cryptology, In press, 13 (2), pp.81--106. ⟨10.1515/jmc-2018-0018⟩. ⟨hal-02053948⟩