Description
Gabidulin codes are the rank metric analogues of Reed?Solomon codes and have found many applications including network coding and cryptography. Interleaving or the direct sum of Gabidulin codes allows both decreasing the redundancy and increasing the error correcting capability for network coding. We consider a transform domain algorithm correcting both errors and erasures with interleaved Gabidulin codes. The transform-domain approach allows to simplify derivations and proofs and also simplifies finding the error vector after solving the key equation. We show that solving the key equation is similar to multi-sequence skew-feedback shift-register synthesis, which can be done effectively using Belekamp-Massey approach or by module minimization.
Next sessions
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Endomorphisms via Splittings
Speaker : Min-Yi Shen - No Affiliation
One of the fundamental hardness assumptions underlying isogeny-based cryptography is the problem of finding a non-trivial endomorphism of a given supersingular elliptic curve. In this talk, we show that the problem is related to the problem of finding a splitting of a principally polarised superspecial abelian surface. In particular, we provide formal security reductions and a proof-of-concept[…]-
Cryptography
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Schéma de signature à clé publique : Frobénius-UOV
Speaker : Gilles Macario-Rat - Orange
L'exposé présente un schéma de signature à clé publique post-quantique inspiré du schéma UOV et introduisant un nouvel outil : les formes de Frobénius. L'accent est mis sur le rôle et les propriétés des formes de Frobénius dans ce nouveau schéma : la simplicité de description, la facilité de mise en oeuvre et le gain inédit sur les tailles de signature et de clé qui bat RSA-2048 au niveau de[…]