Polynomial structures in code-based cryptography

Vlad Dragoi (1, 2) , Pierre-Louis Cayrel (1) , Brice Colombier (1) , Tania Richmond (1)

1 LHC - Laboratoire Hubert Curien
2 LITIS - Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes

In this article we discus a probability problem applied in the code based cryptography. It is related to the shape of the polynomials with exactly t different roots. We will show that the structure is very dense and the probability that this type of polynomials has at least one coefficient equal to zero is extremelly low. We treated this issue in our research of natural countermeasures to a timing attack against the polynomial evaluation.

Domaines: Cryptographie et sécurité [cs.CR]

Vlad Dragoi, Pierre-Louis Cayrel, Brice Colombier, Tania Richmond. Polynomial structures in code-based cryptography. Indocrypt 2013, Dec 2013, India. pp.286-296. ⟨hal-00865355⟩