Algebraic Attack on NTRU using Witt Vectors and Gröbner bases

Gérald Bourgeois (1) , Jean-Charles Faugère (2)

1 GAATI - Laboratoire de Géométrie Algébrique et Applications à la Théorie de l'Information
2 SALSA - Solvers for Algebraic Systems and Applications

We present an algebraic attack on NTRU (restricted to the case where the parameter q is a power of two) using the method of the Witt vectors proposed by Silverman, Smart and Vercauteren [Springer: 278–298, 2005]; the latter considered only the first two bits of a Witt vector attached to the recovering of the secret key in order to reduce the problem to the resolution of an algebraic system over

Domaines: Informatique [cs]

Gérald Bourgeois, Jean-Charles Faugère. Algebraic Attack on NTRU using Witt Vectors and Gröbner bases. Journal of Mathematical Cryptology, 2010, 3 (3), pp.205--214. ⟨10.1515/jmc.2009.011⟩. ⟨hal-01148133⟩