Algebraic attack on NTRU using Witt vectors and Gröbner bases

@inproceedings{Bourgeois2009AlgebraicAO,
title={Algebraic attack on NTRU using Witt vectors and Gr{\"o}bner bases},
author={G. Bourgeois and J. Faug{\`e}re},
booktitle={J. Math. Cryptol.},
year={2009}
}

Abstract 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 𝔽2. The theoretical complexity of this resolution was not studied by the authors. In this… Expand