One improves an algebraic attack of NTRU due to Silverman, Smart and Vercauteren; the latter considered the first 2 bits of a Witt vector attached to the research of the secret key; here the first 4 bits are considered, which provides additional equations of degrees 4 and 8.
@article{arxiv.cs/0605136,
title = {Attaque algebrique de NTRU a l'aide des vecteurs de Witt},
author = {Gerald Bourgeois},
journal= {arXiv preprint arXiv:cs/0605136},
year = {2007}
}