Lattice Base Reduction Attack on Matrix NTRU

NTRU is one of the most important post-quantum cryptosystems nowadays and since its introduction several variants have been proposed in the literature. In particular, the Matrix NTRU is a variant which replaces the NTRU polynomials by integer matrices. In this work, we develop a lattice-based reduction attack on the Matrix NTRU cryptosystem that allows us to recover the plaintext. We also show that this system is completely vulnerable to the proposed attack for parameters that could be used in practice. In addition, we give sufficient conditions to avoid decryption failure for the Matrix NTRU.