We consider the NTRU encryption scheme as lately suggested for use, and study the connection between inverting the NTRU primitive (i.e., the one-way function over the message and the blinding information which underlies the NTRU scheme) and recovering the NTRU secret key (universal breaking). We model the inverting algorithms as black-box oracles and do not take any advantage of the internal wa...

The purpose of this paper is to submit the NSS lattice based signature scheme for consideration for inclusion in the IEEE P1363.1 standard. At the rump session of CRYPTO ’96 the authors introduced a highly efficient new public key cryptosystem called NTRU. (See [4] for details.) Underlying NTRU is a hard mathematical problem of finding short vectors in certain lattices. In this paper we introdu...

In this paper, we propose a new variant of the NTRU public key cryptosystem − the MaTRU cryptosystem. MaTRU works under the same general principles as the NTRU cryptosystem, except that it operates in a different ring with a different linear transformation for encryption and decryption. In particular, it operates in the ring of k by k matrices of polynomials in R = Z[X]/(X−1), whereas NTRU oper...

In this note we describe a variety of methods that may be used to increase the speed and efficiency of the NTRU public key cryptosystem. 1991 Mathematics Subject Classification: 94A60, 11T71. 1. An Overview of NTRU The NTRU Public Key Cryptosystem is based on ring theory and relies for its security on the difficulty of solving certain lattice problems. In this section we will briefly review the...

A property of the NTRU public-key cryptosystem is that it does not provide perfect decryption. That is, given an instance of the cryptosystem, there exist ciphertexts which can be validly created using the public key but which can’t be decrypted using the private key. The valid ciphertexts which an NTRU secret key will not correctly decipher determine, up to a cyclic shift, the secret key. In t...

Abstract. We introduce a generalization of the NTRU cryptosystem and describe its advantages and disadvantages as compared with the original NTRU protocol. This extension helps to avoid the potential problem of finding “enough” invertible polynomials within very thin sets of polynomials, as in the original version of NTRU. This generalization also exhibits certain attractive “pseudorandomness” ...

In 2016, Albrecht, Bai and Ducas and independently Cheon, Jeong and Lee presented very similar attacks to break the NTRU cryptosystem with larger modulus than in the NTRUEncrypt standard. They allow to recover the secret key given the public key of Fully Homomorphic Encryption schemes based on NTRU ideas. Hopefully, these attacks do not endanger the security of the NTRUEncrypt, but shed new lig...

NTRU public key cryptosystem is well studied lattice-based Cryptosystem along with Ajtai-Dwork and GGH systems. Underlying NTRU is a hard mathematical problem of finding short vectors in a certain lattice. (Shamir 1997) presented a lattice-based attack by which he could find the original secret key or alternate key. Shamir concluded if one designs a variant of NTRU where the calculations involv...

NTRU is a public-key cryptosystem based on polynomial rings over Z. Replacing Z with the ring of Eisenstein integers yields ETRU. We prove through both theory and implementation that ETRU is faster and has smaller keys for the same or better level of security than does NTRU.

Author: Daniel Socek Title: Deterministic and Non-Deterministic Basis Reduction Techniques for NTRU Lattices Institution: Florida Atlantic University Thesis Advisor: Dr. Spyros S. Magliveras Degree: Master of Science Year: 2002 Finding the shortest or a “short enough” vector in an integral lattice of substantial dimension is a difficult problem. The problem is not known to be but most people be...