Lattice signatures using NTRU on the hardness of worst‐case ideal lattice problems

NTRUSIGN: Digital Signatures Using the NTRU Lattice

Digital Signatures Based on the Hardness of Ideal Lattice Problems in All Rings

Many practical lattice-based schemes are built upon the Ring-SIS or Ring-LWE problems, which are problems that are based on the presumed difficulty of finding low-weight solutions to linear equations over polynomial rings Zq[x]/〈f〉. Our belief in the asymptotic computational hardness of these problems rests in part on the fact that there are reduction showing that solving them is as hard as fin...

Using the Ntru Lattice

Lattice Attacks on NTRU

NTRU is a new public key cryptosystem proposed at Crypto 96 by Hoffstein, Pipher and Silverman from the Mathematics department of Brown University. It attracted considerable attention, and is being advertised over the Internet by NTRU Cryptosystems. Its security is based on the difficulty of analyzing the result of polynomial arithmetic modulo two unrelated moduli, and its correctness is based ...

Ideal of Lattice homomorphisms corresponding to the products of two arbitrary lattices and the lattice [2]

Abstract. Let L and M be two finite lattices. The ideal J(L,M) is a monomial ideal in a specific polynomial ring and whose minimal monomial generators correspond to lattice homomorphisms ϕ: L→M. This ideal is called the ideal of lattice homomorphism. In this paper, we study J(L,M) in the case that L is the product of two lattices L_1 and L_2 and M is the chain [2]. We first characterize the set...