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

Abstract

Recently, lattice signatures based on the Fiat-Shamir framework have seen a lot of improvements which are efficient in practice. The security of these signature schemes depends mainly on the hardness of solving short integer solutions (SIS) and/or learning with errors problem in the random oracle model. The authors propose an alternative lattice-based signature scheme on the Fiat-Shamir framework over the ring Z[x]/(xn + 1). The key generation in the signature scheme is based on the combination of NTRU and Ring SIS like key generation. Both the signature and the verification are done efficiently by doing polynomial convolutions in the ring Z[x]/(xn + 1). The proposed signature scheme is provably secure based on the hardness of the Ring SIS problem in the random oracle model. The scheme is also efficient up to constant factors as the highly practical schemes which have provable secure instantiation.