Cryptanalysis of lattice-based key exchange on small integer solution problem and its improvement

Abstract

Wang et al. introduced a new variant of small integer solution (SIS), namely, bilateral inhomogeneous small integer solution (Bi-ISIS) which is based on lattice cryptography, and constructed a Bi-ISIS-based key exchange (KE) protocol. In this paper, we indicate that Wang et al.’s Bi-ISIS-based KE protocol is not secure because a common shared key can be recovered directly by using linear algebraic methods. Furthermore, we analysis two simple variants of the Bi-ISIS-based KE and show that they are also insecure. To avoid the shared key attack, we present an improvement of the Bi-ISIS-based KE, whose security is reduced to the learning with error problem over modules (M-LWE).