A New Efficient and Secure Cryptosystem on Lattices

In this paper, we present a new NTRU-Like public-key cryptosystem with security provably based on the worst-case hardness of the approximate lattice problems in order to attain the applicable objectives of preserving the confidentiality of communication and information system resources. Our proposed scheme is an improvement of ETRU cryptosystem. ETRU is an NTRU-Like public-key cryptosystem based on the Eisenstein integers where is a primitive cube root of unity. ETRU has heuristic security and it has no proof of security. We show that our cryptosystem has security stronger than that of ETRU, over Cartesian product of Dedekind domains and extended cyclotomic polynomials. We prove the security for our main algorithm from R-LWE problem.