Amir Hassani Karbasi - Department of Mathematics, University of Guilan
Reza Ebrahimi Atani - Department of Computer Engineering, University of Guilan

In this paper we present a new NTRU-Like public keycryptosystem with security provably based on the worst casehardness of the approximate both Shortest Vector Problem(SVP) and Closest Vector Problem (CVP) in some structuredlattices, called ideal lattices. We show how to modify theNTRUEncrypt cryptosystem to make it provably secure, underthe assumed quantum hardness of standard worst-case latticeproblems, restricted to a family of lattices related to someextended cyclotomic fields. The security then follows from thealready proven hardness of the R-LWE and R-SIS problems bytheir extensions.

Lattice-based cryptography, Ideal lattices, RLWE, R-SIS, Provable security