Elliptic curve and Lattice cryptosystem

Abstract

In this work, we will present a new hybrid cryptography method based on two hard problems: 1- The problem of the discrete logarithm on an elliptic curve defined on a finite local ring. 2- The closest vector problem in lattice and the conjugate problem on square matrices. At first, we will make the exchange of keys to the Diffie-Hellman. The encryption of a message is done with a bad basis of a lattice.