Cryptosystem based on lattice and elliptic curve

Abstract

In this work, we propose a new way to use lattice theory to build a public key cryptosystem and digital signature scheme. This cryptosystem based on the approximate closest vector problem and the problem of the discrete logarithm on an elliptic curve defined on a finite local ring. At first, we choose a point on the elliptic curve and we will make the exchange of keys to the Diffie-Hellman. We transform the coordinates of this point into a matrix which gives us the private key which will serve us for encryption and decryption.