Application of Lowner-John Ellipsoid in the Steganography of Lattice Vectors and a Review of The Gentry's FHE

Abstract: In this paper, first, we utilize the Lowner-John ellipsoid of a convex set to hide the lattice data information. We also describe the algorithm of information recovery in polynomial time by employing the Todd-Khachyian algorithm. The importance of lattice data is generally due to their applications in the homomorphic encryption schemes. For this reason we also outline the general scheme of a homomorphic encryption provided by Gentry.