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

TL;DR

This paper explores using the Lowner-John ellipsoid to embed lattice data for steganography and reviews Gentry's fully homomorphic encryption scheme, highlighting their theoretical and practical significance.

Contribution

It introduces a novel steganographic method using Lowner-John ellipsoids and details an efficient algorithm for data recovery, connecting lattice data applications to homomorphic encryption.

Findings

Successful embedding of lattice data via ellipsoids

Polynomial-time algorithm for data recovery

Comprehensive review of Gentry's FHE scheme

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.