GGH Cryptosystem and Lattice Reduction Algorithms

Abstract

<p>The capability of encrypting top secret information remains as a major research problem in the GGH cryptosystem, which depends on various attacking methods. The early approaches to attacking the GGH cryptosystem mainly relied on special properties of the lattice generated by the vectors of the private key. Consequently, those attacks are not appropriate for general cases.</p> <p>This thesis presents a GGH attacking method for general cases. A lattice basis reduction algorithm is applied to the public key to get a better basis, which is used to decrypt the ciphertext. In the proposed approach, we concentrate on three lattice reduction algorithms: the LLL algorithm, the approximate optimally-reduced algorithm, and the optimally-reduced algorithm. We have implemented a package in MATLAB for the GGH cryptosystem and the three algorithms. We experimented with two groups of experiments and obtained promising results for lattices of low dimensions.</p>