Magliveras, Spyros S.

The main objective of this thesis was to find the full automorphism groups of
finite Desarguesian planes. A set of homologies were used to generate the automorphism
group when the order of the plane was prime. When the order was a prime
power Pa,a ≠ 1 the Frobenius automorphism was added to the set of homologies,
and then the full automorphism group was generated. The Frobenius automorphism
was found by using the planar ternary ring derived from a coordinatization of the
plane.

Finding the shortest or a "short enough" vector in an integral lattice of substantial dimension is a difficult problem. The problem is not known to be but most people believe it is [7]. The security of the newly proposed NTRU cryptosystem depends solely on this fact. However, by the definition NTRU lattices possess a certain symmetry. This suggests that there may be a way of taking advantage of this symmetry to enable a new cryptanalytical approach in combination with existing good lattice reduction algorithms. The aim of this work is to exploit the symmetry inherent in NTRU lattices to design a non-deterministic algorithm for improving basis reduction techniques for NTRU lattices. We show how the non-trivial cyclic automorphism of an NTRU lattice enables further reduction. Our approach combines the recently published versions of the famous LLL algorithm for lattice basis reduction with our automorphism utilization techniques.

The aim of this work is to explore the utilization of permutation-based transformations to achieve compression, encryption and steganography in the domain of digital videos. The main contribution of this dissertation is a novel type of digital video encryption that has several advantages over other currently available digital video encryption methods. An extended classification of digital video encryption algorithms is presented in order to clarify these advantages. The classification itself represents an original work, since to date, no such comprehensive classification is provided in known scientific literature. Both security and performance aspects of the proposed method are thoroughly analyzed to provide evidence for high security and performance efficiency. Since the basic model is feasible only for a certain class of video sequences and video codecs, several extensions providing broader applicability are described along with the basic algorithm. An additional significant contribution is the proposition of a novel type of digital video steganography based on disguising a given video by another video. Experimental results are generated for a number of video sequences to demonstrate the performance of proposed methods.

A recently proposed Chaotic-Key Based Algorithm (CKBA) has been shown to be unavoidably susceptible to chosen/known-plaintext attacks and ciphertext-only attacks. In this paper we enhance the CKBA algorithm three-fold: 1) we change the 1-D chaotic Logistic map to a piecewise linear chaotic map (PWLCM) to improve the balance property, 2) we increase the key size to 128 bits, and 3) we add two more cryptographic primitives and extend the scheme to operate on multiple rounds so that the chosen/knownplaintext attacks are no longer possible. The new cipher has much stronger security and its performance characteristics remain very good.