In this thesis, we provide a summary of fully homomorphic encryption, and in particular, look at the BGV encryption scheme by Brakerski, Gentry, and Vaikuntanathan; as well the DGHV encryption scheme by van Dijk, Gentry, Halevi, and Vaikuntanathan. We explain the mechanisms developed by Gentry in his breakthrough work, and show examples of how they are used. While looking at the BGV encryption scheme, we make improvements to the underlying lemmas dealing with modulus switching and noise management, and show that the lemmas as currently stated are false. We then examine a lower bound on the hardness of the Learning With Errors lattice problem, and use this to develop specific parameters for the BGV encryption scheme at a variety of security levels. We then study the DGHV encryption scheme, and show how the somewhat homomorphic encryption scheme can be implemented as both a fully homomorphic encryption scheme with bootstrapping, as well as a leveled fully homomorphic encryption scheme using the techniques from the BGV encryption scheme. We then extend the parameters from the optimized version of this scheme to higher security levels, and describe a more straightforward way of arriving at these parameters.

In elliptic curve cryptography, cryptosystems are based on an additive subgroup of an elliptic curve defined over a finite field, and the hardness of the Elliptic Curve Discrete Logarithm Problem is dependent on the order of this subgroup. In particular, we often want to find a subgroup with large prime order. Hence when finding a suitable curve for cryptography, counting the number of points on the curve is an essential step in determining its security. In 1985, René Schoof proposed the first deterministic polynomial-time algorithm for point counting on elliptic curves over finite fields. The algorithm was improved by Noam Elkies and Oliver Atkin, resulting in an algorithm which is sufficiently fast for practical purposes. The enhancements leveraged the arithmetic properties of the l-th classical modular polynomial, where l- is either an Elkies or Atkin prime. As the Match-Sort algorithm relating to Atkin primes runs in exponential time, it is eschewed in common practice. In this thesis, I will discuss my implementation of the Schoof-Elkies-Atkin algorithm in C++, which makes use of the NTL package. The implementation also supports the computation of classical modular polynomials via isogeny volcanoes, based on the methods proposed recently by Bröker, Lauter and Sutherland. Existing complexity analysis of the Schoof-Elkies-Atkin algorithm focuses on its asymptotic performance. As such, there is no estimate of the actual impact of the Match-Sort algorithm on the running time of the Schoof-Elkies-Atkin algorithm for elliptic curves defined over prime fields of cryptographic sizes. I will provide rudimentary estimates for the largest Elkies or Atkin prime used, and discuss the variants of the Schoof-Elkies-Atkin algorithm using their run-time performances. The running times of the SEA variants supports the use Atkin primes for prime fields of sizes up to 256 bits. At this size, the selective use of Atkin primes runs in half the time of the Elkies-only variant on average. This suggests that Atkin primes should be used in point counting on elliptic curves of cryptographic sizes.

This thesis explains low temperature operation of an InGaAs Avalanche Photo Diode (APD) cooled using thermoelectric coolers in order to utilize in the quantum cryptographic applications. A theoretical background for the equipment used in the experiment was provided. Circuitry and mechanics used for the low temperature operation were designed. Performance measures for APD were explained and experiment results were presented.

In this thesis I present the investigations of matter-light entanglement in cold atomic samples. Particularly, entanglement of mixed species ensembles and bichromatic light fields is proposed and demonstrated experimentally. This approach avoids the use of two interferometrically separate paths for qubits entanglement distribution. I also present the first implementation of multiplexed quantum memory, and experimentally demonstrate entanglement involving arbitrary pairs of elements within this memory array. Finally, quantum interference of electromagnetic fields emitted by remote quantum memory elements separated by 5.5 m is realized.

Collaborative environments allow users to share and access data across networks spanning multiple administrative domains and beyond organisational boundaries. This poses several security concerns such as data confidentiality, data privacy and threats to improper data usage. Traditional access control mechanisms focus on centralised systems and implicitly assume that all resources reside in the one domain. This serves as a critical limitation for inter-organisational collaborative environments, which are characteristically decentralised, distributed and heterogeneous. A consequence of the lack of suitable access control mechanisms for inter-organisational collaborative environments is that data owners relinquish all control over data they release. In these environments, we can reasonably consider more complex cases where documents may have multiple contributors, all with differing access control requirements. Facilitating such cases, as well as maintaining control over the document’s content, its structure and its flow path as it circulates through multiple administrative domains, is a non-trival issue. This thesis proposes an architecture model for specifying and enforcing access control restrictions on sensitive data that follows a pre-defined inter-organisational workflow. Our approach is to embed access control enforcement within the workflow object (e.g. the circulating document containing sensitive data) as opposed to relying on each administrative domain to enforce the access control policies. The architecture model achieves this using cryptographic access control – a concept that relies on cryptography to enforce access control policies.

Thesis (M.Sc. (Hons.)) -- University of Western Sydney, 2001. / "A thesis submitted for the degree of Master of Science at University of Western Sydney, February 2002" Bibliography : p. 107-113.

Thesis (Ph.D.)--University of Wollongong, 2004. / Typescript. Includes bibliographical references: leaf 195-202.

Univ., Diss.--Hildesheim, 1993. / Literaturverz. S. 371 - 385.

Thesis (M.S.)--Rochester Institute of Technology, 2008. / Typescript. Includes bibliographical references (p. 69-72).

Thesis (M.Sc.) - Carleton University, 2008. / Includes bibliographical references (p. 212-213). Also available in electronic format on the Internet.