Master of Computer Science - Research
School of Computer Science and Software Engineering
Rose, Michael, Lattice-based cryptography: a practical implementation, Master of Computer Science - Research thesis, School of Computer Science and Software Engineering, University of Wollongong, 2011. http://ro.uow.edu.au/theses/3376
Ever since Ajtai's seminal paper Generating Hard Instances of Lattice Problems  there has been much interest in developing Lattice-based cryptography for a number of reasons. Firstly, Lattice-based cryptography provides a much stronger notion of security, in that the average-case of certain problems in lattice-based cryptography are equivalent to the worst-case of those problems . Secondly, there are strong indications that these problems will remain secure under the assumption of the availability of quantum computers, unlike both the integer-factorisation and discrete-logarithm problems as relied upon in many conventional cryptosystems. 
Despite these advantages however, a signi cant hurdle to the widespread adoption of lattice-based cryptography has been that most lattice-based cryptosystems are computationally expensive and hence impractical compared to conventional cryptosystems. In this dissertation, the author will explore various methods to improve the practicality of lattice-based cryptosystems and to optimise the algorithms that make up these cryptosystems for modern computer processors.