Continued Fractions and Torsion on Hyperelliptic Curves. Scientific advance should not blindly add to our knowledge; a true advance brings insights that collapse different issues into one. Understanding more is to need to remember less. For an important class of examples, this project identifies the study of a fundamental invariant of a quadratic number field, its regulator and hence its class number, with maximum torsion on the Jacobian variety of an hyperelliptic curve. The investigator's meth ....Continued Fractions and Torsion on Hyperelliptic Curves. Scientific advance should not blindly add to our knowledge; a true advance brings insights that collapse different issues into one. Understanding more is to need to remember less. For an important class of examples, this project identifies the study of a fundamental invariant of a quadratic number field, its regulator and hence its class number, with maximum torsion on the Jacobian variety of an hyperelliptic curve. The investigator's methods will surprise some longstanding problems into submission and in particular will lead them to reveal full data on torsion on hyperelliptic curves of low genus.
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Security and Privacy of Individual Data Used to Extract Public Information. The project aims to contribute to the development of techniques to allow the harvesting of useful information without compromising personal privacy. Intelligent analysis of personal data can reveal valuable knowledge about a population but at a risk of invading an individual's privacy. This project aims to provide at least partial solutions to some of the problems associated with the protection of private data. In partic ....Security and Privacy of Individual Data Used to Extract Public Information. The project aims to contribute to the development of techniques to allow the harvesting of useful information without compromising personal privacy. Intelligent analysis of personal data can reveal valuable knowledge about a population but at a risk of invading an individual's privacy. This project aims to provide at least partial solutions to some of the problems associated with the protection of private data. In particular, it plans to work on the problem of security of statistical databases and privacy of streaming data. This would be underpinned by a study of anonymisation and homomorphic encryption. The expected outcomes are new theoretical results, new algorithms and protocols applicable to at least some of the current significant problems in information security.Read moreRead less