LE3 .A278 2010

2010

Hooper, Jeff

Acadia University

Master of Science

Masters

Mathematics and Statistics

Mathematics & Statistics

A noncommutative version of the Grobner basis Polly Cracker cryptosystem was proposed in a doctoral thesis by Rai, \Innite Grobner Bases And Noncommutative Polly Cracker Cryptosystems." The description includes a conjecture designed to identify good sources of cryptographically suitable keys. We review the algebraic theory underpinning Grobner basis cryptosystems and describe the various systems that have been proposed. We discuss known attacks on these systems and the countermeasures to defend against their use. Rai's conjecture, designed to counter the problem of having a public key generating an ideal for which a Grobner basis can be found, is the focus of our work. Through computations using GAP software, we explore the viability of this conjecture. The results demonstrate that generating keys at random is not likely to produce suitable results; conversely, following the constraints recommended by Rai is computationally straightforward and produces useful keys. Attempts to nd Grobner bases for ideals generated by keys constructed using this method did not succeed.

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https://scholar.acadiau.ca/islandora/object/theses:142