Computational Complexity and Its Relationship to Number Theory

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This project concentrates on computational problems of a number theoretic nature in order to develop new efficient algorithms or when this is not possible to provide evidence of intractability. A major component of this research will be the further development of new methods arising from algebraic geometry, class field theory, and the geometry of numbers. Whenever possible, results of this research will be applied to the areas of computer security and parallel processing. In particular, an efficient checker' algorithm (see selection 3.2) for Rivest-Shamir-Adleman encryption and decryption will be sought. Also work will continue on the development of parallel algorithms for integer GCD and modular exponentiation. Finally, work will continue on the theory of computer viruses. It is hoped that these efforts will play a role in combatting this growing security threat.