Computational Complexity and Its Relationship to Number Theory

该项目专注于数论性质的计算问题，以开发新的高效算法或当这是不可能提供证据的棘手。这项研究的一个主要组成部分将是进一步发展从代数几何、类场论和数几何中产生的新方法。只要有可能，本研究的结果将应用于计算机安全和并行处理领域。特别是，将寻求Rivest-Shamir-Adleman加密和解密的有效检查器算法（见选择3.2）。此外，还将继续开发整数GCD和模幂的并行算法。最后，将继续研究计算机病毒理论。希望这些努力将在打击这一日益严重的安全威胁方面发挥作用。

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.