NSF-CGP-Fellowship: Concrete Complexity of Number-TheoreticProblems of Importance to Cryptography

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9729662 Peralta This award provides funds to support two three-month research visits by Dr. Rene C. Peralta, Center for Cryptography, Computer and Network Security (CCCNS), University of Wisconsin-Milwaukee, for collaboration with Dr. Eiji Okamoto, School of Information Science, Japan Advanced Institute of Science and Technology (JAIST), Ishikawa, Japan. Their research is concerned with the design and implementation of algorithms which solve, for as large a size as possible, those number-theoretic problems which are the pillars of modern cryptography. Determining what "small-size" is too small to be secure is the main focus of this research project. The project will consider a host of problems such as primality testing, fast arithmetic with large numbers, diophantine approximation, rapid factorization of small numbers, factorization of random numbers, and other problems that may arise as the research progresses. The project will benefit from access to the massive computational resources, five supercomputers, available at the host institution. Collaboration with JAIST also will provide access to untranslated Japanese literature and access to symposia where Japanese research results can be received without the usual delay in availability to the West. The project is mutually beneficial as it will provide ready access by the Japanese collaborators to research results at CCCNS. This project is supported under the Science Fellowship Program between the National Science Foundation and the Japan Foundation Center for Global Partnership. ***