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

9729662 Peralta该奖项提供资金支持威斯康星大学密尔沃基分校密码学、计算机和网络安全中心（CCCNS） Rene C. Peralta博士与日本石川高级科学技术研究所（JAIST）信息科学学院Eiji Okamoto博士进行为期两个月的研究访问。他们的研究涉及算法的设计和实现，以尽可能大的规模解决那些数字理论问题，这些问题是现代密码学的支柱。确定什么“小尺寸”是太小而不安全是本研究项目的主要焦点。该项目将考虑一系列问题，如质数测试、大数快速算法、丢芬图近似、小数快速因数分解、随机数因数分解以及随着研究进展可能出现的其他问题。该项目将受益于访问大量的计算资源，五台超级计算机，可在主办机构。与日本科学技术研究院的合作还将提供查阅未翻译的日本文献和参加研讨会的机会，在这些研讨会上，日本的研究成果可以得到，而不会像通常那样延迟向西方提供。该项目是互惠互利的，因为它将为日本合作者提供CCCNS的研究成果。本项目由美国国家科学基金会和日本财团全球伙伴关系中心科学奖学金计划资助。＊＊＊

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. ***