Mathematical Sciences: Development and Implementation of theNumber Field Sieve

数学科学：数域筛的开发和实现

• 批准号: 9012989
• 负责人: Robert Robson
• 金额: $ 5万
• 依托单位: Oregon State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-05-15 至 1992-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9012989&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Development; Implementation; theNumber

This Small Grant for Exploratory Research supports a project to implement the Number Field Sieve, the newest method for factoring large integers. The principal investigators are Professor Robert Robson of the Mathematics Department and Professor Walter Rudd of the Computer Science Department at Oregon State University, and Professor Joe Buhler of Reed College. The Number Field Sieve has a predicted running time that is so much better than that of the previously known methods of factoring that the Principal Investigators believe that they will be able to factor numbers in the 145-digit range, far larger than has been possible up to now. Except for counting, number theory, which is the study of the properties of the whole numbers, is the oldest branch of mathematics. In modern days, problems in number theory have furnished the driving force to creation of new mathematics in the fields of pure algebra, analysis, and geometry; some of the most recent and most astonishing applications of number theory have appeared in theoretical computer science and coding theory. In particular, the difficulty or ease of factoring large numbers has turned out to have a direct application to the security of public-key codes.

这项探索性研究的小额赠款支持一个项目 实现数字字段筛选，最新的方法， 大整数的分解主要研究人员是 数学系的罗伯特·罗布森教授和 沃尔特·拉德教授，计算机科学系， 俄勒冈州州立大学和里德大学的乔·布勒教授 学院数字字段筛选器具有预测运行时间， 比以前已知的方法好得多， 因为主要研究者认为他们会 能够分解145位数范围内的数字，远远大于 到目前为止是可能的。 除了计数，数论，这是研究 整数的性质，是最古老的分支， 数学在现代，数论中的问题 为新数学的产生提供了动力， 纯代数，分析和几何领域;一些最重要的 数论最近最令人惊讶的应用是 出现在理论计算机科学和编码理论中。在 特别是，分解大数的困难或容易程度 事实证明，它直接适用于 公钥密码