Randomized matrix computations over finite fields

有限域上的随机矩阵计算

• 批准号: 89756-2008
• 负责人: Eberly, Wayne
• 金额: $ 1.97万
• 依托单位: University of Calgary
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2009
• 资助国家: 加拿大
• 起止时间: 2009-01-01 至 2010-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=421570
• 关键词: Randomized; matrix; computations; over; finite

A goal of my research is to design and analyze algorithms for problems in linear algebra. In recent years I have concentrated on algorithms that use randomization, in some way, to solve systems of linear equations over small finite fields. The algorithms that I study are inspired by (and, ideally, closely resemble) methods that are reportedly being used effectively to solve problems in computational number theory - which, in turn, are needed for cryptographic applications - but whose efficiency or reliability has not been rigorously established.

我的研究目标之一是设计和分析线性代数问题的算法。近年来，我一直专注于使用随机化的算法，以某种方式，解决小有限域上的线性方程组。我研究的算法受到了（理想情况下，非常相似）方法的启发，据报道，这些方法被有效地用于解决计算数论中的问题-这反过来又是加密应用所需要的-但其效率或可靠性尚未严格建立。