Cryptography and Group Theory

密码学和群论

• 批准号: 0625271
• 负责人: Gilbert Baumslag
• 金额: $ 0.6万
• 依托单位: CUNY City College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-10-01 至 2007-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0625271&HistoricalAwards=false
• 关键词: Cryptography; Group; Theory

The possibility that quantum computers might eventually make today's cryptographic protocols obsolete and thereby make hitherto private information public, has recently led to an ongoing and very active effort to develop cryptoysystems based on group theory. One such system, using the so--called braid group, was developed in part by Michael Anshel (a member of the City College of New York Computer Science Department and CAISS, the Center for Algorithms and Scientific Software, a research center at CCNY), in 1999, and can be viewed as a group--theoretic analogue of the famous key-exchange idea of Diffie--Hellman. Today, as already indicated, a great deal of research is being carried out in this general area of group theory and cryptography. The Graduate Center of the City University of New York hosts the famous New York Group Theory Seminar, where current research in group theory is discussed on a weekly basis. There is also now a seminar devoted to cryptography at the Graduate Center and the Stephens Institute in Hoboken has a team of researchers working in part on cryptography. So a conference at this time in this general area seems particularly appropriate and important.One tends to marvel at the intricate patterns that one sees in the tiled floors of St. Marks cathedral in Venice and the remarkable symmetry of everyday crystals. Such symmetry also arises in the study of elementary particles and also in knot theory, which surprisingly arises in physics. They also play a part in efforts to understand the intricacies of the three--dimensional world that we live in. There is an algebraic structure known as a group which captures the notion of symmetry in a highly sophisticated way, allowing for the classification of different types of crystals and provides a means for studying and describing the minute particles which make up the material of everyday life.These groups can encode in a remarkably simple way, a huge amount, indeed an infinite amount, of information. Such encodings are often hard to decode and so are extremely promising tools in obtaining secure new ways for hiding and transmitting information.Thus they offer novel means for safe electronic communication.With the birth of the internet and the explosion of commerce over the net, secure transmission of information is now a critical aspect of today's world. The proposed conference will be devoted to bringing some of the ideas involved to the wider mathematical community in the hope that it will lead to broader understanding and application of them.

量子计算机最终可能使当今的加密协议过时，从而使迄今为止私人信息公开的可能性最近导致了基于群体理论开发隐秘系统的持续努力。一种这样的系统，使用所谓的编织组，部分由迈克尔·安塞尔（Michael Anshel）（纽约城市学院的计算机科学系的成员和CAISS的成员，CCNY的研究中心），CCNY的研究中心），可以被视为著名的Key-Exexchange the-exexchange of-exexchange fiffie-bilfie-hellelman的理论类似物。如今，如今已经表明，在小组理论和密码学的这一一般领域正在进行大量研究。纽约市城市大学的研究生中心举办了著名的纽约集团理论研讨会，每周讨论当前的小组理论研究。现在还有一个专门在研究生中心加密术的研讨会，霍博肯的斯蒂芬斯学院有一组研究人员在一部分工作。因此，此时在这个一般地区的一次会议似乎特别适合和重要。一个倾向于惊叹于威尼斯圣马克大教堂的瓷砖地板上看到的复杂模式以及日常晶体的显着对称性。这种对称性也出现在基本颗粒的研究以及结理论中，这在物理学中出现了。他们还在努力了解我们所生活的三维世界的复杂性方面也起着作用。有一个代数结构被称为一个群体，它以高度复杂的方式捕获了对称性的概念，可以分类不同类型的晶体，并提供了一种良好的粒子，可以构成一个庞大的材料。信息。这样的编码通常很难解码，因此在获得安全的隐藏和传输信息的安全新方法方面非常有前途的工具。因此，它们提供了新颖的方法来安全电子通信。随着互联网的诞生和网络上的贸易爆炸，信息的安全传输现在是当今世界的关键方面。拟议的会议将致力于将所涉及的一些想法带到更广泛的数学社区，以期使其能够更广泛地了解和应用它们。