Finite fields and applications in coding theory and cryptography

编码理论和密码学的有限领域和应用

• 批准号: RGPIN-2017-06410
• 负责人: Wang, Qiang(Steven)
• 金额: $ 2.19万
• 依托单位: Carleton University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635187
• 关键词: Finite; fields; applications; coding; theory

The proposed research area is finite fields and applications in coding theory and cryptography. My recent research has centered on the theoretical study of discrete objects/structures and their properties over finite fields, as well as on their applications to other branches of mathematics and information theory. These objects include polynomials and sequences over finite fields, which have a large number of applications in coding theory, communications and cryptography. This is a fascinating and vibrant area of research in the intersection of discrete math, number theory, theoretical computer science and information theory. Many open problems and conjectures over finite fields arise from useful problems in information theory. It is my long term vision to play a significant and lasting contribution to this area of research.

提出的研究领域是有限域及其在编码理论和密码学中的应用。我最近的研究集中在离散对象/结构及其在有限域中的性质的理论研究，以及它们在数学和信息论的其他分支中的应用。这些对象包括有限域上的多项式和序列，它们在编码理论、通信和密码学中有大量的应用。这是一个迷人的和充满活力的研究领域，在离散数学，数论，理论计算机科学和信息论的交叉点。有限域上的许多开放问题和猜想是由信息论中的有用问题产生的。我的长期愿景是为这一领域的研究做出重大而持久的贡献。