Algebraic function fields and cryptography

代数函数域和密码学

• 批准号: 327640-2006
• 负责人: Lee, Yoonjin
• 金额: $ 0.58万
• 依托单位: Simon Fraser University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2006
• 资助国家: 加拿大
• 起止时间: 2006-01-01 至 2007-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=339691
• 关键词: Algebraic; function; fields; cryptography

The proposed research pursues three objectives. The first two objectives are related to the arithmetic of algebraic function fields, and the third one is a practical application of the arithmetic of algebraic function fields to Cryptography. The first proposed research is the development of constructive methods of algebraic function fields whose Jacobians and ideal class groups have nice structures, and investigation of the distribution of class groups of function fields. And the second objective is to determine the image of the Galois representation associated to the Drinfeld modular curves. The last proposed research is developing computationally feasible and efficient methods for computing the Tate-pairing over divisor class groups of hyperelliptic curves for pairing-based cryptography. Cryptography has been getting much attention since information security is one of the very significant issues nowadays. Number Theory has produced nice applications to Cryptography. Funding for this research program will help to ensure that Canada's research in these areas continues to develop and expand, both in terms of basic science related to important applications and the development of highly qualified personnel for academia and industry.

拟议的研究追求三个目标。前两个目标与代数函数域的算术有关，第三个目标是代数函数域的算术在密码学中的实际应用。第一个提出的研究是发展雅可比行列式和理想类群具有良好结构的代数函数域的构造方法，并研究函数域类群的分布。第二个目标是确定与德林菲尔德模曲线相关的伽罗瓦表示的图像。最后提出的研究正在开发计算上可行且有效的方法，用于计算基于配对的密码学的超椭圆曲线除数类组上的泰特配对。由于信息安全是当今非常重要的问题之一，密码学受到了广泛的关注。数论在密码学中产生了很好的应用。该研究计划的资助将有助于确保加拿大在这些领域的研究不断发展和扩大，无论是在与重要应用相关的基础科学方面，还是在学术界和工业界培养高素质人才方面。