Complex Multiplication: Class invariants and cryptographic applications

复数乘法：类不变量和加密应用

• 批准号: 239407529
• 负责人: Professor Dr. Florian Heß
• 金额: --
• 依托单位: Mathematics Institute
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2013
• 资助国家: 德国
• 起止时间: 2012-12-31 至 2016-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/239407529?language=en
• 关键词: Complex; Multiplication; Class; invariants; cryptographic

With the emergence of computer algebra and the need for explicit calculations, the theory of complex multiplication has become subject to algorithmic investigations with a view towards applications in algorithmic algebraic number theory and cryptography. Among the applications are of particular interest primarily proving, explicit classified theory, and curve and pairing based cryptography. A central aspect of algorithmic CM theory is the interplay between numerical and symbolic computations describing discrete objects by analytic means. This project investigates the following three main topics: Class invariants for quadratic and quartic CM-fields, pairing based cryptography and aspects of algorithmic number theory.

随着计算机代数的出现和显式计算的需要，复数乘法理论已成为算法研究的主题，以期在算法代数数论和密码学中应用。其中的应用程序是特别感兴趣的主要证明，明确的分类理论，曲线和配对的密码学。算法CM理论的一个中心方面是通过分析手段描述离散对象的数值计算和符号计算之间的相互作用。本项目主要研究以下三个主题：二次和四次CM-域的类不变量，基于配对的密码学和算法数论方面。