Algebraic function fields and cryptography

点击翻译按钮获取中文摘要

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.