椭圆曲线密码是目前广泛应用的公钥密码体制之一，椭圆曲线上的双线性对以其独特的性质在安全协议设计中有很多重要的应用，如基于身份的密码体制、密钥协商等。基于椭圆曲线上的双线性对的密码系统或协议的执行效率主要取决于适于双线性对计算的椭圆曲线和可有效计算的双线性对。最近十年，在适于双线性对计算的椭圆曲线构造和双线性对的计算的研究上获得了诸多好的结果。本项目构造更多适于双线性对计算的椭圆曲线，同时研究利用 Theta 函数构造计算双线性对的有效算法。该项目的研究成果可为不同安全级别的密码系统实现提供更多的曲线选择，也从根本上提高双线性对密码的实现效率。

Elliptic curve cipher is one of the widely used public key cryptosystems now. Bilinear pairings on elliptic curves have many important applications in the design of secure protocols because of their special properties, such as identity-based encryptions, key agreement protocols,etc.. The most costly operations encountered of pairing-based cryptosystems or protocols mainly depend upon pairing-friendly elliptic curves and efficiently computable bilinear pairings. Many good results on the construction of pairing-friendly elliptic curves and computation of pairings have been yielded in the last decade. This project will study the generation of pairing-friendly elliptic curves and efficient algorithm of pairing computation by using Theta function theory. Implementation of the results of this project can provide more curve selection for different security levels and also fundamentally improve the efficiency of pairing-based cryptosystems.