双线性对在公钥密码学中取得了诸多有趣的应用，比如构造基于身份或者属性的加密方案，三方一轮的密钥协商等等。双线性对的有效计算是实现这些协议或者方案的效率瓶颈。 近年来数域筛法及其变种的迅速发展，一些情形下的有限域上离散对数问题的计算变得更加容易，这影响了配对友善的曲线参数选取。比如，如果BN曲线所在基域的阶为256比特，按照现在的攻击能力，已经不能达到128比特的安全级别。故而为了达到真正的高安全级别，诸多配对友善曲线的具体参数需要增大。本项目主要研究在高安全级别下选择合适的配对友善曲线，加速双线性对的计算效率，以满足密码应用的需求，为我国下一代的基于标识的密码标准提供理论支撑。

Bilinear pairing found many interesting applications in public-key cryptography, for example, constructions of Identity-Based or Attribute-Based encryption schemes, one round key agreement for tripartite and many more. Efficient computations of pairings is the bottleneck of implementations of these protocols or schemes. With the recent development of number field sieves and their variants, discrete logarithm problems in finite fields at special cases become easier, which imposes the selections of parameters of pairing-friendly curves. For example, if the order of the ground field of BN curves has 256 bits, then BN curves can not achieve the 128 bits security level according to the updated estimation. Hence many concrete parameters of pairing-friendly curves should be enlarged for attaining the practical high security level. We will investigate how to choose suitable pairing-friendly curves for high security level, speed up the efficiency of pairing computations such that it can satisfy requirements of cryptographic applications, and provide the theoretical support for Identity-based cryptographic standard of next generations.