有限域上的超椭圆曲线在公钥密码学中取得了重要应用，比如密钥协商和基于身份加密体制。这些密码应用的实现效率由两个核心算法决定，即标量乘运算与双线性对计算。我们拟利用Kummer曲面和超椭圆函数域等理论，改进这些基本运算的计算效率，从而使得基于超椭圆曲线的相关密码协议能够应用于资源受限的环境下，如无线网络或者智能卡中。

Hyperelliptic curves over finite fields find many vital applications in public key cryptography，such as key agreements and Identity-based encryption. The implemental efficiency of these applications depends on the two key algorithms: scalar multiplication and the computation of hyperelliptic pairings. We will optimize the key algorithms by using the theory of Kummer surface and hyperelliptic function fields. This makes the cryptographic protocols or schemes by using hyperelliptic curves satisfy the requirements of resource-constrained environments, such as wireless networks and smart cards.