中文摘要：

对超椭圆曲线上一类非退化的Ate对变种进行研究，使得计算双线性对的Miller算法的循环次数显著减少。通过对此类双线性对与改进Tate对及Ate对的关系的一系列证明，验证了此类双线性对的非退化性；基于广义的Ate对和Vereauteren在椭圆曲线上定义的Ate对，给出了两种超椭圆曲线上的此类双线性对的构造方法；针对此类变种的Miller函数，设计了计算此类变种的Miller算法并对其上的计算进行了详细的研究。

英文摘要：

The non-degenerate variations of the Ate pairing on hyperelliptic curve is studied, The loop length of Miller＇s algorithm for the computation on bilinear pairing is reduced, the non-degeneracy of the HV pairing is proven by the relationship between this pairing and modified Tate pairing, Ate pairing. And based on generalized Ate pairing and the Ate pairings defined by Vercauteren, two methods of construction of this pairing based on hypereliptic curve are given. And then, contraposing to the Miller function on this paring, a Miller algorithm is designed and its computation is studied in detail.