Scalar multiplication is the main operation in the implementation of hyperelliptic curve cryptosystems, where the basic arithmetic of reduced divisor classes is required. In this work, some explicit formulas are proposed for the arithmetic of reduced divisor classes by exploiting Jacobian coordinates when the degenerate divisor is involved. Moreover, an efficiency analysis shows that the degenerate divisor as a base element can be a valid alternative in hyperelliptic curve cryptosystems as well.

中文翻译：

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超椭圆曲线密码系统的简并除数的快速标量乘法

标量乘法是实现超椭圆曲线密码系统的主要操作，在该系统中，需要精简除数类的基本算法。在这项工作中，当涉及简并除数时，通过利用雅可比坐标，提出了一些用于简化除数类算法的显式公式。此外，效率分析表明，简并除数作为基本元素在超椭圆曲线密码系统中也可以是有效的替代方法。