Fast scalar multiplication of degenerate divisors for hyperelliptic curve cryptosystems
作者：
Highlights：
• The arithmetic of reduced divisor classes can be interpreted by the intersection of a quadratic parabola with the hyperelliptic curve.
• Explicit formulas for the arithmetic of reduced divisor classes when the degenerate divisor is involved are proposed by exploiting Jacobian coordinates.
• An efficiency analysis shows that the degenerate divisor as a base element can be a valid alternative in hyperelliptic curve cryptosystems as well.
摘要
•The arithmetic of reduced divisor classes can be interpreted by the intersection of a quadratic parabola with the hyperelliptic curve.•Explicit formulas for the arithmetic of reduced divisor classes when the degenerate divisor is involved are proposed by exploiting Jacobian coordinates.•An efficiency analysis shows that the degenerate divisor as a base element can be a valid alternative in hyperelliptic curve cryptosystems as well.
论文关键词：Hyperelliptic curve,Scalar multiplication,Degenerate divisors
论文评审过程：Received 16 January 2021, Revised 11 March 2021, Accepted 20 March 2021, Available online 3 April 2021, Version of Record 3 April 2021.
论文官网地址：https://doi.org/10.1016/j.amc.2021.126239
