A Fast Jacobian Group Arithmetic Scheme for Algebraic Curve Cryptography : Special Section on Cryptography and Information Security

概要

論文の詳細を見る
The goal of this paper is to describe a practical and efficient algorithm for computing in the Jacobian of a large class of algebraic curves over a finite field. For elliptic and hyperelliptic curves, there exists an algorithm for performing Jacobian group arithmetic in O(g^2) operations in the base field, where g is the genus of a curve. The main problem in this paper is whether there exists a method to perform the arithmetic in more general curves. Galbraith, Paulus, and Smart proposed an algorithm to complete the arithmetic in O(g^2) operations in the base field for the so-called superelliptic curves. We generalize the algorithm to the class oc C_<ab> curves, which includes superelliptic curves as a special case. Furthermore, in the case of C_<ab> curves, we show that the proposed algorithm is not just general but more efficient than the previus algorithm as a parameter a in C_<ab> curves grows large.
社団法人電子情報通信学会の論文
2001-01-01