Generalized Jacobian and Discrete Logarithm Problem on Elliptic Curves

被引：0

作者：

Daghigh, H. ^{[1
]}

Bahramian, M. ^{[1
]}

机构：

[1] Univ Kashan, Fac Sci, Dept Math, Kashan, Iran

来源：

IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS | 2009年 / 4卷 / 02期

关键词：

Elliptic Curve; Discrete Logarithm Problem; Generalized Jacobian;

D O I：

10.7508/ijmsi.2009.02.006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let E be an elliptic curve over the finite field Fq, P a point in E(F-q) of order n, and Q a point in the group generated by P. The discrete logarithm problem on E is to find the number k such that Q = kP. In this paper we reduce the discrete logarithm problem on E[n] to the discrete logarithm on the group F-q(*), the multiplicative group of nonzero elements of F-q, in the case where n | q - 1, using generalized jacobian of E.

引用

页码：55 / 64

页数：10

共 16 条

[1] Quandle cohomology and state-sum invariants of knotted curves and surfaces [J].