TY - JOUR
T1 - Generalized Jacobian and Discrete Logarithm Problem on Elliptic Curves
TT -
JF - IJMSI
JO - IJMSI
VL - 4
IS - 2
UR - http://ijmsi.ir/article-1-88-en.html
Y1 - 2009
SP - 55
EP - 64
KW - Elliptic Curve
KW - Discrete Logarithm Problem
KW - Generalized Jacobian.
N2 - Let E be an elliptic curve over the finite field F_{q}, 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 Fq, in the case where n | q &minus 1, using generalized jacobian of E.
M3 10.7508/ijmsi.2009.02.006
ER -