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 -