دوره 4، شماره 2 - ( 8-1388 )
جلد 4 شماره 2 صفحات 64-55 |
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Daghigh H, Bahramian M. Generalized Jacobian and Discrete Logarithm Problem on Elliptic Curves. IJMSI 2009; 4 (2) :55-64
URL: http://ijmsi.ir/article-1-88-fa.html
URL: http://ijmsi.ir/article-1-88-fa.html
Generalized Jacobian and Discrete Logarithm Problem on Elliptic Curves. مجله علوم ریاضی و انفورماتیک. 1388; 4 (2) :55-64
چکیده:
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.
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