Daghigh, H.; Bahramian, M. Generalized Jacobian and discrete logarithm problem on elliptic curves. (English) Zbl 1301.14016 Iran. J. Math. Sci. Inform. 4, No. 2, 55-64 (2009). Summary: Let \(E\) be an elliptic curve over the finite field \(\mathbb F_{q}\), \(P\) a point in \(E(\mathbb F_{q})\) 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 \(\mathbb F^*_{q}\), the multiplicative group of nonzero elements of \(\mathbb F_q\), in the case where \(n|q-1\), using generalized Jacobian of \(E\). MSC: 14H52 Elliptic curves 94A60 Cryptography 11G05 Elliptic curves over global fields Keywords:elliptic curve; discrete logarithm problem; generalized Jacobian PDFBibTeX XMLCite \textit{H. Daghigh} and \textit{M. Bahramian}, Iran. J. Math. Sci. Inform. 4, No. 2, 55--64 (2009; Zbl 1301.14016) Full Text: Link