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Elliptic divisibility sequences and the elliptic curve discrete logarithm problem
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Abstract: | We use properties of the division polynomials of an elliptic curve $E$ over a finite field $\mathbb{F}_q$ together with a pure result about elliptic divisibility sequences from the 1940s to construct a very simple alternative to the Menezes-Okamoto-Vanstone algorithm for solving the elliptic curve discrete logarithm problem in the case where $\#E(\mathbb{F}_q) = q-1$. |
BibTeX
@misc{eprint-2008-18115, title={Elliptic divisibility sequences and the elliptic curve discrete logarithm problem}, booktitle={IACR Eprint archive}, keywords={public-key cryptography / elliptic divisibility sequences, elliptic curve cryptography, elliptic curve discrete log problem}, url={http://eprint.iacr.org/2008/444}, note={ christine.swart@uct.ac.za 14168 received 16 Oct 2008}, author={Rachel Shipsey and Christine Swart}, year=2008 }