Affiliation:
1. Horst Görtz Institute for IT Security, Ruhr University Bochum, Bochum, Germany
Abstract
AbstractWe give a 4-list algorithm for solving the Elliptic Curve Discrete Logarithm (ECDLP) over some quadratic field 𝔽p2. Using the representation technique, we reduce ECDLP to a multivariate polynomial zero testing problem. Our solution of this problem using bivariate polynomial multi-evaluation yields ap1.314-algorithm for ECDLP. While this is inferior to Pollard’s Rho algorithm with square root (in the field size) complexity 𝓞(p), it still has the potential to open a path to ano(p)-algorithm for ECDLP, since all involved lists are of size as small as$\begin{array}{} p^{\frac 3 4}, \end{array}$only their computation is yet too costly.
Subject
Applied Mathematics,Computational Mathematics,Computer Science Applications
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