Paper 2009/466

The Certicom Challenges ECC2-X

Daniel V. Bailey, Brian Baldwin, Lejla Batina, Daniel J. Bernstein, Peter Birkner, Joppe W. Bos, Gauthier van Damme, Giacomo de Meulenaer, Junfeng Fan, Tim Güneysu, Frank Gurkaynak, Thorsten Kleinjung, Tanja Lange, Nele Mentens, Christof Paar, Francesco Regazzoni, Peter Schwabe, and Leif Uhsadel

Abstract

To encourage research on the hardness of the elliptic-curve discrete-logarithm problem (ECDLP) Certicom has published a series of challenge curves and DLPs. This paper analyzes the costs of breaking the Certicom challenges over the binary fields $\F_{2^{131}}$ and $\F_{2^{163}}$ on a variety of platforms. We describe details of the choice of step function and distinguished points for the Koblitz and non-Koblitz curves. In contrast to the implementations for the previous Certicom challenges we do not restrict ourselves to software and conventional PCs, but branch out to cover the majority of available platforms such as various ASICs, FPGAs, CPUs and the Cell Broadband Engine. For the field arithmetic we investigate polynomial and normal basis arithmetic for these specific fields; in particular for the challenges on Koblitz curves normal bases become more attractive on ASICs and FPGAs.