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


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.

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
ECCbinary fieldsCerticom challenges
Contact author(s)
tanja @ hyperelliptic org
2009-09-26: received
Short URL
Creative Commons Attribution


      author = {Daniel V.  Bailey and Brian Baldwin and Lejla Batina and Daniel J.  Bernstein and Peter Birkner and Joppe W.  Bos and Gauthier van Damme and Giacomo de Meulenaer and Junfeng Fan and Tim Güneysu and Frank Gurkaynak and Thorsten Kleinjung and Tanja Lange and Nele Mentens and Christof Paar and Francesco Regazzoni and Peter Schwabe and Leif Uhsadel},
      title = {The Certicom Challenges ECC2-X},
      howpublished = {Cryptology ePrint Archive, Paper 2009/466},
      year = {2009},
      note = {\url{}},
      url = {}
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