Breaking ECC2K-130

Daniel V.  Bailey; Lejla Batina; Daniel J.  Bernstein; Peter Birkner; Joppe W.  Bos; Hsieh-Chung Chen; Chen-Mou Cheng; Gauthier van Damme; Giacomo de Meulenaer; Luis Julian Dominguez Perez; Junfeng Fan; Tim Güneysu; Frank Gurkaynak; Thorsten Kleinjung; Tanja Lange; Nele Mentens; Ruben Niederhagen; Christof Paar; Francesco Regazzoni; Peter Schwabe; Leif Uhsadel; Anthony Van Herrewege; Bo-Yin Yang

Paper 2009/541

Breaking ECC2K-130

Daniel V. Bailey, Lejla Batina, Daniel J. Bernstein, Peter Birkner, Joppe W. Bos, Hsieh-Chung Chen, Chen-Mou Cheng, Gauthier van Damme, Giacomo de Meulenaer, Luis Julian Dominguez Perez, Junfeng Fan, Tim Güneysu, Frank Gurkaynak, Thorsten Kleinjung, Tanja Lange, Nele Mentens, Ruben Niederhagen, Christof Paar, Francesco Regazzoni, Peter Schwabe, Leif Uhsadel, Anthony Van Herrewege, and Bo-Yin Yang

Abstract

Elliptic-curve cryptography is becoming the standard public-key primitive not only for mobile devices but also for high-security applications. Advantages are the higher cryptographic strength per bit in comparison with RSA and the higher speed in implementations. To improve understanding of the exact strength of the elliptic-curve discrete-logarithm problem, Certicom has published a series of challenges. This paper describes breaking the ECC2K-130 challenge using a parallelized version of Pollard's rho method. This is a major computation bringing together the contributions of several clusters of conventional computers, PlayStation~3 clusters, computers with powerful graphics cards and FPGAs. We also give /preseestimates for an ASIC design. In particular we present * our choice and analysis of the iteration function for the rho method; * our choice of finite field arithmetic and representation; * detailed descriptions of the implementations on a multitude of platforms: CPUs, Cells, GPUs, FPGAs, and ASICs; * details about running the attack.

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Published elsewhere. Unknown where it was published
Keywords: Attacks ECC binary fields DLP Koblitz curves automorphisms parallelized Pollard rho Certicom challenges.
Contact author(s): tanja @ hyperelliptic org
History: 2009-11-18: last of 4 revisions; 2009-11-08: received; See all versions
Short URL: https://ia.cr/2009/541
License: CC BY

BibTeX

@misc{cryptoeprint:2009/541,
      author = {Daniel V.  Bailey and Lejla Batina and Daniel J.  Bernstein and Peter Birkner and Joppe W.  Bos and Hsieh-Chung Chen and Chen-Mou Cheng and Gauthier van Damme and Giacomo de Meulenaer and Luis Julian Dominguez Perez and Junfeng Fan and Tim Güneysu and Frank Gurkaynak and Thorsten Kleinjung and Tanja Lange and Nele Mentens and Ruben Niederhagen and Christof Paar and Francesco Regazzoni and Peter Schwabe and Leif Uhsadel and Anthony Van Herrewege and Bo-Yin Yang},
      title = {Breaking {ECC2K}-130},
      howpublished = {Cryptology {ePrint} Archive, Paper 2009/541},
      year = {2009},
      url = {https://eprint.iacr.org/2009/541}
}