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 G├╝neysu, 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.

Details

Publication typeTechReport
URLhttp://eprint.iacr.org/2009/541
PublisherInternational Association for Cryptologic Research
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