Cryptology ePrint Archive: Report 2009/541

Breaking ECC2K-130

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

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.

Category / Keywords: implementation / Attacks, ECC, binary fields, DLP, Koblitz curves, automorphisms, parallelized Pollard rho, Certicom challenges.

Date: received 5 Nov 2009, last revised 18 Nov 2009

Contact author: tanja at hyperelliptic org

Available format(s): PDF | BibTeX Citation

Version: 20091118:131804 (All versions of this report)

Short URL: ia.cr/2009/541