Breaking ECC2K-130
Additional information
Authors
Bailey D. V.,
Batina L.,
Bernstein D. J.,
Birkner P.,
Bos J. W.,
Chen H. .,
Cheng C. .,
van Damme G.,
Güneysu T.,
Gurkaynak F.,
Kleinjung T.,
Paar C.,
Regazzoni F.,
Niederhagen R.,
Schwabe P.,
Uhsadel L.,
Van Herrewege A.
Type
Journal Article
Year
2009
Language
English
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.
Journal
IACR Cryptology ePrint Archive
Volume
2009
Month
November
Start page number
541
Keywords
Attacks, automorphisms, binary fields, Certicom challenges, DLP, ECC, implementation, Koblitz curves, parallelized Pollard rho
