International Association for Cryptologic Research (IACR)
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\u27s 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
