The extra speed takes advantage of extra hardware,specifically two NVIDIA GTX 295 graphics cards,using a new ECM implementation introduced in this paper.Our implementation uses Edwards curves, relies on new parallel addition formulas, and is carefully tuned for the highly parallel GPU architecture.On a single GTX 295 the implementation performs 41.88 million modular multiplications per second for a general 280-bit modulus.GMP-ECM, using all four cores of a Q6600, performs 13.03 million modular multiplications per second.
This paper also reports speeds on other graphics processors: for example, 2414 280-bit elliptic-curve scalar multiplications per second on an older NVIDIA 8800 GTS (G80), again for a general 280-bit modulus.For comparison, the CHES 2008 paper ``Exploiting the Power of GPUs for Asymmetric Cryptography'' reported 1412 elliptic-curve scalar multiplications per second on the same graphics processor despite having fewer bits in the scalar (224 instead of 280), fewer bits in the modulus (224 instead of 280), and a special modulus (2^{224}-2^{96}+1).
Category / Keywords: Factorization, graphics processing unit, modular arithmetic, elliptic curves, elliptic-curve method of factorization, Edwards curves. Date: received 13 Nov 2008, last revised 27 Jan 2009 Contact author: tanja at hyperelliptic org Available format(s): PDF | BibTeX Citation Version: 20090128:023800 (All versions of this report) Short URL: ia.cr/2008/480 Discussion forum: Show discussion | Start new discussion