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This paper reports record-setting performance for the elliptic-curve method of integer factorization: For example, 926.11 curves/second for ECM stage 1 with B1 = 8192 for 280-bit integers on a single PC. The state-of-the-art GMP-ECM software handles 124.71 curves/second for ECM stage 1 with B1 = 8192 for 280-bit integers using all four cores of a 2.4 GHz Core 2 Quad Q6600. The extra speed takes advantage of extra hardware, specifically two NVIDIA GTX 295 graphics cards, using a new ECM implementation introduced in this paper. The implementation uses Edwards curves, relies on new parallel addition formulas, and is carefully tuned for the highly parallel GPU architecture.
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