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Cofactorization on Graphics Processing Units

Andrea Miele, Joppe W. Bos, Thorsten Kleinjung, Arjen K. Lenstra
LACAL, EPFL, Lausanne, Switzerland
Cryptology ePrint Archive: Report 2014/397, 2014

@misc{cryptoeprint:2014:397,

   author={Andrea Miele, Joppe W. Bos, Thorsten Kleinjung, and Arjen K. Lenstra},

   title={Cofactorization on Graphics Processing Units},

   howpublished={Cryptology ePrint Archive, Report 2014/397},

   year={2014},

   note={url{http://eprint.iacr.org/}}

}

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We show how the cofactorization step, a compute-intensive part of the relation collection phase of the number field sieve (NFS), can be farmed out to a graphics processing unit. Our implementation on a GTX 580 GPU, which is integrated with a state-of-the-art NFS implementation, can serve as a cryptanalytic co-processor for several Intel i7-3770K quad-core CPUs simultaneously. This allows those processors to focus on the memory-intensive sieving and results in more useful NFS-relations found in less time.
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