Paper 2014/397

Cofactorization on Graphics Processing Units

Andrea Miele, Joppe W. Bos, Thorsten Kleinjung, and Arjen K. Lenstra


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.

Note: We fixed a typo

Available format(s)
Publication info
A minor revision of an IACR publication in CHES 2014
CofactorizationGPUsNumber Field Sieve
Contact author(s)
andrea miele @ epfl ch
2015-01-28: last of 3 revisions
2014-05-30: received
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Creative Commons Attribution


      author = {Andrea Miele and Joppe W.  Bos and Thorsten Kleinjung and Arjen K.  Lenstra},
      title = {Cofactorization on Graphics Processing Units},
      howpublished = {Cryptology ePrint Archive, Paper 2014/397},
      year = {2014},
      note = {\url{}},
      url = {}
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