Screaming Fast Galois Field Arithmetic Using Intel SIMD Instructions (2013)

James S. Plank, EECS Department, University of Tennessee,
Kevin M. Greenan, EMC Backup Recovery Systems Division
Ethan L. Miller, UC Santa Cruz.

Appearing in FAST 2013: 11th USENIX Conference on File and Storage Technologies, San Jose, CA, February, 2013.

PDF of the paper.
The software library highlighted by this paper is GF-Complete (http://web.eecs.utk.edu/~plank/plank/papers/CS-13-703.html)

Abstract

Galois Field arithmetic forms the basis of Reed-Solomon and other erasure coding techniques to protect storage systems from failures. Most implementations of Galois Field arithmetic rely on multiplication tables or discrete logarithms to perform this operation. However, the advent of 128-bit instructions, such as Intel's Streaming SIMD Extensions, allows us to perform Galois Field arithmetic much faster. This short paper details how to leverage these instructions for various field sizes, and demonstrates the significant performance improvements on commodity microprocessors. The techniques that we describe are available as open source software.

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Citation Information

• Plain Text:

  .inproceedings  pgm:13:sfg
  author          J. S. Plank and K. M. Greenan and E. L. Miller
  title           Screaming Fast {G}alois {F}ield Arithmetic Using {I}ntel {SIMD} Instructions
  booktitle       FAST-2013: 11th Usenix Conference on File and Storage Technologies
  month           February
  year            2013
  address         San Jose
  where           http://www.usenix.org/events/fast13,http://web.eecs.utk.edu/~plank/plank/papers/FAST-2013-GF.html

• Bibtex:

  @INPROCEEDINGS{pgm:13:sfg,
          author = "J. S. Plank and K. M. Greenan and E. L. Miller",
          title = "Screaming Fast {G}alois {F}ield Arithmetic Using {I}ntel {SIMD} Instructions",
          booktitle = "FAST-2013: 11th Usenix Conference on File and Storage Technologies",
          month = "February",
          year = "2013",
          address = "San Jose",
          where = "http://www.usenix.org/events/fast13,http://web.eecs.utk.edu/~plank/plank/papers/FAST-2013-GF.html"
  }