Screaming Fast Galois Field Arithmetic Using Intel SIMD Instructions

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 (


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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