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IEEE Transactions on Computers - Special issue on fault-tolerant computing
Effective erasure codes for reliable computer communication protocols
ACM SIGCOMM Computer Communication Review
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High-Speed Software Multiplication in F2m
INDOCRYPT '00 Proceedings of the First International Conference on Progress in Cryptology
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STAR: An Efficient Coding Scheme for Correcting Triple Storage Node Failures
IEEE Transactions on Computers
A performance evaluation and examination of open-source erasure coding libraries for storage
FAST '09 Proccedings of the 7th conference on File and storage technologies
POTSHARDS—a secure, recoverable, long-term archival storage system
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Communications of the ACM - Amir Pnueli: Ahead of His Time
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FAST'11 Proceedings of the 9th USENIX conference on File and stroage technologies
Pond: the oceanstore prototype
FAST'03 Proceedings of the 2nd USENIX conference on File and storage technologies
Row-diagonal parity for double disk failure correction
FAST'04 Proceedings of the 3rd USENIX conference on File and storage technologies
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SOSP '11 Proceedings of the Twenty-Third ACM Symposium on Operating Systems Principles
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CLUSTER '11 Proceedings of the 2011 IEEE International Conference on Cluster Computing
Efficient software implementations of large finite fields GF(2n) for secure storage applications
ACM Transactions on Storage (TOS)
Rethinking erasure codes for cloud file systems: minimizing I/O for recovery and degraded reads
FAST'12 Proceedings of the 10th USENIX conference on File and Storage Technologies
NCCloud: applying network coding for the storage repair in a cloud-of-clouds
FAST'12 Proceedings of the 10th USENIX conference on File and Storage Technologies
IEEE Transactions on Information Theory
X-code: MDS array codes with optimal encoding
IEEE Transactions on Information Theory
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USENIX ATC'12 Proceedings of the 2012 USENIX conference on Annual Technical Conference
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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.