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Authors: Prateek Saxena 1 ; Vinay B. Y. Kumar 1 ; Dilawar Singh 1 ; H Narayanan 2 and Sachin B. Patkar 1

Affiliations: 1 Indian Institute of Technology Bombay, India ; 2 Indian Institute of Technology and Bombay, India

ISBN: 978-989-8565-43-3

Keyword(s): Galois Field Matrix Computations and Linear Equation Solvers, GF(2), Block Gaussian Elimination with Pivoting over GF(2), Hardware/Software Co-design, Custom Processor Extensions.

Related Ontology Subjects/Areas/Topics: Embedded Communications Systems ; Telecommunications ; VLSI Design and Implementation

Abstract: Solving a System of Linear Equations over Finite Fields finds one of the most important practical applications, for instance, in problems arising in cryptanalysis and network coding among others. However, other than software-only approaches to acceleration, the amount of focus particularly towards hardware or hardware/software based solutions is small, in comparison to that towards general linear equation solvers. We present scalable architectures for Gaussian elimination with pivoting over GF(2) and higher fields, both as custom extensions to commodity processors or as dedicated hardware for larger problems. In particular, we present: 1) Designs of components---Matrix Multiplication and `Basis search and Inversion'---for Gaussian elimination over GF(2), prototyped as custom instruction extensions to Nios-II on DE2-70(DE2, 2008), which even with a 50MHz clock perform at $\approx$30~GOPS (billion GF(2) operations); and also report results for GF($2^8$) or higher order matrix multipli cation with about 20~GOPS performance at 200MBps. 2) A scalable extension of a previous design [Bogdanov et. al, 2006] for multiple FPGAs and with $\approx$2.5 TrillionOPS performance at ~5GBps bandwidth on a Virtex-5 FPGA (More)

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Paper citation in several formats:
Saxena, P.; B. Y. Kumar, V.; Singh, D.; Narayanan, H. and B. Patkar, S. (2013). Hardware-software Scalable Architectures for Gaussian Elimination over GF(2) and Higher Galois Fields.In Proceedings of the 3rd International Conference on Pervasive Embedded Computing and Communication Systems - Volume 1: PECCS, ISBN 978-989-8565-43-3, pages 195-201. DOI: 10.5220/0004313201950201

@conference{peccs13,
author={Prateek Saxena. and Vinay B. Y. Kumar. and Dilawar Singh. and H Narayanan. and Sachin B. Patkar.},
title={Hardware-software Scalable Architectures for Gaussian Elimination over GF(2) and Higher Galois Fields},
booktitle={Proceedings of the 3rd International Conference on Pervasive Embedded Computing and Communication Systems - Volume 1: PECCS,},
year={2013},
pages={195-201},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004313201950201},
isbn={978-989-8565-43-3},
}

TY - CONF

JO - Proceedings of the 3rd International Conference on Pervasive Embedded Computing and Communication Systems - Volume 1: PECCS,
TI - Hardware-software Scalable Architectures for Gaussian Elimination over GF(2) and Higher Galois Fields
SN - 978-989-8565-43-3
AU - Saxena, P.
AU - B. Y. Kumar, V.
AU - Singh, D.
AU - Narayanan, H.
AU - B. Patkar, S.
PY - 2013
SP - 195
EP - 201
DO - 10.5220/0004313201950201

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