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Cryptographers’ Track at the RSA Conference

CT-RSA 2003: Topics in Cryptology — CT-RSA 2003 pp 158–175Cite as

Efficient GF(p m) Arithmetic Architectures for Cryptographic Applications

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2612))

Abstract

Recently, there has been a lot of interest on cryptographic applications based on fields GF(p m), for p > 2. This contribution presents GF(p m) multipliers architectures, where p is odd. We present designs which trade area for performance based on the number of coefficients that the multiplier processes at one time. Families of irreducible polynomials are introduced to reduce the complexity of the modulo reduction operation and, thus, improved the efficiency of the multiplier. We, then, specialize to fields GF(3m) and provide the first cubing architecture presented in the literature. We synthesize our architectures for the special case of GF(397) on the XCV1000-8-FG1156 and XC2VP20-7-FF1156 FPGAs and provide area/performance numbers and comparisons to previous GF(3m) and GF(2m) implementations. Finally, we provide tables of irreducible polynomials over GF(3) of degree m with 2 ≤ m ≤ 255.

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Author information

Authors and Affiliations

  1. Politecnico di Milano, P.za L. Da Vinci 32, 20133, Milano, Italy

    Guido Bertoni

  2. Communication Security Group, Ruhr-Universität Bochum, 44780, Bochum, Germany

    Jorge Guajardo, Sandeep Kumar, Christof Paar & Thomas Wollinger

  3. General Dynamics Communication Systems, 77 A St., 02494, Needham, MA, USA

    Gerardo Orlando

Authors
  1. Guido Bertoni
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  2. Jorge Guajardo
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  3. Sandeep Kumar
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  4. Gerardo Orlando
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  5. Christof Paar
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  6. Thomas Wollinger
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Editor information

Editors and Affiliations

  1. Gemplus, Card Security Group, La Vigie, Avenue du Jujubier, ZI Athélia IV, 13705, La Ciotat Cedex, France

    Marc Joye

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Bertoni, G., Guajardo, J., Kumar, S., Orlando, G., Paar, C., Wollinger, T. (2003). Efficient GF(p m) Arithmetic Architectures for Cryptographic Applications. In: Joye, M. (eds) Topics in Cryptology — CT-RSA 2003. CT-RSA 2003. Lecture Notes in Computer Science, vol 2612. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36563-X_11

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  • DOI: https://doi.org/10.1007/3-540-36563-X_11

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00847-7

  • Online ISBN: 978-3-540-36563-1

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