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Mastrovito Multiplier for General Irreducible Polynomials

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Book cover Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1719))

Abstract

We present a new formulation of the Mastrovito multiplication matrix and an architecture for the multiplication operation in the field GF(2m) generated by an arbitrary irreducible polynomial.We study in detail several specific types of irreducible polynomials, e.g., trinomials, all-one-polynomials, and equally-spaced-polynomials, and obtain the time and space complexity of these designs. Particular examples, illustrating the properties of the proposed architecture, are also given. The complexity results established in this paper match the best complexity results known to date. The most important new result is the space complexity of the Mastrovito multiplier for an equally-spaced-polynomial, which is found as (m2 - Δ) XOR gates and m2 AND gates, where Δ is the spacing factor.

This research is supported in part by Secured Information Technology, Inc.

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References

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Author information

Authors and Affiliations

  1. i2 Technologies, 565 Technology Square, 9th Floor, Cambridge, MA, 02139, USA

    A. Halbutoğullari

  2. Electrical & Computer Engineering, Oregon State University, Corvallis, OR, 97331, USA

    Ç. K. Koç

Authors
  1. A. Halbutoğullari
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  2. Ç. K. Koç
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering, University of Hawaii, 2540 Dole St., # 483, Honolulu, HI, 96822, USA

    Marc Fossorier  & Shu Lin  & 

  2. Institute of Industrial Science, University of Tokyo, 7-22-1, Roppongi, Minato-ku, Tokyo, 106, Japan

    Hideki Imai

  3. AAECC/IRIT, Université Paul Sabatier, 118, Route de Narbonne, F31067, Toulouse, Cedex, France

    Alain Poli

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© 1999 Springer-Verlag Berlin Heidelberg

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Halbutoğullari, A., Koç, Ç.K. (1999). Mastrovito Multiplier for General Irreducible Polynomials. In: Fossorier, M., Imai, H., Lin, S., Poli, A. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1999. Lecture Notes in Computer Science, vol 1719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46796-3_48

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  • DOI: https://doi.org/10.1007/3-540-46796-3_48

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66723-0

  • Online ISBN: 978-3-540-46796-0

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