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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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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