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Mastrovito Multiplier for All Trinomials
May 1999 (vol. 48 no. 5)
pp. 522-527

Abstract—An efficient algorithm for the multiplication in $GF(2^m)$ was introduced by Mastrovito. The space complexity of the Mastrovito multiplier for the irreducible trinomial $x^m+x+1$ was given as $m^2-1$ XOR and $m^2$ AND gates. In this paper, we describe an architecture based on a new formulation of the multiplication matrix and show that the Mastrovito multiplier for the generating trinomial $x^m+x^n+1$, where $m \not=2n$, also requires $m^2-1$ XOR and $m^2$ AND gates. However, $m^2-m/2$ XOR gates are sufficient when the generating trinomial is of the form $x^m+x^{m/2}+1$ for an even $m$. We also calculate the time complexity of the proposed Mastrovito multiplier and give design examples for the irreducible trinomials $x^7+x^4+1$ and $x^6+x^3+1$.

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Index Terms:
Finite fields, multiplication, standard basis, irreducible trinomial.
B. Sunar, Ç.k. Koç, "Mastrovito Multiplier for All Trinomials," IEEE Transactions on Computers, vol. 48, no. 5, pp. 522-527, May 1999, doi:10.1109/12.769434
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