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Mastrovito multiplier for all trinomials

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2 Author(s)
Sunar, B. ; Dept. of Electr. & Comput. Eng., Oregon State Univ., Corvallis, OR, USA ; Koc, C.K.

An efficient algorithm for the multiplication in GF(2m) was introduced by Mastrovito. The space complexity of the Mastrovito multiplier for the irreducible trinomial xm+x+1 was given as m2-1 XOR and m2 AND gales. 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 xm+xn+1, where m≠2n, also requires m2-1 XOR and m2 AND gates, However, m2-xm/2 XOR gates are sufficient when the generating trinomial is of the form xm+xm/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 x7+x4+1 and x6+x3+1

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Computers, IEEE Transactions on  (Volume:48 ,  Issue: 5 )