<p><b>Abstract</b>—We present a new formulation of the Mastrovito multiplication matrix for the field <tmath>$GF(2^m)$</tmath> 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 <tmath>$(m^2 - \Delta)$</tmath> XOR gates and <tmath>$m^2$</tmath> AND gates, where <tmath>$\Delta$</tmath> is the spacing factor.</p>