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Table 3 Construction parameters of the composite fields \(\mathbb {F}_{(2^8)^2}\)

From: A circuit area optimization of MK-3 S-box

Composite field

The structure of the composite field

\(\mathbb {F}_{2^4}\)

\(\mathbb {F}_{2}[x]/x^{4} + x^{3} + x^{2} + x + 1\)

\(\mathbb {F}_{(2^4)^2}\)

\(\mathbb {F}_{2^4}[x]/x^{2} + 0001x +0010\)