Composite field GF(((22)2)2) Advanced Encryption Standard (AES) S-box with algebraic normal form representation in the subfield inversion

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Composite field GF(((22)2)2) Advanced Encryption Standard (AES) S-box with algebraic normal form representation in the subfield inversion

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In this study, the authors categorise all of the feasible constructions for the composite Galois field GF(((22)2)2) Advanced Encryption Standard (AES) S-box into four main architectures by their field representations and their algebraic properties. For each of the categories, a new optimisation scheme which exploits algebraic normal form representation followed by a sub-structure sharing optimisation is presented. This is performed by converting the subfield GF((22)2) inversion into several logical expressions, which will be in turn reduced using a common sub-expression elimination algorithm. The authors show that this technique can effectively reduce the total area gate count as well as the critical path gate count in composite field AES S-boxes. The resulting architecture that achieves maximum reduction in both total area coverage and critical path gate count is found and reported. The hardware implementations of the authors proposed AES S-boxes, along with their performance and cost are presented and discussed.

Inspec keywords: cryptography; optimisation; algebra

Other keywords: sub-expression elimination algorithm; Galois field; GF(((22)2)2) advanced encryption standard; path gate count; sub-structure sharing optimisation; AES S-box; area gate count; algebraic normal form representation

Subjects: Algebra; Optimisation techniques; Algebra; Cryptography; Data security; Optimisation techniques

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