Abstract
Substitution boxes (S-boxes) are the fundamental mechanisms in symmetric key cryptosystems. These S-boxes guarantee that the cryptosystem is cryptographically secure and make them nonlinear. The S-boxes used in conventional and modern cryptography are mostly constructed over finite Galois field extensions of binary Field \(\mathbb {F}_{2}\). We have presented a novel construction scheme of S-boxes which is based on the elements of subgroups of multiplicative groups of units of the commutative finite chain rings of type \(\frac{\mathbb {F}_{2}[u]}{\langle u^{k}\rangle }\), where \(2\le k\le 8\). Majority logic criterion (MLC) is applied on the apprehended S-boxes owing to, checked their strength.
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Communicated by Antonio José Silva Neto.
This work was partially supported by Fapesp 2013/25977-7.
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Shah, T., Jahangir, S. & de Andrade, A.A. Design of new \(4\times 4\) S-box from finite commutative chain rings. Comp. Appl. Math. 36, 843–857 (2017). https://doi.org/10.1007/s40314-015-0265-9
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DOI: https://doi.org/10.1007/s40314-015-0265-9