Computational and Applied Mathematics

, Volume 36, Issue 2, pp 843–857 | Cite as

Design of new \(4\times 4\) S-box from finite commutative chain rings

  • Tariq Shah
  • Saira Jahangir
  • Antonio Aparecido de Andrade


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.


S-box Finite chain ring Unit elements Subgroup of order 16 Majority logic criterion 

Mathematics Subject Classification

34H10 74H65 90B06 


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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2015

Authors and Affiliations

  • Tariq Shah
    • 1
  • Saira Jahangir
    • 1
  • Antonio Aparecido de Andrade
    • 2
  1. 1.Department of MathematicsQuaid-i-Azam UniversityIslamabadPakistan
  2. 2.Department of MathematicsSão Paulo State UniversitySão PauloBrazil

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