Neural Computing and Applications

, Volume 31, Issue 11, pp 7201–7210 | Cite as

A novel efficient substitution-box design based on firefly algorithm and discrete chaotic map

  • Hussam A. AhmedEmail author
  • Mohamad Fadli Zolkipli
  • Musheer Ahmad
Original Article


Substitution boxes are essential nonlinear components responsible to impart strong confusion and security in most of modern symmetric ciphers. Constructing efficient S-boxes has been a prominent topic of interest for security experts. With an aim to construct cryptographically efficient S-box, a novel scheme based on firefly (FA) optimization and chaotic map is proposed in this paper. The anticipated approach generates initial S-box using chaotic map. The meta-heuristic FA is applied to find notable configuration of S-box that satisfies the criterions by guided search for near-optimal features by minimizing fitness function. The performance of proposed approach is assessed through well-established criterions such as bijectivity, nonlinearity, strict avalanche criteria, bit independence criteria, differential uniformity, and linear approximation probability. The obtained experimental results are compared with some recently investigated S-boxes to demonstrate that the proposed scheme has better proficiency of constructing efficient S-boxes.


Substitution box Firefly algorithm Discrete chaotic map Symmetric ciphers 


Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interests.


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Copyright information

© The Natural Computing Applications Forum 2018

Authors and Affiliations

  • Hussam A. Ahmed
    • 1
    Email author
  • Mohamad Fadli Zolkipli
    • 1
  • Musheer Ahmad
    • 2
  1. 1.Faculty of Computer System and Software EngineeringUniversiti Malaysia PahangKuantanMalaysia
  2. 2.Department of Computer EngineeringJamia Millia IslamiaNew DelhiIndia

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