International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2572

Full Length Research Paper

Statistical analysis of S-box in image encryption applications based on majority logic criterion

Tariq Shah1, Iqtadar Hussain1*, Muhammad Asif Gondal2 and Hasan Mahmood3
1Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan. 2Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Islamabad, Pakistan. 3Department of Electronics, Quaid-i-Azam University, Islamabad, Pakistan.
Email: [email protected]

  •  Accepted: 02 June 2011
  •  Published: 18 August 2011


The S-box is used in various block ciphers and the complexity of encryption essentially depends on the strength of S-box. The strength of an S-box can be measured by analyzing its statistical and algebraic properties. The S-box is the only non-linear component in various block ciphers capable of creating confusion. Many S-boxes have been proposed with similar algebraic and statistical properties. Therefore, it is sometimes difficult to choose an S-box for a particular application. The performances of these S-boxes vary and depend on the nature of data and their application. In this paper, we propose a criterion to analyze the prevailing S-boxes and study their strengths and weaknesses in order to determine their suitability in image encryption applications. The proposed criterion uses the results from correlation analysis, entropy analysis, contrast analysis, homogeneity analysis, energy analysis, and mean of absolute deviation analysis. These analyses are applied to advanced encryption standard (AES), affine-power-affine (APA), gray, Lui J, residue prime, S8 AES, SKIPJACK, and Xyi S-boxes. The results of these analyses are further examined and a majority logic criterion is used to determine the appropriateness of an S-box to image encryption applications.


Key words: S-box, advanced encryption standard (AES), affine-power-affine (APA), SKIPJACK, Lui. J, residue of prime, mean of absolute deviation analysis (MAD), differential/linear approximation probability, bit independence criterion, strict avalanche criterion.