3D Research

, 8:26 | Cite as

A Novel Image Encryption Based on Algebraic S-box and Arnold Transform

  • Shabieh Farwa
  • Nazeer Muhammad
  • Tariq Shah
  • Sohail Ahmad
3DR Express


Recent study shows that substitution box (S-box) only cannot be reliably used in image encryption techniques. We, in this paper, propose a novel and secure image encryption scheme that utilizes the combined effect of an algebraic substitution box along with the scrambling effect of the Arnold transform. The underlying algorithm involves the application of S-box, which is the most imperative source to create confusion and diffusion in the data. The speciality of the proposed algorithm lies, firstly, in the high sensitivity of our S-box to the choice of the initial conditions which makes this S-box stronger than the chaos-based S-boxes as it saves computational labour by deploying a comparatively simple and direct approach based on the algebraic structure of the multiplicative cyclic group of the Galois field. Secondly the proposed method becomes more secure by considering a combination of S-box with certain number of iterations of the Arnold transform. The strength of the S-box is examined in terms of various performance indices such as nonlinearity, strict avalanche criterion, bit independence criterion, linear and differential approximation probabilities etc. We prove through the most significant techniques used for the statistical analyses of the encrypted image that our image encryption algorithm satisfies all the necessary criteria to be usefully and reliably implemented in image encryption applications.


S-box Galois field GF(28Primitive element Arnold transform Image encryption 


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Copyright information

© 3D Research Center, Kwangwoon University and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Shabieh Farwa
    • 1
  • Nazeer Muhammad
    • 1
  • Tariq Shah
    • 2
  • Sohail Ahmad
    • 1
  1. 1.Department of MathematicsCOMSATS Institute of Information TechnologyWah CanttPakistan
  2. 2.Department of MathematicsQuaid-i-Azam UniversityIslamabadPakistan

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