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A highly nonlinear substitution-box (S-box) design using action of modular group on a projective line over a finite field

Author

Listed:
  • Nasir Siddiqui
  • Fahim Yousaf
  • Fiza Murtaza
  • Muhammad Ehatisham-ul-Haq
  • M Usman Ashraf
  • Ahmed M Alghamdi
  • Ahmed S Alfakeeh

Abstract

Cryptography is commonly used to secure communication and data transmission over insecure networks through the use of cryptosystems. A cryptosystem is a set of cryptographic algorithms offering security facilities for maintaining more cover-ups. A substitution-box (S-box) is the lone component in a cryptosystem that gives rise to a nonlinear mapping between inputs and outputs, thus providing confusion in data. An S-box that possesses high nonlinearity and low linear and differential probability is considered cryptographically secure. In this study, a new technique is presented to construct cryptographically strong 8×8 S-boxes by applying an adjacency matrix on the Galois field GF(28). The adjacency matrix is obtained corresponding to the coset diagram for the action of modular group PSL(2,Z) on a projective line PL(F7) over a finite field F7. The strength of the proposed S-boxes is examined by common S-box tests, which validate their cryptographic strength. Moreover, we use the majority logic criterion to establish an image encryption application for the proposed S-boxes. The encryption results reveal the robustness and effectiveness of the proposed S-box design in image encryption applications.

Suggested Citation

  • Nasir Siddiqui & Fahim Yousaf & Fiza Murtaza & Muhammad Ehatisham-ul-Haq & M Usman Ashraf & Ahmed M Alghamdi & Ahmed S Alfakeeh, 2020. "A highly nonlinear substitution-box (S-box) design using action of modular group on a projective line over a finite field," PLOS ONE, Public Library of Science, vol. 15(11), pages 1-16, November.
  • Handle: RePEc:plo:pone00:0241890
    DOI: 10.1371/journal.pone.0241890
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    References listed on IDEAS

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    1. Xinsheng Li & Taiyong Li & Jiang Wu & Zhilong Xie & Jiayi Shi, 2019. "Joint image compression and encryption based on sparse Bayesian learning and bit-level 3D Arnold cat maps," PLOS ONE, Public Library of Science, vol. 14(11), pages 1-29, November.
    2. Silva-García, V.M. & Flores-Carapia, R. & Rentería-Márquez, C. & Luna-Benoso, B. & Aldape-Pérez, M., 2018. "Substitution box generation using Chaos: An image encryption application," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 123-135.
    3. Farwa, Shabieh & Muhammad, Nazeer & Bibi, Nargis & Haider, Sajjad A. & Naqvi, Syed R. & Anjum, Sheraz, 2018. "Fresnelet approach for image encryption in the algebraic frame," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 343-355.
    4. Xiangjun Wu & Yang Li & Jürgen Kurths, 2015. "A New Color Image Encryption Scheme Using CML and a Fractional-Order Chaotic System," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-28, March.
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