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Chaos Meets Cryptography: Developing an S-Box Design with the Rössler Attractor

Author

Listed:
  • Erendira Corona-Bermúdez

    (Centro de Investigación en Computación del Instituto Politécnico Nacional, Ciudad de Mexico 07738, Mexico)

  • Juan Carlos Chimal-Eguía

    (Centro de Investigación en Computación del Instituto Politécnico Nacional, Ciudad de Mexico 07738, Mexico)

  • Uriel Corona-Bermúdez

    (Centro de Investigación en Computación del Instituto Politécnico Nacional, Ciudad de Mexico 07738, Mexico)

  • Mario Eduardo Rivero-Ángeles

    (Centro de Investigación en Computación del Instituto Politécnico Nacional, Ciudad de Mexico 07738, Mexico)

Abstract

The volume of data transmitted over networks has significantly increased in recent years. For that reason, safeguarding the privacy, authenticity, and confidentiality of specific data is imperative, necessitating a type of encryption; symmetric encryption, known for its computational efficiency, is ideal for securing extensive datasets. A principal component within symmetric key algorithms is the substitution box (S-box), which creates confusion between plaintext and ciphertext, enhancing the security of the process. This paper proposes a fashion method to create chaotic S-boxes using the Rössler attractor as a chaotic process and the Rijndael S-box as a permutation box. The proposed S-boxes are evaluated with bijectivity, non-linearity (NL), strict avalanche criterion (SAC), bit independence criterion (BIC), linear approximation probability (LAP), and differential uniformity (DU). The analyses show that the proposed method helps generate a high-resistance S-box to well-known attacks and high efficiency, executing in short computational time.

Suggested Citation

  • Erendira Corona-Bermúdez & Juan Carlos Chimal-Eguía & Uriel Corona-Bermúdez & Mario Eduardo Rivero-Ángeles, 2023. "Chaos Meets Cryptography: Developing an S-Box Design with the Rössler Attractor," Mathematics, MDPI, vol. 11(22), pages 1-16, November.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4575-:d:1276200
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    References listed on IDEAS

    as
    1. B. B. Cassal-Quiroga & E. Campos-Cantón, 2020. "Generation of Dynamical S-Boxes for Block Ciphers via Extended Logistic Map," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-12, March.
    2. Liu, Lingfeng & Wang, Jie, 2023. "A cluster of 1D quadratic chaotic map and its applications in image encryption," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 89-114.
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