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Where octagonal geometry meets chaos: A new S-Box for advanced cryptographic systems.

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This study introduces a novel Substitution Box (S-Box) design using octagonal geometry and chaotic dynamics for enhanced cryptographic security. The new S-Box offers improved resilience against cryptanalytic threats.

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Area of Science:

  • Cryptography
  • Applied Mathematics
  • Computer Science

Background:

  • Substitution Boxes (S-Boxes) are crucial components in modern cryptographic systems.
  • Existing S-Box designs face challenges in maintaining robust security against advanced cryptanalytic attacks.

Purpose of the Study:

  • To introduce a novel S-Box design integrating octagonal geometry and chaotic dynamics.
  • To enhance the security features and resilience of cryptographic systems.

Main Methods:

  • Leveraging octagonal geometric properties for confusion within a matrix.
  • Employing chaotic map unpredictability for S-Box construction.
  • Implementing circular shifts and wrap-around operations on boundary numbers.

Main Results:

  • The proposed S-Box demonstrates strong non-linearity (105.625) and low differential probability (0.0391).
  • Security analyses confirm the S-Box's robustness against various cryptanalytic threats.
  • The design effectively utilizes octagonal properties for confusion and chaotic dynamics for unpredictability.

Conclusions:

  • The novel octagonal-chaotic S-Box offers significant improvements in security.
  • The design provides inherent robustness and resilience against cryptanalytic attacks.
  • This approach presents a promising direction for developing next-generation secure cryptographic systems.