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

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.