A novel systematic byte substitution method to design strong bijective substitution box (S-box) using...

Area of Science:

• Cryptography
• Applied Mathematics
• Computer Science

Background:

• S-boxes are crucial nonlinear components in symmetric encryption algorithms, providing confusion and resistance against cryptanalysis.
• Existing chaos-based S-box designs often exhibit weaker cryptographic performance, particularly in differential probability, compared to algebraic methods.
• Ensuring high nonlinearity and diffusion is key to secure data encryption.

Purpose of the Study:

• To propose a novel 8x8 S-box design methodology utilizing chaos theory and randomization.
• To enhance the differential probability and overall cryptographic strength of S-boxes.
• To introduce a dispersion property within the S-box design loop for systematic dispersal of input data.

Main Methods:

• A piecewise linear chaotic map (PWLCM) was used to generate initial S-box positions.
• The dispersion property was integrated into the design loop for systematic dispersal of the input substituting sequence.
• The proposed S-box was analyzed using nonlinearity, strict avalanche criteria (SAC), bit independence criteria (BIC), differential probability, linear probability, and boomerang connectivity table (BCT).

Main Results:

• The proposed S-box demonstrates superior cryptographic properties, especially in differential probability, achieving an upper bound.
• Controlled randomization effectively altered the probability distribution statistics of S-box differentials, reducing output difference recurrences.
• The generated chaotic trajectories were tested for randomness using the NIST-800-22 test suite, confirming their cryptographic security.

Conclusions:

• The novel approach of integrating chaos and dispersion property within the S-box design loop yields a cryptographically strong S-box.
• The proposed S-box offers enhanced resistance against various cryptanalytic attacks, including differential and boomerang attacks.
• This systematic S-box design, leveraging chaotic mixing and dispersion, represents a significant advancement in secure cryptographic component design.