A Novel Hybrid Chaotic Map and Cryptographic Hash Whitening for Optimized S-Box Design: Construction, Cryptanalysis,...

Area of Science:

• Cryptography
• Applied Mathematics
• Computer Science

Background:

• S-boxes are crucial components in symmetric-key cryptography.
• Existing S-box construction methods face challenges in achieving high nonlinearity and resistance to attacks.
• Chaotic systems offer potential for generating complex, unpredictable sequences suitable for cryptographic applications.

Purpose of the Study:

• To propose a novel method for constructing high-quality S-boxes.
• To leverage delayed nonlinear chaotic systems and a hybrid hash whitening mechanism.
• To evaluate the cryptographic strength of the generated S-boxes.

Main Methods:

• Construction of S-boxes using delayed nonlinear chaotic systems.
• Application of Fisher-Yates permutation to chaotic sequences.
• Enhancement of S-boxes with affine transformations over GF(2).
• Integration of a hybrid hash whitening mechanism.

Main Results:

• Generated S-boxes exhibit strong nonlinear dynamical behavior, evidenced by a positive Lyapunov exponent and uniform statistical distribution.
• Optimized 8-bit → 8-bit S-boxes were achieved.
• Comprehensive cryptographic analysis (nonlinearity, differential uniformity, avalanche effect, etc.) confirmed strong resistance to linear and differential attacks.
• Image encryption demonstrated effective confusion properties.

Conclusions:

• The hybrid approach successfully generates high-quality S-boxes.
• The proposed S-boxes are suitable for symmetric cryptography.
• The method offers a robust alternative for secure S-box construction.