Design of Highly Nonlinear Substitution Boxes Based on I-Ching Operators

Area of Science:

• Cryptography
• Information Security
• Number Theory

Background:

• Substitution boxes (S-Boxes) are crucial components in modern symmetric-key cryptography.
• Designing secure and efficient S-Boxes is an ongoing challenge in cryptosystem development.
• Traditional methods for S-Box generation can be complex and may suffer from vulnerabilities.

Purpose of the Study:

• To propose a novel method for designing S-Boxes using innovative I-Ching operators (ICOs).
• To analyze the properties of these ICOs, including identity, compositionality, and periodicity.
• To demonstrate the effectiveness of ICO-based S-Boxes in cryptographic applications.

Main Methods:

• Developed three I-Ching operators (intrication, turnover, mutual) for S-Box generation.
• Applied operators to modify output positions of Boolean functions, ensuring bijection property.
• Constructed a new network based on the periodicity property of ICOs for S-Box design.
• Evaluated S-Boxes using criteria like nonlinearity, strict avalanche criterion, differential, and linear approximation probabilities.

Main Results:

• The proposed ICOs automatically satisfy the bijection property, avoiding singular values.
• S-Boxes designed using ICOs exhibit enhanced security and performance.
• Comparative analysis shows superior results against other existing S-Box design schemes.
• The ICO-based approach demonstrates potential for broader applications in similar design problems.

Conclusions:

• The I-Ching operator-based approach provides a robust and efficient method for designing high-performance S-Boxes.
• This novel technique offers improved security features crucial for modern cryptographic systems.
• The methodology is adaptable, suggesting potential for wider use in related computational problems.