An optimized substitution box generator based on cubic pell curves and its application in image encryption.

Area of Science:

• Cryptography
• Number Theory
• Computer Science

Background:

• Data security is paramount in the digital age.
• Substitution boxes (S-boxes) are crucial for cryptographic data transformations.
• Designing S-boxes with high nonlinearity and efficiency remains a challenge.

Purpose of the Study:

• Propose a novel S-box generator utilizing cubic Pell curves.
• Enhance data security through advanced S-box design.
• Improve nonlinearity and computational efficiency of S-boxes.

Main Methods:

• Developed a new S-box generator based on cubic Pell curves.
• Employed randomness of points on cubic Pell curves via binary strings.
• Optimized S-boxes using swapping operations to ensure high nonlinearity.

Main Results:

• Achieved optimal nonlinearity (NL) of 108 for the generated S-boxes.
• Demonstrated superior speed and security compared to existing methods.
• S-boxes passed NIST randomness tests and showed robustness in image encryption.

Conclusions:

• The proposed cubic Pell curve-based S-box generator offers significant cryptographic strength.
• The method provides an effective approach to designing highly nonlinear and efficient S-boxes.
• The generated S-boxes are robust against statistical attacks, validating their cryptographic applications.