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A combinatory approach of non-chain ring and henon map for image encryption application
Salman Mohi Ud Din1, Tariq Shah2, Fahad Alblehai3
1Department of Mathematics, Quaid-I-Azam University, Islamabad, Pakistan. salmanmohiuddin3938@gmail.com.
Scientific Reports
|January 13, 2025
Summary
This study introduces a novel image encryption algorithm using complex algebraic structures and the Henon map to improve security and key space. The method enhances data protection against attackers by employing advanced cryptographic techniques.
Area of Science:
- Cryptography
- Algebraic Structures
- Image Processing
Background:
- Algebraic structures are crucial for non-linear components in block ciphers, but can limit key spaces.
- Existing methods may have limitations in confusion and key space size.
Purpose of the Study:
- To enhance security and key space in encryption schemes.
- To develop a robust image encryption system using complex algebraic structures.
Main Methods:
- Utilized complex non-chain rings and the Henon map for a novel algorithm.
- Mapped unit elements from non-chain rings to Galois fields.
- Constructed a substitution box (S-box) from Galois fields for image encryption.
- Employed the Henon map for pixel mixing and XOR operations with a generated key.
Main Results:
- The algorithm demonstrated high effectiveness against potential attackers.
- Evaluated performance using histograms, SSIM, correlation analysis, and NIST tests.
- Analyzed S-box properties including SAC, BIC, LAP, and DAP.
Conclusions:
- The proposed algebraic approach provides a state-of-the-art image encryption system.
- The combination of complex algebraic structures and the Henon map enhances cryptographic robustness.
- The method offers improved security and a larger key space compared to traditional methods.
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