Security Analysis of the Image Encryption Algorithm Based on a Two-Dimensional Infinite Collapse Map

Area of Science:

• Cryptography
• Image Processing
• Applied Mathematics

Background:

• Image encryption algorithms are crucial for secure data transmission.
• The two-dimensional (2D) infinite collapse map is a complex system used in some encryption methods.
• Permutation-diffusion structures are common in modern cryptosystems for enhanced security.

Purpose of the Study:

• To analyze the security weaknesses of an image encryption algorithm utilizing a 2D infinite collapse map.
• To investigate the effectiveness of cryptanalysis on single-round, two-round, and multi-round encryption processes.
• To propose improvements for the analyzed encryption algorithm.

Main Methods:

• Cryptanalysis of the permutation-diffusion structure.
• Mathematical deduction and simplification of encryption/decryption equations.
• Analysis of equivalent keys due to plaintext/ciphertext-independent chaotic sequences.
• Numerical simulations using MATLAB for validation.

Main Results:

• The diffusion process can be merged with the initial permutation, simplifying the structure.
• Equivalent keys were identified, compromising the algorithm's security.
• The algorithm, even with multiple rounds, was successfully cracked.
• Data complexity of the cryptanalysis attacks was evaluated.

Conclusions:

• The analyzed 2D infinite collapse map image encryption algorithm possesses significant security flaws.
• The identified vulnerabilities allow for effective cryptanalysis, even in multi-round configurations.
• The study provides a foundation for developing more robust image encryption techniques.