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

Guanwen Shi¹, Simin Yu¹, Qianxue Wang¹

¹College of Automation, Guangdong University of Technology, Guangzhou 510006, China.

Entropy (Basel, Switzerland)

|July 27, 2022

Summary

This summary is machine-generated.

This study reveals security vulnerabilities in a 2D infinite collapse map image encryption algorithm. Cryptanalysis demonstrates that the permutation-diffusion structure can be simplified, leading to effective attacks on multi-round versions.

Keywords:

2D infinite collapse map chaotic image encryption cryptanalysis equivalent key

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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.