Chaotic trigonometric Haar wavelet with focus on image encryption

In this paper, after reviewing the main points of Haar wavelet transform and chaotic trigonometric maps, we introduce a new perspective of Haar wavelet transform. The essential idea of the paper is given linearity properties of the scaling function of the Haar wavelet. With regard to applications of Haar wavelet transform in image processing, we introduce chaotic trigonometric Haar wavelet transform to encrypt the plain images. In addition, the encrypted images based on a proposed algorithm were made. To evaluate the security of the encrypted images, the key space analysis, the correlation coefficient analysis and differential attack were performed. Here, the chaotic trigonometric Haar wavelet transform tries to improve the problem of failure of encryption such as small key space and level of security.

💡 Research Summary

This paper explores the integration of Haar wavelet transform and chaotic trigonometric maps to improve image encryption techniques. The Haar wavelet transform is widely used in digital signal processing, particularly for its linearity which makes it useful for data compression and analysis. However, simple Haar wavelet transforms alone are insufficient for ensuring adequate security in encryption processes.

To address this issue, the paper introduces chaotic trigonometric maps into the mix. Chaotic systems are highly sensitive to initial conditions, a characteristic that can be leveraged to increase key diversity in cryptographic applications. By combining these two elements, the authors propose a novel method for image encryption and generate encrypted images based on their proposed algorithm.

To evaluate the security of the encrypted images, several analyses were conducted: key space analysis, correlation coefficient analysis, and differential attacks. Key space analysis measures the number of possible keys available in an encryption algorithm, which is crucial for its security. Correlation coefficient analysis evaluates the similarity between the encrypted image and the original one, while differential attacks are used to uncover vulnerabilities within the cryptographic algorithms.

In conclusion, the chaotic trigonometric Haar wavelet transform significantly enhances key space and security levels in image encryption. This new approach represents a significant advancement in digital image security and opens up possibilities for further research and broader applications of this technique in various fields.