[Paper Review] Colored Image Encryption and Decryption Using Chaotic Lorenz System and DCT2

Mohammed Alsaedi|arXiv (Cornell University)|Jan 11, 2017

Chaos-based Image/Signal Encryption4 citations

TL;DR

This paper proposes a secure colored image encryption scheme combining the chaotic Lorenz system for key generation and 2D Discrete Cosine Transform (DCT2) for energy compaction. By exploiting the deterministic chaos for key synchronization and concentrating energy in low-frequency DCT coefficients, the method applies three distinct keys with shift parameters to scramble high-energy components, achieving strong correlation reduction and high security, validated through statistical analysis and simulation results.

ABSTRACT

In this paper, a scheme for the encryption and decryption of colored images by using the Lorenz system and the discrete cosine transform in two dimensions (DCT2) is proposed. Although chaos is random, it has deterministic features that can be used for encryption; further, the same sequences can be produced at the transmitter and receiver under the same initial conditions. Another property of DCT2 is that the energy is concentrated in some elements of the coefficients. These two properties are used to efficiently encrypt and recover the image at the receiver by using three different keys with three different predefined number of shifts for each instance of key usage. Simulation results and statistical analysis show that the scheme high performance in weakening the correlation between the pixels of the image that resulted from the inverse of highest energy values of DCT2 that form 99.9 % of the energy as well as those of the difference image.

Motivation & Objective

• To develop a robust image encryption method that resists statistical attacks by reducing pixel correlation in colored images.
• To leverage the deterministic yet unpredictable nature of the Lorenz chaotic system for synchronized key generation at transmitter and receiver.
• To utilize the energy compaction property of DCT2 to target and modify the most significant coefficients for efficient and secure encryption.
• To introduce a multi-key mechanism with configurable shift parameters to enhance security and key sensitivity.
• To evaluate the scheme’s performance through statistical analysis and simulation, focusing on correlation, entropy, and difference image metrics.

Proposed method

• The Lorenz system generates chaotic sequences used as pseudo-random keys, ensuring identical key streams at both encryption and decryption ends under the same initial conditions.
• Color images are divided into R, G, and B color channels, each processed independently using the DCT2 transform to convert spatial domain data into frequency domain coefficients.
• The DCT2 coefficients are reordered based on energy concentration, with the highest-energy components (accounting for 99.9% of total energy) targeted for modification.
• Three distinct keys are applied with different shift parameters to the high-energy DCT coefficients, introducing non-linear scrambling based on chaotic sequences.
• The inverse DCT2 is applied to the modified coefficients to reconstruct the encrypted image in the spatial domain.
• Decryption reverses the process using the same keys and initial conditions, restoring the original image through inverse DCT2 and key synchronization.

Experimental results

Research questions

• RQ1 Can the chaotic Lorenz system effectively generate synchronized, secure keys for image encryption and decryption?
• RQ2 To what extent does DCT2-based energy compaction enhance the security of encrypted color images?
• RQ3 How effective is the multi-key, multi-shift approach in reducing pixel correlation and improving resistance to statistical attacks?
• RQ4 What is the impact of modifying only the highest-energy DCT coefficients on image quality and security?
• RQ5 How do the statistical properties of the encrypted image and difference image compare to those of the original?

Key findings

• The proposed scheme significantly weakens the correlation between adjacent pixels in the encrypted image, particularly by inverting the highest-energy DCT2 coefficients.
• The difference image between the original and encrypted image shows low correlation, indicating strong resistance to differential attacks.
• The energy compaction property of DCT2 successfully concentrates 99.9% of the image energy in a small subset of coefficients, enabling efficient targeting for encryption.
• The use of three distinct keys with different shift parameters enhances key sensitivity and increases the effective key space, improving security.
• Statistical analysis confirms high entropy and uniform distribution in the encrypted image, indicating strong randomness and resistance to cryptanalysis.
• Simulation results demonstrate that the method achieves high performance in both encryption and decryption with minimal distortion and high fidelity recovery.