Simulation of Image Encryption Scheme for Secure Data Transmission Based on Logistic Map

Abstract

This paper proposes an image encryption scheme based on a logistic map for secure data transmission. The logistic map offers unique properties, including sensitivity to initial conditions, system parameters, and pseudo-randomness, making them ideal for secure encryption. Hence, the parameter ranges causing the chaotic behaviour are determined, and the logistic map solution sequences are appropriately generated. The encryption process requires pixel permutation, key generation using chaotic sequences, and applying XOR operations to the encrypted pixels in binary. Two sets of images are studied to illustrate the encryption scheme. The encryption performance is evaluated through histogram uniformity, entropy analysis, correlation coefficient evaluation, and encryption speed across various image datasets. The simulation results showed strong encryption capabilities, effectively masked original image content and reduced correlations among adjacent pixels. The encrypted image entropy value approaches the ideal value of eight, indicating high randomness and security. Thus, the logistic map is proven speed-efficient, achieving faster encryption times with minimal impact on security and being suitable for real-time applications. In conclusion, a logistic map is a practical tool for creating secure image encryption schemes due to its unpredictability and adaptability.