Leveraging Finite-Precision Errors in Chaotic Systems for Enhanced Image Encryption

Abstract

This research explores the application of chaotic systems in generating pseudo-random numbers for encryption protocols, offering a novel perspective on addressing the challenges posed by limited computer precision in cryptographic applications. Chaotic systems, while promising for encryption, often suffer from degradation in their chaotic properties when implemented on computers with finite precision. Previous studies have primarily aimed to mitigate this issue, with limited consideration of harnessing finite-precision errors as a potential source of randomness. In this study, we propose an innovative encryption method that leverages finite-precision errors within chaotic systems. The algorithm generates a keystream based on lower bound error and employs standard MATLAB routines to describe its main steps, including initialization and image factor addition, Chua’s circuit simulation, error sequence generation, normalization, reshaping of the normalized sequence, and the encryption process. Comprehensive performance evaluations were conducted using benchmark images, including Cameraman, Peppers, and Catherine, each with dimensions of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$256\times 256$ </tex-math></inline-formula> pixels. Evaluation criteria encompassed key space analysis, pixel correlation, entropy of information, histogram analysis, and resistance to noise attacks. The results highlight the effectiveness and security of the proposed method, showcasing its practical utility in real-world encryption scenarios. This research not only contributes a novel approach to encryption but also provides valuable insights into the potential of utilizing finite-precision errors to enhance randomness generation in chaotic systems for cryptographic applications.