A hyperchaotic image encryption paradigm fusing DNA sequence operations with bit-level multi-stage dynamic scrambling

Abstract

Recently, the increasing severity of data breaches has made the security of digital images, as high-capacity visual information carriers, a critical concern. While chaotic maps are widely applied in image encryption due to their high nonlinearity and sensitivity, many existing schemes suffer from degraded chaotic properties or an over-reliance on a single protection mechanism. To address these shortcomings, this paper presents a novel and robust image encryption scheme that synergistically fuses a high-dimensional non-degenerate hyperchaotic map with multi-stage dynamic scrambling and DNA sequence operations. The core of our cryptographic construction is a Lorenz system that changes parameters, where parameters \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma$$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho$$\end{document}, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta$$\end{document} are dynamically modified based on the state trajectory of the system and plaintext information, inducing non-stationary chaos and significantly improving resistance to phase-space reconstruction attacks. The encryption scheme is meticulously architected in four sequential stages: (1) bit-level permutation using a hyperchaotic sequence, (2) DNA encoding with rule selection governed by a second chaotic sequence, (3) a confusion layer employing a DNA-based XOR operation with a key-derived nucleotide stream, and (4) a final confusion layer via chaotic bit masking. We formally prove the perfect reconstructability of the scheme and demonstrate through security analysis that the key space exceeds (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$>2^{456}$$\end{document}, rendering brute-force attacks computationally infeasible. Furthermore, we provide formal proofs for the system’s high sensitivity to both the encryption key and plaintext, achieving near-ideal values for the Number of Changing Pixel Rate (NPCR > 99.61%) and the Unified Average Changing Intensity (UACI \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\approx$$\end{document} 33.46%). Empirical validation on standard test images confirms the algorithm’s effectiveness, exhibiting uniform histogram distribution, near-maximum information entropy (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\approx$$\end{document}7.997), and negligible correlation coefficients between adjacent pixels (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|r_{xy}| < 0.01$$\end{document}). The proposed scheme offers a cryptographically strong framework for secure digital image communication.