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 arewidely applied in image encryption due to their high nonlinearity and sensitivity, many existingschemes suffer from degraded chaotic properties or an over-reliance on a single protectionmechanism. To address these shortcomings, this paper presents a novel and robust image encryptionparadigm that synergistically fuses a high-dimensional non-degenerate hyperchaoticmap with multi-stage dynamic scrambling and DNA sequence operations. The core of ourcryptographic construction is a parameter-hopping Lorenz system, where the parameters σ, ρ,and β are dynamically altered based on the system’s state trajectory and plaintext information,inducing non-stationary chaos and significantly enhancing resistance against phase-space reconstructionattacks. The encryption algorithm is meticulously architected in four sequentialstages: (1) bit-level permutation using a hyperchaotic sequence, (2) DNA encoding with ruleselection governed by a second chaotic sequence, (3) a confusion layer employing a DNAbasedXOR operation with a key-derived nucleotide stream, and (4) a final diffusion layer viachaotic bit masking. We formally prove the scheme’s perfect reconstructibility and demonstratethrough security analysis that the key space exceeds 2^30192, rendering brute-force attackscomputationally infeasible. Furthermore, we provide formal proofs for the system’s high sensitivityto both the encryption key and plaintext, achieving near-ideal values for the Numberof Changing Pixel Rate (NPCR > 99.61%) and Unified Average Changing Intensity (UACI ≈33.46%). Empirical validation on standard test images confirms the algorithm’s effectiveness,exhibiting uniform histogram distribution, near-maximum information entropy (≈7.997), andnegligible correlation coefficients between adjacent pixels (|rxy|<0.01). The proposed schemeoffers a cryptographically strong framework for secure digital image communication.