A Novel Image Encryption Scheme Based on Two-Dimensional Chaotic Map Constructed from Ackley Function and DNA Operations

In contemporary communication systems, digital images occupy an irreplaceable role; however, the privacy-related risks attendant to their prevalent application have grown increasingly salient. This paper presents an image encryption scheme integrating a novel two-dimensional Ackley-Sine chaotic map (2D-ASM) with dynamic DNA operations. First, a two-dimensional Ackley-Sine chaotic map, constructed based on the Ackley function and sine function, is designed and validated through a series of chaotic indicators. Results demonstrate that 2D-ASM exhibits superior chaotic properties compared to several existing state-of-the-art chaotic maps, with its maximum Lyapunov exponent (LE) exceeding 23, Permutation Entropy (PE) close to 1 in the full parameter range, and correlation dimension (CD) significantly higher than comparative chaotic systems. The proposed 2D-ASM-based image encryption scheme leverages the SHA-256 hash value of the plaintext image and four external keys to jointly generate the initial conditions and parameters of the 2D-ASM chaotic system, thereby ensuring a sufficiently large key space of 2²⁵⁶. Subsequently, chaotic sequences generated by 2D-ASM are employed to permute and diffuse the plaintext image, followed by dynamic DNA coding, operations, and decoding to obtain the encrypted image. Security analyses and comparisons with several existing representative algorithms confirm that the proposed encryption scheme achieves excellent encryption performance: the Number of Pixels Change Rate (NPCR) is above 99.6%, the Unified Average Changing Intensity (UACI) approaches 33.4%, and the information entropy of ciphertext images reaches 7.999 or higher. The scheme can effectively resist various potential attacks, including statistical and differential attacks, and outperforms representative algorithms in pixel correlation reduction and anti-interference performance.