An image encryption scheme based on new hyperchaos and encrypted kinoform

Abstract

This paper presents a new hyperchaotic system with excellent chaotic properties and a secure method for generating encrypted kinoforms. Based on these two techniques, a novel image encryption scheme is introduced. First, a two-dimensional (2D) hyperchaotic map, called 2D-SCM, is proposed, which combines the Sine map and the Cubic map. The chaotic properties of the system are evaluated through bifurcation diagrams, Lyapunov exponent spectra, phase diagrams, etc. The results indicate that the system exhibits excellent ergodicity and a broad range of hyperchaotic behavior. Second, to enhance the security and reduce the number of iterations, a method for fabricating encrypted kinoforms in the 2D non-separable linear canonical transform domain by use of the improved Fienup Gerchberg-Saxton algorithm is designed. Finally, an image encryption scheme is developed that combines the 2D-SCM hyperchaotic map with encrypted kinoform techniques. During the encryption process, the plaintext image is first shuffled using a 2D-SCM-based scrambling algorithm. The scrambled image is then used to generate the encrypted kinoform, which is subsequently decomposed into bit-planes and subjected to 2D-SCM-based cyclic shifts and XOR operations to obtain the final ciphertext. Experimental results demonstrate that the proposed image encryption scheme achieves a key space of 10¹⁸⁰, significantly exceeding those of traditional hyperchaos-based and holography-based methods. It also exhibits superior performance in local Shannon entropy tests compared to state-of-the-art algorithms, indicating enhanced randomness in the encrypted images. Furthermore, when the mean-squared error threshold is set to 10⁻³, the scheme offers greater encryption efficiency than the referenced methods, while maintaining reconstructed image quality above 30 dB, ensuring visual acceptability. These attributes contribute to the scheme's robust resistance against statistical, differential, and brute-force attacks.