A novel one-dimensional chaotic map generator and its application in a new index representation-based image encryption scheme

Chaotification of 1D Maps by Multiple Remainder Operator Additions—Application to B-Spline Curve Encryption

In this work, a chaotification technique is proposed for increasing the complexity of chaotic maps. The technique consists of adding the remainder of multiple scalings of the map’s value for the next iteration, so that the most- and least-significant digits are combined. By appropriate parameter tuning, the resulting map can achieve a higher Lyapunov exponent value, a result that was first proven theoretically and then showcased through numerical simulations for a collection of chaotic maps. As a proposed application of the transformed maps, the encryption of B-spline curves and patches was considered. The symmetric encryption consisted of two steps: a shuffling of the control point coordinates and an additive modulation. A transformed chaotic map was utilised to perform both steps. The resulting ciphertext curves and patches were visually unrecognisable compared to the plaintext ones and performed well on several statistical tests. The proposed work gives an insight into the potential of the remainder operator for chaotification, as well as the chaos-based encryption of curves and computer graphics.

CIE-LSCP: color image encryption scheme based on the lifting scheme and cross-component permutation

Encryption of meaningful images into unidentifiable noise-like images can improve the security of images during storage and transmission. In this paper, a novel color image encryption method based on the lifting scheme and cross-component permutation (CIE-LSCP) is introduced. First, original image is divided into red, green and blue components, and then the three components are processed by a preprocessing strategy based on the lifting scheme (PSLS) to change the statistical distribution of the pixels. Second, a block-based cross-component permutation based on index vectors (BCPIV) is presented to divide three preprocessed components into blocks and perform the cross-component permutation operation on them, and three random matrices are utilized to determine the target component, target block and target pixel position of the current pixel to be moved, respectively. Subsequently, a multi stochastic diffusion based on random sequences (MSDRS) is developed to alter the pixel values of the permutated components, and finally a ciphertext image is gotten by merging the three components. Moreover, the SHA256 hash values of the plaintext image are used to obtain the initial parameters of the chaotic system, and the obtained chaotic sequences are applied in the image encryption process. Wherein the generated random sequences are highly reliant on the plaintext image, making the encryption scheme resistant to both known-plaintext attacks and chosen-plaintext attacks. Experimental results demonstrate that the proposed scheme has good security and effectiveness and can be applied for secure transmission of digital images over the Internet.

Image Encryption Algorithm Based on a Novel Wide-Range Discrete Hyperchaotic Map

Existing hyperchaotic systems suffer from a small parameter range and small key space. Therefore, we propose herein a novel wide-range discrete hyperchaotic map(3D-SCC) based on the mathematical model of the Sine map. Dynamic numerical analysis shows that this map has a wide-range of parameters, high sensitive, high sensitivity of sequences and good ergodicity, which proves that the system is well suited to the field of communication encryption. Moreover, this paper proposes an image encryption algorithm based on a dynamic cycle shift scramble algorithm and image-sensitive function. First, the image feature is extracted by the image-sensitive function to input into the chaos map. Then, the plaintext image is decomposed by an integer wavelet, and the low-frequency part is scrambled by a dynamic cyclic shifting algorithm. The shuffled low-frequency part and high-frequency parts are reconstructed by wavelet, and the chaotic matrix image is bitwise XOR with it to obtain the final ciphertext. The experimental results show that the average NPCR is 99.6024%, the average UACI is 33.4630%, and the average local Shannon entropy is 7.9029, indicating that the statistical properties of the ciphertext are closer to the ideal value. The anti-attack test shows that the algorithm can effectively resist cutting attacks and noise attacks. Therefore, the algorithm has great application value in the field of image encryption.

A Hybrid Domain Image Encryption Algorithm Based on Improved Henon Map

A hybrid domain image encryption algorithm is developed by integrating with improved Henon map, integer wavelet transform (IWT), bit-plane decomposition, and deoxyribonucleic acid (DNA) sequence operations. First, we improve the classical two-dimensional Henon map. The improved Henon map is called 2D-ICHM, and its chaotic performance is analyzed. Compared with some existing chaotic maps, 2D-ICHM has larger parameter space, continuous chaotic range, and more complex dynamic behavior. Second, an image encryption structure based on diffusion–scrambling–diffusion and spatial domain–frequency domain–spatial domain is proposed, which we call the double sandwich structure. In the encryption process, the diffusion and scrambling operations are performed in the spatial and frequency domains, respectively. In addition, initial values and system parameters of the 2D-ICHM are obtained by the secure hash algorithm-512 (SHA-512) hash value of the plain image and the given parameters. Consequently, the proposed algorithm is highly sensitive to plain images. Finally, simulation experiments and security analysis show that the proposed algorithm has a high level of security and strong robustness to various cryptanalytic attacks.

A Novel Plain-Text Related Image Encryption Algorithm Based on LB Compound Chaotic Map

Chaos systems have been widely used in image encryption algorithms. In this article, we introduce an LB (Logistic-Baker) compound chaotic map that can greatly improve the complexity of original Logistic map and Baker map, as well as the generated sequences have pseudo-randomness. Furthermore, based on the LB compound chaotic map, an image encryption algorithm is proposed. To resist the differential attack, and enhance the sensitivity of plain-text, the parameters of this algorithm are plain-text related. In this algorithm, the compound chaotic function is influenced by the plain-text image; thus, the specific form of this chaotic map, and its dynamics will be different when encrypting different images. Numerical experiment results indicate that the effect of this novel plain-text related image encryption scheme is excellent, as well as can be competitive with other corresponding algorithms.