Xiaoming Song

The importance of chaotic systems as the main pseudo-random cryptographic generator of encryption algorithms in the field of communication secrecy cannot be overstated, but in practical applications, researchers often choose to build upon traditional chaotic maps, such as the logistic map, for study and application. This approach provides attackers with more opportunities to compromise the encryption scheme. Therefore, based on previous results, this paper theoretically investigates discrete chaotic mappings in the real domain, constructs a general method for a class of quadratic chaotic mappings, and justifies its existence based on a robust chaos determination theorem for S single-peaked mappings. Based on the theorem, we construct two chaotic map examples and conduct detailed analysis of their Lyapunov exponent spectra and bifurcation diagrams. Subsequently, comparative analysis is performed between the proposed quadratic chaotic maps and the conventional logistic map using the 0–1 test for chaos and SE complexity metrics, validating their enhanced chaotic properties.

The chaotic trajectory of the traditional natural chaotic system and the single chaotic system is relatively simple, and the keyspace is small, resulting in low security, low complexity, and poor resistance to attacks based on traditional chaotic design encryption algorithms. This article first constructed a 6th-order cellular neural network hyperchaotic system based on the theory of a 6th-order cellular neural network. Then the Chaotic Sequence Enhancer (CSE) is constructed by using infinite folding mapping. We use CSE to improve our cellular neural network. Compared with the old system, the new system has a larger Lyapunov exponent, higher PE complexity values, and 0–1 test results. Then based on the new chaotic system, a three-dimensional encryption algorithm was designed. The algorithm rearranges the pixels of the image into cubes and performs scrambling and diffusion operations based on the cubes. While making the encryption effect better, the information entropy of the ciphertext image is also above 7.99, and the correlation between adjacent pixels is less than 0.1. At the same time, the encryption algorithm can better resist various corrosion attacks, and the original image can still be better decrypted even when the ciphertext image has received a 25% loss. The result of the NPCR and UACI test is close to the expected values of 99.61% and 33.46%. The ciphertext image produced by the algorithm can pass the NIST SP800-22 statistical tests. The results of various tests and experiments show that our proposed encryption algorithm has high initial value sensitivity, resistance to differential attacks, and resistance to cropping attacks, and has good application prospects in the field of image security.

Multistable dynamics analysis of complex chaotic systems is an important problem in the field of chaotic communication security. In this paper, a new hyperchaotic complex Lü system is proposed and its basic dynamics are analyzed. Owing to the introduction of complex variables, the new system has some structurally distinctive attractors, such as flower-shaped and airfoil-shaped attractors. In addition, the evolution process of the limit cycle is also investigated. Next, the multistable coexistence behavior of the system is researched by the method of attraction basins, and the coexistence behavior of two types of hyperchaotic attractors and one type of chaotic and periodic attractors of the system are analyzed. The coexisting hyperchaotic attractors also show flower and airfoil shapes, and four types of coexistence flower-shaped attractors with different structures are perfectly explored. Moreover, the variation of coexistence attractors in the plane and space with parameters is discussed. Then, by introducing a specific piecewise function determined by a two-element method into the new high-dimensional system, the self-reproduction of the attractor can be realized to generate the multistability, and the general steps of attractors self-reproducing in the higher dimensional system are given. Finally, the circuit design of the new system is implemented, which lays a foundation for the application of complex chaotic systems.

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.

The data space for audio signals is large, the correlation is strong, and the traditional encryption algorithm cannot meet the needs of efficiency and safety. To solve this problem, an audio encryption algorithm based on Chen memristor chaotic system is proposed. The core idea of the algorithm is to encrypt the audio signal into the color image information. Most of the traditional audio encryption algorithms are transmitted in the form of noise, which makes it easy to attract the attention of attackers. In this paper, a special encryption method is used to obtain higher security. Firstly, the Fast Walsh–Hadamar Transform (FWHT) is used to compress and denoise the signal. Different from the Fast Fourier Transform (FFT) and the Discrete Cosine Transform (DCT), FWHT has good energy compression characteristics. In addition, compared with that of the triangular basis function of the Fast Fourier Transform, the rectangular basis function of the FWHT can be more effectively implemented in the digital circuit to transform the reconstructed dual-channel audio signal into the R and B layers of the digital image matrix, respectively. Furthermore, a new Chen memristor chaotic system solves the periodic window problems, such as the limited chaos range and nonuniform distribution. It can generate a mask block with high complexity and fill it into the G layer of the color image matrix to obtain a color audio image. In the next place, combining plaintext information with color audio images, interactive channel shuffling can not only weaken the correlation between adjacent samples, but also effectively resist selective plaintext attacks. Finally, the cryptographic block is used for overlapping diffusion encryption to fill the silence period of the speech signal, so as to obtain the ciphertext audio. Experimental results and comparative analysis show that the algorithm is suitable for different types of audio signals, and can resist many common cryptographic analysis attacks. Compared with that of similar audio encryption algorithms, the security index of the algorithm is better, and the efficiency of the algorithm is greatly improved.

Focused on the problems that the randomness of the noise-adding operation in the de-noising auto-encoder (DAE), and the data matrix does not consider the impact of trusted users on the deep preferences of target users, this paper proposes a recommendation algorithm based on stack de-noising auto-encoder (SDAE) which integrates the preferences of trusted users. Firstly, the score vector is used as the input of the auto-encoder, and the mask vector is designed to train the potential preference of the target user. Secondly, the deep preference of the target user and the trusted user is obtained by the weighted fusion of the features of the two hidden layers of the auto-encoder. Thirdly, in order to reduce the impact of noise on the prediction accuracy, the cascaded auto-encoder model is constructed and trained according to the greedy training method layer by layer training. Finally, SDAE model is compared with other models on different data sets. The experimental results show that SDAE model has better recommendation performance.