Cryptography is one of the most important areas in information security. Cryptography ensures secure communication and data privacy, and it is increasingly being applied in healthcare and related fields. As an important classical cryptographic method, the Hill cipher has always been closely studied by experts and scholars. In order to enhance the security of the conventional Hill cipher (CHC), a novel dynamic Hill cipher (NDHC) is proposed in this work. The proposed NDHC not only replaces the static key matrix of the CHC with a time-varying dynamic key matrix (TVDKM) to change the image pixel values over time t, but also uses the Logistic chaos sequence scrambling the image pixel positions, which greatly enhances the security of the CHC. However, how to effectively obtain the dynamic inversion key matrix (DIKM) of the TVDKM becomes an urgent issue in the NDHC decryption. In order to quickly find the DIKM, a fixed-time convergence fuzzy Zeroing neural network (FTCF-ZNN) model is constructed, and the convergence and robustness of the FTCF-ZNN model for solving the DIKM are verified through theoretical analysis and comparative experimental results. Moreover, the effectiveness and security of the proposed NDHC for medical images encryption and decryption are also validated by experiments.

Zeroing neural network (ZNN) has been applied to various time-varying problems solving, and numerous ZNN models have been developed in recent years, such as power-type varying-parameter ZNN (PT-VR-ZNN) for solving time-varying quadratic minimization problems, adaptive fuzzy-type ZNN (AFT-ZNN) for solving time-variant matrix inversion and fuzzy power ZNN (FPZNN) for solving time-varying quadratic programming problems. As a time-varying problem and imperative research hot spot in science and engineering, the synchronization of chaotic systems has developed for decades. However, the research on chaos synchronization using ZNN method is rarely reported. Therefore, this paper proposes a time-varying fuzzy parameter ZNN (TVFP-ZNN) model to realize chaotic systems synchronization against the external noises. The most prominent feature of the TVFP- ZNN model is that the time-varying fuzzy parameter generated by the fuzzy logic system is applied in this model. Moreover, the above mentioned three models are also applied to realize the same chaotic systems synchronization for comparison. Compared with above three models, the proposed TVFP-ZNN model not only possesses the fastest convergence speed, but also maintains strongest robustness to noises. Besides, the excellent performances of the TVFP-ZNN model are verified by rigorous mathematical validation. Furthermore, the effectiveness and robustness of the proposed TVFP-ZNN model for chaotic systems synchronization are verified by comparative numerical simulation results. Finally, the process of the proposed TVFP-ZNN model for chaotic system synchronization is displayed on the oscilloscope based on the field programmable gate array (FPGA) to further illustrate its practical application ability.

As a classical and effective method for solving various time-varying problems, the zeroing neural network (ZNN) is widely applied in the scientific and industrial realms. In plentiful studies on the ZNN model, its robustness and convergence have been two essential criteria to evaluate the quality of the model. Improvements in the ZNN model have been focused on its convergence speed; however, the adjustability of its convergence speed has been neglected in most prior works, which restricts its extensive promotion in practical application. Considering the above-mentioned issue, a well-designed activation function (WDAF) is designed. Based on the WDAF, a robust predefined-time convergence ZNN (RPTCZNN) model with adjustable convergence speed is proposed to solve the dynamic matrix inversion problem. In addition, the upper bound of the RPTCZNN model’s convergence time is theoretically validated by strict mathematical analysis in a noiseless and noisy environment. Finally, several simulation experiments of the proposed model are conducted to find solutions of dynamic matrix inversion with different dimensions. Moreover, the realization of the tracking control of the robotic manipulator further illustrates the model’s superior convergence and robustness.

As an effective tool for solving dynamic complex value problems, especially dynamic complex value matrix inversion (DCVMI), the complex value zeroing neural network (CVZNN) has been widely applied in various practical industrial fields. However, previous complex value zeroing neural network (PCVZNN) models only achieve unsatisfactory exponential or finite time convergence, which usually does not conform to actual practical situation. Different from PCVZNN models, a complex-valued variant parameter robust ZNN model (CVVPRZNN) with both fixed-time convergence and robustness for solving DCVMI is proposed in this paper. The fixed-time convergence and noise suppression ability of the CVVPRZNN model for solving DCVMI are strictly deduced. Then, three comparative numerical experiments for DCVMI solving, dynamic circuit currents computing and manipulator trajectory tracking of the proposed CVVPRZNN model with other existing PCVZNN models are provided for demonstrating its better solution performances and higher practical application value. It should be noted that the experimental results indicate that regardless of whether it is disturbed by noise or not, the CVVPRZNN model only requires about 0.01 s to complete the corresponding solving task. However, in the same experimental environment, other models either cannot complete the solving task at all, or require about 8 s which is almost 800 times the solving time of the CVVPRZNN model to complete the corresponding dynamic problem solving.

Cryptography is the core of information security. Among various types of ciphers, the traditional Hill Cipher (THC) is a static alternative cipher based on the basic matrix theory. Stuck in the security and real-time issues of the THC with time-invariant key, this paper studies a dynamic novel Hill Cipher (NHC) with time-variant key for the first time. To ensure the fast decryption of the NHC, this work chooses the zeroing neural network (ZNN) which plays vital important role in solving dynamic problems as the decryption algorithm of NHC to solve the time-variant key inversion (TVKI) matrix. Specifically, a new robust fixed-time convergent activation function (NRFT-AF) and a new time-variant convergence factor (NTv-CF) are designed, and thus a new-type zeroing neural network model (NT-ZNN) is constructed by them for solving the TVKI. By virtue of abundant rigorous mathematical derivation, the fixed-time convergence and robustness of NT-ZNN model for solving the TVKI under the cases without noise and with noise are theoretically demonstrated in detail. Moreover, the NHC is also applied to the encryption and decryption experiments of different strings and RGB color image to validate its reliability. Then, comparative simulation results of the NT-ZNN model with conventional-type zeroing neural network (CT-ZNN) models constructed by other existing activation functions (AFs) and convergence factors (CFs) for solving the TVKI are given, and the superiority of the NT-ZNN model in NHC decryption is further verified.