Neural cryptography is a public key exchange algorithm based on the principle of neural network synchronization. By using the learning algorithm of a neural network, the two neural networks update their own weight through exchanging output from each other. Once the synchronization is completed, the weights of the two neural networks are the same. The weights of the neural network can be used for the secret key. However, all the existing works are based on the real-valued neural network model. There are seldom works studying the neural cryptography based on a complex-valued neural network model. In this technical note, a neural cryptography based on the complex-valued tree parity machine network (CVTPM) is proposed. The input, output, and weights of CVTPM are a complex value, which can be considered as an extension of TPM. There are two advantages of the CVTPM: 1) the security of CVTPM is higher than that of TPM with the same hidden units, input neurons, and synaptic depths and 2) the two parties with the CVTPM can exchange two group keys in one neural synchronization process. A series of numerical simulation experiments is provided to verify our results.

By considering that people may immunize their computers with countermeasures in susceptible state, exposed state and using anti‐virus software may take a period of time, a computer virus model with time delay based on an SEIR model is proposed. We regard time delay as bifurcating parameter to study the dynamical behaviors which include local asymptotical stability and local Hopf bifurcation. By analyzing the associated characteristic equation, Hopf bifurcation occurs when time delay passes through a sequence of critical value. The linerized model and stability of the bifurcating periodic solutions are also derived by applying the normal form theory and the center manifold theorem. Finally, an illustrative example is also given to support the theoretical results.

łooseness1These days, the increasing incremental cost consensus-based algorithms are designed to tackle the economic dispatch (ED) problem in smart grids (SGs). However, one principal obstruction lies in privacy disclosure for generators and consumers in electricity activities between supply and demand sides, which may bring great losses to them. Hence, it is extraordinarily essential to design effective privacy-preserving approaches for ED problems. In this article, we propose a two-phase distributed and effective heterogeneous privacy-preserving consensus-based (DisEHPPC) ED scheme, where a demand response (DR)-based framework is constructed, including a DR server, data manager, and a set of local controllers. The first phase is that Kullback-Leibler (KL) privacy is guaranteed for the privacy of consumers' demand by the differential privacy method. The second phase is that (ε, δ)-privacy is, respectively, achieved for the generation energy of generators and the sensitivity of electricity consumption to electricity price by designing the privacy-preserving incremental cost consensus-based (PPICC) algorithm. Meanwhile, the proposed PPICC algorithm tackles the formulated ED problem. Subsequently, we further carry out the detailed theoretical analysis on its convergence, optimality of final solution, and privacy degree. It is found that the optimal solution for the ED problem and the privacy preservation of both supply and demand sides can be guaranteed simultaneously. By evaluation of a numerical experiment, the correctness and effectiveness of the DisEHPPC scheme are confirmed.