On the Security of a Class of Diffusion Mechanisms for Image Encryption.

The need for fast and strong image cryptosystems motivates researchers to develop new techniques to apply traditional cryptographic primitives in order to exploit the intrinsic features of digital images. One of the most popular and mature technique is the use of complex dynamic phenomena, including chaotic orbits and quantum walks, to generate the required key stream. In this paper, under the assumption of plaintext attacks we investigate the security of a classic diffusion mechanism (and of its variants) used as the core cryptographic primitive in some image cryptosystems based on the aforementioned complex dynamic phenomena. We have theoretically found that regardless of the key schedule process, the data complexity for recovering each element of the equivalent secret key from these diffusion mechanisms is only (1). The proposed analysis is validated by means of numerical examples. Some additional cryptographic applications of this paper are also discussed.

New communication schemes based on adaptive synchronization.

In this paper, adaptive synchronization with unknown parameters is discussed for a unified chaotic system by using the Lyapunov method and the adaptive control approach. Some communication schemes, including chaotic masking, chaotic modulation, and chaotic shift key strategies, are then proposed based on the modified adaptive method. The transmitted signal is masked by chaotic signal or modulated into the system, which effectively blurs the constructed return map and can resist this return map attack. The driving system with unknown parameters and functions is almost completely unknown to the attackers, so it is more secure to apply this method into the communication. Finally, some simulation examples based on the proposed communication schemes and some cryptanalysis works are also given to verify the theoretical analysis in this paper.

Selective image encryption using a spatiotemporal chaotic system.

A universal selective image encryption algorithm, in which the spatiotemporal chaotic system is utilized, is proposed to encrypt gray-level images. In order to resolve the tradeoff between security and performance, the effectiveness of selective encryption is discussed based on simulation results. The scheme is then extended to encrypt RGB color images. Security analyses for both scenarios show that the proposed schemes achieve high security and efficiency.

Generalized RLS approach to the training of neural networks.

Recursive least square (RLS) is an efficient approach to neural network training. However, in the classical RLS algorithm, there is no explicit decay in the energy function. This will lead to an unsatisfactory generalization ability for the trained networks. In this paper, we propose a generalized RLS (GRLS) model which includes a general decay term in the energy function for the training of feedforward neural networks. In particular, four different weight decay functions, namely, the quadratic weight decay, the constant weight decay and the newly proposed multimodal and quartic weight decay are discussed. By using the GRLS approach, not only the generalization ability of the trained networks is significantly improved but more unnecessary weights are pruned to obtain a compact network. Furthermore, the computational complexity of the GRLS remains the same as that of the standard RLS algorithm. The advantages and tradeoffs of using different decay functions are analyzed and then demonstrated with examples. Simulation results show that our approach is able to meet the design goals: improving the generalization ability of the trained network while getting a compact network.

Criteria for exponential [corrected] stability of Cohen-Grossberg neural networks.

In this paper, the Cohen-Grossberg neural network models without and with time delays are considered. By constructing several novel Lyapunov functionals, some sufficient criteria for the existence of a unique equilibrium and global exponential stability of the network are derived. These results are fairly general and can be easily verified. Besides, the approach of the analysis allows one to consider different types of activation functions, including piecewise linear, sigmoids with bounded activations as well as C1-smooth sigmoids. In the meantime, our approach does not require any symmetric assumption of the connection matrix. It is believed that these results are significant and useful for the design and applications of the Cohen-Grossberg model.

Robust stability of interval bidirectional associative memory neural network with time delays.

In this paper, the conventional bidirectional associative memory (BAM) neural network with signal transmission delay is intervalized in order to study the bounded effect of deviations in network parameters and external perturbations. The resultant model is referred to as a novel interval dynamic BAM (IDBAM) model. By combining a number of different Lyapunov functionals with the Razumikhin technique, some sufficient conditions for the existence of unique equilibrium and robust stability are derived. These results are fairly general and can be verified easily. To go further, we extend our investigation to the time-varying delay case. Some robust stability criteria for BAM with perturbations of time-varying delays are derived. Besides, our approach for the analysis allows us to consider several different types of activation functions, including piecewise linear sigmoids with bounded activations as well as the usual C1-smooth sigmoids. We believe that the results obtained have leading significance in the design and application of BAM neural networks.

Global exponential stability of hybrid bidirectional associative memory neural networks with discrete delays.

In this paper, the dynamical characteristics of hybrid bidirectional associative memory neural networks with constant transmission delays are investigated. Without assuming symmetry of synaptic connection weights and monotonicity and differentiability of activation functions, Halanay-type inequalities (which are different from the approach of constructing Lyapunov functionals) are employed to derive the delay-independent sufficient conditions under which the networks converge exponentially to the equilibria associated with temporally uniform external inputs. Our results are less conservative and restrictive than previously known results.

Asymptotic stability criteria for a two-neuron network with different time delays.

In this paper, the asymptotic stability of a two-neuron system with different time delays has been investigated. Some criteria for determining the global asymptotically stability of equilibrium are derived from the theory of monotonic dynamical system and the approach of Lyapunov functional. For local asymptotic stability, some elegant criteria are also obtained by the Nyquist criteria. We find that one of them depends on the length of delays while the other ones do not. In the latter case, the delays are sometimes called harmless delays. The results obtained have leading significance in the study of neural networks composed of a large number of neurons with different time delays.