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.

Abstract Key‐based interval splitting arithmetic coding (KAC) possesses both encryption and compression capabilities. However, it possesses vulnerability to chosen‐plaintext attack because the attacker can explore the relationship between the key and the codeword to deduce the secret key. In order to resist this attack, we propose to introduce perturbation into KAC. The perturbation‐based KAC not only avoids the flaw of KAC that the splitting keys are usually located at the endpoint of certain codeword or at the border of two codewords but also removes the restriction that the keys are only allowed in certain sub‐intervals, which result in great convenience to the key scheduler. In addition, based on generalized arithmetic coding using Generalized Luröth Series, we study the phase‐space splitting of a chaotic map for generalized KAC and suggest the generalized perturbation‐based KAC. This leads to the design of a joint compression and encryption scheme with more powerful cryptographic features. Copyright © 2015 John Wiley & Sons, Ltd.

Some pioneering works have investigated embedding cryptographic properties in compressive sampling (CS) in a way similar to one-time pad symmetric cipher. This paper tackles the problem of constructing a CS-based symmetric cipher under the key reuse circumstance, i.e., the cipher is resistant to common attacks even when a fixed measurement matrix is used multiple times. To this end, we suggest a bi-level protected CS (BLP-CS) model which makes use of the advantage of measurement matrix construction without restricted isometry property (RIP). Specifically, two kinds of artificial basis mismatch techniques are investigated to construct key-related sparsifying bases. It is demonstrated that the encoding process of BLP-CS is simply a random linear projection, which is the same as the basic CS model. However, decoding the linear measurements requires knowledge of both the key-dependent sensing matrix and its sparsifying basis. The proposed model is exemplified by sampling images as a joint data acquisition and protection layer for resource-limited wireless sensors. Simulation results and numerical analyses have justified that the new model can be applied in circumstances where the measurement matrix can be reused.

Recent research advances have revealed the computational secrecy of the compressed sensing (CS) paradigm. Perfect secrecy can also be achieved by normalizing the CS measurement vector. However, these findings are established on real-valued measurements while digital devices can only store the samples at a finite precision. Based on the distribution of measurements of natural images sensed by structurally random ensemble, a joint quantization and diffusion approach for the real-valued measurements is suggested. In this way, a nonlinear cryptographic diffusion is intrinsically imposed on the CS quantization process and the overall security level is thus enhanced. It is shown that the proposed scheme is able to resist known-plaintext attack while the original CS scheme without quantization cannot.

In this paper, an improved soft in soft out (SISO) iterative decoding scheme for joint source-channel coding is presented. It is realized as the iterative soft decoding of arithmetic code based on sequential decoding to successively prune the decoding tree. Making use of the forecasted forbidden symbols, an error-resistant arithmetic code with an improved a posteriori probability (APP) metric is adopted to further enhance the error correction performance. Simulation results have validated the superiority of our scheme in terms of packet error rate for the AWGN channel.

We elaborate on the possibility of exploiting the (pseudo)random projection operator, which is at the heart of the most common architecture for compressed sensing, to prevent access to the acquired information by unauthorized receivers. In low-resource applications, this approach may make dedicated cryptographic layers unnecessary when the security requirement is not particularly high. Beyond proving that the proposed system is at least asymptotically immune to straightforward statistical attacks, we also exploit the sensitivity of compressed sensing recovery algorithms to the complete knowledge of the projection matrix to introduce two-class protection. The encoding is such that first-class decoders can retrieve the signal to its full resolution while second-class decoders are able to retrieve only a degraded version of the same signal. Examples are given with reference to ECG signal acquisition.

We propose an improved error correction technique for arithmetic coding. By forecasting the forbidden symbols, the effective forbidden region is expanded and a better error correction performance is achieved. A generalized stack algorithm is employed to detect the forbidden symbol beforehand and the maximum a posteriori (MAP) metric is adopted to preserve the most probable decoding paths in the stack. Simulation results justify the effectiveness of our scheme in improving the error correction performance of arithmetic coding, especially at a low coding rate.

The Arnold cat map is employed in various applications where chaos is utilized, especially chaos-based cryptography and watermarking. In this paper, we study the problem of period distribution of the generalized discrete Arnold cat map over the Galois ring \BBZ2e. Full knowledge of the period distribution is obtained analytically by adopting the Hensel lift approach. Our results have impact on both chaos theory and its applications as they not only provide design strategy in applications where special periods are required, but also help to identify unstable periodic orbits of the original chaotic cat map. The method in our paper also shows some ideas how to handle problems over the Galois ring \BBZ2e.

A chaos-based cryptosystem with compression capability is proposed for lossy image compression. Unlike traditional approaches that require separate compression and encryption programs, our scheme performs these two operations simultaneously in one pass. The tradeoff between reconstructed image quality and compression ratio is controllable by tuning some system parameters. Simulation results show that the compression performance of our approach is encouraging. The secrecy is justified by the security analysis results.

In this paper, we analyze the period distribution of the generalized discrete cat map over the Galois ring where is a prime. The sequences generated by this map are modeled as 2-dimensional LFSR sequences. Employing the generation function and the Hensel lifting approaches, full knowledge of the detail period distribution is obtained analytically. Our results not only characterize the period distribution of the cat map, which gives insights to various applications, but also demonstrate some approaches to deal with the period of a polynomial in the Galois ring.

In this paper, the period distribution of sequences generated by Chebyshev polynomials over the finite field ZNis analyzed. It is found that the distribution is unsatisfactory if N (the modulus) is not chosen properly. Based on this finding, we present an attack on the public-key algorithm based on Chebyshev polynomials over ZN. Then, we modify the original algorithm to make it suitable for practical purpose. Its security under some existing models is also discussed in detail.

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.

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.

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.

The training of neural networks using the extended Kalman filter (EKF) algorithm is plagued by the drawback of high computational complexity and storage requirement that may become prohibitive even for networks of moderate size. In this paper, we present a local EKF training and pruning approach that can solve this problem. In particular, the by-products obtained along with the local EKF training can be utilized to measure the importance of the network weights. Comparing with the original global approach, the proposed local EKF training and pruning approach results in a much lower computational complexity and storage requirement. Hence, it is more practical in solving real world problems. The performance of the proposed algorithm is demonstrated on one medium- and one large-scale problems, namely, sunspot data prediction and handwritten digit recognition.

In combining principal and minor components analysis, a parallel extraction method based on the recursive least square algorithm is suggested to extract the principal components of the input vectors. After the extraction, the error covariance matrix obtained in the learning process is used to perform minor components analysis. The minor components found are then pruned so as to achieve a higher compression ratio. Simulation results show that both the convergent speed and the compression ratio are improved, which in turn indicate that our method effectively combines the extraction of the principal components and the pruning of the minor components.