In this paper, we present a new type of attack on iterated chaotic ciphers using related keys. Based on the fact that a chaotic sequence is not sensitive to the less significant bits of initial conditions and parameters, a divide-and-conquer attack on iterated chaotic ciphers was presented by us before, which significantly reduces the computing complexity of attacks. However, if the information leaked is significant according to the distribution of the coincidence degrees, a measure for the information leakage of chaotic ciphers, or the size of the key is large, then it is difficult for the divide-and-conquer attack to reduce its computing complexity into a realizable level. The related-key attack we present in this paper simultaneously uses the information leaked from different chaotic sequences generated by related keys and combines the ideas of linear cryptanalysis and divide-and-conquer attack together, hence greatly enhances the efficiency of divide-and-conquer attack. As an example, we test the related-key attack on the ZLL chaotic cipher with a 64-bit key on a Pentium IV 2.5 GHz PC, which takes only 8 minutes and 45 seconds to recover all bits of the key successfully.
We address the secure control issue of networked non-affine nonlinear systems under denial of service (DoS) attacks. As for the situation that the system information cannot be measured in specific period due to the malicious DoS attacks, we design a neural networks (NNs) state observer with switching gain to estimate internal states in real time. Considering the error and dynamic performance of each subsystem, we introduce the recursive sliding mode dynamic surface method and a nonlinear gain function into the secure control strategy. The relationship between the frequency (duration) of DoS attacks and the stability of the system is established by the average dwell time (ADT) method. It is proven that the system can withstand the influence of DoS attacks and track the desired trajectory while preserving the boundedness of all closed-loop signals. Finally, simulation results are provided to verify the effectiveness of the proposed secure control strategy.