In this paper, we build a novel chaotic coupled lattice mapping with positive Lyapunov exponent, and introduce a novel chaotic image scrambling mechanism. Then, we propose a chaotic image encryption algorithm which uses the introduced chaotic coupled lattice mapping to apply permutation by iteratively applying the introduced chaotic image scrambling mechanism, and diffusing the pixel values. We use a sorting approach rather than quantizing the chaotic floating-point values to construct the diffusion matrix. We also study the security of the proposed algorithm concerning several security measures including brute-force attack, differential attack, key sensitivity, and statistical attacks. Moreover, the proposed algorithm is robust against data loss and noise attacks.

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Iterative methods are widely used in probabilistic model checking to compute quantitative reachability values. Redundant computation is a significant drawback of iterative methods that affects the performance of probabilistic model checking. In this paper we propose a new approach to avoid redundant computations for reachability analysis of discrete-time Markov processes. Redundant computations can be avoided by considering transitions with Dirac distributions. If two states of a Markov chain are connected with a Dirac transition, the iterative method can postpone the update of the source state until the value of the destination state is computed. Using this approach, we propose two heuristics to improve the performance of iterative methods for computing unbounded reachability probabilities in discrete-time Markov chains and Markov decision processes. The proposed heuristics can be lifted to the computations of expected rewards and have been implemented in PRISM model checker. Several standard case studies have been used and experimental results show that our heuristics outperform most wellknown previous iterative methods.