The property of nonlinearity has high importance for the design of strong substitution boxes. Therefore, the development of new techniques to produce substitution boxes with high values of nonlinearity is essential. Many research papers have shown that optimization algorithms are an efficient technique to obtain good solutions. However, there is no reference in the public literature showing that a heuristic method obtains optimal nonlinearity unless seeded with optimal initial solutions. Moreover, the majority of papers with the best nonlinearity reported for pseudo-random seeding of the algorithm(s) often achieve their results with the help of some cost function(s) over the Walsh–Hadamard spectrum of the substitution. In the sense, we proposed to present, in this paper, a novel external parameter independent cost function for evolving bijective s-boxes of high nonlinearity, which is highly correlated to this property. Several heuristic approaches including GaT (genetic and tree), LSA (local search algorithm), and the Hill Climbing algorithm have been investigated to assess the performance of evolved s-boxes. A performance comparison has been done to show the advantages of our new cost function, with respect to cost functions for s-boxes like Clark’s and Picek’s cost functions.
Data security plays a significant role in data transfer in cloud-based smart cities. Chaotic maps are commonly used in designing modern cryptographic applications, in which one-dimensional (1D) chaotic systems are widely used due to their simple design and low computational complexity. However, 1D chaotic maps suffer from different kinds of attacks because of their chaotic discontinuous ranges and small key-space. To own the benefits of 1D chaotic maps and avoid their drawbacks, the cascading of two integrated 1D chaotic systems has been utilized. In this paper, we report an image cryptosystem for data transfer in cloud-based smart cities using the cascading of Logistic-Chebyshev and Logistic-Sine maps. Logistic-Sine map has been utilized to permute the plain image, and Logistic-Chebyshev map has been used to substitute the permuted image, while the cascading of both integrated maps has been utilized in performing XOR procedure on the substituted image. The security analyses of the suggested approach prove that the encryption mechanism has good efficiency as well as lower encryption time compared with other related algorithms.
Here, a chaotic quadratic oscillator with only squared terms is proposed, which shows various dynamics. The oscillator has eight equilibrium points, and none of them is stable. Various bifurcation diagrams of the oscillator are investigated, and its Lyapunov exponents (LEs) are discussed. The multistability of the oscillator is discussed by plotting bifurcation diagrams with various initiation methods. The basin of attraction of the oscillator is discussed in two planes. Impulsive control is applied to the oscillator to control its chaotic dynamics. Additionally, the circuit is implemented to reveal its feasibility.
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