Abstract
As a kind of spatiotemporal chaos, coupled map lattice (CML) is widely applied into image encryption because of its advantages of more complex dynamical behavior and lower computational overhead. Firstly, this paper proposed a novel spatiotemporal chaos model (MCML) by mixing Logistic, Sine and Tent maps into CML map together. Beyond that, we also change the structure of CML and the coupling method in different lattices. Bifurcation diagram, Lyapunov exponents and NIST test are employed to measure the chaotic behaviors of the MCML system. Secondly, by applying MCML chaos, we design a new key binding and distribution rule, the improved diffusion scheme to encrypt image. Furthermore, the novel bit Z-scan scrambling method also be used to enhance the security of the encryption scheme. Finally, a large number of experimental results prove that our proposed scheme is suitable for image encryption and has high security against common attacks.
Highlights
As a kind of spatiotemporal chaos, coupled map lattice (CML) is widely applied into image encryption because of its advantages of more complex dynamical behavior and lower computational overhead
Zhang et al.[12] improved the dynamic performance of logistic map in every lattice and the CML with parameter q is provided with Euler method
Compared with one-dimensional chaos and CML system, bifurcation diagrams and Lyapunov exponents are analyzed to prove our proposed spatiotemporal www.nature.com/scientificreports model have larger range of parameters and higher Lyapunov exponents which are more suitable for the image encryption
Summary
Mod(4μxn(i)(1 − xn(i)) + 2(1 − μ)xn+1(i − 1) + (1 − μ)sin(πxn(i + 1)), 1), xn(i + 1) 0.5 mod(4μxn(i)(1 − xn(i)) + 2(1 − μ)(1 − xn+1(i + (1 − μ)sin(πxn(i + 1)), 1), xn(i + 1) 0.5, 1)). The results of statistical tests show that the pseudo chaotic sequences generated by MCML system have good randomness. If all pixel’s values of an image are 0, the process of diffusion with using Eq (8) to encryption can be described as follows: c(1) = s(1) ⊕ c(0), c(2) = s(2) ⊕ s(1) ⊕ c(0), c(3) = s(3) ⊕ s(2) ⊕ s(1) ⊕ c(0), c(n) = s(n) ⊕ s(n − 1) ⊕ s(2) ⊕ s(1) ⊕ c(0), we can get the equivalent chaotic sequence s. To enhance the effect of encryption, the control parameter of nonlinear function is decided by decimal chaotic data and keep changing with different images These measures ensure that it’s hard to break the diffusion process and can’t get the equivalent chaotic sequence s. The result shows that our algorithm implements the function of scrambling and diffusion simultaneously
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