In graph theory, Hamiltonian path refers to the path that visits each vertex exactly once. In this paper, we designed a method to generate random Hamiltonian path within digital images, which is equivalent to permutation in image encryption. By these means, building a Hamiltonian path across bit planes can shuffle the distribution of the pixel’s bits. Furthermore, a similar thought can be applied for the substitution of pixel’s grey levels. To ensure the randomness of the generated Hamiltonian path, an adjusted Bernoulli map is proposed. By adopting these novel techniques, a bit-level image encryption scheme was devised. Evaluation of simulation results proves that the proposed scheme reached fair performance. In addition, a common flaw in calculating correlation coefficients of adjacent pixels was pinpointed by us. After enhancement, correlation coefficient becomes a stricter criterion for image encryption algorithms.

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An intrinsic similarity was noted between epidemic spreading models and diffusion operations in cryptography. In this paper, a new image encryption algorithm is proposed based on an epidemic spreading model. The notable feature of the model is the evolution of the network node state. We utilize the evolution of an epidemic spreading model, namely the susceptible-infectious-recovered (SIR) model, to drive the encryption progress by abstracting pixels to the network nodes. In the new cryptosystem, the pixels in plain-text are considered as susceptible individuals, permutation and diffusion are seamlessly integrated rather than having two independent stages, and the encryptions are performed in a two-dimensional and nonlinear manner. Simulation results demonstrate its high encryption speed and excellent encryption security.