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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 Hamiltoniandoi:10.3390/e22010073 pmid:33285848 fatcat:d2vpocx4pzfvnlwdgitk7uui4i