Abstract: According to the features of digital images, a kind of three-dimensional scrambling and encryption algorithm was proposed based on two-dimensional scrambling transformations in a finite integer domain, affine transformations, and integer lifting transformations. This algorithm applies to images with any length and width or at any length-to-width ratio. The feasibility that some parameters of the transformation matrix are negative integers or decimals is taken into account, and the method of parameter setting is explicitly shown. Real number is used in the algorithm, which expands the space of parameters, scrambles the pixel positions and changes their values, makes the scrambling result better, increases the periodicity of scrambling, and improves the security of digital image transformations.