Two new methods for scrambling digital images are introduced. The first is based on the 3-dimensional Arnold transformation and the second method is based on the generalized Gray code transformation. Not only the algorithms for scrambling a digital image are given, but also the periodicity of the 3-D Arnold transformation and the generalized Gray code transformation are discussed. A few theorems that calculate the periods of the two transformations are given. Examples of image scrambling are also given.
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