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We propose the fast algorithms for image scrambling using multi-dimensional orthogonal transform. The multi-dimensional orthogonal sequence can provide an orthogonal transform for image scrambling and descrambling. This scrambling method has the characteristic of high security because the keys for scrambling and descrambling are a set of the parameters to generate the orthogonal sequence. But the disadvantage of this method is that the computing complexity is high. In order to save the computing time, serial and parallel fast algorithms are proposed. When using these fast algorithms, another image can be used as a key to improve the security. For a binary image and a gray scale image, different sequences and fast algorithms are used to scramble. The experimental results show that these fast algorithms can effectively decrease the computing complexity and the histograms of digital image after scrambling have random Gaussian distribution.