  This letter discusses the problem of testing the degree of randomness within
an image, particularly for a shuffled or encrypted image. Its key contributions
are: 1) a mathematical model of perfectly shuffled images; 2) the derivation of
the theoretical distribution of pixel differences; 3) a new $Z$-test based
approach to differentiate whether or not a test image is perfectly shuffled;
and 4) a randomized algorithm to unbiasedly evaluate the degree of randomness
within a given image. Simulation results show that the proposed method is
robust and effective in evaluating the degree of randomness within an image,
and may often be more suitable for image applications than commonly used
testing schemes designed for binary data like NIST 800-22. The developed method
may be also useful as a first step in determining whether or not a shuffling or
encryption scheme is suitable for a particular cryptographic application.
