The quality of image encryption is commonly measured by the Shannon entropyover the ciphertext image. However, this measurement does not consider to therandomness of local image blocks and is inappropriate for scrambling basedimage encryption methods. In this paper, a new information entropy-basedrandomness measurement for image encryption is introduced which, for the firsttime, answers the question of whether a given ciphertext image is sufficientlyrandom-like. It measures the randomness over the ciphertext in a fairer way bycalculating the averaged entropy of a series of small image blocks within theentire test image. In order to fulfill both quantitative and qualitativemeasurement, the expectation and the variance of this averaged block entropyfor a true-random image are strictly derived and corresponding numericalreference tables are also provided. Moreover, a hypothesis test atsignificance-level is given to help accept or reject the hypothesis that thetest image is ideally encrypted/random-like. Simulation results show that theproposed test is able to give both effectively quantitative and qualitativeresults for image encryption. The same idea can also be applied to measureother digital data, like audio and video.
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