  The quality of image encryption is commonly measured by the Shannon entropy
over the ciphertext image. However, this measurement does not consider to the
randomness of local image blocks and is inappropriate for scrambling based
image encryption methods. In this paper, a new information entropy-based
randomness measurement for image encryption is introduced which, for the first
time, answers the question of whether a given ciphertext image is sufficiently
random-like. It measures the randomness over the ciphertext in a fairer way by
calculating the averaged entropy of a series of small image blocks within the
entire test image. In order to fulfill both quantitative and qualitative
measurement, the expectation and the variance of this averaged block entropy
for a true-random image are strictly derived and corresponding numerical
reference tables are also provided. Moreover, a hypothesis test at
significance-level is given to help accept or reject the hypothesis that the
test image is ideally encrypted/random-like. Simulation results show that the
proposed test is able to give both effectively quantitative and qualitative
results for image encryption. The same idea can also be applied to measure
other digital data, like audio and video.
