In this paper we consider the problem of robust perceptual hashing as composite hypothesis testing. First, we formulate this problem as multiple hypothesis testing under prior ambiguity about source statistics and channel parameters representing a family of restricted geometric attacks. We introduce an efficient universal test that achieves the performance of informed decision rules for the specified class of source and geometric channel models. Finally, we consider the practical hash construction, which compromises computational complexity, robustness to geometrical transformations, lack of priors about source statistics and security requirements. The proposed hash is based on a binary hypothesis testing for randomly or semantically selected blocks or regions in sequences or images. We present the results of experimental validation of the developed concept that justifies the practical efficiency of the elaborated framework.