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In the last decade, the increased possibility to produce, edit, and disseminate multimedia contents has not been adequately balanced by similar advances in protecting these contents from unauthorized diffusion of forged copies. When the goal is to detect whether or not a digital content has been tampered with in order to alter its semantics, the use of multimedia hashes turns out to be an effective solution to offer proof of legitimacy and to possibly identify the introduced tampering. We propose an image hashing algorithm based on compressive sensing principles, which solves both the authentication and the tampering identification problems. The original content producer generates a hash using a small bit budget by quantizing a limited number of random projections of the authentic image. The content user receives the (possibly altered) image and uses the hash to estimate the mean square error distortion between the original and the received image. In addition, if the introduced tampering is sparse in some orthonormal basis or redundant dictionary, an approximation is given in the pixel domain. We emphasize that the hash is universal, e.g., the same hash signature can be used to detect and identify different types of tampering. At the cost of additional complexity at the decoder, the proposed algorithm is robust to moderate content-preserving transformations including cropping, scaling, and rotation. In addition, in order to keep the size of the hash small, hash encoding/decoding takes advantage of distributed source codes.