## 1 Introduction  
Digital watermarking is a data hiding technique aimed at identifying and protecting digital multimedia content. In the _embedding_ phase, steganographic data (the watermark) is hidden into the media content, in the _detection_ phase the embedded watermark is extracted. A watermark is meant to not be easily removable or breakable. A classical taxonomy is indeed based on the resilience to alteration or removal by means of image modifications and distinguishes among fragile, semifragile, and robust watermarks. _Robust_ watermarks are designed to resist to transformations. _Semifragile_ watermarks are still retrievable after the image has undergone limited modifications. _Fragile_ watermarks are destroyed by the slightest modification; their typical use is for integrity control. A different taxonomy is related to the capability of recovering the original image exactly as it was before watermarking. In general, watermarking methods induce permanent modifications of the image they act upon. With _reversible_ (also variably referred to as lossless or invertible) watermarks, the original image can, instead, be reconstructed unaltered. Reversible watermarks are especially used in application areas where no modification can be tolerated (e.g., forensics, digital archival of valuable content, or medical imaging). For example, if a watermarking technique induces modifications to medical images, a clinical trial may be necessary before such images can be used for diagnostic purposes. Many watermarking methods rely on domain-specific knowledge. For instance, medical images are often partitioned into two different areas, which are dealt with differently. The ROI (Region of Interest) is defined as the region containing the portions of an image that have clinical significance, while the RONI (Region of Non-Interest) includes the background and possibly a contour. As the RONI contains less relevant data than the ROI, and can thus be subject to heavier modifications, robust watermarks are usually embedded there, leaving the ROI as unaltered as possible. Feature-based image watermarking schemes aim to survive geometric distortions, e.g., scaling, translation, rotation, and cropping. Such schemes isolate salient points of an image, such as corners and edges, which are supposed to be intrinsically bound to the image. Features are thus meant to survive distortions and re-compression. Geometric invariants could be computed from the original image or from a transform of it. A method for selecting the most adequate feature regions for robust watermarking, formulated as a multidimensional knapsack optimization problem (MDKP) and tackled by means of a Genetic Algorithm techniques is presented in [1]. There are situations in which the original image is not available to the embedding agent, who is only given an encrypted image. In such cases, embedding cannot capitalize on regularities and spatial correlation in the image or in some transform of it. Consequently, encrypted images can accommodate smaller payloads. In the context of watermarking encrypted images, assuming that two keys are used for the operations of encrypting and embedding, the property of _separability_ guarantees that the encryption key and the embedding key need not be shared by the same detecting agent [2]. Possession of both keys grants full access, but an agent who only knows the embedding key is able to retrieve the embedded payload and has no access to the original image, whereas an agent who only knows the encryption key will not have access to the embedded payload but will still be able to see a slightly degraded image. The scheme by [PERSON] [2] works with a stream ciphering algorithm. In this work we consider the case of image encryption by means of Identity-Based encryption (IBE) [3]. In addition, the payload that is embedded into the encrypted image is its signature, again via an identity-based cryptosystem.