Perceptual hashing is conventionally used for content identification and authentication. It has applications in database content search, watermarking and image retrieval. Most countermeasures proposed in the literature generally focus on the feature extraction stage to get robust features to authenticate the image, but few studies address the perceptual hashing security achieved by a cryptographic module. When a cryptographic module is employed [1], additional information must be sent to adjust the quantization step. In the perceptual hashing field, we believe that a perceptual hashing system must be robust, secure and generate a final perceptual hash of fixed length. This kind of system should send only the final perceptual hash to the receiver via a secure channel without sending any additional information that would increase the storage space cost and decrease the security. For all of these reasons, in this paper, we propose a theoretical analysis of full perceptual hashing systems that use a quantization module followed by a crypto-compression module. The proposed theoretical analysis is based on a study of the behavior of the extracted features in response to content-preserving/content-changing manipulations that are modeled by Gaussian noise. We then introduce a proposed perceptual hashing scheme based on this theoretical analysis. Finally, several experiments are conducted to validate our approach, by applying Gaussian noise, JPEG compression and low-pass filtering.