Paillier Cryptosystem Based Reversible Data Hiding With Extended Applications In Encrypted Domain

Cloud computing is an advanced information technology infrastructure that pro-vides on-demand ubiquitous access to a pool of configurable computing resources-from high end processing power,storage,networking and artificial intelligence as well as nat-ural language processing.With the development of cloud computing and the drastic in-crease of information size,content owners are greatly motivated to outsource their huge amount of personal multimedia data and computationally expensive tasks to the cloud.The cloud server may embed additional data into the uploaded content such as notation keywords,authentication and integrity related data for managing the uploaded data in the cloud.However,the embedding of such additional data may cause permanent dis-tortion to the original content.The recovery of the original content is pertinent to some sensitive application fields such as military,satellite imagery,medical imagery and law enforcement.Therefore,reversible data hiding(RDH)is needed that embeds confiden-tial data into a cover media in such a way that the embedded data can be extracted error free and the original media content can be restored losslessly.Although,the abundant storage and enormous computation resources of cloud offer many advantages,protect-ing privacy and data confidentiality against unauthorized leakage of information are major concerns of the cloud paradigm.For privacy protection and data confidentiality,the original content is encrypted before outsourcing to the cloud.To this end,reversible data hiding in encrypted domain(RDH-ED)emerges for managing encrypted data in the cloud.At present,most of the RDH-ED methods are based on symmetric key cryptosys-tems.However,with the dramatically increased usage of cloud computing,data en-crypted with symmetric key encryption algorithms are not adequate for cloud based privacy preserving applications because such algorithms do not allow cloud servers to perform mathematical operations directly over encrypted data.On the other hand,the recent development of RDH-ED compatible with partial homomorphic public key cryp-tosystems has intensified the research interest,most of the RDH-ED methods are de-signed for images and less attention is paid to other media types.Moreover,the existing mature RDH methods cannot be transplanted to the encrypted domain due to the limita-tions of the underlying cryptosystems as a limited number of mathematical operations can be performed over encrypted data.Moreover,cloud services allow performing computationally expensive operations over encrypted images for the purpose of image enhancement in the encrypted domain.However,not all processing operations over encrypted images can be performed with-out pre-processing or interactive protocol or without error between the plain domain and encrypted domain operations.This is due to the fact that partial homomorphic cryptosystem allows only limited number of mathematical operations.In this dissertation,the probabilistic and homomorphic properties of the Paillier cryptosystem are effectively utilized to propose RDH-ED methods for 3D mesh mod-els and images.Furthermore,a solution for encrypted domain non-integer mean value computation is proposed,based on which,existing state-of-the-art RDH methods can be realized in the homomorphic encrypted domain.The idea of encrypted domain non-integer mean value is further extended and privacy-preserving processing operations over encrypted images are proposed.The main research work and contributions of this dissertation can be summarized as follows:1.Two-tier RDH-ED for 3D Mesh ModelsWith the rapid development of computer graphics technologies,3D models in the form of 3D meshes or point clouds are increasingly used in numerous applications such as computer aided design(CAD),scientific simulations,video games,movies,virtual reality and 3D printing.However,most of the current RDH-ED methods with homomorphic public key cryptosystems are designed for 2D images and no attention is paid to 3D meshes.In this dissertation,the probabilistic and homomorphic prop-erties of the Paillier cryptosystem are used to propose a two-tier RDH-ED for 3D meshes for end-to-end authentication and cloud data management in the encrypted domain.Experimental results from standard 3D meshes prove that the proposed RDH-ED achieves high embedding rates with improved quality of directly decrypted marked meshes.Moreover,embedded data can be extracted both in encrypted and plain domains.2.Prediction-error Expansion based RDH-ED in Encrypted ImagesCurrent RDH-ED methods with Paillier cryptosystem use the addition and non-encrypted scalar multiplication homomorphic properties to design data embedding methods in encrypted images.However,state-of-the-art embedding methods,such as prediction-error expansion(PEE)and difference expansion(DE),that involve mean value(division)computation in the encrypted domain cannot be realized with the addition and multiplication homomorphic properties without pre-processing or interactive protocol between the content owner and cloud server.Although,fully homomorphic cryptosystem can perform an arbitrary number of mathematical oper-ations in the encrypted domain,it is not efficient for practical applications due to its large ciphertext expansion and computational complexity.In this dissertation,using the homomorphic properties of the Paillier cryptosystem and lattice theory,a solu-tion for mean value computation in the encrypted domain is proposed which does not require any pre-processing or interaction between the content owner and cloud server.Based on the encrypted domain mean value computation,PEE based RDH-ED in encrypted images is proposed.Experimental results from standard test images show that the proposed RDH-ED outperforms other state-of-the-art methods.3.Privacy Preserving Processing Operations over Encrypted ImagesCurrent methods of privacy-preserving processing operations over encrypted images require pre-processing of the plain domain images or interactive protocol between the client and the server in order to perform these operations in the encrypted domain as most of these operations involve mean value computation or division operation which could not be realized with additive homomorphic cryptosystem.Additionally,the processing results of these methods in the encrypted and plain domain were not the same.In this dissertation,the idea of encrypted domain mean value computa-tion is extended to propose privacy-preserving processing operations over encrypted images such as smoothing filter,un-sharp masking and histogram equalization.Ex-perimental results from standard test images reveal that these image processing op-erations can be performed without pre-processing,without client-server interactive protocol and without any error between the encrypted domain and the plain domain.