Research On Key Problems Of Quantum Color Image Security Protection

With the continuous development of quantum computing theory and technology,quantum computer with powerful computing ability is becoming a reality.However,as a tool to solve some difficult problems on classical computer,quantum computer also makes some new requirements and provides novel challenges for the traditional research areas.In the field of image processing,the existing image security protection technology is based on the classic computer framework,so can not be applied into the quantum computer.Researching about image security protection technology on quantum computer is becoming more and more urgent to rich quantum image's theory research content and enhance the security of image in the quantum computer.This paper focuses on two key problems of color image security protection technology on quantum computers: quantum color image scrambling encryption and steganography.The research of these two technologies is based on the quantum color image representation model.Therefore,this paper firstly proposes quantum color image representation model,and then puts forward new methods and new ideas for scrambling encryption and steganography,respectively.The main research work and innovation are summarized as follows:(1)Aiming at the issue of how to store color image on quantum computer,quantum color image representation model NCQI(A Novel Quantum Representation for Color Digital Images)under cartesian coordinate system and quantum color image representation model MCLPQI(Multi-channel Log Polar Quantum Image Representation)under polar coordinate system are proposed.The quantum color image is expressed as a normalized quantum superposition state by using quantum entanglement and superposition characteristic from the viewpoint of encoding color image's color information and position information,so the problem of storing color images on the quantum computer is solved.Compared with the existing models,NCQI model is simple to prepare and flexible.MCLPQI is the first quantum color image representation model under polar coordinates,which is suitable for the study of image registration and so on.In addition,the elementary transformation of these two models is studied,and the unitary matrix and the corresponding quantum circuit are designed.These studies enriched the theoretical content of quantum color image representation.(2)Aiming at the issue of changing the color image's position on quantum computer,an affine transformation algorithm of NCQI based on unitary transform is proposed.We find that moving the qubits to the left can realize the preparation of the quantum state|ax?.On the basis of the state |ax?,the unitary operator can be designed to realize the affine transformation method.Comparing with the existing affine transform method which transforms the multiplication operation involved by affine transform into adder operation and supposing there are only two parameters in the diagonal of affine transform matrix,the form of affine transformation we studied is more general.(3)Aiming at the issue of changing the size of color image on quantum computer,a nearest neighbor interpolation algorithm of NCQI based on halving operation and a nearest neighbor interpolation method of NCQI on the basis of CNOT gate are proposed.The basic principle of these two algorithms is: firstly,the mapping relationship between the interpolated image's position and the cover image's position is established by using the halving operation and the CNOT gate.Then,the unitary operator is utilized to prepare the color value of the corresponding pixel to obtain the interpolated image.Finally,these two algorithms are applied into the quantum gray images FRQI and NEQR.The nearest neighbor interpolation algorithm for FRQI is given for the first time.Comparing with the existing NEQR interpolation algorithm,our NEQR interpolation algorithm's complexity is lower.(4)Aiming at the issue of security protection of color image's content on quantum computer,Arnold scrambling algorithm and Fibonacci scrambling algorithm based on affine transform are proposed,also Arnold and Fibonacci scrambling algorithms based on adder and adder-modular operation are proposed.We find that affine transform and scrambling encryption can both change the position of the image,so the affine transform can be refereed to realize the scrambling.Compared with the existing methods,the complexity of Arnold and Fibonacci scrambling methods based on affine transformation is reduced.In addition,we design the scrambling algorithms based on adder and addermodular operation from the viewpoint of realizing the Arnold and Fibonacci scrambling matrices,which the complexity is lower than the proposed affine-based algorithms and the existing algorithms.The advantages of the proposed algorithms are that they can output a complete scrambled image at the output side of the quantum circuit.The simulation results show that these two algorithms have good visual effect.The proposed algorithms provide new schemes for the realization of color image security protection on quantum computer.(5)A LSQb steganography algorithm based on color coding feature of NCQI is proposed to realize the security protection and the hiding communication behavior of color image on quantum computer.Three qubits comparator and unitary operator are designed based on the color encoding characteristic of NCQI to realize the comparison between the secret qubits and the least significant qubit of the carrier image's pixel,also to achieve the secret qubit's embedding.Compared with the existing algorithms,our algorithm has two advantages: 1)the algorithm is blind,that is,the secret qubits stream is extracted without the help of the original carrier image.2)embedding capacity is large.The simulation results show that the algorithm has good visual effect.In addition,the LSQb steganography algorithm of NEQR based on two qubits comparator and unitary operator is designed,which enriches the content of existing quantum gray image security protection technology.