Quantum Image Encryption Algorithm Based On Chaotic Map And Quadratic Residual Cryptography

With the rapid development of the Internet,image information becomes more and more important in our life.For example,picture dynamics in the circle of friends,fingerprint unlocking of smart phones,face recognition on the threshold,etc.Some of these images can be public information,some is our own personal privacy,and some will be more involving business secrets,national security,therefore,how to protect the safety of the information,how to make the image information is not leaked or stolen by others,these problems become the information security researchers in recent years is the focus of attention.Is one of the best way to protect the safety of image information of image is encrypted,in such a way to encrypt the image information,can better improve the security of some important image information,otherwise attempt to prevent some illegal invaders to steal,damage and tampering with image information,it is also the research significance of image encryption algorithm.With the development of computer science,quantum computer emerges at the historic moment.Some scholars combine the knowledge of quantum mechanics with the traditional image encryption algorithm and put forward the quantum image encryption algorithm.Compared with the traditional image encryption algorithm,quantum image encryption algorithm has the characteristics of quantum mechanics,if in the process of quantum image from outsiders,then quantum image will be because of the characteristics of quantum irreversible change,then the recipient will be found that the image in the process of transmission have been attacked,therefore quantum image encryption algorithm than the traditional image encryption algorithm has higher security,and thus became the scholars at home and abroad in recent years,the research direction.In this paper,quantum affine transform is used as the main encryption method,and logistic mapping and Hoffman coding are combined to propose a quantum image encryption algorithm based on affine transformation.The encryption steps of quantum image encryption algorithm based on quantum affine transformation are described in detail,and the quantum image encryption simulation is carried out with this algorithm,and the security of encrypted quantum ciphertext image is analyzed from several aspects.The main contents of quantum image encryption algorithm based on affine transformation are as follows:First,the plaintext image that needs to be encrypted is digitized to obtain a digital matrix containing image information,and then the digital matrix is quantum coded to obtain the quantum plaintext image.In this paper,the classical Arnold transform is taken as an example to introduce the quantum affine transform.Based on the quantum circuit diagram of the quantum Arnold transform,the quantum circuit diagram of the quantum affine transform used in this encryption algorithm is constructed.On the basis of the successful construction of the quantum circuit diagram,this paper encrypts the quantum plaintext image with the conversion times and variable coefficients as the key,and obtains the quantum image after the first scrambling.Then,carry out logistic mapping to the scrambled quantum image.Will ? and logistic map of initial values as keys,randomly generated two sequences of logistic,inverse trigonometric function transform,respectively,and then the initial value when the sum of pixels in the images of the quantum horizontal ordinate for odd number,scrambling to uselogistic1 sequence,when the sum of pixels in the images of the quantum horizontal ordinate is even,with logistic2 sequence scrambling,finally can get the quantum after secondary scrambling image.Finally,the second scrambled quantum image is Huffman coded and the quantum ciphertext image is obtained.In the process of image decryption,except for quantum affine inverse transformation,the other decryption steps are reverse operations of encryption methods.Finally,the computer simulation experiment and security test of the algorithm are carried out.In this paper,Matlab software image is used to encrypt and decrypt the Lena image with the size of 512.The clear text image Lena is encrypted by the encryption algorithm in this paper,and the effective information in the clear text is well hidden.Compared with the original plaintext image,the decrypted plaintext image has no loss of key information,which shows the better encryption and decryption effect of the algorithm intuitively.Then,the security of the algorithm is analyzed from the aspects of gray histogram analysis,adjacent pixel correlation analysis,key sensitivity analysis and information entropy analysis.It is concluded that the encryption algorithm in this paper has strong anti-histogram attack ability,can resist image attack based on statistical analysis,the key has good sensitivity,and the encryption algorithm in this paper can also resist information entropy attack.From these aspects,it is shown that the encryption algorithm in this paper has good security.By comparing with the corresponding data in other literature,it is concluded that the algorithm has higher security than the encryption algorithm in other literature in resisting image attack and information entropy attack based on statistical analysis.The security advantages of this algorithm are highlighted.