| The image,with its qualities of vividness,intuitiveness,and simplicity,has become an indispensable facet of information transmission.To ensure the safety and quality of the transmission of images in Internet,there is an escalating demand for efficient image encryption algorithms and compatible hardware to attain superior quality.Quantum image encryption stems from digital image encryption and quantum information technologies.Because of its innate parallel computing capabilities,quantum image encryption shows a great promise to satisfy the demands for the safety,quality and speed of image transmission.This dissertation presented the design of several secure image encryption algorithms leveraging the intrinsic properties of quantum images and proposed quantum circuits for quantum image encryption,and elucidated the principles of fundamental quantum logic gates.The specific research endeavors are summarized as follows:To address the concurrent considerations of computational precision,efficiency,and the stability in quantum image encryption algorithms,this dissertation extends the application of the Harr quantum wavelet transform(HQWT)and the iterative quantum Fibonacci transform(IQFT).An algorithm for encrypting multiple color quantum images under the generalized quantum image representation(GQIR)model is introduced.This algorithm exploits HQWT to investigate the impact of this quantum transformation on image characteristics.It analyzes the effects of HQWT on grayscale and color images,as well as the effects on permuting multiple RGB images stored in the generalized quantum image representation,compressing the permuted images into a single composite image.This compression and encryption algorithm employs a measurement matrix comprised of Hadamard gates to compress the composite image at varying ratios.Subsequently,IQFT is employed to interfere with and further compress the already compressed image.The findings reveal that the HQWT algorithm,in comparison to the DQWT algorithm,can reduce the compression ratio to 25% while maintaining a peak signal-to-noise ratio(PSNR)as high as 29.9312 d B.This algorithm demonstrates the feasibility,security,and efficiency of the combined use of HQWT and IQFT in a quantum image encryption algorithm.To efficiently implement chaotic system-based encryption in quantum image algorithms,a quantum image encryption algorithm is proposed based on the Quantum dual-scale triangular(QDs T)mapping and a multilayer short memory fractional order Lotka-Volterra system(MSMFr LVS)to address the issues associated with the fixed starting point characteristic of the traditional Caputo fractional-order Lotka-Volterra system in practical applications,this dissertation employs a prediction-correction method to obtain the chaotic attractor of the Lotka-Volterra system.This leads to the short memory fractional order Lotka-Volterra system(SMFr LVS).Through Poincare sections and frequency power spectra,the chaotic behavior of SMFr LVS is studied.Under same conditions,it was found that compared to the traditional Caputo fractional-order Lotka-Volterra system,SMFr LVS significantly reduced encryption and decryption times.SMFr LVS achieved a decryption time of 1.624 seconds,while the traditional Caputo system required 3256.137 seconds.This not only substantially decreases the time for encryption and decryption processes but also confirms the superiority of SMFr LVS in practical applications.This significant reduction in time demonstrates the superiority of SMFr LVS in practical use.This dissertation introduces a QDs T mapping and designs its corresponding quantum circuit,constructed based on ADDER-MOD.QDs T mapping is applied to disturb quantum images.In the permutation stage,GQIR transforms the plaintext image into a quantum form,and then the quantum image is divided into sub-blocks.Subsequently,operations are performed on the internal and external arrangements of bit planes through sorting pseudo-random sequences and implementing quantum gray code to multiple RGB images stored in generalized quantum image representation.In the diffusion stage,the initial values of MSMFr LVS are generated by plaintext-related mechanisms,and the ciphertext image is obtained by executing a three-level diffusion operation.The combination of QDs T mapping and MSMFr LV has indeed brought about new possibilities in the field of quantum image encryption.The significant enhancements in security,robustness,computational complexity,and encryption speed offer considerable advantages.This not only provides a higher level of protection in image security but also holds potential for significant contributions in future research and applications.To further innovate the combination of HQWT and IQFT in quantum image encryption,a new quantum color image encryption algorithm is introduced in this dissertation,which utilizes the quantum chaotic mapping of cosine and sine operators.The optimal key sequence is generated using hyper-chaotic mapping.The encrypted ciphertext image is obtained by XOR operation between the key sequence composed of the key sequence and the image.The decrypted image is obtained by reconstructing it from the ciphertext image using some reverse quantum operations and the NSL0 algorithm.Such results suggest that the image encryption algorithm based on Clifford chaotic system(with multiple cosine and sine)is superior to the Sprott mathematical model chaotic system(with a single cosine).The histogram of the encrypted image obtained through Clifford chaotic system is evenly distributed,while the histogram of the encrypted image obtained through Sprott mathematical model chaotic system shows peaks influenced by cosine.The results show that the image encryption algorithm based on Clifford chaotic system is feasible,secure,and efficient.In conclusion,this quantum image encryption algorithm based on the fundamental quantum logic gate principles of quantum wavelet transform and hyperchaotic mapping significantly enhances the feasibility,security,and efficiency of image compression and encryption.It provides a new technical route for achieving higher image quality and establishes an experimental foundation for quantum-based image compression and encryption. |
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