Research On Application Of Compressive Sensing Technology To Image Encryption

Compressive sensing(CS)is a new signal sampling model which can effectively capture and recover signals by setting an underdetermined linear system.By utilizing the fact that the nature signals are usually sparse or compressible,CS theory indicates that signals can be reconstructed with high probability using a small number of linear,non-adaptive measurements.The compression process is directly integrated into the sampling process in CS sampling model.Therefore,due to the inherent characteristics of CS,it has attracted extensive research attention in many fields since it was proposed.In the CS sampling system,the measurements obtained by projecting a signal into the random subspace can be considered as a method of information protection.The CS framework can be regarded as a symmetric encryption scheme where the signal,the measurement matrix and the measurements correspond to the plaintext,the secret key and the ciphertext,respectively.As a common presentation form of multimedia data,image is often used in information transmission.CS can not only provide protection mechanism for the signal,but also reduce the redundancy between the pixels of the natural image.As a result,CS is a promising technology to protect image security in image application scenario.However,the security analysis results of the CS framework show that the traditional CS cryptosystem cannot achieve perfect security unless the measurement matrix is a Gaussian matrix and the signals to be measured have the same energy.In addition,if the security of the scheme only depends on CS technology,the image encryption scheme cannot resist the chosen plain attack under the condition that the measurement matrix is reused.Therefore,this thesis studies how to use CS to encrypt images and the main works can be summarized as follows.(1)The security problems and the reconstructed image quality problems of applying various models based on CS to design image encryption scheme are analyzed and summarized.In addition,some cryptographic features that may be incorporated into CS framework are explained from various perspectives such as sparse signal processing and measurement matrix generation,and security mechanisms are introduced to provide more perspectives for designing image encryption schemes using CS.(2)In order to balance the efficiency and security of the cryptosystem under the premise that the measurement matrix are reused,an efficient image encryption scheme using sparse signal transformation and parallel CS is presented.Transformation function is employed to change energy information of the coefficient matrix before CS sampling,which is beneficial for improving the security of the cryptosystem.What's more,as sparse signal transformation is linear operation,it will not increase computational overhead.The experimental results and theoretical analysis show that the encryption scheme can resist the chosen plain attack.(3)In order to achieve visually secure of cipher image,an efficient visually secure image encryption scheme based on parallel CS is proposed.The scheme not only can protect the information of plain image,but also realize the visual security.First,the plain image is encrypted using parallel CS combined with counter mode to obtain the secret image.Then,the secret image is embedded into the cover image to generate the cipher image.The embedding technique is controlled by the chaotic system to enhance the security level of the scheme.It mainly solves two problems in the existing scheme: one is the flexibility of selecting cover image,that is,the quality of reconstructed image is not affected by the cover image,which makes the encryption scheme be potential for practical applications;the other is the reversibility of secret image,that is,the secret image can be extracted accurately from the cipher so that the decrypted image can be stably reconstructed.(4)To realize simultaneous sampling process and diffusion,a parallel CS image encryption scheme based on the embedded diffusion matrix is presented.The proposed scheme can compress and sample images while protecting the privacy of energy information.What's more,the attacker cannot calculate the pixel distribution of the plain image according to the distribution of the measurements.Furthermore,the scheme can resist the chosen plain attack by updating the diffusion matrix.The theoretical analysis and experimental results show that the scheme has good security performance,and the quality of the reconstructed image is not affected by the diffusion matrix.(5)Considering that the data may be attacked in transmission over unsecured channel and the reconstruction process of sparse signal is very time consuming,an image encryption and authentication scheme based on CS is proposed in order to verify the integrity of the data before reconstructing the image.The scheme can verify the integrity of cipher image and locate the tampered region if the cipher image is attacked.