Image Encryption Method Based On GS Algorithm

With the rapid development of network technology, a large amount of information is transmitted through the network, so people pay more and more attention to the problem of information security. The research of the image information security technology, especially the image encryption method has received wide attention, and has been the hot research problem. The research content of this paper is using the transform domain method to establish a new image encryption method, which is to overcome the hidden trouble of the previously established image encryption method in the transform domain, such as several kinds of hidden dangers of the fractional Fourier transform encryption method, and improve the security of image encryption methods.In this paper, a new kind of unitary transformation is proposed, which is called the double parameter vector power weighted unitary transformation. The mathematical properties of the transformation are studied, such as linear additive, order additive,unitary, etc. Based on the double parameter vector power weighted unitary transform theory, this paper studies a new kind of iterative phase recovery algorithm, which is double parameter vector power weighted unitary transformation GS algorithm, and double parameter vector power weighted unitary transforms GS algorithm for image encryption method is proposed. By carrying out digital simulation, the effectiveness,safety and reliability of this new image encryption method have been tested.Firstly, this paper proposes a double parameter vector power weighted unitary transformation. It is a very widely fractional Fourier transform operator, it is depended on the number of the weighted items and three real parameter vectors having the same dimension which is the number of the weighted items. This three real parameter vectors contain a power vector and two free parameters vector. It is easy to verify that power vector weighted unitary transform operator, weighted unitary transforms operator, multi parameter fractional Fourier transform operator, the standard weighted type fractional Fourier transform operator and the classical Fourier operator are the special case of the double parameter vector power weighted unitary transform operator.Secondly, the double parameter vector power weighted unitary transformation GS algorithm is proposed. Double parameter vector power weighted unitary transform GS algorithm is a new kind of iterative phase retrieval algorithm and in the iterative process,transform domain is the double parameter vector power weighted unitary transform which has three high-dimensional real vector parameter. This new phase retrieval algorithm contains the iterative phase retrieval algorithms of almost all the transformation domain as a special case.Thirdly, a double parameter vector power weighted unitary transformation GS algorithm for image encryption is established. The main idea of the new image encryption method is replacing the Fourier transform of the GS algorithm with double parameter vector power weighted unitary transforms to obtain a new phase retrieval algorithm, then through the phase coding and iterative, encrypting the original image into stable phase information, finally we obtain the cipher image which exists in the form of phase.Fourthly, the security, reliability and validity of the double parameter vector power weighted unitary transform GS algorithm is verified by digital simulation.In short, the double parameter vector power weighted unitary transform theory enriched the theory of Fourier transform, and the double power vector weighted unitary transforms GS algorithm which is established based on this new transform theory enriches the iterative phase retrieval algorithm. As an application of this new theory, the double parameter power vector weighted unitary transforms GS algorithm for image encryption method provides new avenues of research to establish image encryption techniques with higher security.