The Study Of Color Image Encryption Technique Based On Fractional Fourier Transform

Image encryption technology for information security is an international frontier research topic of great academic value. The research product can be applied directly to the anti-counterfeit and safety verification. Thus, it has great application value and broad prospect for development. Moreover, it has significant social and economic benefits, and can promote the development of information science in related fields.In practice, color information is very useful, we need to process and transmit plenty of color images. Color image is more fitting for the direct perception of human. In this paper, the theory of fractional Fourier transform (FRT), color model and color transform of the color image have been described, otherwise, several common existing color image encryption technologies have been analyzed. Several single channel color image encryption technologies combing with FRT have been proposed. We have mainly investigated four aspects as follows:First, we propose a single channel color image encryption technology based on FRT and phase retrieval algorithm (PRA), and give the corresponding optical implementation method. We deal with these RGB components as a joint image, fully use of the parallel processing character of optical system, achieving the purpose of parallel processing. Simulation results proved the effectiveness. After a small number of iterations, we could find a good approximate solution, and the security of this method has been analyzed.Second, a color image encryption method based on joint fractional Fourier transform correlator (JFRTC) and PRA has been proposed. Two spatial light modulators (SLM) in the fractional spectrum plane, an amplitude only SLM and a phase only SLM, enable the parallel reconstruction of the joint image. Simulation results show that the algorithm has complex calculation process, large design flexibility and key space. Without knowing the key phase distribution, one can hardly recover the encrypted image through blind deconvolution operations. But this method has a deficiency, the fractional order P1 and phase distribution in input has little effect to the quality of decrypted color image. Therefore, the security is mainly depending on the fractional order P2 and phase distribution in fractional spectrum plane, and the security keys of the system are reduced.Third, to compensate for the deficiency above, a new single-channel fully phase color image encryption method based on JFRTC and PRA is proposed. In this method, the joint fractional spectrum is transformed into pure phase information through a simple nonlinear transform, making the spectrum distribution evenly. The security of the system could be ensured for the phase distributions in the input plane and the fractional Fourier spectrum plane playing the same important role in the decryption progress. The system is simple with lower cost, while its security and reliability is assured for only one phase-only SLM is required in the fractional spectrum plane. In addition, this method could avoid the phase distortion introduced by the gap inevitably existing between two SLMs when they are placed side by side in the previous method. The reconstructed image will obviously degrade while the phase distortions exist.At present, most of the optical encryption technologies are achieved through computer simulation, studies by means of optical experiments are very rare. It is not conducive to the practicality, limiting the further development of optical encryption technology. Comparing with computer system, optical information processing system has the irreplaceable advantage for its inherent characteristic of high speed and parallel processing, especially when processing vast amount of information. Therefore, we propose a double light path JFRTC system combined with double random phase encoding method for color image encryption, and carry out the experimental research. The corresponding optical path and the selection of parameters about optical devices have been introduced. Relevant optical experiment results show that this method could well realize single channel color image encryption. The joint fractional spectrum is recorded by photorefractive material, as the encrypted result. When the phase plate is different, and even if we use correct phase plate but shift a little position, we cannot obtain the correct decrypted result.