Image Encryption Research Based On The Chaos And Digital Transform

With the rapid development of Internet and communications, digital image as a visual form of multimedia data, is used widely. Because of unprecedented openness of today's network and increasingly powerful processing function of computer, it involves threat in personal privacy and the security of digital images which include secret data. Thus, the image encryption algorithm came into being and has made a lot of research results. The security of the encryption algorithm is also rising and strengthened.At present, the main algorithms for image encryption are image scrambling and pixel replacement. Image scrambling does not change the pixels'values; just change the locations of the image pixels, so as to achieve the purpose of encryption. And pixel replacement changes the pixels'values using a reversible calculation method, in order to achieve image encryption. Early image encryption algorithm uses one of them, and later evolved into a combination of these two algorithms. With the development of chaos theory and the introduction of digital transformation, image encryption algorithm steps to a new phase; security has also been greatly improved.Firstly, this paper uses the current research focus-the theory of memristor and analyzes the chaos system which is the Chua's circuit system with memristor. Memristor is known as the fourth basic electronic components following the resistors, capacitors, inductors. Memristor is a resistor with memory, which shows the characteristics that "remember" what charge it had when power runs through it. The Chua's circuit can exhibit chaotic characteristics, and replacing the Chua diode with memristor, the new chaotic Chua's circuit equally performances a certain advantage. Based on this chaotic system, this paper proposes an image encryption algorithm, which combines image scrambling and pixel replacement algorithm. The two algorithms are implemented and based on chaotic sequence. It can be seen from the simulation results, the algorithm has good security:against the brute-force attacks of the encryption key, histogram analysis, statistical analysis of correlation between adjacent pixels, entropy analysis, geometric attacks and other attacks.In addition, with the general development of fractional differential theory, chaotic differential dynamic system and digital transformation theory are studied into a new field. Fractional order chaotic systems and fractional-order digital transformation has been rapidly developed and applied on multimedia information security. In this paper, to be based on the characteristics of fractional differential, and combined with the current common chaotic system, the fractional order chaotic system and its chaotic attractor are simulated. This paper designs an image encryption algorithm with fractional order and is based on transformation theory and fractional order chaotic scrambling algorithm. From the results of simulation, the algorithm has a good performance on statistical analysis, the sensitivity of plaintext, the peak signal to noise ratio and the mean error.