毕业论文之改进蔡氏电路 Image cryptosystem based on a novel memristive chaotic band-pass filter circuit

Image cryptosystem based on a novel memristive chaotic band-pass filter circuitChenyu Yang, Huihui Ma, Yongbin Yu, Yancheng Wang, Nijing YangSchool of Information and Software EngineeringUESTCChengdu, CAbstractIn this paper, a novel image cryptosystem is presented based on an introduced memristive chaotic band-pass filter(BPF). In light of the magic-cube, this proposed cryptosystem treats the RGB image as a “magic-cube” and the processes of encryption and decryption like the magic-cube playing. With the size of picture increasing, the confidentiality of cryptosystem can be strengthened as the high-level magic-cube playing. Simulation results verify the feasibility and the practicability of provided cryptosystem.Keywordsmemristiv; chaotic circuit; band-pass filter; cryptosystem; imageI. IntroductionIn 1971, Leon Chua proposed the fourth fundamental passive element which called memristor 1, although ,it has not been fabricated until 2008 2. A memristor is a two terminal circuit element that has many unique properties, such as nonvolatility, nonlinearity, and nanometer geometries 2-4. Hence, memristor is widely applied to various fields like data storage, neural networks, secure communications, filter circuit, chaotic circuits, and so on 5-11. In particular, the memristive chaotic cryptosystem are a novel research based on memristive circuit 20,22. Images are widely used in various fields. Due to the image include some privacy information, its security has become more important. The traditional image encryption algorithm, such as IDES and RSA, has low efficiency if the image is large 12. To overcome this problem, the chaotic encryption algorithms are proposed by R Matthews in his paper 13. After that, chaotic cryptosystem developed rapidly 14-17.In the recent years, Chaos-based cryptosystems is one of the hotspots of research because of their initial sensitivity and pseudo-randomness 18. Chaotic encryption can be classified as continuous stream data encryption and discrete data encryption，such as voice encryption, text encryption, image encryption and other multimedia encryption 19-22. In addition, Many cryptography researchers mostly focus on traditional one-dimensional chaotic systems like Lorenz system and Logistic map, which have weak security and are easy to be attacked 13. Thus, multi-dimensional chaos which can be produced by memristive circuits is employed in the chaotic cryptosystem 18.Fig. 1. Memristor emulatorFig. 2. Chaotic circuit The memristor-based chaotic circuit has more complex dynamic characteristics because of sensibility of the circuit parameters and the initial values of the memristor 22. Otherwise, the chaotic signal, which generated by the memoristor-based chaotic circuit, has stronger pseudo- randomness. Thus, memoristor-based chaotic circuit has a better application prospect in encryption and decryption.In this paper, a new chaotic cryptosystem named Magic-cube cryptosystem for RGB image and Gray image is proposed based on a novel memristive chaotic band-pass filter. The cryptosystem is an asymmetric encryption algorithm which treat the RGB image as a ”magic-cube” and the Gray image as a ”magic-cube”. In light of the magic-cube playing, the processing of image encryption likes the processing of encrypting a unequal-ordermagic cube by rotatingsemicycle of one sides some rows, and the decryption of image likes the decryption of the unequal-order magic cube with the same rotating rule. The rest of this paper is organized in the following manner. The section 2 mainly analyses the memristor-based chaotic BPF circuit.In section 3, Detailed description of the color picture encryption and decryption system. experimental results and simulation are provided in Section 4. Finally, the conclusions are drawn in Section 5.II. Analyses of chaotic BPF circuitIn this paper, a novel third-order memristive chaotic active BPF circuit is introduced 23, which is built by one single op-amp U, one memristor M as shown in Fig. (1), two capacitors C1 and C2, three resistors R1, R2, and R3, as shown in Fig. (2) .The memristor emulator is described as follows. (1)where the denotes the total scale factor of and .And according to the Kirchhoffs circuit Laws, the memristor circuits state equations are obtained as follows. (2)By giving , , , , , , , . The (2) can be rewrote as follows. (3)where , , , , . By fixing the initial conditions, a chaotic attractor can be obtained as shown in Fig.3, which can provide the chaotic sequences(CS) for cryptosystem. And to connecting the CS with the cryptosystem, the value of parameter is unfixed. Based on the initial sensitivity of chaos, any difference of the value of will result in completely different CS to ensure the cryptosystem. (a) (b)Fig. 3. Chaotic strange attractorsFig. 4. Cryptosystem modelFig. 5. Description of RGB image III. Design of image cryptosystemIn this section, the design of image cryptosystem will be illustrated and the image cryptosystem can be described as shown in Fig.4.As the precondition, a image is made as a cube and an example is supplemented in Fig.5. The cryptosystem process can be presented in detail as follows.l Step 1, a seven digits user key(UK) is obtained like . Theare the deflection-digit(DD) which are used to describe the deflection of each planes. And the denotes the initial-digit(ID) which is employed to calculate the parameter in (3).l Step 2, to obtain the CS, the value of is presented by following calculation. (4) (5)l Step 3, to encrypt the image, the three-dimensional CS (X, Y, Z) is employed from chaotic circuit and both the length of sequences X, Y and Z is equal to . The value of sequences X, Y and Z is mapped to 0255 as shown in Fig. 6. l Step 4, the sequences X, Y and Z plus the red, green and blue color channels equals the new image color channels respectively (mapped in 0255).l Step 5, as shown in Fig. 5, the length , width and height(three color channels) are marked number severally. And the value of and show the turning-circles of the number 1 and number 4 row of . In the same rule, and map the and the height is mapped by and which are mapped in 13. The order of turning agrees with the UK.l Step 6, the same process is realized as shown in step 4.The decryption is partly similar with encryption like playing magic-cube.IV. Experimental resultsIn this section, the simulation result is presented and both of these images are . The parameters of chaotic circuit areelectedas , , and the UK is chosen as 3205789 which sets the as 7.6.In particular, the gray image is treated as a single color channel magic-cube. The cryptosystem and the software interface are programmed by visual studio 2010 and the chaos is created by Matlab simulating.In this cases, the encryption and decryption results of gray image are showed in Fig.7 and the results of RGB images are expressed in Fig.8. The software interface is divided into three parts including loading part, encrypting part and decryption part. The showing and loading of image are realized in loading part, the processing of encryption is established in encryption part and the decryption result is provided in decryption part. (a) sequence X (b) sequence Y(c) sequence ZFig. 6. chaotic sequencesFig. 7. cryptosystem software interface of Lena gray image(a)(b)Fig. 8. Cryptosystem software interface of RGB imagesV. ConclusionIn light of magic playing, a novel cryptosystem is presented in this paper. Based on the initial sensitivity of chaos, we adopt the scheme that the initial parameters of chaotic circuit are instituted by UK to ensure the security of cryptosystem. Simulation results show the feasibility and the practicability of memristor-based chaotic circuit for encryption and decryption.AcknowledgmentThis work is supported by National Natural Science Foundation of China (NSFC Grant No.61550110248). The authors would like to thank the editor and the reviewers for their helpful suggestions and valuable comments.References1 Leon O. Chua, “Memristor-The Missing Circuit Element,” IEEE TRANSCTION ON CIRCUIT THEORY THEORY, vol18, pp. 504-519, 1971.2 D. B. Strukov, G. S. Snider, D. R. Stewart, and R. S. Williams, “The missing memristor found,” Nature, vol453, pp. 8083, 2008.3 Y. Ho, G. M. Huang, and P. Li. Nonvolatile memristor memory: device characteristics and design implications. 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