6, where DNA decoding and recombining selleck are the inverse process of Steps 3 and 2 in Section 3.2. The procedure of acquiring the original image from the encryption image is an inverse operation according to Algorithm 2, where deletion operation is replaced by insertion operation.4. Simulation Result and Security Analysis4.1. Simulation Result In this paper, for standard 256 �� 256 gray image Lena, we use Matlab 7.1 to simulate experiment. In our experiment, we set x0 = 0.95, ��1 = 3.2, ��1 = 0.17, y0 = 0.25, ��1 = 3.3, ��2 = 0.14. The original image is shown in Figure 3(a), Figure 3(b) shows encrypted image, and Figure 3(b) points out that it is difficult to recognize the original image. Figures 3(c) and 3(d) show the decrypted image under the wrong secret keys and the right secret keys, respectively.

From Figure 3(c), we know that it has not any connection with the original image, but Figure 3(d) is as same as the original image.Figure 3Encrypted image and decrypted image. (a) The original image. (b) The encrypted image. (c) The decrypted image under the wrong secret keys. (d) The decrypted image under the correct secret keys.4.2. Secret Key’s Space Analysis In the proposed algorithm, the initial value and the parameter of the system of 2D logistic are identified as secret keys of this algorithm. Therefore, our algorithm has six secret keys x0, ��1, ��1, y0, ��2, ��2. If the precision is 10?14, the secret key’s space is 1014 �� 1014 �� 1014 �� 1014 �� 1014 �� 1014 = 1084 �� 2279. It is shown that the secret key’s space is large enough to resist exhaustive attack.4.3.

Secret Key’s Sensitivity Analysis The chaotic map is very sensitive to the initial value in chaotic state, in other words, it also ensured the sensibility of this encryption algorithm to the secret key. In this paper, if the initial values from three chaotic maps are changed a little, the recovering image is not allowed to be read, but we can get the original image from the encrypted image by using the correct secret keys. The experiment results are shown in Figure 4, where Figure 4(a) shows the decrypted image under the secret keys (0.95000000000001,3.2,0.17,0.25,3.3,0.14). The corresponding histogram is shown in Figure 4(b), and we can see that the histogram of the decrypted image is very uniform. The sensitivity of other parameters is similar.

From Figure 4, we can see that only when all secret keys (the chaotic initial value and system parameter) are correct, the original image can be obtained. Otherwise the decrypted image will have no connection Anacetrapib with the image. Based on the above argument, our algorithm has strong sensitivity to secret key and we can say again that our algorithm can resist exhaustive attack.Figure 4The sensitivity of secret key x0. (a) The decrypted image with secret key (0.95000000000001,3.2,0.17,0.25,3.3,0.14). (b) The corresponding histogram.4.4.