Abstract: In the rapid development of various expertises, the information can be misplaced, misused and damaged. To overcome these vulnerabilities, the information security is eminent. Information security ensures the authorized people to access the precise information when they are needed and cannot be customized without authorization. To prevent the access of information from the illegal user and destruction several encryption techniques are used. Multilevel and double image encryption method are proposed this work to achieve the high level secrecy and better performance. The novel double image encryption technique based on cross image pixel scrambling in Fourier domain and chaotic maps are used to achieve the multilevel encryption. The statistical and security test are tested on Digital Imaging and Communication in Medicine (DICOM) images.
INTRODUCTION
Due to the development of multimedia and network technologies, the information is transmitted through communication network. The intruder can capture the information and it can be altered (Dang and Chau, 2000). Wireless security is used to protect against the illegal copying and distribution of the information (Praveenkumar et al., 2014c). The wireless network provides to access and share the information from any place. Information security such as encryption is used for providing security. Security system is classified into information hiding and cryptography. Steganography and water marking are sub disciplines of information hiding (Amirtharajan et al., 2013).
Cryptography is used for protecting the content of the message from an unauthorized user. The main objective of cryptography is authentication, confidentiality, integrity, non repudiation and availability. It is classified as symmetric key cryptography, asymmetric key cryptography and hashing functions. In symmetric key cryptography identical keys are used for both encryption and decryption. The DES and AES are frequently used techniques in symmetric cryptography. Asymmetric key cryptography uses public key and private key for encryption and decryption. Most popularly used asymmetric cryptography techniques are RSA, DSA and Diffie-Hellman (Wang et al., 2010).
Encryption is the process of altering of information using a secret key which cannot be retrieved by an unauthorized user. Decryption is the reverse process of encryption (Dang and Chau, 2000), with the development in the technology multiple image encryption is proposed in this work. Here double image is encrypted using Arnold cat map and chaotic chebyshev map (Zhong et al., 2012; Li and Dai, 2010). Multiple secret images can be hidden at the same time using multiple image encryptions algorithm. Scrambling is the process of encoding of message in a form which makes the image in an unintelligible form (Aarthie and Amirtharajan, 2014; Amirtharajan et al., 2013; Praveenkumar et al., 2014a,b,c,d, 2015a,b,c,d; Rajagopalan et al., 2014a,b,c). Scrambling of images is defined as the process of change in the position of pixels in a particular order.
Two input images are combined to processed further. This image is split into several bit planes and shuffled iteratively using logistic map algorithm along with Arnold cat map. The Arnold cat map used to scramble and shuffle the pixel of an image (Liu et al., 2012; Veena et al., 2012; Prusty et al., 2013). The properties of the chaos are sensitive to the initial condition and dense orbits. The chaos maps are deterministic dynamical system and have random behaviour. Finally obtain the random binary matrix by chaotic map (Zhe et al., 2009; Li and Liu, 2013; Zhang et al., 2014; Desai et al., 2012).
The chaotic logistic map is depicted by Eq. 1:
| (1) |
The bit xor operation is performed between the unique key and shuffled image by Arnold cat map which produce the ciphered image. The chebyshev map is used to generate the key for shuffled image and generate the row confusion vector. The chaotic state variable is generated by chebyshev map (Fu et al., 2013; Dai and Wang, 2012; Prasadh et al., 2009; Wang et al., 2008). The row and column of the shuffled image are rearranged by row confusion vector and finally produce the scrambled cipher image.
Zhong et al. (2012) proposed double image encryption by scrambling the matrix and encoding one image into phase and other image into amplitude of the complex function. In fractional Fourier domain, double random phase encoding is applied to this complex function and the resultant is the encrypted image.
Liu et al. (2012) proposed the encryption method for double image using Arnold and discrete fractional angular transform. The two images are converted into phase and amplitude of the complex function. Arnold transform is used to scramble the pixel position and it is transformed into fractional angular domain. In this process phase is considered as the key and amplitude of the image is the encrypted image.
In this study, a combination of two images into single image using Arnold transform to scramble the pixel position using chaotic logistic sequence is proposed. It is used as the key for encryption. Further image is encrypted using chaotic chebyshev map. The chaotic logistic and chebyshev maps are used as the key for both encryption and decryption process.
MATERIALS AND METHODS
In this study, a combination of two images into single image using Arnold transform to scramble the pixel position using chaotic logistic sequence is proposed shown in Fig. 1. It is used as the key for encryption. Further image is encrypted using chaotic chebyshev map. The chaotic logistic and chebyshev maps are used as the key for both encryption and decryption process.
Encryption algorithm:
| • | Read the double input DICOM images of size 256×256 |
| • | Split the image into 8 bit planes and apply Arnold cat map to shuffle the bit planes |
| • | Then the resultant image forms the encrypted image of level 1 |
| • | The chaotic logistic key is generated by Eq. 1 and Bit xor with the previous cipher from step 2 |
| • | Then the resultant image forms the encrypted image of level 2 |
| • | Row confusion vector is calculated by Eq. 2: |
| (2) |
| Fig. 1: | Block diagram of encryption and decryption |
The values of rm is restricted within the region (m, M). The chaotic state variables are generated from chebyshev map as expressed by Eq. 3:
| (3) |
| • | Apply this row confusion vector to step 6 then it forms the resultant image as the scrambled image of level 3 |
| • | Store the resultant image as the multilevel encrypted image |
The block diagram of encryption and decryption is shown in Fig. 1.
Decryption algorithm:
| • | Read the double input multilevel encrypted image |
| • | Decrypt the image using the key generated by chaotic chebyshev map Eq. 3 |
| • | The resultant image is the descrambled image of level 1 |
| • | Generate the key using chaotic logistic map Eq. 2 |
| • | Bit Xor is applied between the step 3 and 4 then the resultant image is the decrypted image of level 2 |
| • | Then to the decrypted image obtained from step 5 apply Arnold cat map to reshuffle the image to form the final decrypted image of level 3 |
| • | Combine 8 bit planes into single plane |
| • | Store the resultant image as the decrypted image |
RESULTS AND DISCUSSION
In this study a double image encryption is proposed. Double image is encrypted using Arnold logistic cat map and chaotic chebyshev map. To prove the performance of the proposed method various metrics were calculated such as correlation coefficient, Number of Changing Pixels Rate (NPCR) and information entropy.
Several metrics were calculated for sample images shown in Table 1 and compared with recent work on image encryption (Zhang et al., 2014; Dai and Wang, 2012). Consider image 1 and 2 as the double input image for which horizontal, vertical, diagonal correlation, NPCR and entropy were calculated as -0.0044, -0.00046, 0.0039, 99.5750 and 7.9962, respectively and these values are comparable with various studies (Praveenkumar et al., 2015a , b, c, d; Zhang et al., 2014; Dai and Wang, 2012), the correlation values, NPCR and entropy are better.
In Fig. 2a depicts the double input medical image and Fig. 2b depicts the uniform pixel distribution of Fig. 2a. The encryption using Chaotic Arnold cat map of Fig. 2a is depicted in Fig. 2c. The encryption using chaotic chebyshev of Fig. 2c is illustrated in Fig. 2d. The uniform pixel distribution of Fig. 2d is represented in Fig. 2e. There is no correlation between the original and ciphered image. The decryption using chaotic chebyshev of Fig. 2e is illustrated in Fig. 2f. The final decrypted image is depict in Fig. 2g. The uniform pixel distribution of Fig. 2g is illustrated in Fig. 2h.
NPCR: Number of pixel change rate (NPCR) is used to find the effect one pixel modification on the entire image. It used to find the difference between original and encrypted image pixels. NPCR, correlation coefficients and entropy were calculated using the Eq. 4:
| (4) |
X, Y is the adjacent pixel from original image and encrypted image:
| • | |
| • |
| Table 1: | Metrics considering images of size 256×256 |
| Fig. 2(a-h): | Sample double image with their multiple encrypted decrypted outputs and histograms (a) Original double image, (b) Histogram of Fig. 2a, (c) Encryption using Arnold cat map, (d) Encryption using chaotic chebyshev, (e) Histogram of Fig. 2d, (f) Decryption using chaotic chebyshev, (g) Final decrypted image and (h) Histogram of Fig. 2g |
Correlation coefficient: Correlation is used to find the degree of similarity between the two adjacent vertical, horizontal and diagonal pixels are given in Eq. 5:
| (5) |
where, μ is the mean value, s is the standard deviation, E [.] is the expected value.
Entropy: Average quantity of information enclosed in the each received message and the formula is given in Eq. 6:
| (6) |
| H(X) | = | Information entropy |
| X | = | Information source X |
| L | = | Length |
| p(xi) | = | Probability of symbol |
CONCLUSION
To tackle the robustness, tamper detection and security issues double image multilevel encryption scheme is proposed. The double image is scrambled using Arnold cat map and chaotic Chebyshev map. The bit-XOR operation is performed between unique key generated by chaotic chebyshev map and scrambled image. The resultant image is the multi level encrypted image. The various metrics such NPCR, information entropy and correlation values of horizontal, vertical, diagonal were calculated for various medical image and compared with available literature and found to be superior. The negative correlation values expose that they defend against discrepancy and brute force attack.