Abstract: In this study, RGB based image encryption was proposed. Initially the RGB components are separated, to each plane logistic mapping was employed. Then permutation was done for number of iterations given by the user and then the bitplanes are combined form a single image. Circular shift operation was performed on either left/right then up/down of the permuted pixels. As a final module, bitwise operation are applied based on two keys for row and column, respectively. To analyse the robustness of the proposed method correlation values, Unified Average Changing Intensity (UACI), Number of Pixels Change Rate (NPCR) and histogram tests were estimated.
INTRODUCTION
The place where mathematics and engineering meets can be called ‘cryptography’. It is one of the means by which a readable data or text is made unreadable (for the eavesdropper) by encrypting the readable data. A sender transforms an original text (plaintext) into a modified text (cipher text) by means of a cryptographic key using encryption. The receiver performs the reverse operation to retrieve back the original message by decryption. So, an interloper cannot tamper the concealed information. The remarkable cryptosystem services are confidentiality, legitimacy, access control, veracity and nonrepudiation. A good encryption method should thrive for two fundamental attributes, viz., confusion and diffusion (Diaconu and Loukhaoukha, 2013; Akhshani et al., 2012).
According to the keys used, cryptography can be classified as public key cryptography and private key cryptography. The two ciphers used in this mechanism are block ciphers and stream ciphers. In former, the operation is done on blocks of ciphers while in the latter operation is done bit by bit. The time taken for encryption and decryption is the disadvantage of cryptography (Amirtharajan and Rayappan, 2013). The effective solution to this problem will be ‘steganography’ (Amirtharajan and Rayappan, 2012a, b; Amirtharajan et al., 2013a-h; Ramalingam et al., 2014) and watermarking. “Steganography”-We can’t say that this sounds alien. It has been in use since very ancient times, term coined from Greek and is nothing but secret message in disguise, putting it simple, hidden writing. Now it is used in digitalized version. So, what exactly does it mean? The phenomenon by which one digit file is hidden or embedded in other. (Amirtharajan and Rayappan, 2013; Janakiraman et al., 2012; Padmaa and Venkataramani, 2014; Praveenkumar et al., 2012a, b, c, 2014a-k). Rajagopalan et al., 2012; Thanikaiselvan et al., 2012, 2013a, b; Thenmozhi et al., 2012).
Cryptography concept dates back to 2000 BC through hieroglyphics, an Egyptian practice. In modern world, cryptography has become a combat zone of top computer scientists and mathematicians. Because today, the decisive issue in business, online communication, war etc is the capability to safely hoard and transmit perceptive data. Cryptography is a significant classification of security system. It is characterized by plain text (original text), encryption (encoding), cipher text (modified text), decryption (decoding), key (tool with which plaintext is turned to cipher text).
Yang et al. (2010a) propose block encryption, universal modular transform with chaotic mapping to improve entropy and security. Luo et al. (2010) uses Lagrange’s equation on RGB plane to provide color image encryption. Huang and Zhang (2013) implements permutation based on six keys and utilizing chaotic maps to ensure encrypted image output. Amirtharajan et al. (2013a) reveals that how encryption can be applied to store secret information in a better way. Wireless communication with its enhanced efficiency, greater flexibility, mobility and reduced cost has encompassed human needs and sophistications to a greater extent. Several techniques adopted in the wireless standards solely contribute to its heightened demand.
Orthogonal Frequency Division Multiplexing (OFDM) is one such technique adopted to provide robust and high speed networks by countenancing signal overlap for secure communication using OFDM, steganography and encryption. Praveenkumar et al. (2014b) proposes image encryption in OFDM wireless environment to provide secure data transmission. A new chaos-based fast image encryption algorithm proposed and explained in (Kwok and Tang, 2007; Amin et al., 2010, Wang et al., 2011; Yang et al., 2010b; Xu et al., 2012) proposed a chaotic system based on circular bit shift and XOR operations. Ye (2010) gives out scrambling based on chaos Zhu et al. (2011) introduces bit-level permutation based on chaos combination. Yoon and Kim (2010) and Zheng and Gao (2011) introduce image encryption with permutation and chaotic maps.
Literature survey has been done on the existing RGB based image encryption algorithms. In this proposed methodology, to the individual bitplanes, logistic chaotic map has been applied to create shuffling. To the shuffled result, Rubik’s cube encryption process to get the final encrypted image. The next section provides the proposed methodology and followed section deals with results and discussion and finally section present the conclusion of this study.
METHODOLGY
In the proposed methodology, chatic logistic mapping was employed to the RGB planes of the original image to provide shuffling and Rubick’s cube encryption was employed on the shuffled image to get the final encrypted output. Figure 1 provides the block diagram of the proposed scheme.
Chaotic logistic mapping: The initial conditions and the system parameters are to be known to use any chaotic system. The chaotic map exhibits diffusion and confusion properties. Logistic mapping is a non linear polynomial dynamic mapping which has a degree of 2.
| Fig. 1: | Proposed methodology |
| Rubik’s cube encryption algorithm: | |
Figure 2 represents the sequential operations performed in the Rubik’s cube principle in order to obtain the encrypted image.
As proposed in the algorithm circular shifts are performed on the individual rows and columns of the image matrix in order to obtain the maximum possible confusing over the original image. This way of rotating the rows and columns in right/left and up/down directions, respectively resembles the technique used to shuffle and solve the Rubik’s cube.
| Fig. 2: | Block diagram of Rubik’s cube encryption |
RESULTS AND DISCUSSION
This study was implemented on MATLAB 7.1 platform considering Lena, Baboon, camera man and peppers images of dimensions 256x256 in 8 bit format. Figure 3a provides the original Lena image, Fig. 3b provides the chaotic logistic map output after applying to R plane. Figure 3c provides the chaotic logistic map output after applying to G plane, Fig. 3d provides the chaotic logistic map output after applying to B plane. Figure 3e provides the combined output of R+G+B planes. Figure 3f provides the final encrypted Rubick’s cube output of the combined RGB plane. Figure 3g provides the histogram of the final encrytpted output and Fig. 3h provides the decrypted Lena image.
Figure 4a provides the original Baboon image, Fig. 4b provides the final encrypted output of Fig. 4a and c provides the histogram of Fig. 4b and d provides the decrypted output. Figure 5a provides the original cameraman image, Fig. 5b provides the final encrypted output of Fig. 5a and c provides the histogram of Fig. 5b and d provides the decrypted output. Figure 6a provides the original peppers image, Fig. 6b provides the final encrypted output of Fig. 6a and c provides the histogram of Fig. 6b and d provides the decrypted output. Table 1 provides the matrices like Horizontal, vertical, diagonal correlation values, NPCR and UACI of the final encrypted image with that of the original image.
NPCR and UACI: NPCR and UACI are the two metrices to estimate any encryption algorithm. They are considered to validate the pixel change rate and the average intensity change between the original and the encrypted image. Higher the values indicates that the proposed scheme reveals high resistance to differential and brute force attacks.
If A1 (i, j) and A2 (i, j) represents the pixel values in ith row and jth column of the two images XxY, respectively.
Then:
| Fig. 3(a-h): | |
| Fig. 4(a-d): | (a) Original baboon image, (b) Encrypted output of Fig. 4a, (c) Histogram of Fig. 4b and (d) Secrypted image |
The propsed study provides NPCR and UACI values of 99.6 and 33.44, respectively.
Correlation analysis: In general, to examine the efficiency of the proposed cryptosystem, the correlation between adjacent pixels are calculated.
| Fig. 5(a-d): | (a) Original cameraman image, (b) Encrypted output of Fig. 5a, (c) Histogram of Fig. 5b and (d) Decrypted image |
| Fig. 6(a-d): | (a) Original peppers image, (b) Encrypted output of Fig. 6a, (c) Histogram of Fig. 6b and (d) Decrypted image |
| Table 1: | Image encryption matrices for various images |
The correlation co-efficient ρ can be given by:
where, x and y are adjacent pixels of the original images. To calculate the value of ñ the following discrete formulas can be used:
where, I is the number of pixel pairs. From Table 1, the correlation values are nearing zero indicates that there exists no correlation between the original and the ciphered image.
CONCLUSION
In this study, chaotic logistic map on individual bit planes of RGB image followed by rubick’s encryption principle to provide the final encrypted image. Image encryption has become a combat zone of top computer scientists and mathematicians and encrypted image secret is safely hoarded and transmit. In this study, the computed horizontal, vertical and diagonal correlation values reveals that there exists no correlation between the original image and the shuffled image. The proposed encryption provides NPCR of 99.6, UACI of 33.5 and negative correlation values revels that resists against differential and brute force attacks.