QISLSQb: A Quantum Image Steganography Scheme Based on Least Significant Qubit

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1 06 International Conference on Mathematical, Computational and Statistical Sciences and Engineering (MCSSE 06) ISBN: QISLSQb: A Quantum Image Steganography Scheme Based on Least Significant Qubit Tie-un ZHANG, Bassem Abd-El-Atty, Mohamed Amin and Ahmed A. Abd El-Latif,* School of software, Harbin niversity of Science and Technology, Harbin, China Department of Mathematics, Faculty of Science Menoufia niversity Shebin El-Koom 35, Egypt *Corresponding author Keywords: Quantum steganography, Quantum image processing, LSQb, Image scrambling. Abstract. In this paper, a new quantum image steganography scheme to embed quantum secrete gray image into quantum cover image is proposed. In the proposed scheme, the quantum secret image scrambled utilizing Arnold cat map and embedding the result into quantum cover image using two least significant qubit (LSQb).The extracting process need only stego image to extract the embedded secret image. The simulation results demonstrate that the proposed scheme has good invisibility and high capacity. Introduction Quantum steganography utilizes the effects of quantum mechanics such as quantum computation and quantum communication to achieve tasks of information hiding. Quantum steganography, can be defined as the classical steganography in the viewpoint of quantum mechanics, has become important researching area of quantum cryptography. Quantum image steganography based on quantum image processing techniques to improve many tasks in classical image steganography. The first step is to represent and store the classical images on quantum computers. There are many representations for classical images on quantum computers, such as flexible representation of quantum images (FRQI) [], which uses X + number of qubits to represent a gray image with size x x and the NEQR model for represent quantum images []. In spite of the used qubits of NEQR increases from x + qubits used in FRQI to X + q qubits, it is excellent for processing quantum image because the quantum representation is very similar to the representation of a classical image. In the earlier works, there is no quantum image steganography scheme to embed quantum gray image into quantum image. The quantum image steganography algorithms [3, 4] embed binary image or message as binary image with maximum capacity one bit per pixel. However, quantum image steganography algorithms [3, 4] broken to embed quantum gray image into quantum image. In [5], Wang et al. proposed an LSQb information hiding algorithm for quantum image, which embeds the secret information without scrambling into the first qubit of the cover image. Sang et al. In [6] proposed LSQb information hiding algorithm to embed quantum information into quantum color image. In [7], AL-Salhi et al. Presented a quantum image steganography algorithm based on the least significant Qu-block (LSQB). Heidari et al. In [8] proposed a Quantum watermarking technique based on least significant bit (LSB) to embed quantum binary image into cover image. In this paper, we propose a quantum image steganography scheme to embed quantum gray image instead of binary image into the quantum cover image. It utilizes NEQR for quantum representation, two LSQb and quantum image scrambling to increase the capacity and security of the proposed scheme. Experimental results demonstrate that, the maximum capacity increases from -bit per pixel in [3, 4, 5, 6, 8] to -bit per pixel in the proposed scheme and the invisibility is good. The rest of this paper is as follows. In section, we give a brief background on the NEQR representation, Arnold image scrambling and LSQb. Section 3 gives the proposed quantum 40

2 steganography approach. Section 4 is devoted to analysis and results in terms of visual quality and payload capacity. In section 5, we present a comparison with related algorithms. Finally, conclusions drown in section 6. Preliminaries NEQR for Quantum Images. The NEQR model has information about the pixels color and its related position of each pixel in the image. The mathematical representation of a quantum image for n n an image can be expressed as follows. where the binary sequence I ci i n () i0 q 0 k ci ci... ci ci, ci { 0,}, k q,...,,0, i 0,,..., q 0 ci... cici 0,,, encodes the color value, and the color range is q, i for i, are n dimension computational basis quantum states. Arnold Image Scrambling. The basic idea of image scrambling is to transform a meaningful image into a meaningless image by permutation the positions of pixels into new positions. Arnold image scrambling matrix is defined as x x modn y y () where N is the size of image. The input is the position information x and y of original image, and the output is the position information x and y of Arnold scrambled image. The inverse of Arnold image scrambling is defined as follows x x modn y y (3) Zhou et al. [9] gives a quantum Arnold image scrambling that can be defined as I S S ( I ci S ( i ) n i 0 S( i) can be defined according to Eq. as (4) S( i) S( y x) S( y) S( x) where S( x) = x + ymod N S( y) = x + ymod N (5) Least Significant Quantum Bit. In this way LSQb information hiding can be described by substituting the last qubit of cover image with the secret information. In [5], Wang et al. proposed least significant qubit information hiding algorithm for quantum image. In [5], the qubit of secret information c M 0 is compared with the last qubit color of cover image c0 in Eq.. If the output of comparison is the same apply to I otherwise apply i toi. 4

3 (6) q q i I X i i I 0, i (7) q I 0, i Where X 0 0 and 0 I 0 Proposed Quantum Image Steganography Scheme Here, we propose a quantum image steganography scheme based on NEQR for quantum images by utilizing quantum Arnold image and two least significant qubits. We assume that the cover image n n with size n n and secret image with size. The embedding procedures of the proposed quantum image steganography consist of three phases, which are given by the following steps. Phase : Preprocessing Images. Preprocessing images is given by the following steps. n n Step : The secret image with size and 8-bit is expanded to image with size n n and -bit. Step : The NEQR representations of the cover image and the secret image after expanding is I and J, respectively are shown as follows: I n q 0 k ci i, ci ci... cici, ci i 0, {0 } (8) 0 k J c, c c c, c { 0,} n 0 (9) Phase : Scrambling for Quantum Secret Image J. The quantum secrete image J scrambled using Arnold transformation as follows JS S ( J c S ( ) n (0) 0 Phase 3: Embedding Scrambled Image JS into Cover Image I. The quantum scrambled image JS embedded into quantum cover image I utilizing two least significant qubits. The two qubits of scrambled secret image JS color encoding information c and c0 in Eq. 0 compared with the two last qubits of cover image I color encoding information c and c0 in Eq. 8. If the output of comparison for c is the same apply to I otherwise apply i toi and if the output of comparison for c0 is the same apply to I otherwise apply 0 i toi. () q q i I X I i i I 0, i () q q 0i I X i i I 0, i 4

4 (3) q I 0, i Analysis and Results on Classical Computer Visual Quality. Visual quality is the amount of difference between the stego image and the original cover image in pixels values. There are many quantities to measure the difference of pixels between the stego image and the original cover image; one of the most used quantities is PSNR (peak signal to noise ratio). It is defined as the MSE (mean squared error) for two images X and Y with size i. MSE [ (, ) (, )] i i X x y Y x y (4) x0 y0 PSNR is defined as follows. MAX X PSNR 0 log 0( ) MSE Where, MAX X is the maximum value of pixels in the cover image X. In this scheme, Y related to the stego image and X related to the original cover image. In our experiments, we use images of size 8 8 as cover image and as secret image to simulate the proposed scheme. The following Figure describes experimental results of our scheme and Table gives the PSNR value between the original image and the stego image for different images. Table. PSNR (in db) values for different text messages. Cover image Secret image Lena Baboon Barbara Lena Baboon Barbara (5) Obviously, from Figure, human eyes cannot detect the difference between stego image and original image. From Table, we can see that the PSNR values are high enough. So we can conclude that our scheme has a good visual effect. Payload Capacity. The steganography capacity can be stated as the ratio between the number of embedded bits of the text message and the number of pixels for cover image. The proposed schemes capacity is given as follows: numberof embedded image pixels 0.5n 0.5n pixel C pixel / pixel number of cover image pixels n n pixel 4 The capacity of the proposed scheme is -bit per pixel, which is higher than of most of quantum image steganography algorithms. So we can conclude that our scheme has high capacity. Original cover image Stego image Secret image Extracted image (6) Figure. The visual effects of proposed scheme. 43

5 Comparison with Related Algorithms From the above section, the simulation results demonstrate that the proposed scheme has high capacity compared to the algorithms of [3-5]. The capacity of the proposed algorithm is -bit per pixel, while the capacity of algorithms in [3-5] is -bit per pixel. From Table, we can conclude that the proposed algorithm has high capacity, good visual effect and embedding quantum gray image instead of binary image. Table. Comparison with related algorithms. Items Proposed scheme Algorithm in [3] Algorithm in [4] Algorithm in [5] Maximum Capacity bit/pixel bit/pixel bit/pixel bit/pixel Embedding data Gray-scale image Binary image Message as binary image Any information Scrambling Quantum Arnold Quantum Hilbert - Image scrambling Image scrambling - Visual quality (PSNR) using Lena as cover image Conclusion In this paper, a quantum image steganography scheme based on the novel enhanced quantum representation (NEQR) for quantum images, quantum Arnold image scrambling and two least significant qubits have been proposed. The advantages of the proposed scheme are the extracting operation does not need the original cover image or the original secret image, good visibility and high capacity. Simulation results show the efficiency of the proposed quantum image steganography scheme. Acknowledgement This work is supported by Menoufia niversity under the proect number: A-WSN06, Guangdong Natural Science Foundation: 05A and Natural Science Foundation of Heilongiang Province, China: QC04C076, JJ06ZR068. References [] P.Q. Le, F. Dong, K. Hirota, A flexible representation of quantum images for polynomial preparation, image compression and processing operations, Quantum Inf Process, 0 (0) [] Y. Zhang, K. Lu,Y.H. Gao, M. Wang, NEQR: a novel enhanced quantum representation of digital images, Quantum Inf Process, (03) [3] Nan Jiang, LuoWang, A Novel Strategy for Quantum Image Steganography Based on Moir epattern, Int J TheorPhys, 54 (05) [4] Nan Jiang, Na Zhao, LuoWang, LSB Based Quantum Image Steganography Algorithm, Int J TheorPhys. 55 (06)07-3. [5] S. Wang, J. Sang, X. song, X. Niu, Least Significant Qubit (LSQb) Information Hiding Algorithm for Quantum Image, Measurement, 73 (05) [6] J. Sang, S. Wang, Q. Li, Least significant qubit algorithm for quantum images, Quantum Inf. -0 (06) 5 Process. [7] Y.E. AL-Salhi, S. Lu, Quantum Image Steganography and Steganalysis Based On LSQu-Blocks (06) 55 TheorPhys. Image Information Concealing Algorithm, Int J 44

6 [8] S. Heidari, M. Naseri, A Novel LSB Based Quantum Watermarking, Int J TheorPhys. 55 (06) [9] Nan Run Zhou, Tian Xiang Hua, Li Hua Gong, Dong Ju Pei, Qing Hong Liao, Quantum image encryption based on generalized Arnold transform and double random-phase encoding. Quantum Inf Process. 4 (05)