一种新型的量子水印策略，张伟伟，高飞，随着量子计算机和量子网络的发展,量子数据的安全越来越重要。量子水印是一种可以将包括身份信息等的不可见信号嵌入到包括音频,视�
国利技论文在线 http://www.paper.edu.cn principle and quantum no-cloning theorem. Recently, quantum cryptography has obtained a great deal of attentions because it can stand against the threat from an attacker with the abil ity of quantum computation. Quite a few branches of quantum cryptography develops greatly in recent years, including quantum key distribution(QKD)[5-10, quantum secret sharing (QSS)11-13, quantum secure direct communication(QSDC)[14-18, quantum identity authentication [19-21, and so on Different from cryptography, which is used to protect the secrecy of the message's content steganography aims at hiding the existence of message. Quantum watermarking is a kind of steganography, which is used to embed some symbolic quantum information into quantum multimedia content. It will not affect the usage of multimedia and others cannot feel the watermark s existence. The watermark in the carrier is used to protect the copyright Compared with the flourishing quantum cryptography, quantum steganography is still in its infancy. Inages are good carriers and always used in steganography. Recently, a few strategies or quantum images' storing and retrieving have been proposed 22),126,[27]. Based on the presentations of quantum images, Le et al. proposed the strategies for quantum images geometric transformations 25 ,[28-30]. Besides, some quantum watermarking schemes[23 24,25,32 were proposed, where 24 is the only and first one based on quantum images But a significant limitation is that the proposed schemes in 24 based on quantum images can only be used to vertify the identity of carrier images true owner. That means we can onl find out soneone is using illegal carrier image, but we can not find out where his/her inages come from. This is a real limitation in practical application. In this paper we propose a novel quantum watermarking strategy which is more universal, in the sense that it can be used to find out who is the real owner(or who leaks the carrier images to the illegal users) according to the watermark extracted from the carrier image The rest of this paper is organized as follows. The next section introduces quantum information 31, the flexible representation of quantum images(FRQI)27, which will be used n the following sectiOns, and the watermarking scheine proposed by Le et al.. In section IIl, we describe our quantum watermarking strategy detailedly and present the results and analysis of simulation-based experiments to demonstrate the realization of the watermarked carrier image Finally, a short conclusion is given in Section IV 1 Preliminaries 1.1 Quantum information quantulnl coinputer is a device for coMputations that Inakes direct use of quantulnl mechanical properties. Quantum computation and quantum information are based on the fundamental concept, the quantum bit, or qubit for short. Just like there exist a classical bit 国利技论文在线 http://www.paper.edu.cn 1o以 屮 K 1: Bloch sphere representation of a qubit l )=cos j0)+eip sin 5| 1)311 either 0 or l, a qubit also has a state. Their difference is that a qubit can be in any linear combinations of state 0) or 1. It is often called superpositions: β1).The number a and B are complex numbers, and satisfy a/2+1B12= 1. The computational basis states 0) and 1 form an orthonormal basis for a special vector space. We can think the qubit as the following geometric representations, which can be rewrite as the form of qubit as follows l/)=cos 210)+e y sin 21), where the 6 and 4 are real numbers and define a. point on the unit three dimensional sphere, as shown in Fig. 1. In principle, there are infinitely many points on the unit sphere, so that one could store an entire text of Shakespear in the infinite binary expansion of 0 31 1.2 Flexible representation of quantum images Based on the human perception of vision and the classical images' pixel representation the fexible representation for quantum images(FRQI), a representation for quantum images, was proposed in 27. FRQI contains the color information and corresponding position of ever pixel in image. According to the FrQi, a quantum image's representation can be written as the form shown below ()=∑c)81), )=cos|0)+sine1),6;∈[0,],=0, 2n ere 0,1are 2-D computational basis quantum states.(00, 01, 22m-1) is the vector of angles encoding colors, and i), for i=0,, 22n-1, are(22n-1)-D computational basis. There 国利技论文在线 http://www.paper.edu.cn 00 01 10 2: A simple image and its FRQI state: I)=5[(cos Bol0)+sin Bo 1))00)+(cos 010)+ sin61|1)01)+(cos20)+sin2|1)②10)+(cos30)+sin1)②11)24 are two parts in the FRQI of an image: Ci and i, which encode information about the colors and their corresponding positions in the image, respectively For 2-D images, the location information encoded in the position qubit i) includes two parts: the vertical and horizontal coordinates. For preparing quantum images in 2n-qubit systems, or n-sized images, the vector )=|y)x)=y=19m-2…,90)|xn-1n-2…xo), yh)|x)∈{0,1} for every i=0, 1,,n,(3n-1, 1n-2, ,o) encodes the first n-qubit along the vertical location and(am-1, n-2,. o)encodes the second n-qubit along the horizontal axis. An example of a 2x2 FRQJ image is shown in Fig. 2 27,128-[30,[33, the methods for storing and retrieving quantum images are proposed 1.3 Le et al.,s strategy based on restricted geometric transformations In 24, Le et al. proposed an algorithm for watermarking and authentication of quantum images based on restricted geometric transformations (including two-point swapping, the verti- cal flip, the horizontal flip, the coordinate swap operations). It is a great progress for quantum images processing that they utilize the restricted va riants(of the quantum versions)[28 of these transformations as the basic resources of the watermark embedding and authentication circuits. These procedures are available for the various stages by the copyright owners and users of the published(watermarked) images. The copyright owner has access to both the classical and quantum versions of the image and watermark signal. The end-users on their parts are 国利技论文在线 http://www.paper.edu.cn Authentication Embedded carrier image Watermark cIrcul mage Watermark image Carrier image K 3: The outline of Le et al.'s watermark authentication procedure[24] restricted to only the published quantuM versiOns of the watermarked inages The outline of quantum watermark image's embedding procedure consists of two parts the first part decides the watermark map with the classical versions of carrier and watermark images as input, the second part transforms the watermark map into quantum circuit accord ing to a simple mapping between the map's value(O, 1 or-1)and the quantum geometric transformations. The watermark authentication procedure, whose outline is shown in Fig. 3, is only available to the copyright owner. Ile/she uses the inverse watermark-embedding circuit (comprising of the same gate sequence as the watermark-embedding circuit but in the reverse order)to authenticate the true ownership of an embedded carrier image. That means if the copyright owner want to authenticate some embedded carrier image, he/ she has to know which watermark image is in the carrier image, i.e the unique embedding circuit. Therefore this cheme can only be used to verify the identity of a true owner of the carrier image. In this scheme, the copyrighters can only find out someone is using illegal images, but they can not find out where his /her images come from. This is a real limitation in practical application 2 Quantum watermark embedding and extracting procedure Our waternark enbedding procedure is based on the idea that Flaking a subtle change to the carrier image according to the watermarking image. The embedded carrier image and the original carrier image are indistinguishable by naked eyes. The extracting procedure can only be executed by the embedder, because the key used to decide the position of watermark and the original carrier image is only known to the embedder 2.1 The embedding procedure of quantum watermark image As we known, an image consists of many pixels which are all pure colors. According to the FRQI, a pixel's color in a quantum image can be written as I(0)=cos 80)+sin 81, where 0 represents the color of the pixel. The outline of the embedding procedure is shown in Fig 4 国利技论文在线 http://www.paper.edu.cn kev Watermark Imaqe Embedding algorithm H Embedded carrier image Iage 4: The outline of watermark image's embedding procedure The concrete procedure is as following (1)If the waternark image's size is less than the carrier's image, the emnbedder should polish it to the size of carrier image. Concretely, the embedder randomly cover the carrier image with the watermark image. The area in watermark image corresponding to the exposed region in carrier image is replenished with the corresponding pixels in the carrier image, thus the watermark image is the same size with the carrier image. Here the white pixels' position are only known to embedder (2) The embedder produces a sequence of key k(unique to the carrier image). Thi will be used to determine the position that the watermark image's pixel will be embedded, and it is only known to the embedder. Specifica lly, if h =0 the watermark image's pixel is embedded in the cosine part, otherwise the sine part (9) The embedder embeds the watermark image into the carrier image according to the following method, which makes a subtle change to the Taylor series expression of the carrier mages pixels le taylor series of cos and SillI k 2k cos r= 1 2!4! (2k)! +.(-∞C<x<+) h-1 sIn (2k-1) +…(-∞<x<+∞) Assume the watermark image's pixel is cos p0)+sin p 1). If the key in step(2 )is 0, the original pixel is approximated with a0)+B 1), where a= cos 6=1 02 A4 g6 2!4!6 thus the pixel embedding watermark's pixel is a0)+B 1). here a'=co5=1624 4!6! If the key in step(2)is 1, the original pixel is approximated with a 0)+B> 国利技论文在线 http://www.paper.edu.cn Embedded carrier image Extracting Watermark kev algorithm Image Original carrier Image Rl 5: The outline of watermark image's extracting procedure 6= sin=6 thus the embedding watermarks pixel is a0)+B1), here 6=6 3!5!7! (4) Implement the above three steps for every carrier image's pixel and watermark image's p 2.2 Quantum watermark images extracting procedure In our scheme, the watermark extracting procedure is only available to the copyright owner(the embedder). He/ She uses the key and the original carrier image to extract the watermark image from an embedded carrier image according to the extracting procedure(see Fig 5). Assume the color of the original carrier image's pixel is I(0=cos 00)sin 0 1,the color of the enbedded carrier image 's pixel is (0)+61. The concrete steps are as following (1)According to the key (unique to the carrier image), the embedder get the position of watermark image' s every pixel (2) If the key in step (1)is 0, the extracted watermark pixel is cos ( p0)+sin '1, where 2!+4! )×6:) If the key in step(1) is 1, the extracted watermark pixel is cos '0)+sin '1),where y′=(63,02 5! )×7) (3)Implement the above two steps for every pixel of the embedded carrier image and get every pixel of the watermark image 国利技论文在线 http://www.paper.edu.cn 2. 3 Simulations of quantum watermark embedding and extracting pro- cedure Due to the condition that the physical quantum hardware is not affordable for us to execute our protocol, we just make the simulations of the input quantum carrier images and watermark images. The tools needed and results obtained in our simulation experiments are presented and reviewed in this section MATLAB MATrix LABoratory) is a useful software tool for matrix manipulations, plot ting of functions and data, implementation of algorithms, creation of user interfaces, and in- terracing with programs. It is flexible in the representation and manipulation of large arrays of vectors and matrices. Because it is reasonable to treat the quantum images as large matrices and the transformations as matrix computations. Therefore, MATLAB is suitable to simulate quantum states(such as quantum images), although it has some limitations in simulating the image of huge size MATLABs Image Processing Toolbox provides a comprehensive set of reference-standard algorithms and graphical tools for image processing, analysis, visualisation anld algorithIn development. By using Matlab, qualltuln images anld their transformationS can be effectively simulated [24]. We demonstrate our quantum watermark embedding and ex- tracting procedure with a classical computer with Intel(R) Core(TM)2 Duo CPU E7500 2.93 GHz, 1.98 GB Ram equipped with the MATLAB 2009a environment. The peak-signal-to-noise ratio (PSNr), being one of the most used metrics in classical images for comparing the fidelit of a watermarked image with its original version, will be used as our watermarked image eval- uation metric by transforming the quantum images into classical forms, though there may be some influence on the results. It is most easily defined via the mean squared error(MSE), which for two mxn monochrome images(the original carrier image i and its watermarked version k) is defined as MSE I ∑∑(I(,)-K( The PsnR is defined by PSNR=20log( MAXI √MSE Here, MAXI is the maximum possible pixel value of the image[24 2.3.1 Simulation of gray images In the simulation. we use 256x256 images of different types as carrier images and water mark images. In Fig. 6, a part of the embedded carrier images are shown at left and the right 国利技论文在线 http://www.paper.edu.cn K 6: The left are embedded carrier images. The right are extracted watermark images from the left side is the waternark iMages extracted fron the corresponding left images. And the PSnr is presented in Table i 表1: gray images's PSNR carrier image watermark image PSNR aera sailboat 50.8418 baboon ena 63.4885 boat pepper 63.5384 lena baboon 64.8810 pepper boat 64.2690 sailboat aerial 56.347 2.3.2 Simulation of color images In the simulation, we use 756x 504 and 768x512 images of different types and colors as carrier images and watermark images. In Fig. 7, a part of the embedded carrier images are at left and the right side is the watermark images extracted from the corresponding left images And the PSnr is presented in Table II 2.3.3 Analysis From Fig. 6, Fig. 7, Table I and Table il, we can see that the watermark image's embedding doesnt affect the carrier image's visual effect. And the PSNR is obviously higher than the average level of the classical algorithms