一种新型的量子水印策略 英文

一种新型的量子水印策略

张伟伟12，高飞1，刘斌1，贾恒越1，温巧燕1，陈晖3

1北京邮电大学网络与交换技术国家重点实验室，北京　100876

2信息安全国家重点实验室(中国科学院软件研究所)，北京100190

3现代通信国家重点实验室，成都，610041

摘要：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，视频和图像等的量子多媒体数据中，起到版权保护的作用。本文提出一种基于灵活量子图像表示的的新型水印策略。之前提出的策略（唯一的一个基于量子图像的策略）只能用来验证载体图像的拥有者是否为所已知的身份。与其相比，本文提出的策略能够找出真正的版权所有者，并且除版权所有者以外的任何人都不能清除或提取除水印图像。

关键词：量子计算，量子图像，量子水印

中图分类号：O59

A Novel Watermark Strategy For Quantum

Images

Wei-Wei Zhang12，Fei Gao1，Bin Liu1，Heng-Yue Jia1，Qiao-Yan Wen1，Hui

Chen3

1the State Key Laboratory of Networking and Switching Technology,Beijing University of

Posts and Telecommunications,Beijing100876

2the State Key Laboratory of Information Security(Institute of Software,Chinese Academy

of Sciences),Beijing100190

3Science and Technology on Communication Security Laboratory,Chengdu,610041 Abstract:With the development of quantum computer and quantum network,the security

of quantum data becomes more and more important.Quantum watermarking is the technique which embeds the invisible quantum signal such as the owner’s identi?cation into quantum multimedia data(such as audio,video and image)for copyright protection.In this paper,a novel watermark strategy for quantum images is proposed based on?exible representation for quantum images(FRQI).Compared with the former strategy(only one based on quantum 基金项目：NSFC(Grant Nos.61170270,61100203,60903152,61003286,60821001),NCET(Grant No.NCET-10-0260),SRFDP(Grant Nos.200800131016,20090005110010),Beijing Natural Science Foundation(Grant No.4112040),

the Fundamental Research Funds for the Central Universities(Grant Nos.BUPT2011YB01,BUPT2011RC0505, 2011PTB-00-29,2011RCZJ15),Science and Technology on Communication Security Laboratory Foundation(Grant No.

9140C110101110C1104).

作者简介：Zhang Wei Wei（1987-），female，Master Student，major research direction：quantum key distribution, quantum secret sharing,and quantum images processing.Correspondence author：Gao Fei（1980-），male，professor，major research direction：quantum key distribution,quantum secret sharing,and quantum secure direct communication.

images)which can only be used to verify the identity of the true owner of a carrier image,the proposed method can also be used to?nd out who is the real owner.And it is impossible for anyone except the copyrighter to clear o?or extract the watermark images.

Key words:Quantum computation,Quantum image,Quantum watermarking.

0Introduction

THE high integration of the traditional computer has resulted in the appearing of quan-tum e?ects which greatly restricts the development of the classic computer.Recently,the quantum computer(QC)and the quantum network are developing rapidly.In2001,IBM de-veloped the world’s?rst7-qubit QC to give a demonstration.In2007,D-wave corporation in Canada announced that they had?nished the16-qubit commercial QC for the?rst time and it was improved to48-qubit in2008.In2011,D-wave announced their achievement of 128-qubit commercial QC.The company had set goals for developing1024-qubit QC and pro-posed QC’s further application(such as releasing the quantum computing software system, providing interface for application program including SQL Prolog Lisp etc,developing the on-line commercial computation service).D-wave’s development implies that the principle of quantum computer has been matured and the practical technology also has made substantial progress.In the meantime,the quantum networks are?ourishing.In2004,Raytheon BBN Technologies and Harvard university cooperatively constructed a quantum cryptography net-work Defense Advanced Research Projects Agency(DARPA)and successfully accomplished the mutual connection using the communication optical?ber.Secure communication based on quantum cryptography(SECOQC)network was accomplished in2008,which was cooperatively ful?lled by41research institutions and enterprises from the European Union,Switzerland and Russia.In2010,based on the latest QKD technology,the Tokyo QKD network making use of JGN2plus(Japan’s Gigabit Network)was con?gured as a star network.This network con-nected the JGN2plus operation center in Otemachi with National Institute of Information and Communications Technology(NICT)’s Headquarter in Koganei as well as Tokyo University in Hongo and NICT’s research facility in Hakusan.

With the development of quantum computer and quantum network,the security of quan-tum data becomes more and more important.Cryptography is the approach to protect data’s secrecy in public environment.As we know,the security of most classical cryptosystems is based on the assumption of computational complexity.But this kind of security is susceptible to the strong ability of quantum computation[1],[2].It means that many existing cryptosys-tems’s security will be threatened by quantum computer.Fortunately,this di?culty can be overcome by quantum cryptography[3],[4].Di?erent from its classical counterpart,the secu-rity of quantum cryptography is assured by physical principles such as Heisenberg uncertainty

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.

Di?erent 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 a?ect 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?ourishing quantum cryptography,quantum steganography is still in its infancy.Images are good carriers and always used in steganography.Recently,a few strategies for quantum images’storing and retrieving have been proposed[22],[26],[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?rst one based on quantum images. But a signi?cant limitation is that the proposed schemes in[24]based on quantum images can only be used to vertify the identity of carrier image’s true owner.That means we can only ?nd out someone is using illegal carrier image,but we can not?nd out where his/her images 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 ?nd 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?exible representation of quantum images(FRQI)[27],which will be used in the following sections,and the watermarking scheme proposed by Le et al..In section III,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.

1Preliminaries

1.1Quantum information

A quantum computer is a device for computations that makes direct use of quantum 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

图1:Bloch sphere representation of a qubit|ψ?=cosθ

2|0?+e iφsinθ

2

|1?[31].

either0or1,a qubit also has a state.Their di?erence is that a qubit can be in any linear combinations of state|0?or|1?.It is often called superpositions:|ψ?=α|0?+β|1?.The numberαandβare complex numbers,and satisfy|α|2+|β|2=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:

|ψ?=cosθ

2|0?+e iφsinθ

2

|1?,where theθandφare real numbers and de?ne a point on the

unit three–dimensional sphere,as shown in Fig.1.In principle,there are in?nitely many points on the unit sphere,so that one could store an entire text of Shakespear in the in?nite binary expansion ofθ[31].

1.2Flexible representation of quantum images

Based on the human perception of vision and the classical images’pixel representation, the?exible representation for quantum images(FRQI),a representation for quantum images, was proposed in[27].FRQI contains the color information and corresponding position of every pixel in image.According to the FRQI,a quantum image’s representation can be written as the form shown below.

|c i?=n?1,

where|0?,|1?are2-D computational basis quantum states,(θ0,θ1,...,θ22n?1)is the vector of angles encoding colors,and|i?,for i=0,...,22n?1,are(22n?1)-D computational basis.There

图2:A simple image and its FRQI state:|I?=1

[(cosθ0|0?+sinθ0|1?)?|00?+(cosθ1|0?+

2

sinθ1|1?)?|01?+(cosθ2|0?+sinθ2|1?)?|10?+(cosθ3|0?+sinθ3|1?)?|11?][24]

are two parts in the FRQI of an image:c i and|i?,which encode information about the colors and their corresponding positions in the image,respectively.

For2-D images,the location information encoded in the position qubit|i?includes two parts:the vertical and horizontal coordinates.For preparing quantum images in2n-qubit systems,or n-sized images,the vector

|i?=|y?|x?=|y n?1y n?2...y0?|x n?1x n?2...x0?,

|y i?|x i?∈{0,1},

for every i=0,1,...,n,(y n?1,y n?2,...,y0)encodes the?rst n-qubit along the vertical location and(x n?1,x n?2,...,x0)encodes the second n-qubit along the horizontal axis.An example of a 2×2FRQJ image is shown in Fig.2.

In[27],[28]-[30],[33],the methods for storing and retrieving quantum images are proposed.

1.3Le 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?ip,the horizontal?ip,the coordinate swap operations).It is a great progress for quantum images processing that they utilize the restricted variants(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

图3:The outline of Le et al.’s watermark authentication procedure[24].

restricted to only the published quantum versions of the watermarked images.

The outline of quantum watermark image’s embedding procedure consists of two parts: the?rst 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(0,1or-1)and the quantum geometric transformations.The watermark authentication procedure,whose outline is shown in Fig.3,is only available to the copyright owner.He/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 scheme can only be used to verify the identity of a true owner of the carrier image.In this scheme,the copyrighters can only?nd out someone is using illegal images,but they can not ?nd out where his/her images come from.This is a real limitation in practical application.

2Quantum watermark embedding and extracting procedure

Our watermark embedding procedure is based on the idea that making 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.

2.1The 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(θ)=cosθ|0?+sinθ|1?,where θrepresents the color of the pixel.The outline of the embedding procedure is shown in Fig.4.

图4:The outline of watermark image’s embedding procedure.

The concrete procedure is as following:

(1)If the watermark image’s size is less than the carrier’s image,the embedder 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).This key will be used to determine the position that the watermark image’s pixel will be embedded,and it is only known to the embedder.Speci?cally,if k=0the watermark image’s pixel is embedded in the cosine part,otherwise the sine part.

(3)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 image’s pixels.

The Taylor series of cos x and sin x is

cos x=1?x2

2!

+

x4

4!

?...+(?1)

k x2k

(2k)!

+...(?∞

sin x=x?x3

3!

+

x5

5!

?...+(?1)

k?1x2k?1

(2k?1)!

+...(?∞

Assume the watermark image’s pixel is cosφ|0?+sinφ|1?.If the key in step(2)is0,the original pixel is approximated withα|0?+β|1?,where

α=cosθ=1?θ2

2!

+

θ4

4!

?θ

6

6!

,β=

√

thus the pixel embedding watermark’s pixel isα′|0?+β′|1?,here

α′=cosθ′=1?θ2

2!

+

θ4

4!

?φ

6

6!

,β=

√

1?α′2

If the key in step(2)is1,the original pixel is approximated withα|0?+β|1?,where

图5:The outline of watermark image’s extracting procedure.

β=sin θ=θ?θ33!+θ55!?θ6

7!

,α=√1?β2thus the embedding watermark’s pixel is α′|0?+β′|1?,here

β′=sin θ′=θ?θ33!+θ55!?φ67!

,α′=√1?β′2(4)Implement the above three steps for every carrier image’s pixel and watermark image’s pixel.

2.2Quantum watermark image’s 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 (θ)=cos θ|0?+sin θ|1?,the color of the embedded carrier image’s pixel is α′|0?+β′|1?.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 φ′|0?+sin φ′|1?,where

φ′

=((1?θ22!+θ44!

?α′)×6!)16If the key in step (1)is 1,the extracted watermark pixel is cos φ′|0?+sin φ′|1?,where φ′=((θ?θ33!+θ55!

?β′)×7!)17(3)Implement the above two steps for every pixel of the embedded carrier image and get every pixel of the watermark image.

2.3Simulations of quantum watermark embedding and extracting pro-

cedure

Due to the condition that the physical quantum hardware is not a?ordable 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-terfacing with programs.It is?exible 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.MATLAB’s Image Processing Toolbox provides a comprehensive set of reference-standard algorithms and graphical tools for image processing,analysis,visualisation, and algorithm development.By using MATLAB,quantum images and their transformations can be e?ectively simulated[24].We demonstrate our quantum watermark embedding and ex-tracting procedure with a classical computer with Intel(R)Core(TM)2Duo CPU E75002.93 GHz,1.98GB Ram equipped with the MATLAB2009a environment.The peak-signal-to-noise ratio(PSNR),being one of the most used metrics in classical images for comparing the?delity 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 in?uence on the results.It is most easily de?ned via the mean squared error(MSE),which for two m×n monochrome images(the original carrier image I and its watermarked version K) is de?ned as

MSE=

1

mn

m?1

∑

i=0

n?1

∑

j=0

[(I(i,j)?K(i,j))2]

The PSNR is de?ned by

P SNR=20log10(MAX I √

MSE

)

Here,MAX I is the maximum possible pixel value of the image[24].

2.3.1Simulation of gray images

In the simulation,we use256×256images of di?erent 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

图6:The left are embedded carrier images.The right are extracted watermark images from the left.

side is the watermark images extracted from the corresponding left images.And the PSNR is presented in Table I.

表1:gray images’s PSNR

carrier image watermark image PSNR

aerial sailboat50.8418

baboon lena63.4885

boat pepper63.5384

lena baboon64.8810

pepper boat64.2690

sailboat aerial56.3347

2.3.2Simulation of color images

In the simulation,we use756×504and768×512images of di?erent 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.

2.3.3Analysis

From Fig.6,Fig.7,Table I and Table II,we can see that the watermark image’s embedding doesn’t a?ect the carrier image’s visual e?ect.And the PSNR is obviously higher than the

average level of the classical algorithms.

图7:The left are embedded carrier images.The right are extracted watermark images from the left.

表2:color images’s PSNR

carrier image watermark image PSNR

sea lake78.6989

green tree bar57.2443

dancers building68.5769

house boat76.6030

temper huts76.0906

mural wall in?nity

wall mural78.9717

Due to the Minute changes to the original carrier images,users of the carrier images will not feel the exist of watermark images.Because the unique key of carrier image,the original carrier image and the embedding algorithm are only known to the embedder,the illegal operations of clearing away or extracting the watermark image are impossible.

3Conclusion

In this paper,a novel watermarking algorithm for images on quantum computers is pro-posed based on?exible representation for quantum images(FRQI).Compared with the previous strategy[24]which can only be used to verify the identify of true owner of the carrier image, our method is more universal.It can be used to?nd out who is the real owner.And it is impossible for a illegal users to clear o?or extract the watermark images.

Since the quantum computer and the quantum images study is only in their infancy,we

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