外文翻譯--數(shù)字圖像隱寫技術(shù)的隨機調(diào)制

1、<p><b>　　外文資料</b></p><p>　　Digital image steganography using stochastic modulation</p><p>　　Jessica Fridrich? and Miroslav Goljan</p><p>　　Department of Electrical

2、and Computer Engineering, SUNY Binghamton, Binghamton, NY</p><p>　　13902-6000, USA</p><p><b>　　ABSTRACT</b></p><p>　　In this paper, we present a new steganographic parad

3、igm for digital images in raster formats. Message bits are embedded in the cover image by adding a weak noise signal with a specified but arbitrary probabilistic distribution.This embedding mechanism provides the user wi

4、th the flexibility to mask the embedding distortion as noise generated by a particular image acquisition device. This type of embedding will lead to more secure schemes because now the attacker must distinguish statistic

5、al anoma</p><p>　　Keywords: Steganography, steganalysis, stochastic modulation, device noise</p><p>　　1. INTRODUCTION</p><p>　　The purpose of steganography is to hide the very prese

6、nce of communication by embedding messages into innocuous-looking cover objects, such as digital images. To accommodate a secret message, the original cover image is slightly modified by the embedding algorithm to obtain

7、 the stego image. The embedding process usually incorporates a secret stego-key that governs the embedding process and it is also needed for the extraction of the hidden message.</p><p>　　In contrast to wate

8、rmarking when the embedded message has a close relationship to the cover image supplying data,such as sender or receiver information, authentications codes, etc., in steganography, the cover image is a mere decoy and ha

9、s no relationship to the hidden data. The most important requirement for a steganographic system is undetectability: stego images should be statistically indistinguishable from cover images. In other words, there should

10、be no artifacts in the stego image that c</p><p>　　The early steganographic schemes focused on introducing as little distortion in the cover image as possible utilizing the seemingly intuitive heuristics tha

11、t the smaller the embedding distortion is, the more secure the steganographic scheme becomes. However, recent advances in steganalysis clearly showed that this is not the case. The Least Significant Bit embedding (LSB) w

12、ith sequential or random message spread has been successfully attacked even for very short messages2,3,11. In essence, the L</p><p>　　The +–1 embedding is a special case of our stochastic modulation when the

13、 noise η added to the cover image has the following probability distribution P: P(η = –1) = p/2, P(η = 1) = p/2, P(η = 0) = 1?p (assuming the message is a random bit-stream and 100p % of pixels were used for embedding).

14、Notice that in +–1 embedding, the message bits are still encoded and extracted as LSBs of pixels. In this paper, we show how to extend this embedding archetype to a noise with an arbitrary probabilistic dist</p>&

15、lt;p>　　The embedding party (Alice) can use stochastic modulation, for example, in the following way. Alice will carry out experiments on her source of cover images and estimate the properties of the noise present in t

16、hem. If Alice’s acquisition device is a digital camera, the noise depends on the exposition time, the amount and type of ambient light at the scene, usage of a flash, the specific CCD sensor and camera circuitry, interpo

17、lation algorithms in camera’s hardware, etc. The sensor and hardware n</p><p>　　Determining the actual security of stochastic modulation, however, is not an easy task due to the fact that we are adding a qua

18、ntized noise to an already quantized (and processed) signal rather than at the point of acquisition when the light hits the CCD sensor. This issue is also discussed in the paper.</p><p>　　Before we close thi

19、s introduction, we note that, similar to stochastic modulation, DSSS (Direct Sequence Spread Spectrum) embedding, that is widely used for robust watermarking, also superimposes message-modulated noise on the image. Howev

20、er, DSSS cannot be simply turned into a high-capacity non-robust embedding needed for steganography due to the correlation-based message extraction.</p><p>　　The paper is organized as follows. In the next se

21、ction, we give a brief overview of related methods proposed in the past. Then, in Section 3, we describe the main ideas behind stochastic modulation and in Section 4 we discuss some important implementation issues that n

22、eed to be considered to establish practical communication. In Section 5, we investigate the security of the proposed algorithm from the point of view of recent advances in steganalysis.</p><p>　　Stochastic m

23、odulation is extended to a content-dependent noise in Section 6. Finally, in Section 7 we conclude the paper and outline possible future research directions.</p><p>　　2. RELATED METHODS</p><p>　

24、　In the past, several researchers attempted to design steganographic schemes that embed messages by adding Gaussian noise to the image. Marvel et al.7 describe a high-capacity method for embedding message bits in uncompr

25、essed raw image formats. A special non-linear transformation together with the message bits is used to generate a Gaussian signal that is added to the cover image. The purpose of the transformation is to maximize the sep

26、aration between two samples of a random Gaussian variable tha</p><p>　　Alturki’s1 approach is a simple bit-replacement of quantized DCT coefficients calculated from a randomly permuted image. The key-depende

27、nt permutation serves as a pre-whitening and distributes the image energy evenly over the whole spectrum. Consequently, the quantization noise appears to be Gaussian although no formal proof of this is given. In Alturki’

28、s method, truncation of grayscales at 0 or 255 may introduce read-out errors during the decoding.</p><p>　　The author mentions that the problem can be dealt with by applying error-correction to his scheme. H

29、owever, the error-correcting scheme will further decrease the capacity of the method. Because the maximal bit error rate highly depends on the image, it is not easy to find fixed error bounds. Also, the method cannot be

30、easily generalized to make the distortion follow an arbitrary probability distribution that would approximate a non-Gaussian device noise.</p><p>　　According to the best knowledge of the authors of this pape

31、r, no steganographic method has so far been proposed that would provide a high embedding rate (e.g., above 0.5 bpp) and could be interpreted as adding noise of predefined properties, including the proof that the distorti

32、on really has the required statistical properties. In the next section, we describe a simple high-capacity steganographic method that embeds message bits by adding a noise signal with an arbitrary distribution or even a

33、c</p><p>　　3. STOCHASTIC MODULATION</p><p>　　In Subsection 3.1, we describe a high-capacity steganographic method that embeds message bits into individual pixels by adding to the cover image a n

34、oise signal with a probabilistic distribution that is symmetrical about zero. Generalization to an arbitrary noise distribution is presented in Subsection 3.3. Throughout this text, we assume that the cover image is an 8

35、-bit grayscale image.</p><p>　　First, note that if {si} is a normally distributed Gaussian sequence N(0,σ) and if zi is a random variable uniformly distributed in {–1, 1}, then {zisi} is also N(0,σ). In othe

36、r words, a Gaussian sequence with randomized signs stays Gaussian. This statement is true for any random variable with a distribution symmetrical about zero.</p><p>　　Suppose the message mi consists of a ran

37、dom sequence of 1's and –1's (mi has zero mean). Consider a naïve steganographic scheme in which we add the signal {misi} to the image. Unfortunately, in order to recover the message, the original image or a

38、t least its approximation (e.g., using low-pass filtering) is necessary. Errors in estimating the original image necessitate employment of error-correction schemes, which in turn may dramatically decrease the steganograp

39、hic capacity. Below, we show a si</p><p>　　We define a parity function P on pixel values, P(x, s) ∈ {–1,1}, for x∈{0, …, 255} and s > 0, where s is an integer parameter, and P(x, s) = 0 for s = 0. This fu

40、nction applied to the stego image pixel values will produce message bits. The parity function is required to satisfy the following “anti-symmetric” property for all x</p><p>　　P(x+s,s)=-P(x-s,s), x∈[1,2s]

41、 (1)</p><p>　　For example, for s = 1, we can define P(x, 1), x = 0, 1, 2, … as P(x, 1) = 1, 1, –1, –1, 1, 1, –1, –1, …. In general, for s > 0, the first segment of 2s parities can be arb

42、itrary, but every next segment of 2s values must be the negative copy of the previous segment. Thus, it is enough to define P on the set [1, 2s]. A good choice for the parity function is</p><p>　　P(x,s)=（-1）

43、x+s，x∈[1,2s]. (2)</p><p>　　This parity function ensures that P changes its sign as often as possible. We will find this property useful when x+s or x–s should get outside of their dynamic

44、 range during embedding.</p><p>　　Notice that besides the pixel value x, the parity function depends on the second parameter s. This is important because otherwise we could not find a function P(x) satisfyin

45、g P(x+s) = – P(x–s) for all pixel values x and all positive integers s.</p><p>　　3.1 Embedding method</p><p>　　Having defined the parity function, we can now continue with the description of the

46、 embedding method. The image pixels can be visited either sequentially or along a pseudo-random walk generated from the stego-key. A pseudorandom number generator (PRNG) is seeded with a secret seed derived from the steg

47、o-key. The PRNG should produce numbers with a distribution that matches the distribution of the noise that will be superimposed on the cover image during embedding. We will call the noise generated</p><p>　　

48、For each pixel x along the random walk, we generate one sample of the stego noise rounded to an integer s. If s = 0,we do not modify x and move to the next pixel. If s ≠ 0, we check if P(x+s, s) = m, where m is the messa

49、ge bit to be embedded. In this case, we modify x to x + s and move to the next pixel and embed the next message bit. If P(x+s, s)= –m, we modify x to x – s. Denoting the pixel values of the stego image as xi’, the embedd

50、ing process can be expressed using the formula</p><p>　　xi’ = xi + miP(xi + si , si) si (3)</p><p>　　In this formula, the message bits mi are duplicated as necessary to accoun

51、t for the cases when si = 0. We can say that instead of adding the signal {misi} to the cover image as we did in the beginning of this section, we add {visi}, where vi = miP(xi + si, si). According to our assumption, the

52、 message bits mi form a pseudo-random sequence of 1’s and – 1’s. Because the image and the stego noise sequence si are independent of the message, the variable vi is also a pseudo-random sequence of 1’s and</p>&l

53、t;p>　　There is a slight complication at the boundaries of the pixels’ dynamic range at 0 and 255. The amplitude of the noise that is added to the image should be truncated as it would happen during the image acquisiti

54、on process.Whenever xi + si > 255 the xi’ will be the nearest value less or equal to 255 with the desired parity mi. A similar measure is applied when xi + si < 0.</p><p>　　3.2 Message extraction</p

55、><p>　　In the decoding process, we generate the same stego noise sequence {si} from the stego-key as was done during message embedding, follow the same pseudo-random path in the stego image, and apply the parit

56、y function P to the pixel values. The non-zero parity values form the secret message</p><p>　　mi = P(xi, si) (4)</p><p>　　We note that the stego-key can determine both

57、 the random embedding walk and the sequence si.</p><p>　　If the device noise is Gaussian, the embedding distortion can be expressed using the Peak-Signal-to-Noise-Ratio(PSNR) as</p><p>　　PSNR=10

58、log10（2552/σ2） (5)</p><p>　　To obtain the expected capacity C measured as the number of bits-per-pixel, bpp, we have to subtract the probability of occurrence of ‘0’ in the stego noise

59、sequence si from the maximum bit rate of 1 bit per pixel (bpp):</p><p>　　C=1-erf（） (6)</p><p>　　where erf is the statistical error function erf（x）=。</p><p>　

60、　On the other hand, if the user specifies the capacity C in bpp, the standard deviation σ of the noise that needs to be added to the image to carry such payload must be greater than</p><p>　　σ=

61、 (7)</p><p>　　where erf -1 is the inverse error function.</p><p>　　3.3 Improved stochastic modulation</p><p>　　The steganographic method as described in the previous su

62、bsection works with one stego noise sequence si that is either added or subtracted from the pixel value based on the match between the message bit and the parity function. It is possible to obtain a higher embedding capa

63、city with the same distortion by considering two stego noise sequences rather than one and always add one or the other, again based on the match between the message bit and a parity function. Furthermore, the improved te

64、chn</p><p>　　First, we generate two independent stego noise sequences rounded to integers ri, si (for example, we can seed the PRNG with two different seeds derived from the stego-key). For each pixel xi, if

65、 ri ? si = 0, we do not embed a message bit but we do modify xi to xi+ri and embed the same message bit in the next pixel. If ri ? si ≠ 0, we verify whether P2(xi+si, ri?si) = mi, where mi is the message bit to be embedd

66、ed, and P2 is a parity function defined so that P2(x+k, k) = ?P2(x, k) for all x∈[0, 2</p><p>　　P2(x+r, r?s) = – P2(x+r–(r?s), r?s) = – P2(x+s, r?s) ≠ 0, whenever r?s ≠ 0 (8)</p><p>　　Denoting

67、the pixel values of the stego image as xi’, the embedding process can be expressed using the formula</p><p><b>　　(9)</b></p><p>　　Thus, the pixel value is modified by adding the valu

68、e of one of the stego noise sequences to it. Because the selection of the values ri vs. si is governed by the match between two uncorrelated quantities – the parity function P2(xi+si,ri?si) and the message bit mi – the n

69、oise added to the image has the same characteristics as the stego noise.</p><p>　　The parity function P2: ([0, 255], Z) → {–1,1} is periodic with the period 2|k| and is defined similarly to the previous pari

70、ty function P requiring</p><p>　　P2(x+k, k) = –P2(x, k), for all x∈[0, 255] and k≠0 (10)</p><p>　　Again, it will become advantageous to define P2 so that it frequently changes sign to m

71、inimize deviations from thestego noise signal at 255 and 0:</p><p>　　P2(x, k) = (–1)x+k, x∈[1, k], k≠0 is an integer,P2(x, 0) = 0 (11)</p><p>　　The embedding distortion for the new method

72、 is still the same as when just one stego noise sequence was used because we are adding a signal selected at random from two stego noise sequences of the same distribution. But now the probability of not embedding a mess

73、age, which occurs when r ? s = 0, is smaller. This is because in general the distribution of the sum of two random variables is the convolution of both and is thus “flatter” than for a single variable. In the case of a G

74、aussian stego noi</p><p>　　Pr（r=n）= (12) </p><p>　　Thus the probability that r ? s = 0 is (Pr?Ps)(0), where ? denotes the convolution.Finally, the capacity of the modified st

75、ochastic modulation algorithm is C = 1 – (Pr?Ps)(0) (13)</p><p>　　The improvement in capacity is quite obvious from Figures 1 and 2 (the broken line corresponds

76、to the embedding method with one Gaussian sequence and the continuous line to the new two-sequence method). </p><p>　　Figure 1: Capacity as a function of the PSNR </p><p>　　Figure 2: Capacity as

77、 a function of the Gaussian variance σ2. </p><p><b>　　中文譯文</b></p><p>　　數(shù)字圖像隱寫技術(shù)的隨機調(diào)制</p><p>　　杰西卡·弗里德里希和米羅斯拉夫·戈連</p><p>　　電氣

78、工程和計算機系，紐約州立大學(xué)賓漢姆頓，賓漢姆頓，紐約州13902-6000，美國</p><p><b>　　摘要</b></p><p>　　本文中，在光柵格式下我們?yōu)閿?shù)字圖像提出了一種新的隱寫模式。信息比特是通過添加一個指定的但任意概率分布的弱噪聲信號從而嵌入封面圖片中的。這個嵌入機制為用戶提供的靈活性，可以把嵌入失真掩蓋成為一個特定的圖像采集設(shè)備產(chǎn)生的噪聲。這種

79、嵌入模式將會使計劃更加安全，因為現(xiàn)在攻擊者必須區(qū)分那些可能由圖像采集本身所引入的嵌入過程所產(chǎn)生的統(tǒng)計異常。與之前提出的方案不同，這一新的方法，我們稱之為隨機調(diào)制，實現(xiàn)無噪聲提取算法或差錯收集的未察覺的數(shù)據(jù)傳送。這將會提供更高的容量（達到0.8比特每像素），方便和簡單的實現(xiàn)復(fù)雜度低的嵌入和提取。但是最主要的，是因為嵌入噪聲具有隨機特性，近似一個給定的設(shè)備噪聲，新的方法比現(xiàn)有的方法具有更高的安全性。本文的最后部分，我們擴展隨機調(diào)制到一個內(nèi)容

80、相關(guān)的設(shè)備信號，同時我們還討論了基于隱寫分析就這項方案可能的攻擊的最新進展。</p><p>　　關(guān)鍵字：隱寫技術(shù)；隱寫分析；隨機調(diào)制；設(shè)備噪聲；</p><p><b>　　1.引言</b></p><p>　　隱寫技術(shù)是通過把信息嵌入數(shù)字圖像這類看似平淡無奇的覆蓋物中，從而達到隱藏通訊信息本身的目的。為了可以容納一個秘密信息，原本的封面圖片

81、會通過嵌入算法這一方式來稍加修改從而得到隱秘的圖片。嵌入過程通常包括一個秘密的隱寫密鑰管轄的嵌入過程，并且它也需要隱藏信息的提取。</p><p>　　水印嵌入信息時，通常被嵌入的信息都與表面圖片所提供的數(shù)據(jù)，例如收件人或發(fā)件人的信息，驗證碼等等這些有著密切的聯(lián)系。而隱寫技術(shù)嵌入信息時正好與之相反，表面圖片僅僅是一個單純的誘餌并且與被隱藏數(shù)據(jù)無關(guān)。對于一個隱寫技術(shù)系統(tǒng)的最重要的要求是不可被檢測性：也就是隱秘圖片在

82、統(tǒng)計方面無法從表面圖片中區(qū)分出來。換句話說，在隱秘圖像中應(yīng)該沒有能讓攻擊者發(fā)覺的比隨機猜測擁有更高可能性的人為痕跡。除非給與對嵌入算法進行了充分的了解的隱秘關(guān)鍵（科克霍夫法則）。</p><p>　　早期隱寫技術(shù)方案的重心在于引進使表面圖片盡可能小的失真，利用表面上直觀的經(jīng)驗知識——嵌入失真越小，隱寫技術(shù)方案就會越安全。然而，隱寫技術(shù)分析的最新進展表明情況并非如此。嵌入連續(xù)或隨機分布的信息的低通濾波器已經(jīng)被成功的

83、攻擊即使信息相當(dāng)?shù)亩?。本質(zhì)上講，低通濾波器嵌入是很容易被發(fā)覺，因為它引進的失真對于圖片來說是極其不自然的，并且在適當(dāng)?shù)拇_定的統(tǒng)計學(xué)特性方面產(chǎn)生了不平衡。更好的辦法是通過對像素的隨機加1或者-1來替換LSB的翻轉(zhuǎn)操作（+-1嵌入），并從LSB中提取信息比特，就像經(jīng)典的LSB嵌入一樣。這就是Hide的嵌入算法，他已經(jīng)被JPEG版本接受為隱寫技術(shù)（一個稍微不同的版本）。事實上，它已經(jīng)證明LSB嵌入模式的輕微修改是更加難以被發(fā)覺的。</p

84、><p>　　當(dāng)噪聲η加入表面圖片時，+-1嵌入方式是隨機調(diào)制的一種特殊情況，并且P的分布概率為：P（η=-1）=p/2，P（η=1）=p/2，P（η=0）=1-p（假設(shè)信息是隨機位流并且像素的100p%都被用于嵌入）。請注意，在+-1嵌入方式中，信息位依舊像像素的LSBs一樣被編碼和提取。本文中，我們將展示如何將一個嵌入原型擴展成為一個擁有在任意一個整數(shù)集定義的任意概率分布P的噪聲?？梢赃_到這種效果的算法稱為隨機調(diào)

85、制。</p><p>　　嵌入部分（Alice）可以使用隨機調(diào)制，例如，以下方式。Alice將對她的表面圖片的來源進行試驗，并估計其中當(dāng)前的噪聲性能。如果Alice的采集設(shè)備是一臺數(shù)碼相機，噪聲取決于曝光時間、現(xiàn)場環(huán)境光的數(shù)量與種類、閃光燈的使用、具體的CCD傳感器和照相機電路，以及照相機硬件的插值算法等等。眾所周知，傳感器和硬件的噪聲可以很好地被獨立同分布的高斯噪聲所模仿。因為通常來說圖片中噪聲數(shù)量的大的變動是

86、由于上述提到的眾多的促進作用所造成的。這種促進作用可以無需引進可被輕易察覺的統(tǒng)計方面的人為痕跡而輕微地提高噪聲的數(shù)量。這個想法是本文中提出的隨機調(diào)制的基礎(chǔ)。</p><p>　　然而測定隨機調(diào)制的實際的安全性不是一件簡單的工作，因為事實上我們正在將一個量化噪聲加入一個已量化（和加工過的）信號中，而不是對光照時的傳感器進行點采集。這一觀點在本文中也進行了討論。</p><p>　　結(jié)束引言之

87、前，我們注意到，類似隨機調(diào)制，擴頻（直接序列擴頻）嵌入，廣泛用于魯棒水印，也將圖像調(diào)制噪聲疊加如圖像中。然而，由于相關(guān)信息需要提取，直接序列擴頻無法輕易成為需要隱寫技術(shù)的大容量非穩(wěn)固的嵌入。</p><p>　　本文的結(jié)構(gòu)如下。下一節(jié)中，我們對于過去提出的相關(guān)方法給予了簡要的概述。在第3節(jié)中，我們描述了隨機調(diào)制背后的主要的觀點。在第4節(jié)中，我們討論了如何去實施建立切實可行的溝通的重要問題。第5節(jié)中，我們從隱寫分析

88、的最新進展這一角度來研究所提出的算法的安全性。第6節(jié)中，隨機調(diào)制技術(shù)擴展成為一個內(nèi)容相關(guān)的噪聲。最后，在第7節(jié)中我們總結(jié)了本文并概述了未來可能的研究方向。</p><p><b>　　2.相關(guān)方法</b></p><p>　　在過去，一些研究人員嘗試去設(shè)計以向圖片中加入高斯噪聲來嵌入信息的隱寫技術(shù)的方案。馬弗爾等人將這種高容量的方法形容為在無壓縮未加工的圖片格式中嵌入

89、信息位。由一種特殊的非線性變換與信息位一起生成的高斯噪聲被加入表面圖片。變換的目的是最大限度分離兩個樣品之間的編碼0和1的隨機高斯變量。信息探測器首先用于自適應(yīng)的維納濾波器對圖片的噪聲成份分析。噪聲成份然后通過反嵌入功能來決定嵌入位。然而，附加的高斯信號的振幅必須足夠大，以盡量減少位提取過程中的錯誤。這迫使用戶增大附加的噪聲的幅度，這反過來又降低了隱寫技術(shù)方案的安全性。即使目前沒有失真，糾錯對于保證無差錯位提取也是必要的。這進一步降低了

90、該方法的實用性。我們承認這一工作的重點是魯棒能力性的問題，而不是安全性問題。Alturki的方法是一個簡單的從一個隨機置換的圖像中得出量化后的DCT系數(shù)的位替換的算法。相關(guān)的關(guān)鍵性的移位看做預(yù)白化，并且將圖片能量均勻地分布在整個光譜上。因此，量化噪聲成為高斯型的，盡管這沒有被正式證明。在Alturki的方法中，在解碼過程中，對于0或255灰度級的截斷可能會引進結(jié)果傳達錯誤。作者提到這一問題可以通過在他的方案中應(yīng)用</p>

91、<p>　　據(jù)本文作者所知，迄今為止已提出的隱寫方法沒有一個可以提供高嵌入率（例如，高于0.5bpp）并且可以被理解為附加噪聲的預(yù)定義屬性，包括失真確有必要的統(tǒng)計特性方面的證明。在下一節(jié)中，我們描述了一種通過加入任意分布的噪聲信號甚至是自相關(guān)噪聲來嵌入信息位的簡單的高容量的隱寫方法。該方法不需要任何糾錯方案或任何計算昂貴的圖像處理或轉(zhuǎn)換。</p><p><b>　　3.隨機調(diào)制</b&

92、gt;</p><p>　　在3.1小節(jié)中，我們描述了一種通過向表面圖片加入關(guān)于零對稱的概率分布的噪聲信號來實現(xiàn)將信息位嵌入單個像素的隱寫技術(shù)方法。在3.3小節(jié)中推廣到任意的噪聲分布。縱觀這段文字，我們認為，表面圖片是一個8位灰度圖像。</p><p>　　首先，需要注意的是，如果{Si}是一個正態(tài)分布的高斯序列N（0，σ），并且如果Zi是在{-1,1}上均勻分布的隨機變量，那么{ZiSi

93、}也是N（0，σ）。換句話說，隨機信號性的高斯序列還是高斯的。這種說法對于任意關(guān)于零對稱的隨機變量都是正確的。</p><p>　　假設(shè)消息Mi由1與-1的隨機序列組成（Mi具有零均值）?？紤]我們將信號{MiSi}加入圖像的固有的隱寫技術(shù)方案。不幸的是，為了恢復(fù)消息，原始圖像或者至少是相當(dāng)相似的圖像是必需的。估計原始圖像時產(chǎn)生的錯誤迫使我們需要用到糾錯方案，這反過來有可能大幅度的降低隱寫的可實施性。下面，我們將展

94、示一類參數(shù)化的校驗功能被用于明顯實現(xiàn)這一方案的簡單的想法。</p><p>　　我們定義奇偶函數(shù)P的像素值，P（x，s）∈{-1，1}，其中x∈{0，…，255}且s>0，s是一個整數(shù)參數(shù)，同時，s=0時，P（x，s）=0。適用于隱寫圖像像素值的這一函數(shù)將會產(chǎn)生信息位。奇偶函數(shù)必須滿足以下反對稱特性，其中所有的x滿足</p><p>　　P(x+s,s)=-P(x-s,s), x∈[

95、1,2s]. (1)</p><p>　　例如，當(dāng)x=1時，我們可以把P（x,1）,x=0,1,2,…定義為P（x,1）=1,1,-1,-1,1,1,-1,-1,…。一般情況下，當(dāng)s>0時，2s奇偶校驗的第一部分可以是任意的，但是每下一個2s的值，必須是上一部分的負的形式。因此，足夠?qū)定義在集[1,2s]上。奇偶函數(shù)的一個很好的選擇是</p><p

96、>　　P（x，s）=（-1）x+s，x∈[1,2s]. (2)</p><p>　　這個奇偶函數(shù)可以確保P盡可能多的改變其信號。我們發(fā)現(xiàn)嵌入過程時當(dāng)x+s或者x-s處于動態(tài)范圍以外這一特性相當(dāng)有用。</p><p>　　請注意，除了像素值x，這奇偶函數(shù)還取決于第二個參數(shù)s。這相當(dāng)重要，因為否則我們無法為所有像素值x和所有正整數(shù)s找到一個滿足P(x+

97、s)=-P(x-s)的函數(shù)P（x）。</p><p><b>　　3.1嵌入方法</b></p><p>　　定義奇偶函數(shù)后，現(xiàn)在我們可以繼續(xù)進行嵌入方法的描述了。無論是按順序還是沿著密鑰產(chǎn)生的偽隨機走，圖片像素都可以被訪問。偽隨機數(shù)字發(fā)生器（PRNG）是密鑰所產(chǎn)生的一種秘密的種子。PRNG將產(chǎn)生一些數(shù)字，這些數(shù)字是按在嵌入時將要疊加在表面圖片上的噪聲的分布方式分布的

98、。我們把產(chǎn)生于PRNG的噪聲稱為隱寫噪聲。</p><p>　　對于每一個隨機移動的像素x，我們生成一個把隱寫噪聲四舍五入為一個整數(shù)的樣本。如果s=0，我們不會修改x并移動到下一個像素。如果s≠0，我們會檢驗P(x+s)是否等于m，其中m是作為信息位被嵌入。在這種情況下，我們把x修改為x+s，同時移動到下一個像素，并嵌入下一個信息位。如果P(x+s，s)=-m，我們把x修改為x-s。把隱寫圖像的像素值表示為xi

99、，，嵌入過程可以用公式表示為</p><p>　　xi，= xi+miP（xi+ si，si）si (3)</p><p>　　在這個公式中，當(dāng)si=0是信息位mi必須重復(fù)的原因。我們可以認為，就像我們在本節(jié)開始時所做的那樣，我們向表面圖片中加入了{visi}，而不是加入信號{misi}，其中vi=miP（xi+si，si）。根據(jù)我們的假設(shè)，信息位m