Image Bitsllipped RS Steganalyzerreported value0.02070.02490.02160.02040.02050.02960.02400.0246

Baboon

Clock

Hats

Lena

New York

Parrot

I~TeaDOt340

Table 4: Performance of RS Steganalyzer when message bits embedded only in active regions of image.

s. CONCLUSION

In this paper we have examined ways in which Alice and Bob can practice adaptive steganography in order to escapedetection by known steganalysis techniques. We show that even if the warden is aware of the specific adaptive mechanismbeing used, Alice and Bob still gain in the sense that they can embed larger messages while escaping detection. Wedemonstrate the validity of our approach using RS steganalysis as an example and design some experimental ways to escapedetection.

6. REFERENCES[1] G. I. Simmons, "Prisoners' Problem and the Subliminal CI1annel", CRYPTO 83- Advances in Cryptology, August

22-24.1984. pp. 51-67. ,

[2] N. F. Johnson, S. Katzenbeisser, "A Survey of steganographic techniques", in S. Katzenbeisser and F. Petitco1as (Eds.):Infonnation Hiding, pp. 43- 78. Artech House, Norwood, MA, 2000.

[3] N. F. Johnson, S. Jajodia, "Steganalysis: The investigation of Hidden Information", IEEE Infonnation TechnologyConference, Syracuse, NY, USA, 1-3 September 1998.

[4] N. F. Johnson, S. Jajodia, "Steganalysis of Images created using current steganography software". in David Aucsmith(Ed.): Info17nation Hiding. LNCS 1525. pp. 32-47. Springer-Verlag Berlin Heidelberg 1998.

[5] A Westfeld, A. Pfitzmann. "Attacks on Steganographic Systems'., in Andreas Pfitzmann (Ed.): Infonnation Hiding.LNCS 1768. pp. 61-76, Springer-Verlag Berlin Heidelberg, 1999.

[6] I. Fridrich, R. Du, M. Long, "Steganalysis ofLSB Encoding in Color Images.', Proceedings of ICME2000. New YorkCity. July 31-August 2. New York, USA .

[7] I. Fridrich. M. Goljan and R. Du. "Reliable Detection ofLSB Steganography in Color and Grayscale Images". Proc. ofthe ACM Workshop on Multimedia and Security, Ottawa. CA. October 5.2001, pp. 27-30.

[8] I. Avcibas, N. Memon and B. Sankur, "Steganalysis Using Image Quality Metrics... Security and Watennarking ofMultimedia Contents, SPIE. San Jose, CA. February 2001.

[9] R. Chandramouli and N. Memon, "Analysis of LSB Based Image Steganography Techniques." Proceedings of theInternational Conference on Image Processing, Thessaloniki, Greece, October 2001.

[10] Andreas Westfeld. F5-A Steganographic Algorithm: High Capacity Despite Better Steganalysis. S. 289-302 in Ira S. i

Moskowitz (Hrsg.): Information Hiding. 4th International Workshop. IHOI, Pittsburgh, USA. April 2001, Proceedings.LNCS 2137. Springer- Verlag Berlin Heidelberg 2001.

[11] Faisal Alturki and Russell M. Mersereau. Secure blind image steganographic technique using discrete fouriertransformation. In Proceedings of the IEEE International Conference on Image Processing, lCIP '01, Thessaloniki, Greece,October 2001.

[ 12] http:/ /www .cl.cam.ac.uk/ -fapp2Jwatennarking/benchmark/image_database.hbnl

78 Prac. SPIE Val. 4675

subjective visual quality of a suspected stego-image.. In this paper we restrict our attention to the passive warden caSe aIJassume that no changes are made to the stego-object by the warden Wendy.

Figure 1: Framework for Secret Key Passive Warden Steganography. Alice embeds secret message in cover imag(left). Wendy the warden checks if Alice's image is a stego-image (centre). If she cannot determine it to be so, sbpasses it on to Bob who retrieves the hidden message based on secret key (right) he shares with Alice.

It should be noted that the main goal of steganography is .to communicate securely in a completely undetectable manner. Th;is, Wendy should not be able to distinguish in any sense between cover-objects (objects not containing any secret messag~and stego-objects (objects containing a secret message). In this context, "steganalysis" refers to the body of techniques th~aid Wendy in distinguishing between cover-objects and stego-objects. It should be noted that Wendy has to make thidistinction without any knowledge of the secret key which Alice and Bob may be sharing and in some cases (pUIsteganography) without knowledge of the specific algorithm that they might be using for embedding the secret messaglHence steganalysis is inherently a difficult problem. However, it should also be noted that Wendy does not have to gleaanything about the contents of the secret message m. Just determining the existence of a hidden message is enough. This fac

makes her job a bit easier.

Given the proliferation of digital images, and given the high degree of redundancy present in a digital representation of aimage (despite compression), there has been an increased interest in using digital images as cover-objects for the purpose (steganography. The simplest of such techniques essentially embed the message in a subset of the LSB (least significant biplane of the image, possibly after encryption [2]. It is well known that an image is generally not visually affected when ileast significant bit plane is changed. Popular steganographic tools based on LSB like embedding vary in their approach fihiding information. Methods like Steganos and Stools use LSB embedding in the spatial domain, while others like Jsttembed in the frequency. For brevity, we collectively refer to these techniques as LSB steganography techniques. For a gocsurvey of steganography techniques, the reader is referred to [2]. In this paper we restrict our attention to LSB steganograpllwhere digital images are being used as cover objects. However, the principles developed here are more general and apply ~well to ?ther t~s of steg.anograp~y techniq~es and with other types of cover-data like video and audio-., .

The development of techniques for image steganography and the wide-spread availability of tools for the same have led to ~increased interest in steganalysis techniques for image data. The last two years have seen many new and powerlsteganalysis techniques reported in the literature. Perhaps some of the earliest work in this regard was reported by Johns<and Jajodia [3],[4]. They mainly look at palette tables in GIF images and anomalies caused therein by common stego-too]A more principled approach to LSB steganalysis was presented in [5] by Westfeld and Pfitzmann. They identify Pairs ,Values (poV's) which consist of pixel values that get mapped to one another on LSB flipping. For example the value 2 gemapped to 3 on LSB flipping and likewise 3 gets mapped to 2. So (2, 3) forms a PoV. Now LSB embedding causes tIfrequency of individual elements of a Po V to flatten out with respect to one another .So for example if an image has 50 pixethat have a value 2 and 100 pixels that have a value 3, then after LSB embedding of the entire LSB plane the expect(frequencies of2 and 3 are 75 and 75 respectively. This of course is when the entire LSB plane is modified. However, as 101as the embedded message is large enough, there will be a statistically discernible flattening of PoV distributions and this fa

70 Proc. SPIE Val. 4675

However, this,is the main limitation of their technique. LSB embedding can only, ., .

Wendy.

lines but with higher detection rate even for short messages was proposed by Fridrich,, , ..~

color planes. They then show that the ratio of close colors to the total number of unique colors increases

image as opposed to when the same message is". It is this difference that enables them

cover-images from steg-images for the case of LSB steganography. A more sophisticated technique thataccuracyeven for short messages was presented by Fridrich et. al. in [7]. Since we make

for obtaining our experimental results, we give a detailed explanation of it in sub-

Memon and Sankur [8] present a general purpose technique for steganalysis of images that works with a wideof embedding techniques including but not limited to LSB embedding. They demonstrate that steganographic

., , c~

, ' The steganalyzermultivariate regression on the selected quality metrics and a training set of cover and stego images.. In the

, , ., , , ..-, -J

results with the chosen feature set and well-known watermarking and steganographic techniques indicate their, -1 cover images and stego-images for a wide variety of stego-

They report moderately successful results eyen when the stego-technique was unknown to the detector and not

l analysis of LSB steganography and investigate under what conditions can anbetween stego-images and cover-images. They derive a closed form expression of the probability of

, , ., ., ; ...

, ' , ~the steganalysis problem as a multiple hypothesis testing problem and pool results at individual pixels to

detection rule. Although this work is interesting from an academic point of view, il;resul~sin loose uppersteganographic capacity of LSB encoding in general. Some of the specific techniques described above for LSB, , , , .

2. ANAL YSIS OF ADAPrIVE STEGANOGRAPHY

framework described so far Alice and Bob have no knowledge of the steganalyzer that the wardenis using to detect stego-images, whereas Wendy can have knowledge of their embedding algorithm (but not their

-Alice and Bob are well aware about the capabilities of Wendy and may take explicit: will employ. This awareness could be in the

of general knowledge about the current state-of-the-art in steganography. For example, if Alice and Bob are aware, -.1 make sure that the message embedded in 'each image is short and- also

., Having some knowledge about Wendy's detection mechanisms,

that Alice and Bob will adapt their embedding algorithm accordingly in order to avoid detection. Intuitivelythis is what we mean by adaptive steganography. Now, it would violate one of the basic principles ofc- .steganography) if we assume that Wendy is ignorant of Alice's and Bob's adaptive embedding strategy.

' steganalyzer, we show in this

Alice and Bob can practice adaptive steganography depending on the amount and type ifthey have about Wendy's detector and the constraints governing their communication abilities. We can

-.-, --,

Prac. SPIE Val. 4675

1

2.

3.

4.

Alice and Bob use a technique that cannot be detected with Wendy's steganalyzer. So if Wendy is usingsteganalyzer for LSB detection, Alice and Bob can use a technique other than LSB embedding. For example, th'could embed in the next significant bit plane. Or they could embed in the transform domain using a techniqsimilar to [10] and [11]. However, this situation is really not of interest from a theoretical point of view as Wendwho we assume has full knowledge of Alice's and Bob's strategy, can develop anew steganalyzer that will det(the technique and we are back to square one.Alice can restrict the number of bits that they embed such that Wendy is not able to detect the message given tparameters she is using in her steganalyzer. In this case Alice and Bob need not share any extra information otlthan the secret key which they use to embed the message.Alice and Bob embed the message only in locations where it is hard for Wendy to detect. For example, Alice aBob can only embed in pixel locations where the immediate neighborhood has high activity and any statistimeasurement that Wendy may attempt to make would be affected by the high degree of "noise" present in 1neighborhood. Note, that in order to use such a strategy Alice and Bob have to pre-decide the specific mechanisto be employed.Alice can first embed the message and then further process the stego-image in order to mask the hidden message ~hence avoid detection. The post-processing could be as simple as addition of Gaussian noise or could be somethilmore involved that makes explicit use of Alice's knowledge of Wendy's steganalyzer.

As we stated above, the first case presented above is ad-hoc and not of further interest. In the rest of this section we exalIthe remaining cases in a mathematical setting and show that indeed Alice and Bob can gain something by using any ofthree strategies. We defer the analysis of case 3 to the full version of the paper as it really turns out to be very similar to (4. In the rest of this section we take a closer look at cases 2 and 4 and show how Alice and Bob could benefit by using san approach.

Let us examine case 2 of adaptive steganography, where we assume that Alice and Bob know Wendy's detection techruand try to escape detection using a smart strategy that does not give sufficient information to Wendy. From statisldetection theory point of view we can state that in order to detect the presence of a hidden message within a celprobability of error, Wendy has to observe at least N features or samples [9]. Therefore, if Alice chooses the numbefeatures that carry the hidden message to be less than N, Wendy's detection probability will decrease. Of course this oalso mean a reduction in the hiding capacity for Alice since the number of message carriers will be less in this case.

formulate this problem as follows. For Wendy's detector let Ho and H 1 respectively denote that hypothesis that the obse

signal does not contain a message and the contrary. Now, Wendyobserves a total 'of Lfeatures in the image presented t<by Alice and performs a statistical hypothesis test on each of these features (or a subset) to determine if a message is preIn general, each of these tests on the individual features could be different in their approach or the parameters used. u

denote by aiand Pt,i=1,2,...Lthe respective false alarm (P(HliHo»and miss probabilities (P(HoIHl»of

individual statistical detectors. For simplicity, in the following analysis we assume ai = Pt,i = 1,2,...L .After W

chooses these parameters and performs the corresponding tests, she arrives at L decisions. The question now for Wendhow to combine these L decisions for a fmal decision such that a global false alarm and miss probability is attained'immediately see that this problem is combinatorially hard. The reason for this is as follows: Wendy has to design a gfusion detector (function) that takes L binary inputs and gives a binary output (final decision about the presence or absen

a hidden message). It is easy to see that there are 22L such global fusion rules! Picking the optimal fusion rule from SUIexponential growing class of functiOOs in L is an enormous task indeed. For example, consider the case when WeJ)dyeach pixel in a 256x256 image for the presence of a LSB message. This means, Wendy has to fmd the optimal fusion de1

from 226"36 possibilities! ! Of course, some trivial fusion detection functions can be immediately discarded such as th'that decides no message is hidden when all the features test positive for its presence. But, such trivial functions are smnumber compared to the problem at hand. In order to alleviate this problem, Wendy can use heuristics such as majoritythat agrees with the decision outcomes of the majority of the local statistical tests performed on the features. We observeheuristics mayor may not be optimal. Nevertheless, from adaptive steganography view-point this is not critical. SuWendy uses the K-out-of-L global detector heuristic that decides the presence/absence of a hidden message if K oul

detectors agree with this decision. Then, it is easy to see that the global detection probability (Pd) and the false

probability ( P f ) are given by:

72 Proc. SPIE Val. 4675

(0.1)

I'L) Since Alice knows the detection strategy of Wendy, it is reasonable to assume that Alice knows theL!=

i!(L-i)!of Wendy as a function of K (as shown in Figure 2) and the actual value of

her detection. Then, Alice's strategy will be to choose a message length such that Wendy will be unablecurve. This essentially leads to the notion of steganography capacity, an

[9]. For example, consider the ROC curve in Figure 2. If Wendy chooses to maximize her detection(K=I in Eq. (0.1» at the expense of maximizing her false alarm probability, then she detects a hidden message

, This means, theoretically, that Alice's steganography capacityto zero. On the other hand, if Wendy decides to minimize her false detection (therefore minimize her detection

K=20 in Eq. (0.1), then, the steganography capacity of Alice is nearly 20 times the number of bitsfeature. Of course, for the other non-extreme cases, Alice and Wendy play the game of not allowing the other

operate in the desired point on the ROC curve. Specifically, Alice's strategy would be to choose a value of K as theof features where she will hide the message (how these features are chosen is an entirely different question) such that

a detection probability that. is less than what she aimed for. Assuming, Alice is more concerned, we can reason that the value of K in the ROC curve that Wendy chooses serves as an upper

on Alice's steganography capacity. We point out here that the tightness of this bound needs further investigation.

we note that since Wendy's global detector deals with discrete random variables, not all possible values-of Pj and

by it.

0.9

0.8

0.7

0.6

a.""'0.5

0.4

0.3

O.Z

0.

n.0.2 0.4 0.6 0.80

PI

Figure 2: ROC for the global detector as a function of K when a = 0.45, /3 = 0.25, L = 20.

now consider the last adaptive steganography case. There are many possible strategies for Alice to increase the..~1~'~ ~ For example, after embedding a message, Alice can add zero-mean noise to those samples (or

that do not carry the message. This way, when Wendy attempts to search for a message using local statisticalin most steganalysis techniques) of the stego signal, she will find it difficult to estimate or detect the

This is clear because the additional noise will increase the variance of the local statistical measures being used inmechanism thereby increasing the estimation error and probability of detection error .We study this effect from

.

Proc. SPIE Vol. 4675

an information theoretic formalism using a cascaded channel model as shown in Figure 3. In this figure, M stands for th~secret message, X is the stego signal and y is the stego'signal after modification by Alice to achieve adaptive steganographyThe cover signal serves as the first channel and the processing undergone by X can be thought of as a second channelClearly, X is obtained from M and y fl:om X~

M x yCover

(Channel 1)?;

Process stego

signal( Channeil:L

Figure 3: A cascaded channel model for adaptive steganography.

It is reasonable to assume that,

I(M;YIX)=o

where I(.) denotes mutual information. In plain terms, Eq. (1.1) means that output of Channel 2 depends statistically only onits input and this happens to be true for this case of adaptive steganography. Now, we know that [6],

I(M;X)=H(M)-H(M IX)

I(M;Y) = H(M)-H(M IY)

where H(.) stands for the unconditional entropy. It is enough to show that I(M;X) ~ I(M;Y) since this means that the

amount of information Wendy gets about M from y (as a result of adaptive steganography) is less than what she will getfrom X (non-adaptive steganography). To prove the required inequality we resort to information theory for cascade channels[6]. We start with the following well-known equation [6],

I(M;YX)= I(M;Y)+I(M;X IY)

=I(M;X)+I(M;Y I X

and equate the right hand sides and use Eq. (1.1) to obtain

I(M;X)=I(M;Y)+I(M;X IY)

Since I(M;X IY)~Ofrom Eq. (1.4) we see that I(M;X)~ I(M;Y) showing that there is something to be gained by

adaptive steganography. Of course, the amount of gain will depend on various factors such the embedding algorithm, thesteganalysis technique, the stego signal processing etc.

3. EXPERIMENT AL RESUL TS

In this section we show practical examples of adaptive steganography. We develop our examples for the RS Steganalysistechnique proposed in [7]. However similar examples can be constructed for other techniques too. The reason we chose theRS steganalysis technique to demonstrate the practical feasibility of adaptive steganography is first because to the best of ourknowledge the RS steganalyzer is currently the state-of-the-art in LSB steganalysis. Second, the technique is very simple toimplement. In the rest of this section we examine the four cases of adaptive steganography identified in section 2 and for eachof them give a practical realization within the framework of LSB steganography and RS steganalysis. For our experimentswe used the watermarking benchmark image database from [22]. The database contains a variety of images includingcomputer generated images, images with bright colors, images with reduced and dark colors, images with textures and fine

74 Proc. SPIE Vol. 4675

and edges, and well-known images like l:.ena, peppers etc. All the images were converted to grey scale and

experiments.

-~subsection we describe in more detail the RS steganalyzer which despite its simplicity provides very accurate

of LSB steganography. Given an 8 bit grayscale image (so assumed for ease of exposition) an RS steganalyzer

-'I pixel in the group. The pixel group is defined as:

G = (XI, X2, X3, ..., Xn}

a discrimination function, f constructed such that it captures the smoothness of a particular group of pixels, is defined

three invertible operations, Fn (x), n = -1,0,1, on pixel values x, are defined as follows:

I. F1(x) is defined as the operation that performs flipping of the LSB of an image pixel. It effectively maps pixel

values as follows:

F; : OH 1, 2 H ~, ..., 254 H 255

2. F_1(x) maps pixel values in the opposite direction as compared to F1. Specifically the mapping F_1 is defined asfollows:

F -I: -I ~ 0, I ~ 2~ ., 255 H 256

3. Identity function, Fo{x) that simply maps a pixel value to itself.

or F -1 are extended to a group of pixels G by using a mask M, which specifies what operation will bewhich pixel in the group. For example, ifG = (39,38,40,41) and M = (-1,0,-1,0), then FM(G) = (F-1(39), Fo(38), F-

using the operations F1, F-l and the discrimination functionf, three types of pixels groups are defined as follows:

Ge R ~ f(F;(G» > f(G)

Ge S ~ f(r;(G»< f(G) .

qe U ~ f(r;(G» = f(G)

group, s is a Singular group, and U is an Unusable group.

steganalysis technique consists of the following simple steps:

1. Calculate the number of Regular Groups (RM) and Singular GrOUPS(SM) using a positive mask M and a negativemask M. A negative mask is the positive mask with its operations negated, meaning: IfM = (-1,0, -1,0) then -M =

(1,0,1,0).

2. Invert the LSBs of all of the image pixels and repeat step I.

3. Based on the observations made on the distribution of the computed values RM RM SM and S.M arrive at anestimate of the length of the steganographic message embedded.

I we show the results obtained with RS steganalyzer for different message lengths. It can be seen that the technique,- ; accm:ate in predicting not only the presence of a message but also the length of the message. It should be

Proc. SPIE Vol. 4675 75

noted that the results given in Table 1 are for 256 x 256 images and in general the larger the image the better RS steganalysiworks. This explains the relatively larger number of false alarms and misses we see in Table I. fu actual tests conducted bthe authors of [7] over more than 10,000 images, RS Steganalysis gives highly accurate detection and predicts the messa~length with remarkable accuracy. FUrthermore, with an optimized selection of parameter settings, the authors of [7] ha,obtained better results on the test set shown below. Hence, to be fair to RS Steganaysis, we do not consider the imaglbuildings, jup, eins, pills, SARimage and tolicon in the rest of our experimental results. The first four of these images resuin false positives as the RS algorithm reports significantly high message length even when there is no message embedd((first column). The last two images result in false negatives as they report a message length of 0 even when 20% of the bjhave been used for embedding a message.

In the rest of this section we examine different ways in which Alice and Bob can communicate when Wendy is using an ISteganalyzer to detect stego-images. Although we discuss examples with respect to RS Steganalysis the principles discu~sare general and can be applied with suitable modifications to other techniques as well.

Table I: Performance of RS Steganalysis technique on image test set with LSB embedding.

If we assume that Alice and Bob know exactly what type of steganalysis technique(s) will Wendy be using then it is c1quite easy for them to communicate covertly despite the presence of Wendy. So for example if it is known that Wenusing the RS steganalysis technique then there are many different ways, in which they can foil the detector. Perhapsimplest way is not to embed in the LSB but in the next bit plane. That is in the case of 8 bit images, they can embesecret message in the 71h bit plane instead of the glh bit plane. This completely foils RS steganalysis and also the relatedsteganalysis technique described in the introduction. This is because both these techniques critically rely on changes m2the distribution of pixel value pairs that are closed under LSB flipping operation. However, embedding in the 71h LSBway affects these distributions. In Table 2 we show the performance of RS steganalysis when a: message of different leis embedded in the 71h bit plane. As can be seen the messages will go completely undetected if Wendy were employin~RS steganalysis.

Now of course if Wendy also looks for messages in the 71h bit then she will be able to easily detect them. One simple vdo this is simply strip the 81h bit and apply RS or PoV steganalysis to the new LSB which is the 7tb bit. However, A1i(Bob can do something more sophisticated that renders Wendy's steganalyzer ineffective even if she knows the new tectbeing employed. To make this point clear we conducted another experiment where we embed a message bit in LSB of 2only if the difference between the pixel and all its immediate neighbors is greater than 2. It so tums out that RS stegarrelies on the peculiar structure of the mapping created by LS:B flipping and the strategy we describe preserves this strand hence goes completely undetected. That is, we can embed significantly large secret messages without being detecan RS steganalyzer. Table 2 lists results obtained with such an approach. Again it can be seen that the RS steganalyzc

76 Prac. SPIE Val. 4675

,2R. Cha,ndrainouli1, Grace Li2 and Nasir Memon

1 Stevens Institute of Technology

Hoboken, NJ 07030U.S.A

and

2polytechnic University,Brooklyn, NY 11201,

U.S.A

ABSTRACT

techniques attempt to differentiate between stego-objects and cover-objects. In recent work we developed ananalytic upper bound for the steganographic capacity of LSB based steganographic techniques for a given false

of detection. In this paper we look at adaptive steganographic techniques. Adaptive steganographic techniquessteps to escape detection. We explore different techniques that can be used to adapt message embedding to the

content or to a known steganalysis technique. We investigate the advantages of adaptive steganography within anframework. We also give experimental re~ults witb a state-of-the-art steganalysis technique demonstrating that

, of bits elpbedded without detection.

Steganography, Steganalysis, Adaptive Steganography, RS Steganalyzer.

I. INTRODUCTION

refers to the science of "invisible" communicatioli. Unlike cryptography, where the goal is to securefrom an eavesdropper, steganographic techniques strive to hide the very presence of a message from an

Although steganography is an ancient subject, the modem formulation of it is often given in terms of the prisoner's[I] where Alice and Bob are two inmates who wish to communicate in order to hatch an escape plan. However, all

between them is examined by the warden, Wendy, who will punish them at the slightest suspicion of theof secret messages in their communication. Specifically, in the general model for steganography, we have Alice

to send a secret message m to Bob. In order to do so, she "embeds" m into a cover-object c, to obtain the stego-The stego-object s is then sent through the public channel. In a pure stt;ganography framework, the technique for

message is unknown to Wendy and shard as a secret between Alice and Bob. However, it is generally notas good practice to rely on the secrecy of the algorithm. In private key steganography Alice and Bob share a

key which is used to embed the message. The secret key is usually a password that can be used to seed a--~ : ---g~eratoc to se.~ct ~ocation$ ip the cover-object for embedding the secret message (possibly encrypted).

has no knowledge about the secret key that Alice and share, although she might be aware of the algorithm that they---, ---~~~~ ~~ , In public key steganography, Alice and Bob have private-public key pairs and

, s public key. In this paper we restrict our attention to private key steganography.

warden Wendy who is free to examine all messages exchanged between Alice and Bob can be passive or active. A..simply examines the message and tries to determine if it potentially contains a hidden message. If it appearsit does, she suppresses the message and/or takes appropriate action, else she lets the message through without any action.active warden, on the other hand, can alter messages deliberately, even though she does not see any trace of a hidden

:;0 order to foil any secret communication that can nevertheless be occurring between Alice and Bob. The amount of.For example,

images, it would make sense that the warden is allowed to make changes as long as she does not alter significantly the

Edward J. Delp 111, Ping Wah Wong,~ .0277-786X/02/$15.00

69