[PDF] Secure and Invisible Data Hiding in 2-Color Images

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Secure and Invisible Data Hiding in 2-Color

Images

Yu-Chee Tseng

and Hsiang-Kuang Pan Department of Computer Science and Information Engineering

National Chiao-Tung University

Hsin-Chu, 30050, Taiwan

Email: yctseng@csie.nctu.edu.tw

Department of Computer Science and Information Engineering

National Central University

Chung-Li, 32054, Taiwan

Abstract—In an earlier paper [1], we propose a steganography scheme for hiding a piece of critical information in a host binary image. That scheme ensures that in each ??image block of the host image, as many as ???????bits can be hidden in the block by changing atmost 2 bits in the block. As a sequel of that work, in this paper we propose a revised scheme that can maintain higher quality of the host image by sacrificing some data hiding space. The new scheme can still offer a good data hiding ratio. It ensures that for any bit that is modified in the host image, the bit is adjacent to another bit which has a value equal to the former"s new value.

Thus, the hiding effect is quite invisible.

Keywords:binary image processing, coding, cryptography, in- formation hiding, prisoners" problem, security, steganography.

I. INTRODUCTION

As digital media are getting wider popularity, their security- related issues are becoming a greater concern. One central is- sue isconfidentiality, which is typically achieved byencryp- tion. However, as an encrypted message usually flags the im- portance of the message, it also attracts cryptanalysts" interests. The sometimes confusing terminologystagenographyhas a dif- ferent flavor from encryption; its purpose is to embed a piece of critical information in a non-critical host message (e.g., web- pages, advertisements, etc.) to distract opponents" attention [2], [3]. One less confusing name for steganography would bedata hiding. It should be understood that steganography is orthogo- nal to encryption, and it may be combined with encryption to achieve a higher level of security. The study of this subject may be traced back to [4], where the Prisoners' Problemwas proposed. In this scenario, Alice and Bob are in jail, and wish to hatch an escape plan. All their com- munications must go through the warden, Willie, and if Willie detects any encrypted messages, he will frustrate their plan by throwing them into solitary confinement. So they must find some way to hide their plaintext(or ciphertext)in an innocuous- looking covertext. The history and bandwidth concerns of the subliminarl channelare discussed in [5], [6]. Information hid- ing has applications in many commercial-, military-, and anti-? This work is supported by the National Science Council of the Republic of China under grants # NSC89-2218-E-008-003, # NSC89-2218-E-008-012, and # NSC89-2218-E-008-013, and the Ministry of Education, the Republic of China, under grant # 89-H-FA07-1-4 (Learning Technology). criminal-related issues. Classifications and surveys of informa- tion hiding can be found in [7], [8]. In the context of images, data hiding is usually achieved by alternating some nonessential information in the host image. Given a color image, one simple approach is to use the least- significant bit (LSB) of each pixel to hide information [9]. As this is not likely to degrade the quality of the image much, a number of software packages have adopted this approach [10]. format. Thus, such a picture can hide about 2.36 megabytes of data. To further reduce the hiding effect on the image quality, a genetic algorithm is proposed in [11]. A hiding scheme based on the conventionalkeystreamgeneratoris proposedin [12]. In- formation hiding for security documents (such as currency and bill) is discussed in [13]. References [14], [7] consider how to apply public-key cryptography to steganography. A review of data hiding techniques in image, audio, and text is in [15] One less frequently addressed, but very challenging, problem is data hiding in a two-color/black-and-white image (such as facsimiles, xeroxs, and bar codes). The reason is that chang- ing a pixel in such a image can be easily detectable. One such scheme is proposed in [16]. However, this scheme is shown to be easily breakableanda morerobust schemeis proposedin [1], where it is shown that for each???block of the host image, the block can accommodateas many as secret data by changing at most 2 bits in the block. As a sequel of the work in [1], in this paper we propose a revised versionof the scheme in [1]. By takingthe qualityof the image after hiding into consideration,the new scheme can make the hiding effect quite invisible. It ensures that for any bit that is modified in the host image, the bit must be adjacent to another bit that has the same value as the former"s new value. This will be achieved by sacrificing some data hiding space, but the new scheme still offers a good data hiding ratio. Implementation results are also demonstrated to verify the idea. The rest of this paper is organized as follows. Section II re- views our earlier scheme [1]. The revised new scheme is pre- sented in Section III. Implementation results are in Section IV.

Conclusions are drawn in Section V.

II. BACKGROUND ANDMOTIVATION

Steganography, or data hiding, can be defined as follows.

Given a host message

?and a guest message?, a steganog- raphy scheme should provide a data hiding function ??and a data retrieving function ??such that where?is a secret key. That is,??can extract the guest message from the host message hidden by ??. Further, to dis- tract the opponents, it should be hardly detectable that ?has been hidden with information. Under the context of using au- dio/video/image as the host message, this could mean that sounds/looks almost like the original?.

A. A Review

Below, we review the data hiding scheme proposed by Chen, Pan, and Tseng [1], which is shown in Fig. 1 and is abbreviated as theCPTscheme. Through the review, we will identify some image quality problems associated with it. This will motivate the work in this paper. In the CPT scheme, we are given a host binary image will be partitionedintoblocksoffixedsize???(forsimplicity, we assume that ?"s size is a multiple of???). The scheme is able to hide as many as ???????bits of the guest message in each host block by modifying at most 2 bits in the block. The secret key has two components: ??: a randomly selected binary matrix of size???. ??:aweightmatrixwhichis anintegermatrixofsize???. ?satisfies the condition that???????

Note that since

it is trivial to find a matrix that can serve as a weight matrix. In fact, the number of choices for ?can be calculated as:

For instance, if?????and???, there are?

possible?"s. This number should be large enough to prevent a brute-force attack. The data hiding is achieved by modifying some bits of

Below, we show how to hide a bit stream

?????into an ???host block, say,??. More details can be found in [1].

S1. Compute

??, where?means the bitwise exclusive-

OR of two equal-size binary matrices.

S2. Compute

??????, where?means the pairwise multiplication of two equal-size matrices and means the sum of all elements in a matrix.

S3. From the matrix

??, compute for each?????? the following set: Intuitively,??is the set containing every matrix index??? ?? such that if we complement??? ????, we can increase the sum in step S2 by ?. There are actually two possibilities to achievethis: (i)if ??and??? ??, thencomplementing ????will increasethe weightby?, and (ii) if?????? and??? ??, then complementing??? ????will decrease the weight by ???, or equivalently increase the sum by? (under?? ? ? ?). Also, define?? ?for any??? .S4. Define a weight difference If???, there is no need to change??. Otherwise, we run the following program to transform ??to? a) Randomlypickan ????such that??? b) Randomly pick a ??? ??????and complement the bit c) Randomly pick a bit To summarize,the abovesteps ensure the followinginvariant: I1: In the above step S4, we pick two nonempty sets???and complement ??to increase the weight by??and???????, respectively. The overall effect is an increase of the weight by ?. It is proved in [1] that step S4 will always succeed. How- ever, there are logical flaws in the above program, which we left out intentionally for ease of presentation. First, the set ??(and similarly ?, etc.) is not yet defined. Like other ??"s, we can regard??as the set of indices such that comple- mentingthese locations in ??will result in an increase of weight by ?. Since this can be achieved by changingnothingon??, we can always regard ??as nonempty and whenever the state- ment “complement the bit ????" is encountered, we simply skip this step. This amendment will make the program logically complete.

To reflect the invariantI1, the receiver of

??simply recovers the hidden data as follows.

S5. Onreceiving

??,thereceivercomputes?? ???? to find the hidden bit stream??

For example, let the host image

?, secret key?, and weight matrix ?be as shown in Fig. 2(a). First,?is partitioned into two ???blocks,??and??. We can hide??????? bits in each block. Let???, and??????the secret data to be hidden. The results of ??and?? ??arein Fig. 2(b). Since ???, theweight difference ???????. Thus, swapping??? ????will increase the weight by ??.For??, since?? ????? . Thus, swapping??? ????and??? ????will increase the weight by ???and?????? ??, respectively.

Fig. 2(c) shows the resulting

?(with the modified bits in gray).

B. Some Observations

In the above scheme, although at most two bits can be modi- fied in each host block, there is no control on the quality of the image after modification. Specifically, the bits that are modi- fied are selected from a random process. It does not takewhere the modified bits are located, into consideration. The develop- ment only focuses on the weight management. This motivates the work in this paper.

Opponent

DataHi?i?g

Proce?ure

?x? ?x? ?x? ?x?

DataRetrieval

Proce?ure

Hosti?ageF

CriticalinformationB

Critical

information B r Fig. 1. Block diagram of the CPT data hiding scheme. W = 1234
5 671
2 345
6 712

K =F =

1 1 1 00 000 0

000000

1 F 1F2 (a) (b) (c) F' 2 F' 1 FK 1 2 Fig. 2. An data hiding example: (a) the inputs, (b)?? ??and?? ??, and (c) the modified image.

III. DATAHIDING WITHQUALITYCONTROL

In this section, we propose a revised version of the CPT scheme [1]. Our goal is to improve the quality of the image after data hiding. This will be achieved by sacrificing some data hiding space.

A. Control of Image Quality after Data Hiding

Since we are working on a 2-color image, changing any bit in the image may be easily detectable. To maintain the quality of the image, certainly we should change as few bits as possi- ble. A completely black or blank host block will not be used to hide data. Also, if a bit has to be changed, we expect that its location be very close to a bit who shares the same value as the former"s new value. For instance, consider an image ?repre- sented by a matrix, which is modified into two images ?and ??, as follows: ???(1) (2) Both ?and? ??differ from?in one bit. We would regard? and? ?as more alike than?and? ??, because? ?differs from? in a location which is adjacent to an area of 1"s. The modified 1 in ??is more visible. To formulate the above observation, given an image ?,we define a distance matrix ???????, which is an integer matrix of the same size as ?such that element ??????such that the complement of??????is equal to ??????. The matrix will later be used to reflect the priority in choosing a bit to be modified. For example, in the earlier exam- ple, we have (3)

B. The Scheme

Now we present our scheme. We are given a host image

Still,

?will be partitioned into blocks of size???. For sim- plicity, we assume that the size of ?is a multiple of???. As mentioned earlier, our scheme will trade some data hiding space for better image quality. Specifically, for each host image block ??, we will hide, if possible,?bits of data in??, where that in the CPT scheme. Let ?????be the binary stream to be hiddenin??, and? be the modified image after the hiding. If? ??is not completely black or blank, the scheme will ensure the following invariants: I2:

I3:??? ????

data hidden in

Definition 1:An

???matrix?can serve as a weight ma- trix if ??????and for each ???sub-block of?, the sub-block contains at least one odd element. To be shown later, this definition will improve the quality of the image after data hiding. For example, the following shows three possible ways to define a ???weight matrix: (4) (5) where “ ?" means an odd number, and “?" an even number. For instance, the number of legal weight matrices based on any of these patterns is where the first part is for choosing those odd numbers, and the second part for those even numbers.

The detailed data hiding steps are as follows.

S1. If

??is completely black or blank, simply keep??intact (not hidden with data) and skip the following steps. Otherwise, perform the following.S2. Compute

S3. Fromthe matrix

??,computeforeach?????? the following set: ?is for the bit corresponding to??? ????in block ??(note that??is only a block in the original image?).

Also, define

?for any??? Intuitively, in the above step, we try to control the quality of the image after modification. A bit can be swapped only if it has a neighbor which shares the same value as its new value. Here we define a neighbor to be one at a distance ??, i.e., a bit has

8 neighbors.S4. Define a weight difference

If? ???, there is no need to change??. Otherwise, we run the following program to transform ??to? if(there exists an ?such that? ???and? then

Randomly pick an

?which satisfies the above condition;

Randomly pick a

?and complement the bit

Randomly pick a

?and complement the bit else ??no data will be hidden?? if(?? ????? Keep ??intact; else

Select a

??? ??such that??????is odd and its corresponding ?is the smallest;

Complement the bit

end if; end if;

However, note that if the resultant

??is completely black or blank, we will regard the data hiding as invalid. That is, ??will be regarded as not hidden with data, and we will try to hide the same bit stream ?????again in the next host block. (See the discussion below.)

S5. On receiving the block

??, the receiver computes the hid- den data to be 2 ,if? ??is not completely black or blank and ??????is even. Otherwise,? contains no hidden information.

Note that in the above steps, we still regard

??as non-empty. However, this set still represents those elements by changing which we can increase the total weight by 0. Since we canquotesdbs_dbs1.pdfusesText_1

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