Novel Non-expanded Visual Cryptography Scheme with Block Encoding

Yi-Jing Huang1, ＊, Chih-Chiang Lee2, Hsien-Chu Wu3, Jun-Dong Chang4, Chwei-Shyong Tsai1,and Ya-Ting Tsao3

1 Department of Information Management,

National Chung Hsing University,

Taichung 402, Taiwan

yjhang1221@gmail.com;tsaics@nchu.edu.tw2 Information and Communication Research Laboratories,

Industrial Technology Research Institute,

Chutung Hsinchu 310, Taiwan

ccianglee@itri.org.tw3 Graduate School of Computer Science and Information Technology,

National Taichung Institute of Technology,

Taichung 404, Taiwan

wuhc@ntit.edu.tw, winds2012@gmail.com4 Department of Computer Science and Information Engeineering,

National Chung Hsing University,

Taichung 402, Taiwan

phd9607@cs.nchu.edu.tw

Received 5 December 2010; Revised 15 March 2011; Accepted 25 May 2011

Abstract. In the traditional visual cryptography, secret pixels are expanded to cause the size of the recov-ered image is larger than the original one. Although many researches successfully solve expansion prob -lem, the quality of the recovered image is not better. In order to improve quality of reconstruction, this pa -per proposes a novel non- expansion scheme. The principle of the proposed scheme is to divide the secret image into a number of blocks in the first place and then each block generates a number of combinations of share blocks by using same color pixels. After generating combinations of share blocks, two pixels with a corresponding position are executed by the “OR” operation when stacking two share images. In spite of solving the expansion problem and increasing the clearly visible of the recovered image, the result of the proposed scheme tends towards dark. In order to increase contrast of the recovered image, the second scheme is proposed by modifying original secret blocks before dividing the secret image into blocks, and then the further processes are in common as the first scheme. From the experimental results, the image quality of the second scheme is clearer than the first scheme.

Keywords: Visual cryptography, non expanded, block encoding

1 Introduction

Visual cryptography (VC) was introduced by Naor and Shamir [1], and it decrypts the secret image by using human visual system without any cryptography computations. In VC, the secret image can be revealed by stacking two share images, so nobody can get the secret image with one of them. Besides, share images are noise-like that means each of them does not reveal any information about the secret such as (b) and (c) of Fig. 1. Briefly, the secret image is encrypted by generating two shares, and the secret image can be revealed by stacking them when decryption. Besides, combining VC with the (k, n)-threshold concept of secret sharing is also called as Visual Secret Sharing (VSS). The (k, n)-threshold means that a secret owner would like to gener -ate n shares for n participants, so that the original secret image is visible when least k (2≦k≦n) of them are stacked together. Afterwards, there are many studies of secret sharing are proposed sequentially such as [2], [3].

＊ Correspondence author

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In 1995, Naor and Shamir proposed the (n, n)-threshold VC that the binary secret image is encoded into n shares with noise-like, and the secret image is recovered by stacking these n shares together. The basic princi -ple of VC is succeeded by (2, 2)-VC scheme which means that the scheme constructs two shares, and the se -cret image is recovered by stacking two shares together. In tradition, shares are expanded twice, that is to say, each secret pixel is encoded into 1×2 pixels (as shown in Fig. 1).

(a) (b) (c)

(d)

Fig. 1. An example of VC: (a) the secret image “Lena”; (b) and (c) the shares; (d) the recovered image

(a) (b)

Fig. 2. An example of four times size: (a) Secret image; (b) Recovered image

In order to decrease distortion of the recovered image, each secret pixel is encoded into two blocks with 2×2 pixels, consisting of two black pixels and two white pixels, and these two blocks are distributed to two shares respectively. Finally, two pixels with a corresponding position are executed like the “OR” operation when stacking two shares. Although the expansion of twice becomes into four times, it also has an expansion problem. Pixel expansion causes space consuming because the one pixel of share is larger than the original one that means larger space to store pixels is needed. In addition, when a secret block with one pixel is trans-formed into a block with 2×2 pixels, the recovered image is four times larger than the original secret image (as shown in Fig. 2), and shares are consisted of two white and two black pixels.

The meaning of the pixel expansion is definite; Although VC is a secure encryption mechanism, the recov-ered image is not the same size as the original image. To overcome the pixel expansion problem, many ways are proposed. Afterwards, many studies attempt to improve the quality of the recovered image by adopting dif -ferent methods to deal with the pixel expansion problem [2], [4]-[8]. Kafri and Kaeren [4] proposed a novel visual secret sharing scheme based on random grids and Lin [3] proposed a non-expansion method using halftone technology to reconstruct the secret image. The principle of random grids is that a white pixel is prob-abilistically equal to the black pixel such that the average light transmission of probability is 1/2. The principle of non-expansion method using halftone technology is that the grayscale image of the W × H size is divided into (W/2) ×H blocks, and each block is average of every two pixels of the original secret image. Subse -quently, the researchers improve the traditional visual cryptography to share gray secret images with non-ex -pansion. Nevertheless, recovered images of these schemes are less clear. In this paper, in order to improve the quality of the reconstructed image, the proposed scheme shares gray secret images not only with non-expan -sion but also the reconstructed image is more similar to the original secret image.

In this paper, a non-expansion VC for sharing secret grayscale image is proposed. First, the secret image is transferred into halftone image. Then, the halftone image is divided into a number of blocks with n×n pixels. In each block, the pixels are classified into two-pixel groups according to the pixel color, and then each block can be generated a number of combinations of shares by block encoding. However, the image quality of the proposed scheme tends towards dark. In order to increase contrast of the recovered image, the second scheme 62

Huang et al: Novel Non-expanded Visual Cryptography Scheme with Block Encoding

is proposed. The second scheme modifies the n×n blocks in halftone image and makes the stacked image clear. The further processes are all in common as the first scheme. The result of the second proposed scheme is clearer than the first proposed scheme and other existing methods.

The rest of this paper is organized as follows. The related works of non-expanded visual cryptography are introduced in Section 2. In Section 3, we present the first and second proposed schemes in detail. Experimental results and comparisons are shown in Section 4. Finally, a brief conclusion is given in Section 5.

2 Related Works

2.1 Kafri et al.’s Scheme

Random Grids proposed by Kafri and Keren [4] in 1987 is one of the non-expanded techniques. The principle of this scheme supposes the binary secret image I with the size of H × W is encrypted into share 1 and share 2 with the same size as the binary secret image I. Firstly, the share 1 is generated by randomly assigning each pixel, the color 0 or 1, i.e., white and black. Let denote the generalized OR operation which describes the relation of the superimposition of two random grids (or two random pixels). Table 1 presents the results of su -perimposition and two corresponding random pixels. The S1 is a pixel of share 1 and the S2 is a pixel of share 2.

Table 1. The results of superimposition and two corresponding random pixels, S1 belongs to share 1 and S2 belongs to share 2

S1 S2 S1 S21 1 11 0 10 1 10 0 0

The algorithm is that a black or white pixel (1 or 0) is selected with probability half and half for the first share. In a word, a white pixel of the secret image is divided into shares; a white pixel of share 1 is probabilis -tically equal to a black pixel because it is random, and each pixel of share 2 is corresponded to share 1. If a se -cret pixel is white, the probability of black of S1 is 1/2, and S2 must be black. Hence, a white pixel is proba -bilistically equal to a black pixel so the average light transmission of probability is 1/2 when the white pixel is recovered.

Since the four possible combinations occur with an equal probability, the probability of white for S1 S2 to be transparent is 1/4. That is, the average light transmission of the superimposition of S1 S2 is 1/4. Fur-thermore, white pixel of original would generate same color pixel of two shares and black pixel of original would generate different color pixel of two shares. The process of random grids is described in Table 2.

Table 2. The principle of random grids and operation process

Secret pixels S1 S2 S1 S2 probability

1/2

1/2

1

1

2.2 Lin’s Scheme

In order to reconstruct the secret image with non-expansion, Lin’s non-expansion method [5] first reduce the grayscale image size into half of the original image by using the average operation. Each pixel of the reduced image is the average value of two pixel values of the original secret image. The detailed procedures of this scheme are presented as follows. Input: grayscale secret image S with W × H size.Output: two shares S1 and S2.

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Step 1: Divide secret image into two-pixel blocks, and compute the average of each two-pixel blocks by Eq. (1). Then, the secret image with size W × H is reduced into size (W/2) × H.

avg = (p1+p2)/2, where and are pixel value of the two-pixel block (1)

Step 2: The method transforms the reduced image into a binary image by error diffusion which is a halftone technology proposed by Floyd [9], it is about the error values are dispersed into the surrounding pixels. By raster scan, if the average value is smaller than the threshold 128, the corresponding pixel value of halftone image is 0, otherwise is 255. Then, calculates the error by Eq. (2) and (3), and disperse the error with weight 1/16, 3/16, 5/16, and 7/16 to neighboring pixels in different directions. Repeat above operations until all aver -age value of two-pixel blocks done.

(2)

(3)

Step 3: In common with traditional VC, the characteristic of the method is that a pixel of the original image is expanded into double size. In phase of generating shares, the share has the same size as the original secret im -age. The unit(x,y) will be used to generate sharing blocks by using Table 3. The sharing block of S1 can be

or randomly. According to Table 3, the sharing block S2 is determined by unit(x,y) and S1.

Table 3. Determining the share block S2

unit(x,y)S1

S2

Fig. 3. The structure of the proposed first scheme

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3 The Proposed Scheme

3.1 The First Scheme

In this section, a new visual cryptography method without pixel-expansion is proposed. The main purpose is to let the recovered image can have the same size with original image and improve visual quality. The major pro-cessing flow of the proposed first scheme is shown in Fig. 3. The secret image is divided into a number of blocks. In order to get a better recovered image, we proposed the block encoding method to construct share images. The block encoding estimates the position of black pixel in each block and classifies pixels into groups by pixel values. Each block can generate two share blocks s1 and s2 by block encoding. For decrypting, we can superimpose the share blocks. The pixels with corresponding position are executed with the “OR” op -eration when stacking two shares. Finally, each block of original secret images will be reconstructed by human eyes.

This scheme contains three steps. The first step separates the original secret image into a number of blocks. For each block, the second step takes two pixels with the same color as a group and each group generates a number of combinations of share blocks. That is to say, we can take two black pixels as a group and two white pixels as another group, and then generate share blocks for each group. The final step is superimposition phase. We superimpose the combination of each share block, and each block of original secret image will be reconstructed. We will describe each process of scheme in detail.

Table 4. 16 types of 2×2 pixel blocks in the original secret image

Secretblock

Array

Secretblock

Array

Step 1: Division phaseDivide the original secret binary image into a number of blocks with 2×2 pixels. If secret image is M×N

size, there will be M×N /2×2 blocks. There are totally 16 different types of block. We suppose 0 denotes black pixel and 1 denotes white pixel and use arrays to represent combinations of black and white. The following Table 4 illustrates 16 different types of a secret block. For example, if the secret block is and the array

representation is .

Step 2: Grouping phaseIn this step, two pixels with same color are classified as a group. Before the introduction of this phase, we

explain the representation of grouping array. Here, we use an example to illustrate the corresponding position of image pixels and the grouping array.

For example:: , : , : , : , : , :

If secret block contains two black and two white, such as , we take same color pixels as a group and

obtain group1 and group2 , and then it will generate two share blocks for each group, such as sh1

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and sh2 . In addition, if secret block is , we take same color pixels as a group to have

group1 and group2 , and then it generates two share blocks, such as s1 and s2 .

In addition, if the secret block has odd number of black pixels, we change one white pixel to be black pixel to let the number of black pixels in the secret block be even, and then according to the above mentioned shar -ing method, use same color pixels to decompose the secret block. The following Table 5 is used to show how

to change white pixels to black pixels. If secret block is , it is changed to . Then the new

changed block can generate two share blocks such as and . If secret block is , it is

changed to . And it can generate two share blocks and . Table 5 shows all types of

blocks containing odd black pixels and the corresponding changed ones.

Table 5. Block containing odd black pixels and its changed form

One black pixel Changed block Three black pixel Changed block

Step 3: Sharing phaseFor each group, this scheme generates a number of combinations of share blocks by traditional visual cryp -

tography. After sharing phase, two pixels in group have the same color black or white. The visual cryptogra -phy with black and white group is shown in Table 6.

The examples of grouping and sharing phase are explained in Table 7.

Table 6. Visual cryptography with black and white group

group S1 S2 S1 S2

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Huang et al: Novel Non-expanded Visual Cryptography Scheme with Block Encoding

3.2 The Second Scheme

Due to the result of the first scheme, it tends towards dark. In order to increase the contrast of the recovered image, we proposed the second scheme. The process of the second scheme is shown in Fig. 4. In grouping phase of the first scheme, if the secret block has odd number of black pixels, we change one white pixel to be black. It will make the recovered image dark; hence we modify the secret block by considering the number of black pixels. If the block has odd number of black pixels, we modify the block. And then the next process is same as the first scheme, that is, use same color pixel in block to decompose the block. Each block can be gen -erated a lot of combinations of share blocks of s1 and s2. Finally, one of them will be selected randomly and recovered each block of original secret images by stacking two share images. Finally, each block of original secret images will be reconstructed by human eyes.

Table 7. Examples of share blocks generation

Secret block

grouping S1 S2

group1 group2 group1 group2 group1 group2

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Fig. 4. The structure of the second scheme

The second scheme has four steps. It different from the previous is that it has one more step --- modification phase. The principle is that we consider the number of black pixels in secret image after dividing. Here, the first step, division phase, is same as previous method. The second step is modification phase. After dividing, we take secret blocks to be adjusted. The grouping phase and sharing phase are Step 3 and Step 4, respec -tively. We describe each process in detail as follows.

Step 1: Division PhaseWe take the original secret image into a number of blocks with 2×2 pixels. Therefore, if the original secret

image is sized M×N, there will be M×N / (2×2) blocks. There are 16 types of blocks and we can refer to the di-vision phase of the first scheme.

Step 2: Modification PhaseAfter dividing secret image into a number of blocks, we modify it by considering the number of black pix-

els in secret image. If the block has odd number of black pixels, we will modify it into containing even num -ber of black pixels. If the block with odd number black pixels occurs first, randomly change its one black pixel to white. If the block with odd black pixel second appears, randomly modify one white pixel in the block into black. We can use a logical variable to determine that one black and one white pixels change into two black or two white. The modified block has even number of black pixels.

For example, assume that X is a logical variable, if the first original secret block is , we randomly

select two pixels of three white pixels as group1 and take the other as group2 . We change group2 into or by the value X. When X is 0, the group will be set to , and set the variable X to 1. If

the next secret block is , group2 will be changed to , and then set the variable X to 0. We use the

above algorithm to represent the process for determining group. Therefore, the first modified block is

when X is 0, and the next modified block is for X = 1.

Table 7. The modification result of the block with odd number of black pixels

Original secret blockModified block

X=0 X=1

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Huang et al: Novel Non-expanded Visual Cryptography Scheme with Block Encoding

Steps 3 and 4: Grouping and sharing PhasesWe can refer to the grouping and sharing phases of the first scheme. After modification phase, all secret

blocks have even number of black pixels. Then, the processes of grouping and sharing secret block into two share block are as same as the first scheme.

(a) (b) (c) (d)

Fig. 5. The original images for secret image sharing

4 Experimental Results

This paper makes effort to generate shares without pixels expansion and recover the secret image with high visual quality. There are many literatures related to VC with non-expansion, however, just few literatures have high quality for reconstruction secret image. In order to illustrate the visual quality of the recovered image with the performance of the proposed schemes, this paper not only implements the proposed scheme but also compares the results with the other two non-expansion schemes from the existing literatures. Sections 2.1 and 2.2 detail the procedures of these two schemes, respectively. In the experiment, the original images are all bi -nary images which are shown in Fig. 5. The size of the secret image is 512×512.

Furthermore, sizes of the shares and the recovered images are the same as the original one in the proposed scheme and two compared schemes. In Fig. 6, there are the comparisons about reconstruction of the secret im -age among Kafri et al.’s scheme, Lin’s scheme, and the proposed schemes. Although these recovered images of Kafri et al.’s and Lin’s schemes solve problem of expansion, the recovered image of quality is not better than the proposed scheme. The recovered images of the proposed scheme are clearly visible than Kafri et al.’s and Lin’s. Thus the purpose of this paper not only solves expansion problem but also makes recovered image clear.

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(a-1) (b-1) (c-1) (d-1)

(a-2) (b-2) (c-2) (d-2)

(a-3) (b-3) (c-3) (d-3)

(a-4) (b-4) (c-4) (d-4)

Fig. 6. Experimental results of Kafri et al.’s scheme [4], Lin’s scheme [5] and the proposed scheme

In Fig. 6, the first row is the result of Kafri et al.’s scheme. Obviously, these recovered images of are not clear. Besides, results of Lin’s scheme (as shown at the second row in Fig. 6) are clearer than Kafri et al.’s, but reconstructed images have no better image quality. In order to obtain the recovered image with high quality, the proposed schemes achieve this purpose. The results of the proposed scheme are shown at the third and the fourth row in Fig. 6. The third row is the first proposed scheme. Although these recovered images are clear, it tends towards dark. In order to increase contrast, the second scheme is proposed, and the results of the second scheme are shown at the fourth row in Fig. 6. They show that the proposed approach has better effect than other schemes.

5 Conclusions

An extended visual cryptography without pixel-expansion for the original image is proposed in previous re -searches. However, the non-expansion in previous researches is not clear at all. In order to increase the visual quality of reconstructed images, a novel scheme to construct shares and let recovered secret image with better quality is proposed. The process of the proposed scheme divides the secret image into a number of blocks in the first place, and then same color pixels are selected as a group, and each group is generated a number of combinations of shares. In short, the proposed method not only solves the problem of pixels expansion but also

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let recovered image clearly. However, the result of the first proposed scheme tends towards dark. In order to increase brightness of the recovered image, the second scheme is proposed. It considers the number of black pixels of the secret image, thus the secret image with high quality can be revealed. The experimental results confirm that the proposed scheme has the distinguished outcomes compared with other extended visual secret sharing schemes. In conclusion, the proposed scheme achieves several purposes successfully: the shares and the recovered image have no pixel expansion, and the quality of the recovered image is better than previous re -searches.

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