EXTENDED VISUAL CRYPTOGRAPHY SCHEME FOR COLOR

IMAGES WITH NO PIXEL EXPANSION

Xiaoyu Wu, Duncan S. Wong and Qing Li

Department of Computer Science, City University of Hong Kong, Tat Chee Avenue, Hong Kong, China

Keywords:

Information hiding, Extended visual Cryptography, Secret sharing.

Abstract:

A k-out-of-n Extended Visual Cryptography Scheme (EVCS) is a secret sharing scheme which hides a secret

image into n shares, which are also some images. The secret image can be recovered if at least k of the shares

are superimposed, while nothing can be obtained if less than k shares are known. Previous EVCS schemes

are either for black-and-white images or having pixel expansion. In this paper, we propose the ﬁrst k-out-of-n

EVCS for color images with no pixel expansion. The scheme also improves the contrast of the n shares and the

reconstructed secret image (i.e. the superimposed image of any k or more shares) by allowing users to specify

the level of each primary color (i.e. Red, Green and Blue) in the image shares as well as the reconstructed

secret image.

1 INTRODUCTION

In (Naor and Shamir, 1994), Naor and Shamir in-

troduced the notion of Visual Cryptography Scheme

(VCS) which allows an image to be encrypted so that

the decryption can be done simply by the human vi-

sual system without any other computation. A k-out-

of-n VCS splits an image to n shares so that they look

indistinguishable from random noise. These shares

are then printed on transparencies as images. From

any less than k shares, nothing (other than the size) of

the secret image can be obtained. Only by superim-

posing k or more shares, the secret image will become

visible.

In (Naor and Shamir, 1994), an extension of

VCS called Extended Visual Cryptography Scheme

(EVCS) was also introduced. In an EVCS, besides

generating n shares for a secret image, these n shares

also carry n meaningful and independently chosen

images. To generate these shares, a user arbitrarily

chooses n meaningful images which have the same

size as the secret image. Then the user splits the se-

cret image and embed the share information into the n

meaningful images in such a way that given any k− 1

or less shares, no information about the secret image

can be obtained, while given any k or more shares,

the secret image will be revealed when the shares are

superimposed. In (Ateniese et al., 1996), Ateniese et

al. proposed the ﬁrst k-out-of-n EVCS for black-and-

white images using the hypergraph coloring method.

It is for black-and-white images. Since then, there

have been some other EVCS schemes proposed, e.g.

(Nakajima and Yamaguchi, 2002; Wang et al., 2009;

Sirhindi et al., 2009). To the best of our knowl-

edge, there is no EVCS for color images that supports

the general k-out-of-n secret sharing while having no

pixel expansion, that is, the pixel expansion rate being

equal to one.

In this paper, we solve this problem by propos-

ing the ﬁrst k-out-of-n EVCS for color images with-

out pixel expansion. We use a probabilistic technique

(Yang, 2004) for achieving no pixel expansion. The

scheme also allows a user to choose the number of

color levels for each primary color (i.e. Red, Green

and Blue) that the reconstructed image and each share

image could have. The reconstructed image refers to

the image obtained by imposing k or more share im-

ages. We ﬁnd that this ‘tunable’ feature is very useful

(in practice), as the user is able to use it for maximiz-

ing the quality of the reconstructed image, given that

different types of images may best appear with differ-

ent color levels (more details will be given in the later

part of the paper).

2 A BRIEF REVIEW OF K-OUT-

OF-N BLACK-AND-WHITE VCS

In this section, we brieﬂy review a generic represen-

tation of the k-out-of-n VCS scheme for black-and-

423

Wu X., S. Wong D. and Li Q. (2010).

EXTENDED VISUAL CRYPTOGRAPHY SCHEME FOR COLOR IMAGES WITH NO PIXEL EXPANSION.

In Proceedings of the International Conference on Security and Cryptography, pages 423-426

DOI: 10.5220/0002936904230426

 SciTePress

white images(Naor and Shamir, 1994). A k-out-of-

n VCS scheme for black-and-white images is repre-

sented by two collections of n × l boolean matrices.

The two collections are denoted by C

and C

. Matri-

ces in C

(resp. C

) are obtained by permuting all the

columns of a Basic Matrix B

(resp. B

). Formally,

and C

are represented as follows.

= {matrices obtained by permuting the columns of







0,0

0,1

... p

0,l−1

n−1,0

n−1,1

... p

n−1,l−1







= {matrices obtained by permuting the columns of







0,0

0,1

... p

0,l−1

n−1,0

n−1,1

... p

n−1,l−1







where p

i, j

, p

i, j

∈ {0,1} for 0 ≤ i ≤ n − 1 and

0 ≤ j ≤ l − 1.

Due to the page limitation, we refer readers to

(Naor and Shamir, 1994) for details of the represen-

tation. In the next section, we use a black-and-white

VCS described above as a building block to build a

k-out-of-n color EVCS which does not have pixel ex-

pansion. Note that the pixel expansion rate of the

VCS above is l > 1.

3 OUR K-OUT-OF-N EVCS FOR

COLOR IMAGES

We now propose a k-out-of-n EVCS for color images.

The scheme is the ﬁrst EVCS for color images with

no pixel expansion. For a color secret image, suppose

that n meaningful images have already been chosen.

These images are color images chosen arbitrarily and

will be used for generating n share images. Also, the

choosing processing is totally independent as long as

the image size is the same as that of the secret image

since our scheme does not have any pixel expansion.

Our scheme consists of the following steps: 1. His-

togram Generation; 2. Color Quality Determination;

3. Grouping; 4. Share Creation. These steps are elab-

orated in detail as follows.

3.1 Histogram Generation

For the secret image and each of the n images which

will be used as share images, we ﬁrst generate three

primary-color (i.e. R, G, B) component images for

each of them and then create a histogram for each

primary-color component image. As an example,

suppose that the secret image is the Lena image which

is encoded in 24-bit RGB. Figure 1 shows the secret

image (Lena) and the three RGB primary-color com-

ponent images of it. In each component image, there

are 256 levels of intensity of the corresponding pri-

mary color. Figure 2 shows the histogram of the red

component generated in this step. In the histogram of

R (resp. G and B), the horizontal axis represents the

intensity of R (resp. G and B) ranging from 0 to 255

and the vertical axis represents the number of pixels

in the R (resp. G and B) component image that have

the intensity value.

Figure 1: The secret image (Lena) and its RGB component

images.

Figure 2: Histogram of the red component image.

3.2 Color Quality Determination

In this step, the user is to choose the number of in-

tensity levels that the reconstructed image will have

when at least k share images are superimposed and

the number of intensity levels of each share image.

First, the user is to determine the number of intensity

levels for maximizing the quality of the reconstructed

image or shares. Let N be the number of intensity

levels that the reconstructed image will have. As the

reconstructed image has three primary-color compo-

nents, we set N = N

× N

, where N

denotes

the number of the intensity levels of X ∈ {R,G,B}

primary-color component of the reconstructed image.

For the n share images, let M

be the number of in-

tensity levels of the i-th share image (for i = 1, ...,n),

where M

= M

× M

, where M

denotes the

number of intensity levels of X ∈ {R, G,B} compo-

nent of the i-th share. In Sec. 4, we provide more dis-

cussions on how to choose the number of color levels.

SECRYPT 2010 - International Conference on Security and Cryptography

424

3.3 Grouping

As of the previous step, this step is carried out on each

of the n share images as well as the secret image. In

the following, we use the secret image as an example

to describe how the grouping works. For each pri-

mary color X ∈ {R,G,B}, we partition the histogram

of X of the secret image into N

groups so that each

group has the same area as other groups on the his-

togram, where N

is the number of color intensities

for the X component of the (to-be)-reconstructed se-

cret image determined in the previous step. By the

same area on a histogram, it implies that there will be

an equal number of pixels in each of the N

groups

on the histogram. Figure 3 shows the histogram of

the red primary-color component images of Lena af-

ter grouping where N

= 4 . In the ﬁgure, we use dif-

ferent color intensities to represent different groups.

Figure 3: Histogram of R illustrating the 4 × 4 × 4 color

levels.

3.4 Share Creation

The ﬁnal step of the scheme is to create the n share

images. To create these shares, we start with by cre-

ating n shares for each primary color. After creating

all the shares of the three primary colors, we then su-

perimpose the three shares corresponding to the three

primary colors of the i-th share, 1 ≤ i ≤ n, for forming

the n ﬁnal shares. In the following, we describe how

the n shares of each primary color X ∈ {R, G,B} are

created.

1. We ﬁrst construct a k-out-of-n black-and-white

EVCS. The construction can be viewed as an ex-

tension of the k-out-of-n black-and-white VCS re-

viewed in Sec. 2. The extension is similar to

the method due to Wang, Yi and Li (Wang et al.,

2009).

(a) Take a k-out-of-n black-and-white VCS which

satisﬁes the conditions in Sec. 2. Let the Basic

Matrices B

and B

are of dimension n× l.

(b) Then, we construct 2

boolean matrices de-

noted by A

,...,c

for c

,... ,c

∈ {b,w}, where

b stands for black and w stands for white. Each

of A

,...,c

will be n × t for some integer t ≥

⌈

k−1

⌉. In each row of A

,...,c

, for example, the

i-th row, all the t bits but one must be 1. The

remaining bit is 1 if c

= b and is 0 if c

= w.

We denote this bit as ∗ in the following. In

other words, each row of A

,...,c

has only one

∗. Besides, the number of ∗ in each column of

,...,c

should be at most k−1.

ﬁned as the following Basic Matrices:

,...,c

= B

◦ A

,...,c

and T

,...,c

= B

◦

,...,c

for c

,... ,c

∈ {b,w}. Therefore,

there are altogether 2

n+1

Basic Matrices and

they can be considered as two sets of Ba-

sic Matrices, that is, {T

,...,c

}

,...,c

∈{b,w}

and

,...,c

}

,...,c

∈{b,w}

, each set has 2

Basic

Matrices. Each of these matrices is n× m where

m = l +t where B

and B

are n× l and A

,...,c

are n×t. We refer readers to (Wang et al., 2009)

for the details of how this k-out-of-n black and

white EVCS works.

In the next step, we use the Basic Matrices

,...,c

and T

,...,c

in a probabilistic way on

each RGB primary-color component image so

that the share images created will have the same

size as the original secret image (i.e. no pixel

expansion or having the optimal pixel expan-

sion rate of 1).

2. This step is carried out pixel by pixel for the se-

cret image. For each primary color X ∈ {R,G, B}

of a pixel in the secret image, we carry out the

following steps:

(a) On the X histogram of the secret image, sup-

pose that the color intensity of the pixel with

respect to primary color X is in the k-th group

(where 0 ≤ k ≤ N

− 1). We compute a proba-

bility value P

= k/(N

− 1) which determines

the likelihood of going through one of the fol-

lowing steps.

(b) With probability P

, we carry out the following

two steps:

• We look into n × l Basic Matrix B

of the k-

out-of-n black-and-whiteVCS and the general

form A

,...,c

– With probability P

, which is determined by

the user as follows, we randomly pick a col-

umn from B

; The trade-off between the

quality of share images and the reconstructed

image is the result of adjusting the value of

. The greater (less) the P

is, the higher

(lower) the quality of the reconstructed im-

age would be and the lower (higher) the qual-

ity of the share images would be.

– With probability 1 − P

, suppose the color

intensity of the X primary-color component

EXTENDED VISUAL CRYPTOGRAPHY SCHEME FOR COLOR IMAGES WITH NO PIXEL EXPANSION

425

of the corresponding pixel in the i-th mean-

ingful image is in the k

-th group (where

0 ≤ k

≤ M

− 1 and 1 ≤ i ≤ n), we com-

pute a probability value Q

= k

/(M

−1).

We then set the ∗ in the i-th row of the gen-

eral form A

,...,c

to 0 with the probability

and to 1 with the probability 1-Q

and

randomly choose a column from it.

• Consider the column chosen as an n-bit vec-

tor. For the ﬁrst bit, we assign the black color

(i.e. 0 color intensity) if the bit is 1, otherwise

we assign X primary color (i.e. 255 color in-

tensity) to the correpsonding pixel in the ﬁrst

share image. This continues until we have as-

signed colors to the corresponding pixel on all

the n share images.

steps to the above, but change B

to B

3. Finally, we superimpose the i-th R share with the

i-th G share and the i-th B share, for i = 1,...,n,

to form the ﬁnal i-th color share image.

4 DETERMINING THE NUMBER

OF COLOR LEVELS

In this section, we discuss how to choose the number

of color levels (i.e. N = N

× N

) in the recon-

structed secret image and the share images. As the

scheme allows a user to arbitrarily choose the number

of color levels, we observe that the number of color

levels has a signiﬁcant impact on the quality of the

reconstructed image and the share images. The num-

ber of color levels should be chosen depending on the

number of colors of the original n+ 1 images. In the

following, we take the reconstructed image as an ex-

ample.

We ﬁrst identify the secret image as belonging to

one of the following two categories: in category 1, the

number of levels of a particular primary color is small,

for example, less than 4; and in category 2, the num-

ber is large, say at least 4. For images in category 1, if

the image on a particular primary color X ∈ {R,G, B}

is OriginalN

, since OriginalN

in this case is small,

there is no need to try with different color levels. We

should just set N

to OriginalN

. Images that fall into

this category could be texts or logos. Figure 4 and

Figure 5 show the images of text, their corresponding

shares and the reconstructed image (Lena) for the case

of 2-out-of-2 EVCS, N

= N

= M

= 2 (where i = 1,2).

For images in category 2, one may try the color

level N

from a small value, say 2 or 4, to the “full”

Figure 4: The images of the text.

Figure 5: The two shares and the reconstructed image of the

text.

level, i.e. OriginalN

. Based on our experimental

results, we observe that for photos or color cartoon

images with large number of color levels, trying these

three values (namely 2, 4 or OriginalN

) for the value

of N

can already attain one of the best results in the

reconstructed images.

REFERENCES

Ateniese, G., Blundo, C., Santis, A. D., and Stinson, D. R.

(1996). Visual cryptography for general access struc-

tures. Inf. Comput., 129(2):86–106.

Nakajima, M. and Yamaguchi, Y. (2002). Extended visual

cryptography for natural images. Journal of WSCG,

10(2):303–310.

Naor, M. and Shamir, A. (1994). Visual cryptography. In

Advances in Cryptology - EUROCRYPT ’94, pages 1–

12. Lecture Notes in Computer Science, Vol. 950.

Sirhindi, R., Afzal, M., and Murtaza, S. (2009). An ex-

tended secret sharing scheme for colour images with

ﬁxed pixel expansion. International Journal of Elec-

tronic Security and Digital Forensics, 2(1):58–67.

Wang, D., Yi, F., and Li, X. (2009). On general construc-

tion for extended visual cryptography schemes. Pat-

tern Recognition, 42(11):3071–3082.

Yang, C. N. (2004). New visual secret sharing schemes us-

ing probabilistic method. Pattern Recognition Letters,

25(4):481–494.

SECRYPT 2010 - International Conference on Security and Cryptography

426