LEARNING WITH FUN

An Application of Visual Cryptography

Young-Chang Hou and Zen-Yu Quan

Department of Information Management, Tamkang University

151 Ying-Chuan Road, Tamshui, Taipei County, Taiwan 251, R.O.C., Taiwan

Keywords: Visual Cryptography, Information Sharing, Computer-Aided Instruction.

Abstract: Visual Cryptography, an emerging cryptography technology, exploits the characteristics of human visual

system to decrypt the overlapping images without mass and complicated computations. Almost all the

related studies of visual cryptography were concentrated on the topics of the information security. In this

paper, we propose to use the technique of visual cryptography to teach young kids counting. It can stimulate

the curiosity of the kids and increase the fun of learning.

1 INTRODUCTION

It is not uncommon to transfer multimedia data via

the Internet recently. With the coming age of

Electronic Commerce, it is urgent to solve the

problem of how to ensure the information safety in

the open network environment. The encrypting

technologies of the traditional cryptography are

usually used to protect the information content. The

data become disordered after encrypting and then are

recovered by the correct key. After encrypting, the

content can hardly be recognized even though

unauthorized persons steal the data. Hence it can

achieve the goal of protecting information safety.

Naor and Shamir proposed a new cryptography

area, Visual Cryptography, in 1995 (

Naor and Shamir,

1995)

. The most notable feature is that it can recover

the secret image without any computing. It exploits

the human visual system to read the secret message

from the overlapping shares and thus overcome the

disadvantage of huge and complex computation in

the traditional cryptography. The (k, n)-threshold

scheme (

Naor and Shamir, 1995, 1996) makes the

application of visual cryptography more flexible.

The manager can first produces n copies of

transparency drawn from one secret image for his

members. Each one holds only one transparency. If

any t of them stacks their transparencies together,

the content of the secret image will show up. If the

number of transparencies is less than t, the content

of the secret image still keeps hidden.

There have been many published studies

(

Ateniese et al, 1996, 2001, Blundo et al, 1996, Naor and

Shamir, 1995, 1996)

of visual cryptography. All of

them, however, concentrated on discussing the

topics about information security. In this paper, we

use the technology of visual cryptography to

generate shares with numbers on them. When

playing with kids, we can show them two shares,

and ask for the answer. The correct answer will

show automatically when you superimpose one

share over another. This can stimulate the curiosity

of the kids and increase the fun of learning.

2 VISUAL CRYPTOGRAPHY

2.1 Basic Theorem of Visual

Cryptography

The output media of visual cryptography is

transparency, so the white pixels are treated as

transparent. The most common way of black-and-

white visual cryptography is to decompose every

pixel in the secret image into a 2*2 block on the two

transparencies according to the rules in the Table 1.

When the pixel is white (black), randomly choose

one of the first (last) two rows of the Table 1 to form

the corresponding content of the block on the two

transparencies.

As to the security of the shares, there are six

possible patterns of every block on the transparency,

456

Hou Y. and Quan Z. (2009).

LEARNING WITH FUN - An Application of Visual Cryptography.

In Proceedings of the First International Conference on Computer Supported Education, pages 456-459

DOI: 10.5220/0002018104560459

 SciTePress

Table 1: Sharing and stacking scheme of black and white

pixels.

Secret

image

Share1 Share2

Stacked

image

and they are chosen randomly, so the secret image

cannot be identified from a single transparency.

Because every block on the transparencies consist of

two white pixels and two black pixels, no matter it

comes from white pixel or black pixel of the secret

image, there is no clue of revealing the secret image

on the shares.

When stacking two transparencies, the block

corresponding to the black pixels in the secret image

will be full black, and that corresponding to the

white pixels will be half-black-and-half-white,

which can be seen as gray pixel (50% black). This

gives enough contrast to recognize the secret

information on the stacked shares by human eyes.

Take Figure 1 for example, a secret image with the

words of “淡江資管” are decomposed into two

shares. When we stack them together, we can get the

reconstructed image. Though the contrast of the

stacked image is degraded to 50%, human eyes can

still identify the content of the secret image easily.

(a) Secret image

(b) Share image 1

(d) Recovering image

Figure 1: Visual cryptography for “淡江資管”.

2.2 Visual Cryptography for Grey-level

and Colour Images

Every kind of the media has different ways to

represent the colour level of an image according to

its physical characteristic. The general printer, such

as dot matrix printers, laser printers, or jet printers

etc., can only control a single pixel to be printed

(black pixel) or not to be printed (white pixel).

Hence one way to represent the gray level of an

image is to control the density of the printed dots;

for example, the printed dots of the bright part are

sparse, but those of the dark part are dense. Such

method that uses the density of the net dots to

simulate the gray level is called “Halftone”. Hou

might be the first researcher to use the concepts of

colour decomposition and halftoning technology to

produce shares needed by visual cryptography for

both grey-level and colour images (Hou, 2003). By

means of halftone, we can transform an image with

gray level into a binary image (Figure 2). Because

human eyes cannot identify too tiny printed dots and

will mix with the nearby dots, though the

transformed image has only two colours - black and

white, we can simulate different gray levels through

the density of printed dots.

(a) Continuous tone (b) Halftone

Figure 2: Grey-level image and black-and-white image.

The transformed halftone image (Figure 2b) is a

black-and-white image, such image format is very

suitable to apply the traditional visual cryptography

method to generate the shares (Figure 3). Secret

image Figure 3c is hidden into Figure 3a and 3b.

As for colour image, most colour printers use

cyan, magenta and yellow inks to display colour.

These three components of a colour image can be

decomposed to form three monochromatic images.

This monochromatic image is like a single gray-

level image which can be handled by the above

mentioned method. Each participant will get a

colour share which is composed of cyan, magenta

and yellow monochromatic shares. After stacking

these shares, colour secret image can be revealed.

LEARNING WITH FUN - An Application of Visual Cryptography

457

2.3 Extended Scheme of Visual

Cryptography

The shares generated by visual cryptography (Naor

and Shamir, 1995) are noise-like and meaningless.

There is no clue of the secret image on the share. It

meets the requirement of security. But the

meaningless shares will cause adversary’s attention

and invite the illicit attempts. Ateniese (Ateniese et

al, 2001) proposed an extended visual cryptography

scheme (Table 2) to hide a secret image into two

meaningful sharing transparencies. When stacking

the transparencies generated from Table 2 together,

we will get the secret message with no trace of the

original cover image on the shares.

Table 2: Sharing and stacking scheme of black and white

pixels.

Secret

image

Share1 Share2

Stacked

image

white (W)

(W)

(W) (B)

(B) (W)

(B) (B)

Black (B)

(W) (W)

(W) (B)

(B) (W)

(B) (B)

According to Table 2, blocks with 2 white pixels

and 2 black pixels on the share image represent a

white pixel of the cover image. Blocks with 1 white

pixel and 3 black pixels on the share image represent

a black pixel of the cover image. There is 25%

contrast between black and white pixels on the

sharing transparencies. Hence, we can disclose the

content of the cover image.

When the pixel of the secret image is white

(black), choose one of the first (last) four rows of the

Table 2, depending on the corresponding colours on

the cover images, to form the content of the block on

the two transparencies. As to the security, there are

six possible white patterns and four possible black

patterns to be chosen as the content of every block in

the transparency, and they are determined randomly.

Therefore, to have share1 or share2 alone, there is no

clue of revealing the secret image on the sharing

transparencies.

When stacking two transparencies, the block

corresponding to the black pixel in the secret image

will be full black, and those that corresponding to

the white pixel in the secret image will be 3-black-

and-1-white, which can be seen as gray pixel (75%

black). There is also 25% contrast between black

and white pixels on the stacked transparencies.

Hence, the content of the secret image can be

disclosed easily by our visual system.

Take three colour-level images for example,

Figures 3d and 3e are two meaningful sharing

transparencies produced by using the sharing

scheme of the Table 2. Figure 3f is the reconstructed

secret image produced by superimposing Figure 3d

and 3e. In other words, secret image Figure 3f is

hidden into Figure 3d and 3e or Figure 3d and 3e

cover secret image Figure 3f. Though the contrast of

the sharing images and stacked secret image are

degraded to 50% and 75% respectively, human eyes

can still identify the content of the cover images and

the secret image easily

(a) Share image 1

(b) Share image 2

(d) Share image 1

(e) Share image 2

(f) Stack (d) and (e)

Figure 3: Visual cryptography with meaningless an

meaningful shares.

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3 POSSIBLE SCENARIOS IN

EDUCATION

Teaching of counting has created significant

difficulties to both teachers and young kids. Class

size is one of the major barriers to effective

instruction. As the lowering cost of the computer

hardware and widely spread of the Internet, pupils

might have their own laptop personal computers for

homework and instruction, especially in some highly

computerized cities or countries. A well-designed

pedagogy, such as Computer-Assisted Instruction

(CAI), can make the instruction most effective.

In the information security field, visual

cryptography is used as one of the technologies to

implement the topics about watermarking,

information hiding and information sharing. It can

generate shares, stack them together, the secret

information will automatically show up and

recognize by human eyes. Therefore, it is a good

tool to be used to practice counting for kids.

For example, the sum of two numbers can be

treated as a secret number, the generated share 1 and

share 2 can be treated as the summand and the

addend. When kids are doing their counting

exercises, they can select one number share,

dragging it to another share, stacking them together,

magically, the number on these two meaningful

shares disappears, the correct answer shows up on

the stacked shares. When you shift these two shares

a little bit, pixels are not stacked properly, the

answer will fade away. It can stimulate the curiosity

of the kids and increase the fun of learning.

Figure 4 and Figure 5 are examples of the sum

and the product of two numbers, respectively.

(a) Share image 1

(b) Share image 2

Figure 4: Sum of 3 and 5.

(a) Share image 1

(b) Share image 2

Figure 5: Product of 4 and 6.

A set of programming exercises have been

designed with help of computer assisted instruction.

The demo system can pose questions to students,

return feedbacks, and select additional questions

based on the kids' responses. By using this system,

kids can practice counting and learn the basic

principle of the visual cryptography.

4 CONCLUSIONS

Visual Cryptography exploits the characteristics of

human visual system to decrypt the overlapping

images without mass and complicated computations.

Traditionally, visual cryptography is used as one of

the technologies to implement the topics about

watermarking, information hiding and information

sharing. In this paper, we propose a teaching system

which uses the technique of visual cryptography to

teach young kids counting. The technology of visual

cryptography can be used to generate numbers, stack

them together, the result will automatically show up

and recognize by human eyes. It can stimulate the

curiosity of the kids and increase the fun of learning.

ACKNOWLEDGEMENTS

This work was supported in part by a grant from

National Science Council of the Republic of China

under the project NSC96-2221-E-032-027.

REFERENCES

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1996, “Visual Cryptography for General Access

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

2001, “Extended Capabilities for Visual

Cryptography,” Theoretical Computer Science, Vol.

250, pp. 134-161.

Blundo, C. A. De Santis and D. R. Stinson, “On the

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ftp://theory.lcs.mit.edu/pub/tcrypto1/96-13.ps.

Y.C. Hou, 2003, “Visual Cryptography for Color Images,”

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Naor, M. and A. Shamir, 1995, “Visual Cryptography”,

Advances in Cryptology: Eurpocrypt’94, Springer-

Verlag, Berlin, pp. 1-12.

Naor, M. and A. Shamir, 1996, “Visual Cryptography II:

Improving the Contrast Via the Cover Base”. Theory

of Cryptography Library Report 96-07,

ftp://theory.lcs.mit.edu.tw/pub/cryptol/96-07.ps.

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