Design and implementation of hierarchical visual

International Journal of Network Security & Its Applications (IJNSA), Vol.6, No.1, January 2014

Design and Implementation of Hierarchical Visual
Cryptography with Expansionless Shares
Pallavi Vijay Chavan1, Dr. Mohammad Atique2 and Dr. Latesh Malik3
1

2

Research Scholar-Dept. of Comp. Sci. & Engg., GHRCE, Nagpur, MH, India
Associate Professor-PG Dept. of Computer Science, SGBAU, Amravati,MH, India
3
Professor- Dept. of Comp. Sci. & Engg., GHRCE, Nagpur, MH, India

ABSTRACT
Novel idea of hierarchical visual cryptography is stated in this paper. The key concept of hierarchical
visual cryptography is based upon visual cryptography. Visual cryptography encrypts secret information
into two pieces called as shares. These two shares are stacked together by logical XOR operation to reveal
the original secret. Hierarchical visual cryptography encrypts the secret in various levels. The encryption
in turn is expansionless. The original secret size is retained in the shares at all levels. In this paper secret is
encrypted at two different levels. Four shares are generated out of hierarchical visual cryptography. Any
three shares are collectively taken to form the key share. All shares generated are meaningless giving no
information by visual inspection. Performance analysis is also obtained based upon various categories of
secrets. The greying effect is completely removed while revealing the secret Removal of greying effect do
not change the meaning of secret.

KEYWORDS
Visual cryptography, greying effect, shares, key share.

1. INTRODUCTION
Visual cryptography is the art of encrypting visual information such as handwritten text, images
etc. The encryption takes place in such a way that no mathematical computations are required in
order to decrypt the secret. The original information to be encrypted is called as secret. After
encryption, ciphers are generated and referred as shares. The part of secret in scrambled form is
known as share. Fundamental idea behind visual cryptography is to share the secret among group
of n participants. In order to share the secret, it is divided into n number of pieces called shares.
These shares are distributed among the participants. To reveal the original secret, each participant
provides his own share. Complete knowledge of n-1 shares is unable to decrypt the secret. Many
visual cryptographic schemes exist. The basic scheme is 2 out of 2 visual cryptography in which
the secret is partitioned into exactly two parts. To reveal the secret these two shares must
participate. Following figure indicates simple example of 2 out of 2 visual cryptography scheme.

DOI : 10.5121/ijnsa.2014.6108

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Figure 1. Example of basic visual cryptography

In above figure, graying effect is observed at background. Additional black pixels at the
background are forming some pattern and giving raise to greying effect. Due to this effect,
meaning of secret remains undisturbed. Hence, greying effect does not have any impact on
original secret. Another scheme known as 2 out of n scheme, the secret is divided into exactly n
shares. To reveal the secret any two shares must participate. Third scheme of VC is formally
known as K out of n scheme in which the secret is divided into exactly n parts. To reveal the
secret any K shares are sufficient. Multiple shares are generated out of visual cryptography.
Extended version of third visual cryptography scheme is n out of n where in secret is divided into
n shares. All n shares must participate while revealing the secret. Hierarchical visual
cryptography abbreviated as HVC is specialization of visual cryptographic schemes. HVC is
based upon basic 2 out of 2 visual cryptographic scheme. As the secret is encrypted in multiple
levels in HVC, the secrecy of data tends to increase. Now a day’s many authentication system
exists based upon biometric, passwords but each authentication system is having pitfalls related to
the secrecy of data. The idea stated in this paper is further utilized to design the authentication
mechanism based on Hierarchical visual cryptography. In this work the size of shares is also
reduce giving the expansionless shares. This paper is organized as follows: Section II deals with
related work in the area of visual cryptography. Section III describes the key concept of
expansionless visual cryptography. In section IV the detailed idea of hierarchical visual
cryptography along with experimentation is stated. Experimental results are also represented in
this section. The last section V describes conclusion of the overall experimentation.

2. RELATED WORK
The concept of visual cryptography formally known as secret sharing was developed by Adi
Shamir in 1979. He stated that the secret D is divided in n pieces and easily reconstructable from
any k pieces. He claimed that data is protected after encryption but the key used for encryption
could not be protected. He suggested secret sharing to protect the keys used for encryption.
According to Shamir, the scheme is k out of n secret sharing scheme [1]. With the help of basic
idea behind visual cryptography, many researchers performed the survey based on various
cryptographic schemes. In the survey of VC schemes it has been found that the colorful secret
also be shared using visual cryptography [2, 3]. Che Wei Lee used visual cryptography for
authentication based on the binary document images with the constraint that the binary document
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image must follow portable network graphics format. In binary documents there are only two
possibilities of pixel values viz. black and white. Here authors used 0 to represent black
information and 1 to represent white information [4]. Stegenography and visual cryptography
concepts were combined by George Abboud to share the hidden message. The idea was quite
novel but increased complexity during the computation of shares [5]. In 2008 the concept was
proposed to use visual cryptography for banking applications. The authors stated that visual
cryptography based signature authentication is more secured than password based authentication.
Individual pixel value in the secret is indicated by f(x, y) before processing and by g(x, y) after
processing. In any situations for binary secret the values of these two functions are either 0 or 1
[6]. In 2010, cheating prevention mechanism was stated using visual cryptography by Bin Yu [7].
In the same year Li Fang proposed that multiple secrets could be encrypted in the same pairs of
shares [8]. Contrast enhancement in visual cryptography was proposed by Thomos Monoth
efficiently increased the contrast level of revealed secret [9]. The motivation for Hierarchical
visual cryptography oriented from visual cryptography and the need of secured authentication
mechanism based on visual cryptography. In 2000, Yang C.n and Laih C.S stated color visual
cryptography scheme. According to these authors color information like image is easily encrypted
using color VC scheme. Time Complexity was the major issue of discuss in this paper [10]. A
segment-based visual cryptography suggested by Borchert [11] can be used only to encrypt the
messages containing symbols, especially numbers like bank account number, amount etc. [11]. In
2013, Omprasad and Sonavane developed visual cryptography encoder and decoder by employing
the concept of stegenography. Stegenography hides the secret information in such a way that no
one information looks like an image. The authors combined visual cryptography with
stegenography to obtain better results. The application proposed by authors was Quick Response
code [12]. Application of Visual Cryptography to biometric authentication was proposed in 2011
by K. Suryadevara and Naaz. The authors stated that biometric characters are most feasible for
authentication. In order to secure the authentication process, the authors applied visual
cryptography to biometric character. Every biometric character was acceptable in this technique
including fingerprint, iris and tongue. The process of enrollment, verification and identification of
biometric character was introduced in this paper. The technique followed 2 out of 2 secret sharing
scheme representing 2 out of 2 visual cryptography. The shares generated by this method were
expanded version of original secret with expansion ratio of 1:4[13]. In the year 2012, Yi Hui
Chen and Pei Yu Lin proposed a novel secret sharing scheme using low computations for
authentication. The valuable advantage in this scheme was pixel expansion ratio of 1:1. The secret
was reconstructable without loss. The problem identified with this method was authentication
with half secret which is infeasible for signature based authentication. The authors used Boolean
operations to encrypt the secret [14].

3. EXPANSIONLESS VISUAL CRYPTOGRAPHY
In earlier work of visual cryptography, we encrypted the secret with the expansion ratio of 1:4
and later 1:2. The expansion indicates that if original secret is of size AXB then with expansion
ratio 1:4 the shares have size 4AX4B and with expansion ratio 1:2 the shares reflected are found
to be of size 2AX2B. Due to this expansion hierarchical encryption of secret gets affected. During
encryption using HVC initially secret is encrypted using 1:2 expansion ratio giving two shares S1
and S2. If S1 and S2 are encrypted with the same expansion ratio independently then the resultant
four shares are again expanded forms of S1 and S2 (S1 and S2 are already expanded in first level
of encryption). This huge expansion in shares affects the space complexity. While superimposing
the shares of HVC, the larger transparencies are required. Expansion-less hierarchical visual
cryptography is the solution to reduce this expansion in the shares. The requirement of this
proposed method is that the secret should be in binary form i.e. black and white passwords,
signatures, handwritten text etc. Before encrypting, the original secret is mapped into the size
which is multiple of 4. Before encrypting the secret, it is normalized. The resize function of
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OCTAVE/MATLAB is chosen to convert any secret whose size is multiple of 4. After resizing
the secret starting with top left corner of secret every 2X2 pixel block is selected for encoding
independently. The encoding of 2X2 block is done among various random combinations. If 2X2
block in original secret is entirely black then this block is encrypted using 4 possibilities
represented by equation 1 - 8. There are multiple possibilities for the 2X2 pixel blocks. The
encoding combinations for share1 of entire black block of pixels are represented as below:
[1 0; 0 1]
[0 0; 1 1]

(1)
(2)

[1 1; 0 0]

(3)

[0 1; 1 0]

(4)

The encoding combinations appearing in share2 are given by:
[0 1; 1 0]

(5)

[1 1; 0 0]

(6)

[0 0; 1 1]

(7)

[1 0; 0 1]

(8)

Similarly, if 2X2 block of secret is found to be entirely white then such block is encrypted with 4
random combinations. Share1 of encoding for white block of pixels is given by:
[1 0; 0 1]

(9)

[0 0; 1 1]

(10)

[1 1; 0 0]

(11)

[0 1; 1 0]

(12)

Above combinations also represents share2 as the basic property of encrypting white pixel
indicates that the pattern of share1 and share2 must be same. Third possibility for 2X2 pixel
block is neither pure white nor pure black. In such cases the encryption is done using following
combinations. share1 for random combinations is given below:
[0 1; 1 0]

(13)

[1 0; 1 0]

(14)

[0 1; 1 1]

(15)

[1 0; 1 1]

(16)

Corresponding share2 combinations are represented by following matrices:
[0 1; 0 1]

(17)
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[1 1; 0 1]

(18)

[1 0; 1 0]

(19)

[0 1; 0 1]

(20)

3.1. Expansionless Visual Cryptography Algorithm
Input: Secret in binary form
Output: Meaningless shares
1. Read the secret.
2. Covert secret size AXB to exact multiple of 4.
3. Determine the size of converted secret: [s1 s2]< ¡size(secret)
4. For each i in s1 with step size 2
For each j in s2 with step size 2
if(2X2 block is entirely black)
Randomly select the pattern from equation 1-4 to generate share1 and from equation 5-8
to generate share2.
Else
if(2X2 block is entirely white)
Randomly select the pattern from equation 9-12 to genrate share1 and share2
Else
Encrypt the block using random selection among equations 13-16 to generate share1 and
using equations 17-20 to generate share2.
End for
End for
5. Exit.

4. HIERARCHICAL VISUAL CRYPTOGRAPHY EXPERIMENTATION
Hierarchical visual cryptography encrypts the secret in two levels. Initially the secret is encrypted
in two different meaningless shares called share1 and share2. This is the first level of
Hierarchical visual cryptography. In the second level, these two shares are encrypted
independently. Share1 is encrypted to yield share11and share12. Similarly, share2 is encrypted
to yield share21 and share22. At the end of second level of HVC four shares are available. The
key share formation takes place here. Among these four shares any three shares are taken and
mapped to yield the key share. Table 1 shows the mapping of key share. With the help of
mapping stated here, the key share found to have blacker tendency.
Table 1. Key Share Generation

Share12 Share21 Share22
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1

Key Share
1
1
0
0
0
1
95


1
1

1
1

0
1

0
0

Another mapping method is stated here with soft computing approach. While mapping these three
shares to key share, following inference rules are applied. These inference rules are defining the
intelligence of an algorithm. The concentration of black and white pixels in key share is
determined based upon concentrations of three input shares. These if-then rules are applicable to
each pixel of the share12, share21, share22.
1. If (share12, share21, share22 is black) then keyshare pixel is black;
2. If (share12, share21 is black and share22 is white) then keyshare pixel is black;
3. If (share12, share22 is black and share21 have white) then keyshare pixel is black;
4. If (share12 is black and share21, share22 is white) then keyshare pixel is black;
5. If (share12 is white and share21, share22 is black) then keyshare pixel is black;
6. If (share12, share22 is white and share21 is black) then keyshare pixel is white
7. If (share12, share21 is white and share22 is black) then keyshare pixel is black;
8. If (share12, share21, share22 is white) then keyshare pixel is black.

4.1. Methodology for Hierarchical Visual Cryptography
Hierarchical visual cryptography is defined on basis of visual cryptography. Simple visual
cryptography divides original secret in two parts. Each part is known as share. To reconstruct the
secret, both shares are stacked together. This technique is known as 2 out of 2 visual
cryptography. Hierarchical visual cryptography also encrypts the secret information in two shares
at the first stage. Later, these two shares are encrypted individually to generate subsequent shares.
This is the second level of hierarchy in HVC. At the end, four resultant shares are found. Out of
these four shares, any three shares are taken to generate the key share. This stage is identified as
third level of HVC. Finally, HVC scheme gives two resultant shares out of which one is handed
over to the user for authentication and another share is along with database. The shares are
generated using Naor and Shamir scheme of two out of two visual cryptography. Algorithm for
Encrypting Secret using hierarchical visual cryptography is given below:
1. Begin
2. Read original secret.
3. Resize the secret to standard size.
4. Encrypt resized secret using 2 out of 2 VC scheme.
Share 1 and Share 2 are generated here.
5. Share 1 is encrypted using 2 out of 2 VC.
Share 11 and share 12 are generated here.
6. Share 2 is encrypted separately using 2 out of 2 VC.
Share 21 and share 22 are generated here.
7. Share 11, Share 12 and Share 21 are combined to form key share
(Inference rules are defined to generate key share pixel value.)
8. Output remaining share and key share.
9. End.

4.2. Experimental Results
The experimentation with expansionless hierarchical visual cryptography is done with reference
to the following secret shown in figure 2. Above secret is encrypted using expansionless visual
cryptography. After encryption, share1 and share2 are generated at the first level of HVC which
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are represented by figure 3. Encryption at the second level is shown in figure 4. The key share is
shown in figure 5. Finally figure 6 indicates revealed secret.

Figure 2. Original secret

Figure 3. Shares at first level of hierarchy

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Figure 4. Shares at second level of hierarchy

Figure 5. Key share

98


Figure 6. Revealed secret

4.3. Experimental Analysis
Concentration of black and while pixels in the shares and revealed secret are analyzed. Each
entity involved in hierarchical visual cryptography represents different concentration of black and
white information. As the secret changes over time, corresponding concentration varies with
respect secret. Percentage of black and white pixels remains constant for different category of
secrets like images, handwritten text and textual passwords. Following Table denotes exact
concentration of black and white pixels in shares and secret. It has been analyzed that the
concentration of white pixels decreases drastically in first level of hierarchical visual
cryptography. This concentration remains steady for second level and later increases at the end of
hierarchy. Key share reflects high concentration of black pixels. The revealed secret represents
high concentration of white pixels. High concentration in reconstructed secret is helpful to detect
the secret easily during authentication. It leads to removal of graying effect observed in basic
Shamir scheme.
Table 2. Statistics of pixels in HVC encoder
Entity
Secret
Resized
Secret
Share1
Share2
Share11
Share12
Share21
Share22
Revealed
secret

No. of black pixels
2364

No. of white
pixels
6744

Total
pixels
9108

4989

15159

20148

10479
10463
10479
10463
6716
6716

9669
9685
9669
9685
13484
13432

20148
20148
20148
20148
20148
20148

2024

18124

20148

Following graph indicates white pixel concentration in encrypting entity and corresponding
shares. The statistics of hierarchical visual cryptography encoder are mapped in this graph.

99


Figure 7. Representation of black pixels in entities

Figure 7. Representation of white pixels in entities

5. CONCLUSIONS
In this paper, we proposed and experimented hierarchical visual cryptography. Related work in
area of visual cryptography is also discussed in this paper. Encryption at each level of HVC is
expansionless. A share generated out of HVC represents the same size of secret. The keyshare
generated is having random nature. It has been observed that the expansionless shares consume
less memory. Graying effect is reduced to zero. In earlier work of visual cryptography it has been
observed that expansion of secret taking place after encryption. Thus reflects some greying effect.

100


The authentication mechanism based on hierarchical visual cryptography is identified as a future
scope of this work. The authors encrypted various categories of secrets to compare the results.

ACKNOWLEDGEMENTS
The authors are thankful to Shamir for providing basic platform of visual cryptography. We are
also thankful to all the authors those who contributed in the area of visual cryptography.

REFERENCES
[1]

Adi Shamir, How to share a secret. Communications of ACM, Volume 22, No. 11, Pages 612-613,
1979.

[2]

Wangarce G.,R. Zhongnin, Halftone visual cryptography by iterative half toning. Proceedings of 2010
IEEE International Conference on Acoustics Speech and Signal Processing, pages 1822-1825, March
2010.

[3]

W. Gandhare P. S. Revenkar, Anisa Anjum, Survey of visual cryptography schemes. International
Journal of Security and Its Applications, Volume 4, No. 2 pages 49-56, April 2010.

[4]

Wen Tsai Che Lee, Authentication of binary images in png format based on a secret sharing
technique. Proceedings of IEEE International Conference on System and Engineering, pages 506-510,
July 2010.

[5]

Yampolskiy R.V. Abboud G, Marean J, Steganography and visual cryptography in computer
forensics. Proceedings of 5th IEEE International Workshop on Systematic Approaches to Digital
Forensic Engineering, pages 25-32, 2010.

[6]

Hegde C, Manu S, and Patnaik L, M Shenoy, P D, Venugopal , Secured authentication using image
processing and visual cryptography for banking applications. Proceedings of 16th IEEE International
Conference on Advanced Computing and Communications, pages 65-72, 2008.

[7]

Li Fang, Bin Yu, Jin Lu, A co-cheating prevention visual cryptography scheme. Proceeding of 3rd
IEEE International Conference on Information and Computing, pages 157-160, 2010.

[8]

Bin Yu, Li Fang, Ya-Min Li, Multi secret visual cryptography based on reversed images. Proceeding
of 3rd IEEE International Conference on Information and Computing, pages 195- 198, 2010.

[9]

Babu Anto P. Thomas Monoth, “Contrast enhanced visual cryptography schemes based on additional
pixel pattern”, Proceeding of IEEE International Conference on Cyberworlds, pages 171-178, 2010.

[10] Yang C.n and Laih C.S, “New colored visual secret sharing schemes”, Design, Codes and
Cryptography, Vol. 20, pp. 325- 335, 2000.
[11] B. Borchert, .Segment Based Visual Cryptography,. WSI Press, Germany, 2007.
[12] S. S. Omprakash Deshmukh, “Multishare crypt stego authentication system”, International Journal of
Computer Science and Mobile Computing, Volume 2 No.2, Pages 80–90, February 2013.
[13] K. Suryadevara and Naaz, “Visual cryptography improves the security of tongue as a biometric in
banking”, Second International Conference on Computer and Communication Technology, Pages
412–415, 2011.
[14] P. L. Yi Chen, “Authentication mechanism for secret sharing using boolean operation”, International
Journal of Electronic Science and Technology, Volume 10 No.3, Pages 195–198 September 2012.

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Authors
Ms. Pallavi Vijay Chavan is a research scholar at G. H. Raisoni College of Engineering,
Higna, Nagpur, MH, India and working as an assistant professor (Sr.Gr.) at Bapurao
Deshmukh College of Engineering, Sevagram, MH, India. She did her BE in Computer
Engineering in 2003 from Nagpur University, Nagpur and ME in Computer Science and
Engineering from SRTMNU, Nanded. She is having 9 years of teaching experience. She
has published 10 research papers in International conference s, 4 research papers in International journals
and 6 papers in national conferences. She is a life member of ISTE.
Dr. Mohammad Atique is working as an associate professor in P.G. Department of compu
ter science at Sant Gadge Baba Amravati University Amravati, MH, India. He has
published many research papers in International journals and conferences as well as in
national journals and conferences. He is member of many professional bodies like ISTE.
His area of interest is soft computing and operating system. He is recipient of research
grants from research agencies like AICTE and UGC.
Dr. Latesh Malik is professor and head of computer science and engineering department at
G. H. Raisoni College of Engineering, Nagpur. She has published many research papers in
the area of pattern recognition. Her area of interest is Handwritten text recognition.

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Design and implementation of hierarchical visual

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