03-08-2012, 10:13 AM
A New Visual Cryptography Scheme for Color Images
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Abstract
Visual cryptography is a method for protecting image-based secrets that has a computation-free decoding
process. In this paper, we proposed a visual cryptographic system which can be used to hide the original image
information from an intruder or an unwanted user. The images can be in any standard format. The encrypted image
is sent to the destination through the network and then the image is decrypted. We used symmetric key
cryptography. Experimental results indicate the proposed method is a simple, practical and effective cryptographic
system.
Key Words: Image sharing, Visual cryptography, Image processing.
I. Introduction
Visual cryptography [1] is a cryptographic technique which allows visual information (pictures, text, etc) to be
encrypted in such a way that the decryption can be performed by the human visual system without the aid of
computers. As network technology has been greatly advanced, much information is transmitted via the Internet
conveniently and rapidly. At the same time, the security issue is a crucial problem in the transmission process. For
example, the information may be intercepted from transmission process. This method aims to build a cryptosystem
that would be able to encrypt any image in any standard format, so that the encrypted image when perceived by the
naked eye or intercepted by any person with malicious intentions during the time of transmission of the image is
unable to decipher the image.
Firstly an image and key is fed into cryptosystem. The encryption algorithm produces a cipher image which is
sent into receiver through a communication channel. When the cipher image reaches the destination, the receiver
enters the key and the original image is decrypted. Figure 1 shows the block diagram of the cryptosystem. The key
we used is the symmetric key with minimum size of 47 bits. Two important factors are used to determine the
efficiency of any cryptographic scheme [2], namely: 1) the quality of the reconstructed image and 2) the resizing
factor (“fac”). Any loss of information during the reconstruction phase leads to reduction in the quality of the
recovered image. On the other hand resizing factor refers to enlarging or reducing the original image. To enlarge an
image, specify resizing factor greater than 1. To reduce an image, specify resizing factor between 0 and 1.For
bandwidth constrained communication channels it is desirable to keep resizing factor (“fac”) as small as possible.
For color images, reducing resizing factor is of paramount importance since they occupy more space and consume
more band width compared to grayscale and binary images.
This paper is organized as follows: Section II describes the theoretical formulations, Section III describes the
mathematical function, Section IV describes the encryption algorithm, Section V describes the decryption algorithm,
Section VI gives the experimental results and finally Section VII gives the conclusion.
ISSN: 0975-5462 1997
B.SaiChandana.et. al. / International Journal of Engineering Science and Technology
Vol. 2(6), 2010, 1997-2000
Figure 1: Block diagram of our Cryptosystem
II. Theoretical Formulations
A color image is usually represented in the RGB color space [3,4] , because most of the computer input and
output devices use this color system. Each vector consists of three components, which are the intensity values in the
Red, Green and Blue channel. The combination of these values delivers one particular color. A change in the
intensity value will change the information stored in the picture. So by performing some changes in intensity values
we can encrypt the image and doing the reverse in decryption. If the changes are performed separately on Red,
Green and Blue layers, we can have more robust visual cryptographic system. This is because of the fact that when
an intruder goes for complete analysis of the image will try to know these basic intensity values. These intensity
values will help him to generate the original image. So if the encryption is done at this basic level then it will be
hard to break the system. All the changes in the intensity values are performed using a mathematical function.
III. Mathematical Function
The function used in this cryptosystem should have a bijective mapping i.e. the function should have one-one and
onto mapping. This indicates the inverse of the function exists. Hence the original information of the image can be
retrieved back during decryption without any error. The function is given as
g(u)= abs(1/log(tan((exp(k) * cos(exp(1)) * sin(exp(U))))))
here ‘k’ and’ l’ are the keys and ‘U’ is the gcd of the two keys which are used for encryption.
IV. Encryption Algorithm
Step 1: Ask for the image and the keys X1 and Y1 and the resizing factor “fac”.
Step 2: Generate the function g( ) which will contain the values generated from a function in an array.
Step 3: Find the absolute value of the function g( ). Here U=gcd(X1,Y1).
Step 4: Pass it through a low pass filter.
Step 5: Resize the image using bi-cubic interpolation and get the RGB layer in a separate matrix with the factor
“fac”.
Step 6: Multiply the pixel values with the absolute values calculated.
Step 7: Flip the new formed Red matrix upside-down.
Step 8: Flip the new formed Green matrix left-side right.
Step 9: Rotate the Blue matrix by twice of the “fac”.
Original
Image
Key
Encryption
Cipher
Image
Key
Decryption
Original
Network Image
ISSN: 0975-5462 1998
B.SaiChandana.et. al. / International Journal of Engineering Science and Technology
Vol. 2(6), 2010, 1997-2000
Step 10: Generate the image again save it in .bmp format. (The image is saved in .bmp format because actual values
of the pixel are retained and the number of pixels is also the same which is in contrast with the other compressed
images like jpeg, gif, etc.)
Step 11: Send the image with the resizing factor to the receiver.
V. Decryption Algorithm
Decryption is just the reverse process of encryption. The aim of decryption is to make the encrypted information
readable again (i.e. to make it unencrypted).
Step 1: Receive the image and ask for the key and resizing factor.
Step 2: Break the received image into Red Green and Blue parts/layers.
Step 3: Flip the new formed Red matrix upside-down.
Step 4: Flip the new formed Green matrix left-side right.
Step 5: Rotate the Blue matrix by twice of the “fac”.
Step 6: Generate the function depending upon the keys. Here U=gcd(X1,Y1).
Step 7: Find the absolute value of function and pass it through low pass filter.
Step 8: Divide the pixel values of the received image with the absolute value of the function.
Step 9: Form the image.
Step 10: Resize the image by multiplying its rows and column with the “fac” using bi-cubic interpolation.
VI. Experimental Results
This section presents the simulation results illustrating the performance of the proposed cryptosystem. The test
image employed here is the true color image “parrot” with 290×290 pixels. The key size is of 47 bits. The
encryption and decryption algorithm are implemented in MATLAB 7.0 [5,6] in core2duo of 2.66 GHz machine. The
decryption algorithm takes 40 seconds to get executed. Now if an intruder goes for the exhaustive search for the
keys then it will take around 2.2*1022 years to get the keys. This is the long time for secret information to lose its
secrecy. Hence the proposed system is a strong one. If the key length is increased the system will become more
secure. The results for our system are shown in figure 2 and in figure 3.
a) Original image b) Encrypted image c) Decrypted image
Figure 2: Encryption and Decryption process
ISSN: 0975-5462 1999
B.SaiChandana.et. al. / International Journal of Engineering Science and Technology
Vol. 2(6), 2010, 1997-2000
a)Original image b) Encrypted image c) Decrypted image
Figure 3: Encryption and Decryption Process
As stated earlier, the efficiency of any cryptosystem depends on the quality of the reconstructed image. We used
the Structural Similarity (SSIM) index [7] for measuring the quality between two images. The SSIM index can be
viewed as a quality measure of one of the images being compared provided the other image is regarded as of perfect
quality. The quality measures are calculated between the original image and the encrypted/decrypted image. Table 1
shows the quality measures of the images in figure 2 and in figure 3.
Table 1: SSIM index
Image SSIM Index
( for figure 2)
SSIM Index
( for figure 3)
Original
Image
1 1
Encrypted
Image
0.0004 0.0003
Decrypted
image
0.98 0.99
VII. Conclusion
In this paper, we have presented a new visual cryptographic system which can be used to hide the original image
information from an intruder or an unwanted user. The advantages of the proposed method are its resizing factor and
its capability of perfect reconstruction of the secret image. This work is an attempt to make a secured transfer of
valuable images between two trusted parties. The confidentiality is maintained and the authentication can be
checked by digital signatures. The proposed method can be considered as a good candidate for secure visual data
transmission in systems with limited bandwidth. This work is highly applicable in military field.