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					 International Journal of Application or Innovation in Engineering & Management (IJAIEM)
                     Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 3, Issue 5, May 2014                                                                              ISSN 2319 - 4847

              Pixel Transformation based on Rubik’s
                          Cube Principle
                                              M.Sirisha1, SVVS Lakshmi2
                       1,2
                         Department of MCA, ANITS Engineering College, Sangivalasa, Tagarapuvalasa,
                                         Visakhapatnam, Andhra Pradesh, India.

                                                            Abstract
Technology today evolves at a faster rate than it could have been predicted. The benefits of the these rapid changes has not
diminished the concerns for security of data. The paper deals with implementation of security measures for images based on the
principles of Rubik's cube. Here the image is encrypted by scrambling of pixels and performing XOR operations and it is
decrypted similarly. This technique enables a better procedure for ensuring security for the image files that are being transmitted
literally every second. The algorithm has been tested on different kinds of images and the obtained results have been presented.

Keywords: Encryption, Decryption, Rubik’s Cube.

1. INTRODUCTION
Images have been the fundamental source of conveying ideologies right from the start of mankind which stands true even
today. In this day and age of accelerated and convenient media for transmission and use of data resources the need for
security has never been more profound. This has led to the development and analysis of several encrypting algorithms
that come with their own distinct characteristics.
In recent years, several encryption schemes have been proposed [1] – [12]. Image encryptions are broadly classified into
three types. They are
1. Pixel Transformation
2. Value Transformation
3. Chaotic Transformation

Value Transformation:
Based on Intensity Hue Saturation (IHS), the transformation of pixel can be done. The total image is divided into different
color spaces and each color space is encrypted by using the different approach.

Pixel Transformation:
The transformation is possible by using different mechanisms such as Peano-Hilbert curves and permutation
diffusion architecture. These types of processes may use the pixel transformation or pixel shuffling, depends on the
criteria.

Chaotic Transformation:
The origin for this one is pixel transformation only. It is novel pixel shifting method which generates chaotic sequences
and is used as an encryption sequences. It used 3D cat map to shuffle pixels within image.
The paper presents encryption techniques for secure transfer of images from one port to another. It has been designed
based on the Principles established by Rubik’s cube. The technique involves encrypting the image by dividing into a
sequence of byte arrays and applying XOR operations to obtain a scrambled image. The image is decrypted by taking the
same sequence of byte arrays and applying the before mentioned techniques to obtain the original image.

2. RUBIK’S CUBE PRINCIPLE AND PROCEDURE
The very concept of Rubik’s cube depends on rows and columns. The principle is applied to rows and these rows rotated
according to the requirement. The image is divided into rows and each row pixel transformation is applied.

2.1 Rubik’s Cube Image Encryption
In this section, the proposed encryption algorithm based on Rubik’s cube principle is described along with the decryption
algorithm.

2.1.1 Rubik’s Cube Based Encryption Algorithm
Let Io represent a α-bit image of the size M × N. Here, Io represents the pixels values matrix of image Io. The steps of
encryption algorithm are as follows:
(1) Generate randomly two byte arrays BR and BK of variable length.

Volume 3, Issue 5, May 2014                                                                                         Page 273
 International Journal of Application or Innovation in Engineering & Management (IJAIEM)
                     Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 3, Issue 5, May 2014                                                                           ISSN 2319 - 4847

(2) Store all the pixel values of a selected image in a byte array BR
(3) Divide the byte array BR into three parts and store it in three different byte arrays.
         (a)The first byte array B1 will store pixel values from 0 to one-third part of BR
         (b)The second byte array B2 will store pixel from the end of B1 till one-sixth of BR.
         (c)The third byte array B3 will store remaining pixel from end of B2 till end of BR
(4) For each byte array i of image Io,
          (a) Compute the sum of all elements in the byte array i, the sum is denoted by α (i)
                      N
               α(i) = ∑ Io i, j , i = 1, 2, ... , M, (1)
                      j=1

         (b) Compute modulo2 of α (i), denoted by M α (i)
         (C) Byte array i is left or right shifted depending on the M α (i)
                  If M α (i) =0          right circular shift
                    else                     left circular shift
(5)Using byte array BK, the bitwise XOR operator is applied to first and third byte array of the scrambled image.
(6) Combine all the byte arrays B1, B2, B3 into another byte array Ienc in order to obtain an encrypted image.

2.1.2 Rubik’s cube decryption Algorithm.
The decrypted image is Idec is recovered from the encrypted image Ienc. The steps for decryption algorithm is
(1) Divide the byte array Ienc into three parts and store it in three different byte arrays.
(a)The first byte array B1 will store pixel values from 0 to one-third part of BR
(b)The second byte array B2 will store pixel one sixth part of BR
(c)The third byte array B3 will store remaining pixel values of BR

(2) Using byte array BK, the bitwise XOR operator is applied to first and third byte array of the scrambled image.
(3) For each byte array i of image Io,
           (a) Compute the sum of all elements in the byte array i, the sum is denoted by α (i)
                           N
                 α(i) = ∑ Io i, j , i = 1, 2, ... , M, (1)
                         j=1
           (b) Compute modulo2 of α (i), denoted by M α (i)
           (c) Byte array i is left or right shifted depending on the M α (i)
                If M α (i) =0            right circular shift
                        else               left circular shift

(4) Combine all the byte arrays B1, B2, B3 into another byte array Idec in order to obtain an original image.

3. RESULT AND ANALYSIS
In this section, we present the tests that were conducted to assess the efficiency and security of the proposed image
encryption algorithm. These tests involve visual testing and security analysis [13].

3.1Visual Testing
For visual testing we test by using different types of images with different sizes. These selected images will be encrypted
using our proposed Rubik’s cube encryption. From this we can observe the difference in pixel position of the encrypted
images and original images shown in figure 1(a) to figure 1(f). There will be a drastic change between the encrypted and
original images.

3.2 Analyzing Security
Security is a major concern in any image encryption. There are certain major methods that will help in breaking the
image encryption. Methods such as Brute force, Plain text and cipher text attack etc are some of the major methods for
breaking the encryption. The assessment of these security issues can be done mainly by KEY SPACE and KEY
SENSIBILITY.

3.2.1Key Space
A brute force attack is an attack that basically works on guessing. So practically speaking, larger the key space, the harder
it will be the for the brute force to break the encryption. In our proposed Rubik’s cube image encryption, a brute force


Volume 3, Issue 5, May 2014                                                                                     Page 274
 International Journal of Application or Innovation in Engineering & Management (IJAIEM)
                     Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 3, Issue 5, May 2014                                                                      ISSN 2319 - 4847

attack is practically impossible because the key space huge. The key which we use to encrypt the image is multiplied by
fifteen times. Since the key space is too big to break using brute force our image encryption is very secure.

3.2.2Key Sensibility
A good encryption should always have a high sensibility feature. Which means any small change should lead in a huge
difference in the encrypted image. In our encryption the each pixel’s position depends on each byte present in the secret
key which we provide for encryption shown in figure 2(a) to figure 2(c). Since there will be a huge change in the image
for every small change in the key, key sensibility is very high in our encryption.




            Figure 1(a): Leena (original)                       Figure 1(b): Leena (encrypted) using key k1




              Figure 1(c):Penguins (original)                 Figure 1(d):Penguins (encrypted) using key k1




                                                                Figure 1(f): Murali (encrypted) using key k1
               Figure 1(e):Murali (original)


Volume 3, Issue 5, May 2014                                                                                Page 275
 International Journal of Application or Innovation in Engineering & Management (IJAIEM)
                     Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 3, Issue 5, May 2014                                                                      ISSN 2319 - 4847




 Figure 2(a):
   Leena (encrypted)                Decrypted image                    Leena(encrypted)               Decrypted image
                                     using correct key k1                                                 using wrong
key k2




         Figure 2(b):
  Penguin(encrypted)                 Decrypted image                      Penguin(encrypted)          Decrypted image
                                       using correct key K1                                               using wrong
keyk2




Figure 2 (C):                 Decrypted image                 Murali (encrypted)               Decrypted image using
Murali(encrypted)             using correct key K1                                             wrong key k2

3.3 Speed Test
One more important aspect that should be kept in mind is the speed at which the encryption of the image is done. Our
proposed Rubik’s cube image encryption is very fast compared to other image encryptions. Our encryption’s average
speed is less than a second when it runs on a normal Intel Core I3 (3.06 GHZ) Processor on a .Net framework 4.0. Speed
test is performed on images with various resolutions, but the encryption was finished in less than a second.

4.CONCLUSION
This paper explains the encrypting and decrypting techniques using the principles of Rubik. Performance assessment
tests demonstrate that the proposed image encryption algorithm is highly secure. It is also capable of fast
encryption/decryption which is suitable for real-time Internet encryption and transmission applications. The before
mentioned algorithms are efficient and have been repeatedly tested for concrete results, but, the ethical aspect of the
solution must not be forgotten. The techniques mentioned above need to be implemented ethically to produce desired
results without breaching any established security protocols.

References
[1] Z. Liu, L. Xu, C. Lin, J. Dai, and S. Liu, “Image encryption scheme by using iterative random phase encoding in
    gyrator transform domains,” Optics and Lasers in Engineering, vol. 49, no. 4, pp. 542–546, 2011.

Volume 3, Issue 5, May 2014                                                                                Page 276
 International Journal of Application or Innovation in Engineering & Management (IJAIEM)
                     Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 3, Issue 5, May 2014                                                                        ISSN 2319 - 4847

[2] Q. Guo, Z. Liu, and S. Liu, “Color image encryption by using Arnold and discrete fractional random transforms in
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[3] Z. Liu, H. Chen, T. Liu et al., “Image encryption by using gyrator transform and Arnold transform,” Journal of
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AUTHOR
           M.SIRISHA completed her graduation from Andhra University, Visakhapatnam. She is currently pursuing
           her final semester post graduation in MCA in ANITS Engineering college a premier private engineering
           college in Visakhapatnam.


           SVVS LAKSHMI has received her MCA from Andhra University, Visakhapatnam. Presently she is perusing
           her MTECH in Andhra University. She is working as Assistant Professor in ANITS Engineering College,
           Visakhapatnam.




Volume 3, Issue 5, May 2014                                                                                   Page 277

				
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Description: International Journal of Application or Innovation in Engineering & Management (IJAIEM) Web Site: www.ijaiem.org Email: editor@ijaiem.org Volume 3, Issue 5, May 2014 ISSN 2319 - 4847