A Modified Binary Encryption Algorithm based on Diffuse Representation

International Journal of Advanced Engineering, Management and Science (IJAEMS) [Vol-3, Issue-8, Aug- 2017]
https://dx.doi.org/10.24001/ijaems.3.8.1 ISSN: 2454-1311
www.ijaems.com Page | 825
A Modified Binary Encryption Algorithm based
on Diffuse Representation
Dr. S. Radhakrishnan1
, R. Arthy2
, M. Sivasankari3
, B. Jegajothi4
, Dr. M. Mohamed
Sathik5
1,2,3,4
Department of Information Technology, Kamaraj College of Engineering and Technology, Virudhunagar, India
5
Pricipal, Sathakathulla Appa College, Tirunelveli, India
Abstract— In the era of Internet, the multimedia data can
be used by anyone. There is a chance that unintended
users get access to the data so, encryption is needed to
hide the multimedia data from the unauthorized users.
This paper proposes a modified binary encryption
algorithm based on diffuse representation. Here a binary
image is XORed with a random matrix and is divided into
more number of non-overlapping sub-images. The
modified encryption algorithm will produce an encrypted
image with ¼th of dimension and increased number of
bits. The proposed encryption algorithm is a symmetric
encryption algorithm. The number of keys generated is
equal to the number of non-overlapping sub-images. The
key shall be transmitted by a private key encryption
algorithm. The encryption of the key is not of interest in
this paper. The proposed algorithm has high performance
that it gives BER as 0% and infinite PSNR. Even
grayscale images can be encrypted using this algorithm
considering each bit-plane as a binary image.
Keywords— BER, Encryption, Private Key Encryption,
PSNR, Symmetric Encryption.
I. INTRODUCTION
Internet is accessible by anyone in the world. When a
multimedia data is shared through the internet there is a
danger of unintended users getting access to it. To avoid
this encryption is used. The visual cryptography
technique is to support the encryption process where the
secret information is converted into a unreadable form
[2]. Encryption is a method in which the meaningful data
is transformed into meaningless data and is sent through
the internet. To get access to the data one should do the
reverse process called the decryption to get the data in the
original form.
Encryption is originally done for the text data where the
transformed content is not understandable. Encryption
algorithms are divided into two major categories:
Symmetric and asymmetric encryption. In symmetric
encryption, the key that is used for encryption and
decryption are same. But in the asymmetric encryption,
the key used during encryption differs from that used
during decryption.
The key that is used during the cryptographic process can
be categorized into various types. The symmetric
encryption uses secret key that is shared between sender
and receiver for encryption and decryption. The
asymmetric encryption uses (private key, public key) pair
to perform the cryptographic operations. The key pair is
generated by the user and the public key is made available
to anyone. The sender encrypts the message using private
key of their own and receiver decrypts the encrypted
message using sender’s public key which is available in
public.
The various visual cryptographic schemes are mentioned
in [6], [10] for binary image, gray-colored images. [4]
address the Extended Hamming Code to generate key for
encryption and decryption through which the code is self-
correcting. A new symmetric key cryptographic algorithm
is proposed in [5] where the algorithm withstands the
security. A lossless and reversible encryption algorithm
was introduced in [1] to address the pixel oversaturation
by embedding the secret data into the several least
significant bit planes of cipher text pixels by wet paper
coding.
The algorithm [7] presents the probabilistics model which
adopts the (t, n) visual cryptography scheme. This model
efficiently manages the dynamically changing user group.
The security level is improved using the bit level
permutation technique in [8] for chaos based image
ciphers. This technique proves better performance
because the bits are shuffled between different bit planes.
The error diffusion method [9] is used to provide the
solution for management problem. This method adds a
cover image to each share to make the share visible. The
error diffusion method is also used for shadow images
[11]. This improves the quality of shadow image when
compared to the existing algorithms.
The proposed algorithm in this paper is a symmetric
encryption algorithm for binary images. The key used in
symmetric encryption algorithm should not be disclosed
publicly. The work in the paper is inspired from [3] which

uses a diffuse representation for encryption. A similar
method is used to encrypt the binary image. However, the
encryption algorithm used to encrypt the random matrix
and the key is not the intent of this paper. Any
asymmetric encryption algorithm may be used.
The rest of the paper is organized in the following
manner. Section II discusses the existing algorithm from
which this paper has been developed. Section III
discusses the proposed algorithm of encryption and
decryption. Section IV discusses some theoretical aspects
by which the security in the algorithm can be increased.
Section V discusses about the experimental results and
Section VI gives the conclusion of the paper.
II. EXISTING ALGORITHM
A novel binary encryption algorithm based on diffuse
representation is been proposed by Houas et al. In this
paper a binary image has been taken and encryption
algorithm is applied. The encryption algorithm can be
described as follows:
2.1 Encryption
(a) A binary image (I) is taken
(b) Divide the image into n non-overlapping sub-
images (I1, I2) each sub-image is taken to the size
of the full image with the remaining partitions of a
sub-image as zeros. Let it be called a share.
(c) The key for encryption β is calculated from all the
shares by using the equation (1)
β(i, j) =
1
2
[(a1(i, j) +
||I1||1
√64
) + (a2(i, j) +
||I2||1
√64
)]
(1)
(d) The encrypted shares are formed from the key and
the share by the equation (2) and (3)
𝑏 = β(i, j) − 𝑎1(𝑖, 𝑗) (2)
𝑏 = β(i, j) − 𝑎1(𝑖, 𝑗) (3)
The encrypted shares are formed by subtracting the share
from the key. Knowing the key β, the random matrix and
the encrypted shares the decryption can be done with the
following decryption algorithm.
2.2 Decryption Algorithm
(a) The encrypted shares are taken
(b) The key β is taken
(c) All the encrypted shares are subtracted from the
key and added together to from the decrypted
binary image
Here a single key is used and the number of encrypted
shares denotes the numbers of subimages. So once the
key is hacked, then the image can be easily decrypted. To
overcome this disadvantage the modified encryption
algorithm based on diffuse representation is proposed.
The proposed algorithm is discussed in section III.
III. PROPOSED ALGORITHM
The possibility of the hacker decrypting the encrypted
image can be reduced by applying the proposed modified
encryption algorithm.
Algorithm 1:
[Ien, Irm, Ikey] = Encryption [Im]
/* Notation: Im – Binary Image, Irm – Random Matrix,
Ixor – Resultant Image after XOR, Idec – Share with
Decimal values, Ikey – Key, Iencrypt – Encrypted Image
Shares, Ien – Encrypted Image
*/
1. Read the Binary image (Im)
2. Generate a random matrix (Irm) of size equal to the Im
3. Ixor = Irm XOR Im
4. Divide the Ixor into 8 shares
// Perform for 8 shares
5. For i = 1 to row(Ixor) incr 2
For j = 1 to column(share) incr 2
Idec[i, j] = decimal_conversion(Ixor)
Endfor
Endfor
6. Calculate Ikey
7. Iencrypt = Ikey – Idec
8. Concatenate all the encrypted shares to obtain Ien
Fig. 1 – Proposed Encryption Algorithm
The Fig. 1 shows the encryption algorithm in detail. The
input image is read as the binary image and a random
matrix is generated to perform XOR operation. This
converts the image matrix into a random matrix. The
matrix is scanned from left to right and top to bottom by
taking a 2 x 2 sized matrix each time and converted into a
decimal numbers. The resultant matrix is of m/2 x n/2
sized matrix of decimal numbers.
The key for each non overlapping matrix (share) is
calculated using the equation (4)
𝐵 𝑘 =
4||𝐼 𝑘||1
√𝑠𝑖𝑧𝑒
(4)
The Ikey is used to encrypt the shares and finally all the
shares are concatenated to obtain the encrypted image.
The decryption process is the reverse of the encryption
algorithm. The random matrix and keys are shared with
the end user. The share of keys are not a part of this paper.
The decryption algorithm is stated in the Fig 2.

Algorithm 2:
[Idecrypt] = Decryption [Ien, Irm, Ikey]
/* Notation: Irm – Random Matrix, Idec' – Share with
Decimal values, Ikey – Key, Ien – Encrypted Image, Ien –
Encrypted Image, Ibin - Share with Binary values, Idbin -
Binary Decrypted Image, Idecrypt - Decrypted Image
*/
1.Read the Encrypted image (Ien)
2. Divide the Ien into 8 shares
// Perform for 8 shares
3. Idec' = Ikey - share
4. For i = 1 to row(Idec')
For j = 1 to column(share)
Ibin = binary_conversion(Idec')
Endfor
Endfor
5. Concatenate all the decrypted Ibin's to obtain Idbin
6. Idecrypt = Idbin XOR Irm
Fig.2 - Proposed Decryption Algorithm
IV. THEORETICAL ASPECTS
4.1 Random matrix
The hacker when hacks the encrypted image can easily
view the original image. To avoid this situation a random
matrix is generated to increase the security level in
encryption. The matrix is a formed with 0’s and 1’s and
then XORed with the original image.
4.2 Number of Keys
The proposed algorithm uses the symmetric encryption
algorithm which takes the secret key for encryption and
decryption. As per the theory of cryptography, the
security increases when the size and number of keys
increases. The proposed algorithm has 8 keys for 8
different shares that makes the hacker feel difficult to
hack the key and identify the respective key for each
share. Since, the secret key has to be shared among the
users it has to be secured using private key cryptosystem.
4.3 Joining all the shares and shares of variable sizes
The encrypted image is a combination of all shares. The
shares can be decrypted with the respective keys. If the
keys are not in the order then it is not feasible to decrypt
the image. The keys can be send to the receiver by
shuffling and encrypting which may be baffle the hacker
to rearrange the key. There are (8! - 1) ways to shuffle the
key.
4.4 Mapping of the 2 x 2 pixel matrix to a decimal
number
The 16! ways of mapping 0000 – 1111 binary to decimal
1 – 16. One such mapping is as follows
0000 - 15 0100 - 11 1000 - 7 1100 - 3
0001 - 14 0101 - 10 1001 - 6 1101 - 2
0010 - 13 0110 - 9 1010 - 5 1110 - 1
0011 - 12 0111 - 8 1011 - 4 1111 - 0
A random mapping can be used so that the mapping may
not be deciphered by the hacker. These are some of the
methods by which security has been added to encryption
algorithm.
V. EXPERIMENTAL RESULTS
The proposed algorithm is tested with the standard images
like lena, cameraman, Barbara, baboon and Peppers.
These image are converted into binary images and taken
as test images. The binary images (I1) are encrypted and
then decrypted (I2) using the proposed algorithm. The
performance of the algorithm is calculated by using the
metrics like Bit Error Rate (BER) and Peek Signal to
Noise Ration (PSNR).
The PSNR is Peak Signal to Noise Ratio is an error
comparison metrics to ensure that the decrypted image
looks similar to the encrypted image. The PSNR value is
calculated using the formula mentioned in equation (5)
and (6).
(5)
(6)
Where,
L - Maximum fluctuation of input image
H - Height of the object
W - Width of the object
The Bit Error Ratio (BER) is the number of bit errors
divided by the total number of transferred bits during a
studied time interval. The equation (7) shows the
calculation of BER value.
(7)
Table.1: BER and PSNR of Decrypted Image
Image BER PSNR
Lena 0 Inf
Cameraman 0 Inf
Barbara 0 Inf
Baboon 0 Inf
Pepper 0 Inf
The Table 1 tabulates the BER and PSNR values for various
input binary images. The ideal value of BER is 0% and this
has been achieved by the proposed algorithm when
comparing the original binary image I1 and the decrypted
image I2. Since, the ideal value is achieved it need not be

compared with any algorithm. Similarly, PSNR is infinity for
all images which is also the ideal value. Since, the
dimensions of the original image is altered the performance
measures like Number of Pixels Change Rate (NPCR) and
Unified Average Changing Intensity (UACI) may not be
used.
VI. CONCLUSION
The security is a major factor in the data transmission.
The hacker should not be able to decipher the data even if
it is hacked. A novel algorithm is proposed to increase the
complexity of the encryption. The complexity of the
algorithm has been increased by having 1) Random
matrix XORing 2) Number of Keys Used 3) Joining all
the Shares and Shares of Various Sizes 4) Wide Range of
Mapping Function of the 2 x 2 pixel matrix to a decimal
number. The results show that the algorithm is more
secure. Also, BER and PSNR value proves that the
algorithm decrypts perfectly.
REFERENCES
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[8] Chong Fu, Jun-Bin Huang, Ning-Ning Wang, Qi-Bin
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[9] ShekhaChenthara, Deepika M.P., Dr. Varghese Paul, “A
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