Security analysis of fbdk block cipher for digital images

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
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Volume: 03 Issue: 02 | Feb-2014, Available @ http://www.ijret.org 387
SECURITY ANALYSIS OF FBDK BLOCK CIPHER FOR DIGITAL
IMAGES
M. Kiran Reddy1
, K. J. Jegadish Kumar2
1
M.E-Communication Systems, 2
Assistant Professor, Electronics and Communication Department, SSN College of
Engineering, Tamilnadu, India
Abstract
Network security is one of the major concerns in the modern world. In this regard, a strong security technique is required to protect
user data. Cryptography techniques plays an important role in secured transmission through encryption of data and thus ensuring
integrity, authenticity, confidentiality of information. Several encryption algorithms have been proposed like AES (Advanced
Encryption Standard), DES (Data Encryption Standard) and RSA. These provide very good encryption for text applications. However,
these encryption schemes appear not to be ideal for image applications. Some algorithms like GKSBC and RC6 provide very good
encryption for digital images. New techniques are emerging that are aimed at providing secured transmission of images over
networks. The FBDK (Fixed Block with Dynamic Key Size) block cipher is a new cryptography technique designed using simple
operations like XOR, substitutions, circular shifting. The FBDK algorithm is applicable for blocks of any size with key size being
dynamic for each block. It does not involve any complex mathematical operations like modular exponentiation. It is a hybrid
cryptography technique based on symmetric key and asymmetric key cryptosystems. This paper investigates the security of FBDK
block cipher for digital images against brute-force attack, statistical analysis and Differential analysis attacks. In this paper, various
security analysis tests has been discussed which are helpful in finding out whether the FBDK encryption algorithm can do secure
encryption or not. Experimental results proves the security and efficiency of FBDK cipher for images against all aforementioned
types of attacks which justifies its consideration for real time image applications.
Keywords: Cryptography, Ciphers, Encryption, Security, and cryptanalysis.
----------------------------------------------------------------------***------------------------------------------------------------------------
1. INTRODUCTION
The security of digital images is more important since the
communication of digital products over open networks occur
more and more frequently. Special and efficient technique is
needed for storage and transmission of data securely.
Encryption is the most practical security technique for digital
data in computer systems.
In order to fulfill such a task, many encryption methods have
been proposed such as DES, AES and RSA. However, these
encryption schemes appear not to be ideal for image
applications, due to bulk data capacity and high redundancy.
Also, they involve complex mathematical calculations that
require more time. In [2], FBDK block cipher was proposed,
which is capable of handling any block size with dynamic key
size based on the size of the message. The design procedure of
the FBDK algorithm is given in detail in [2]. This paper
explores the security of FBDK algorithm regarding brute
force, statistical attacks and Differential analysis in secured
transmission of digital images. The experiments carried out
along with their outcomes are discussed in detail in the
following sections.
2. SECURITY ANALYSIS AND TEST RESULTS
A good encryption technique has thoroughly rearranged pixel
positions, values transformed and visually transformed
processes. Some security analysis parameters [1] which are
done on FBDK algorithm are:
1. Statistical analysis
2. Key space analysis
3. Encryption quality
4. Differential analysis
2.1 Statistical Analysis
Shannon introduced two methods known as diffusion and
confusion which will make intruders and their attackers more
bewildered [1]. Diffusion means spreading out the influence of
a single plain image pixel over many cipher image pixels.
Confusion means, using transformations that Complicate the
dependence of statistics of the cipher image on the statistics of
the plain image [1]. The statistical analysis test is done by
finding out histogram and correlation of encrypted image with
respect to original image. The tests were performed using
Microsoft Windows 2008 on Intel(R) core(TM) i3-2350 CPU,
2.3 GHz to 2 GB of RAM using Matlab 7.0.

_______________________________________________________________________________________
2.1.1 Histogram
These are the first visual test performed by the intruders as
well as sender and receiver while decryption [1]. The
histogram of original and encrypted image must totally be
different, so that no sort of information about the original
image can be obtained from the encrypted image. Figure 1
shows the histograms of the original image “Cameraman.tif”
and its encrypted image. From the figure 1 it can be seen that
the histogram of encrypted image is completely different from
that of the original image and hence the FBDK algorithm is
highly resistant to histogram analysis and intruder can gain no
information from the encrypted image through visual tests.
Fig -1: Histogram analysis using FBDK algorithm. (a)
Original Image, (b) Histogram of Original Image, (c)
Encrypted Image, (d) Histogram of Encrypted Image.
2.1.2 Correlation Coefficient
Correlation coefficient gives the degree of similarity or
relationship between original and encrypted images [7]. Let A
be the original image and B be the encrypted image of size
MXN. Then the correlation coefficient denoted by ϓ is
calculated as,
ϓ =
 



m m n
mmn
n
mmn
m n
mmnmmn
BBAA
BBAA
))(
2
())(
2
(
))((
Where, Amn is pixel intensity at mth
row and nth
column of
original image, Bmn is pixel intensity at mth
row and nth
column
of encrypted image. Am is mean of all elements in original
image A and Bm is mean of all elements in encrypted image B.
The table 1 shows the correlation coefficient values obtained
for various images encrypted using FBDK algorithm.
Table -1: Correlation coefficient of standard Images
encrypted with FBDK algorithm
Image Size ϓ
Singer.jpg 256X256 -0.0005
Lena.tif 512X512 -0.0022
Pirage.tif 512X512 0.0006
The range of ϓ is -1 to +1. If the correlation coefficient value
is close to -1 or +1 then the original and encrypted images are
highly correlated and a significant information about original
image can be easily obtained from encrypted image. If ϓ is
close to zero then the original image and encrypted image are
highly uncorrelated and this implies the encryption efficiency
is high. From Table 1 the ϓ values obtained by encrypting
various standard images are very low (nearly zero) which
indicates that the original image and encrypted image are
highly uncorrelated and hence statistical attacks using
correlation is very difficult. The results of Histogram analysis
and Correlation coefficient tests prove that the FBDK
algorithm is highly resistant to statistical attacks. In the next
section, the algorithm’s resistance to key space analysis is
investigated.
2.2 Key Space Analysis
The key space refers to the number of bits used to encrypt
image. The key size should be large enough to tackle key
space analysis also known as brute force search attack. Here,
all possible key combinations are tried on the encrypted
message. Suppose, if the original key length used by the
receiver is of N bits, then 2N
combinations of key are possible.
If the N is very large, then it will be very difficult for the
attacker to try all the combinations. In the worse case, the
minimum number of searches the intruder must perform in
order to get the original key should be 2N/2
. The security of an
algorithm depends on its resistance to brute force search. The
proposed algorithm is analyzed against brute force search and
the experimental results prove it to be more resistant to key
space analysis. The table 1 shows the brute force search time
required with different N values and at an average decryption
time of 2.456. In the proposed algorithm the key length varies
for each block and hence it is very difficult for the attacker to
know the key length and to perform key analysis. Since, the
text and image data is highly encrypted and there is no pattern
of input seen in the encrypted output, the proposed algorithm
is also resistant to traffic analysis and release of message
content attacks.

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Table -2: Brute Force search analysis of FBDK algorithm
Key Length (in bits) Brute Force search time
(years)
128 5.61e+36
136 5.28e+38
144 1.29e+41
152 3.36e+43
The table 2 shows that if a key of length 128 bits is used then
the time required to perform brute for search is 5.61e+36
years. This is very large when compared with the lifetime of
the message that is being transmitted. Hence proposed
algorithm is highly resistant to brute force search attack or key
space analysis.
2.3 Encryption Quality
A good encryption scheme must posses high encryption
quality and low execution time [7]. In this section, encryption
quality and performance analysis tests were conducted on
FBDK algorithm using text and image files. The tests were
performed using Microsoft Windows 2008 on Intel(R)
core(TM) i3-2350 CPU, 2.3 GHz to 2 GB of RAM using
Matlab 7.0.
2.3.1 Encryption Analysis
To determine the encryption quality two tests Viz., EQ
measure, and PSNR (Peak Signal to Noise Ratio) value
calculation is performed.
2.3.1.1 Encryption Quality (EQ) measure
When an image is encrypted there will be a change in its grey
scale values. The EQ [7] measure gives the amount of
deviation of grey scale values in original and encrypted
images. Let I denote the original image and I’ denote the
encrypted image each of size M*N pixels with L grey levels.
Let HL(I) denote the number of occurrences of each grey level
L in the original image and HL(I’) denote the number of
occurrences of each grey level L in the encrypted image. The
encryption quality [7] represents the average number of
changes to each grey level L and is expressed mathematically
as,
Encryption Quality = 256
)()'(
255
0


L
LL IHIH
The table 3 gives a comparison between GKSBC and FBDK
in terms of EQ. All the images are of size 512X512 and FBDK
has high EQ values compared to GKSBC [7]. Hence, the
proposed algorithm proves to be efficient for image encryption
when compared with GKSBC.
Table -3: EQ comparison between GKSBC and FBDK
Image File EQ (GKSBC) EQ (FBDK)
Lena (512X512) 663.82 714.65
Baboon (512X512) 773.90 823.71
Girl (512X512) 894.89 939.71
2.3.1.2 PSNR Value
An efficient encryption algorithm produces an unintelligible
image [3] as output. The parameter that can be used for
determining the encryption efficiency of the algorithm is the
PSNR (peak signal to noise ratio) [4] value in decibels (dB).
Ideally, PSNR value between the actual image and encrypted
image (PSNR_A_E) should be 0 dB and between the actual
image and decrypted image (PSNR_A_D) it should be infinity
[7]. Practically an efficient algorithm give a PSNR value less
than 9 dB between actual image and encrypted image, a PSNR
value between (30-60) dB between actual image and
decrypted image. Table 2 shows the PSNR values obtained
with various standard test images taken as input to the
proposed algorithm. For all the images the PSNR value is
quite good, this also indicates that the algorithm can tolerate
various statistical attacks like the traffic analysis,
autocorrelation analysis etc. The PSNR values for decrypted
image show that the original image can be reconstructed
efficiently from the encrypted image.
Table -4: PSNR values for different Standard test images
encrypted using FBDK
Image name Dimensions PSNR_A_E
(dB)
PSNR_A_D
(dB)
Cameraman.tif 256 X 256 8.389 37.8532
Singer.jpg 225 X 225
X 3
8.6653 46.9137
Pirate.tif 512 X 512 8.9183 36.6502
2.4 Differential Analysis
Generally, the intruder tries to make slight changes such as
modifying one pixel of the encrypted image, and then
observes the change of the result. After such changes, if the
attacker is able to obtain any relevant information about
original image from the encrypted image then the algorithm
used for encryption is practically inefficient. Also, the
encrypted image must be sensitive to small changes in original
image. If a change in original image can cause a significant
change in the cipher image with respect to diffusion and
confusion, then the differential attack becomes very inefficient
on that image. The methods [1] used to study the influence of
one-pixel change on the whole image, encrypted by FBDK
are: Number of Pixels Change Rate (NPCR) and Unified
Average changing Intensity (UACI). NPCR gives the number
of pixels change rate in encrypted image when one pixel

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change occurs in original image [1]. Consider two encrypted
images T1 and T2, whose original images have only one pixel
difference. Then, NPCR of two images is defined as [1]:
NPCR=
%100*
*
),(
,
vw
jiS
ji

Where, S (i, j) = 




),(),(if,1
),(),(if,0
21
21
jiTjiT
jiTjiT
w=number of rows in an image, v=number of columns in an
image, (i,j)=Position of Pixels
Another method, UACI is unified average changing intensity
which measures the average intensity of differences between
original image and ciphered image [1]. The formula for UACI
is:
UACI =
%100*
255
),(),((
*
1
,
21


ji
jiTjiT
vw
NPCR or UACI are random variables dependent on
parameters such as the image size and format of image rather
than statistical values. For UACI the typical value taken on an
average for different image sizes is 34% and for NPCR score
the upper bound is 100% (ideal value) which indicates, it is
difficult to establish relationship between the images. One
performed test is on the one-pixel change influence on a 256
grey-scale image “cameraman.tif” of size 256X256. The
Figure 2 (b) shows the encrypted image and figure 2 (c) shows
the encrypted image obtained after one pixel value in the
original image is changed. The NPCR and UACI values for
different image sizes are listed in Table 5.
Fig -2: (a) Original Image, (b) Encrypted Image, (c) Encrypted
Image after pixel value change.
The encrypted images before and after pixel change are
completely scrambled. There is no significant information
about the original image is available in these images. From
table 5, we can find the values of NPCR and UACI to be very
close to ideal value for all size of images. This indicates that
no sort of relationship can be established between the
encrypted images.
Table 5 NPCR and UACI values for images of different sizes
encrypted with FBDK
Size NPCR UACI
128X128 99.2432% 33.254%
256X256 99.2523% 33.384%
512X512 99.3147% 33.462%
The NPCR and UACI tests prove that the FBDK algorithm is
resistant to differential analysis and hence it can be used
efficiently for digital image encryption for secured
transmission through the communication networks. Also, the
clearance of the differential analysis tests indicates that the
algorithm is also resistant to attacks like chosen plaintext,
chosen ciphertext, traffic analysis.
3. CONCLUSIONS
In modern communication world, image encryption plays a
crucial role, and hence, an efficient encryption algorithm is
necessary. The paper provides encryption efficiency analysis
and security evaluation of FBDK algorithm. The various
security analysis tests shows that FBDK block cipher can be
considered to be a real-time encryption technique for digital
images.
ACKNOWLEDGEMENTS
The authors wish to express heartful thanks to the faculty of
ECE, SSN College of Engineering, Chennai for their support
to this research.
REFERENCES
[1]. Taranjit Kaur, Reecha Sharma, “Security Definite
parameters for image encryption techniques”, International
journal of Emerging Technology and Advanced Engineering,
Volume 3, Issue 5, May, 2013.
[2]. M.Kiran Reddy and K.J.Jegadish Kumar,
“Implementation of Novel Hybrid Cryptography Algorithm”,
In press.
[3]. M. Ashwak AL-Abiachi, Faudziah Ahmad, Ku Ruhana, “
A Competitive Study of Cryptography Techniques over block
cipher”, UKSim 13th International Conference on Modelling
and Simulation, 2011.
[4]. Amitesh Singh Rajput, Nishchol Mishra, Sanjeev Sharma,
“Towards the Growth of Image Encryption and Authentication
Schemes”, International Conference on Advances in

_______________________________________________________________________________________
Computing, Communicactions and Informatics (ICACCI),
2013.
[5]. G. Chen, Y. Mao and C.K. Chui, “A symmetric image
encryption scheme based on 3D chaotic cat maps”, Chaos
Solitons Fractals 2004; 21:749-61, 2004.
[6]. Nitty Sarah Alex and L. Jani Anbarasi, “Enhanced Image
Secret Sharing via Error Diffusion in Halftone Visual
Cryptography”, IEEE International Conference on ICASSP,
1985.
[7]. S. Arul jothi and M. Venkatesulu, “Encryption Quality
and Performance analysis of GKSBC algorithm”, Journnal of
Information Engineering and Applications, vol 2, No.10,
2012.
BIOGRAPHIES
M.Kiran Reddy is currently pursuing his
Masters degree in communication systems
in SSN Collegeof Engineering,
Email-id: kiran.reddy889@gmail.com
K.J.Jegadish Kumar is working as
Assistant Professor in SSN college of
Engineering, Chennai in ECE Department.
Email-id: jegadishkj@ssn.edu.in

Security analysis of fbdk block cipher for digital images

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Security analysis of fbdk block cipher for digital images