2012 International Conference on Image and Information Processing (ICIIP 2012)
IPCSIT vol. 46 (2012) © (2012) IACSIT Press, Singapore
A New Efficient Image Encryption Technique Based on Arnold and
IDEA Algorithms
Amr M. Riad 1 +, Amr H. Hussein 2, Hossam M. Kasem 2 and Atef Abou El-Azm 1
1
Faculty of Electronic Engineering, Menofia University, Menuof, Egypt
2
Faculty of Engineering, Tanta University, Tanta, Egypt.
Abstract. In this paper, a newefficient image encryption technique ispresented.It is based on a combination
between chaotic Arnold’s cat map and the international data encryption algorithm (IDEA) in order to meet
therequirements of secure image transfer. First, the IDEA accepts a 128 bits secret key which is used to
generate an encryption key. The encryption key length equals the original image width (w). Second, the
encryption key is used to generate the encryption matrix. The rows of the encryption matrix are formed by
making successive (N-decimal) rotations from the encryption key. Third, the encryption matrix is simply
XORed with the original image to produce a primary encrypted image. Finally, the Arnold cat map is used to
shuffle thepositions of the primary encrypted image pixels to produce the final encrypted image. The results
of several experimental, statistical analysisand key sensitivity tests showed that the proposed image
encryptionscheme provides an efficient and secure way for imageencryption.
Keywords: image encryption, arnold cat map, international data encryption algorithm (IDEA).
1. Introduction
Among the many expressions of information, the image isbecoming a mainstream means of expression
with its uniquevisual, direct-viewing, lively and other characteristics. In orderto ensure the security of digital
images, researchers have putforward a lot of encryption algorithms. In recent years, with thechaos theory
carried out and rapidly developed, many scholarsbegan to turn their sights on chaotic cryptography, and
haveproposed many image encryption algorithms chaos-based [1].
Arnold’s cat map (ACM) [2-4] in recognition of Russian mathematician Vladimir I. Arnold, who
discovered it using an image of a cat. It is a simple and elegant demonstration and illustration of some of the
principles of chaos – namely, underlying order to an apparently random evolution of a system. An image (not
necessarily a cat) is hit with a transformation that apparently randomizes the original organization of its
pixels.
The pixels rapidly degenerate into a television-static of chaos by iteration number five, with some
unintelligible order prominent in a number of iterations prior to the original image reappearing on the
fifteenth iteration. Therefore, the image is said to have a period of fifteen. From point of view, the ACM has
two main disadvantages that are; after a number of iterations of the ACM, the original image will return, and
the histogram of the encrypted image is the same as the histogram of the original image. This is due to the
fact that the pixel values themselves didn’t change [5].
A well-known cryptographic algorithm is the IDEA. It came into picture in 1990. IDEA uses algebraic
operations completely and it entirely avoids the use of any lookup tables or S-boxes [6-8]. IDEA most of
which are used in text or binary data. It is difficult to use them directly in multimedia data. Multimedia data
are often of high redundancy, of large volumes and require real-time interactions, such as displaying, cutting,
+
Corresponding author. Tel.: +2 01224751185.
E-mail address: amr_riad@msn.com.
140
copying, bit rate conversion, etc. videos with these ciphers directly are time consuming and not suitable for
real-time.
In this paper, a new efficient image encryption technique based on a combination between Arnold’s cat
map algorithm and the international data encryption algorithm (IDEA) is presented. The proposed technique
follows four steps; first, the IDEA accepts a 128 bits secret key which is used to generate an encryption key.
The encryption key length equals the image width (w). Second, the encryption key is used to generate the
encryption matrix. The rows of the encryption matrix are formed by making successive (N-decimal) rotations
from the encryption key. Third, the encryption matrix is simply XORed with the original image to produce a
primary encrypted image. Finally, the Arnold cat map is used to shuffle thepositions of the primary
encrypted image pixels to produce the final encrypted image.
The performance of the proposed technique is measured through a series of statistical tests. These tests
included entropy measurement, histogram analysis, processing time measurement, irregular deviation,
histogram deviation, correlation analysis, key sensitivity, and exhaustive key search. The results of these
experimental, statistical analysisand key sensitivity tests showed that the proposed image
encryptiontechnique provides an efficient and secure way for imageencryption. The proposed technique run
time is much smaller than the individual IDEA algorithm.
On the other hand, compared to the Arnold algorithm, the proposed technique provides higher entropy,
relatively uniform distributed encrypted image histogram, better irregular deviation, higher histogram
deviation, and extremely high NPCR tests values greater than 99. Furthermore, the image decryption with a
slightly different key fails completely to recover the original image. So, the proposed image encryption
technique is highly key sensitive.
2. Statistical Analysis Used to Test the Proposed Technique
Different statistical tests are used to evaluate the performance of the proposed techniqueentropy,
Irregular Deviation, Histogram Deviation, Correlation, Correlation, Key sensitivity Test and NPCR and
UACI [9-10].
3. Proposed Image Encryption Technique
In this paper, a new efficient image encryption technique based on a combination between chaotic
Arnold’s cat map and the international data encryption algorithm (IDEA) is presented.Fig.1 shows the block
diagram of the proposed image encryption technique. The proposed scheme follows these steps:
1. The image is transformed into a square × matrix.
2. The IDEA accepts a 128 bits secret key which is used to generate an encryption key from the input
1 vector “0, 1, 2, 3, 4, 5, …….., W”.
encryption matrix. The rows of the encryption matrix are formed by
3. Generation of the ×
making successive (N-decimal) rotations from the encryption key.
4. The encryption matrix is simply XORed with the original image to produce a primary encrypted
image.
5. Arnold cat map is used to shuffle thepositions of the primary encrypted image pixels to produce the
final encrypted image.
Fig. 1: The block diagram of the proposed image encryption technique.
141
4. Experiimental Analysis
A
In this section, the performancee of the propposed techniq
que is measuured throughh a series of tests. Thesee
tests includded entropy measurement
m
t, histogram analysis, prrocessing tim
me measurem
ment, irregulaar deviation,,
histogram deviation,
d
corrrelation anaalysis, key seensitivity, and
d exhaustive key search.
4.1. Statisstical analyysis
Some experimental
e
results are given in thiis section to demonstratee the efficienncy of our scheme.
s
Thee
original-imaage with thee size 256 256 is shown in Fig. 2(a) and thee histogram of the origin
nal-image iss
shown in Fiig. 2(b).
(a)
(b)
F 2: Originaal-image and its
Fig.
i histogram (a) original-im
mage; (b) histoogram of the ooriginal-imagee.
Fig.3 shhows the enccryption proccedure of thee cameraman
n image usingg the propossed techniquee. The secrett
key is takenn as 128 bitss key “'3032';'3334';'35366';'3738';'393
30';'3032';'33334';'3535'” ((in hexadecim
mal). In thiss
case, only 5-decimal suuccessive rootations of thhe encryptio
on key are used.
u
The sttatistical anaalysis of thee
proposed teechnique are listed in tabble (1) comppared to the ACM. The proposed
p
tecchnique resu
ults in higherr
entropy thann ACM, goood correlation between thhe original im
mage and thhe encrypted image, smalller and thuss
better irreguular deviatioon than ACM
M, high histtogram deviaation of 1.00031 which iss much greaater than thee
ACM histoggram deviatiion which eqquals zero. The
T NPCR teests indicate that the propposed techniique is moree
efficient andd immune too differential attacks thann ACM as listted in table (1).
( The propposed techniq
que providess
a uniform histogram
h
com
mpared to ACM as show
wn in Fig. 4.
Fig. 3: Thhe encryptionn procedure off the cameram
man image.
(a)
(
(b)
Fig.4: Thhe histogram of
o the encryptted image usin
ng (a) Proposeed technique, ((b) ACM.
142
Tablle. 1: Statisticcal Analysis off the Proposed
d Technique compared
c
to A
ACM.
Statistical Analysis
En
ntropy
Coorr2
Irrregular Deviaation (DI)
Hiistogram Devviation (DH)
Time Consuming (Hole Proocess)
NP
PCR (first pixxel change)
NP
PCR (Middlee pixel changee)
NP
PCR (Last pixel change)
Prroposed Tech
hnique
7.9940
0.0024
0.5934
1.0031
0.534 secc
99.9985
99.9985
99.9985
A
Arnold
Chaottic Map (ACM
M)
7.00097
0.00006
0.77165
0
0.0944963 sec
0
0
0
4.2. Key sensitivity
s
t
test
In this section we introduced several
s
key sensitivity
s
teests using thhe secret keyy with differrent decimall
rotations off the generateed encryptionn key.
For 5-ddecimal rotattions, the keyy sensitivity analysis sho
ows that chaanging one bbit in the seccret key willl
result in a completely different cippher image. In Fig. 5, we
w have shoown the resuults of some attempts too
encrypt imaage with sligghtly differennt secret keyys than the on
ne used for the
t encryptioon of the original image..
Particularlyy, in Fig. 5(aa) and Fig. 5(b)
5
respectively, the oriiginal imagee and the enccrypted imag
ge producedd
using the secret
s
key “'3032';'3334
“
4';'3536';'37338';'3930';'3032';'3334';'35535'” (in heexadecimal) are shown,,
whereas Fig. 5(c) annd Fig. 5(d) show thhe encrypteed images produced uusing the secret keyss
“'2032';'33334';'3536';'3738';'3930';'30032';'3334';'33535'”and“'3
3032';'3334';'3536';'3738';;'3930';'3032
2';'3334';'353
4'” respectivvely.
In Fig. 5, we have shown the original imaage as well as the threee encrypted images prod
duced in thee
aforesaid stteps. It is noot easy to coompare the encrypted
e
im
mages by sim
mply observing these images. So forr
comparisonn, we have calculated
c
thhe correlationn between the
t corresponnding pixelss of the threee encryptedd
images. Forr this calculaation, we havve used the saame formula as given in Eq.
E (5) exceppt that in thiss case A andd
B are the vaalues of corrresponding pixels
p
in the two encryptted images too be comparred. In Tablee 2, we havee
given the results
r
of thee correlationn coefficientts between the
t corresponnding pixelss of the threee encryptedd
images A, B and C. It is clear from
m the table that
t
no correelation existss among the three encry
ypted imagess
even thoughh these have been producced by using slightly diffe
ferent secret keys.
k
The imaages after the decryptionn of the encryypted image (shown in Fig.
F 6(c)) witth the originaal secret keyy
“'3032';'33334';'3536';'3738';'3930';'30032';'3334';'33535'” and Fig.
F 6(d) shows the deccrypted imag
ge using thee
key “'30322';'3334';'35336';'3738';'39930';'3032';'3334';'3534'”.. It is clear that the deccryption witth a slightlyy
different key fails comppletely and heence the propposed image encryption procedure
p
is highly key sensitive.
s
(a) Original
O
imagee
(b) Encrypteed image with original key
'3032';'3334';'3536'';'3738';'3930';'3032';'3334';;'3535'
(c) Encrypted image witth key
(d) Encrrypted image w
with key
'2032';'33334';'3536';'33738';'3930';'33032';'3334';'3353
'3032';'3334';'3536'';'3738';'3930';'3032';'3334';;'3534'
5'
Fig. 5: Encrypted image with 5-decimal rotattions.
143
Table. 2: Coorrelation coeffficients betweeen the corressponding pixells of the threee different encrypted imagess obtained by
using slighttly different secret key of th
he image show
wn in Fig. 5.
Image 1
Imaage A of Fig. 5(a)
5
Imaage A of Fig. 5(a)
5
Imaage B of Fig. 5(b)
5
( Original im
(a)
mage
Image 2
Imagge B of Fig. 5(b)
5
Image C of Fig. 5(c)
5
Image C of Fig. 5(c)
5
Corrrelation coeffiicient
0.0217
-0.0819
0.1028
(b) Encrypted im
mage with origginal key
'3032';'3334';'3536';'33738';'3930';'33032';'3334';'
3535'
(c) Decryppted image wiith original key
(d) Decrypteed image with key
'3032';'33344';'3536';'37388';'3930';'3032';'3 '3032';'3334';'3536';'33738';'3930';'33032';'3334';'
334';'35355'
3534'
Fig. 6: Keey sensitivity test
t results forr the 5-decimaal rotations.
In the same way, the key sensitiivity tests forr 10, 15, 20, and 25 decim
mal rotationss are made. The
T resultantt
correlation coefficients are listed in table (3).
Table. 3: Coorrelation coeffficients betweeen the corressponding pixells of the threee different encrypted imagess obtained by
using sligghtly differentt secret key off the cameram
man image.
Imagee 1
Image 2
Correelation
coefficieents at 10
decimalss rotation
Correlation
n
coefficients att 15
d
decimals
rotattion
Correlation
coeffiicients at 20
decimals rotation
Correlattion
coefficientss at 25
decimals ro
otation
Imagee A
Imagee A
Imagee B
Image B
Image C
Image C
0.00213
-0.00792
0.11039
0.0211
-0.0786
0.1041
0
0.0212
-00.0788
0
0.1032
0.0186
6
-0.0802
0.1035
5
5. Conclu
usions
In this paper, a neew efficient image encrryption techn
nique based on a combination betw
ween chaoticc
orithm (IDEA
A) is presentted. The perrformance off
Arnold’s caat map and thhe internatioonal data enccryption algo
the proposeed techniquee is measured through a series of teests. These tests includedd entropy measurement,
m
,
histogram analysis,
a
proocessing tim
me measurem
ment, irregu
ular deviatioon, histogram
m deviation,, correlationn
analysis, keey sensitivityy, and exhausstive key seaarch. The results of these experimentaal, statisticall analysisandd
key sensitivvity tests shoowed that thhe proposed image encry
yptiontechniqque providess an efficientt and securee
way for im
mageencryption. The prooposed technnique run tim
me is muchh smaller thaan the indiv
vidual IDEA
A
algorithm. On
O the otherr hand, com
mpared to thee Arnold alg
gorithm, the proposed tecchnique prov
vides higherr
entropy, unniformly disstributed enccrypted imagge histogram
m, better irrregular deviation, higheer histogram
m
deviation, and
a extremely high NPCR
R tests valuees greater thaan 99. Furthermore, the image decry
yption with a
slightly diff
fferent key fails
f
complettely to recovver the origiinal image. So, the propposed imagee encryptionn
procedure iss highly key sensitive.
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