TELKOM
NIKA
, Vol.12, No
.3, Septembe
r 2014, pp. 6
75~682
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v12i3.106
675
Re
cei
v
ed Ma
rch 6, 2
014;
Re
vised July
21, 2014; Accepted Augu
st
2, 2014
Performance of Chaos-Based Encryption Algorithm for
Digital Image
Sur
y
adi
MT,
E
v
a Nurpeti, Dhian Widy
a
Dep
a
rtment of Mathemati
cs,
Univers
i
tas Ind
ones
ia, De
pok,
1642
4, Indon
e
s
ia
*Corres
p
o
ndi
n
g
author, em
ail
:
{yad
i.mt, eva.nurp
e
ti}@sci.u
i
.
ac.id
A
b
st
r
a
ct
Presentati
on of
informatio
n
in digit
a
l form is
hig
h
ly vul
nera
b
l
e ag
aints infor
m
ati
on a
busi
n
g
.
Digita
l
imag
e is one
of digita
l infor
m
ati
on w
h
ich i
s
frequently
b
e
co
mes a targ
et of crim
e. T
herefor
e, relia
ble,
secure, an
d fast security techni
ques ar
e re
quir
ed in
d
i
git
a
l image i
n
for
m
ation. In this study, chaos-
b
a
s
ed
encrypti
on a
l
g
o
rith
m for di
git
a
l i
m
a
ge is b
u
i
l
t to im
pr
ove e
ndur
ance fro
m
brute
force a
n
d
know
n pl
ai
ntext
attack. T
he alg
o
rith
m use l
ogi
stic map as a
rand
o
m
nu
mb
er gen
erator fo
r key stream. Accordi
ng to test
and
ana
lysis, this al
gorit
hm
h
a
s key spac
e
of
10
, key sensitivity up to
10
, the key strea
m
is
proved
rand
o
m
, and the distrib
u
tio
n
of pixels val
ue from
e
n
cry
p
ted i
m
a
ge is
proved
un
ifor
m. So, it can be
concl
ude
d that
, the algorit
h
m
is very difficult
to be
cracke
d by brute force
attack and a
l
s
o
know
n pl
aint
ext
attack.
Ke
y
w
ords
: ch
aos, log
i
stic map, encrypti
on
alg
o
rith
m, dig
i
tal i
m
a
g
e
1. Introduc
tion
Perform
a
n
c
e
of an al
gorith
m
ca
n be
see
n
from th
e al
g
o
rithm e
ndu
rance security
again
s
t
attacks and
comp
utation time.
The
t
r
a
d
itional cip
h
e
r
like
Data
Encryptio
n
S
t
andard
(DE
S
),
Internation
a
l
Data En
crypt
i
on Algo
rithm
(IDEA),
Ad
vanced En
cryption Standa
rd
(AES), and
Rivest-S
ham
ir-Adlem
an
Algorithm
(RSA) requi
re
a la
rge
comp
utational time
an
d
high
computi
n
g
power. Ho
we
ver, the image encrypti
on ciph
ers are p
r
eferable whi
c
h take lesse
r
amount of time
and at the same time without
compromi
sing security
[1],[2]
To p
r
ovide
a
better
sol
u
tio
n
for the
se
cu
rity pro
b
lem
o
f
digital im
ag
e, a
numb
e
r
of imag
e
encryption
te
chni
que
s
hav
e be
en
propo
sed
in
cludi
ng
the chao
s
-b
a
s
ed
imag
e
en
cryption.
The
s
e
techni
que
s provide a goo
d
combi
nation
of spee
d,
hig
h
se
cu
rity, complexity, and comp
utation
a
l
power, et
c [
3
]-[6] Ch
ao
s-ba
sed
en
cryption also
been
extensi
v
ely studi
ed
by re
se
archers
becau
se of its su
peri
o
r in
safety and co
mplexity
[2],[
3],[6]-[12].
Cha
o
s i
s
the
type of behav
ior of a
syste
m
or fu
n
c
tion
that is rand
o
m
, sen
s
itive to initial
values,
and
ergo
dicity. F
unctio
n
that has
ch
ao
s propertie
s
wa
s called
ch
ao
s fun
c
tion. Chao
s
function have been proved very suitable to desig
n facilities for dat
a protection [
4
],[5],[13]. Wi
th
these p
r
op
erti
es, ch
ao
s fun
c
tion can be
use
d
as a ran
dom num
ber
gene
rato
r. One of the sim
p
le
function
th
at sho
w
s
the ch
aos prope
rtie
s is the lo
gisti
c
eq
uation
or comm
only
called the
logi
stic
map.
Lo
gisti
c
map fu
ncti
on is d
e
fined
as a fun
c
tio
n
:
→
,
1
which i
s
a
function of one variable
and
is a fixed param
eter. The value
of variable
in the interval
0,
1
and
in the interval
0,4
. Mea
n
whil
e, the prese
n
tation of
logistic ma
p function i
s
in the
form of iterative. It
is
:
1
(1)
whe
r
e
0
,
1
,
2
,
3
...
.
and
is
the initial value of iteration [2],[3].
In this pa
pe
r, we will
discu
ss
abo
ut se
curity of d
i
gital image
usin
g chao
s -ba
s
e
d
encryption m
e
thod, by u
s
i
ng the lo
gisti
c
map as a cha
o
s
fu
nctio
n
.
Te
sting of
algorith
m
was
done b
a
sed
on the en
cry
p
tion and d
e
c
ryption ave
r
age
time, si
ze of the key spa
c
e, an
d ke
y
sen
s
itivity analysis. Be
sid
e
that, we
condu
ct
ed a
random
ne
ss analysi
s
of key
stre
am which
gene
rated
by
these
alg
o
rit
h
m, and
unifo
rm di
strib
u
ti
o
n
analy
s
is of
pixel value
s
in the ima
ge t
h
a
t
has be
en
en
crypted.
The
analy
s
is wa
s
carrie
d o
u
t to see th
e resi
stan
ce
ag
aints
brute
fo
rce
attack a
nd kn
own pl
aintext attack.
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ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 3, September 20
14: 67
5 – 682
676
2. Encr
y
p
tio
n
Algorithm
Encryptio
n
al
gorithm fo
r
digital ima
g
e
in this pap
er u
s
e
s
lo
gi
stic m
ap
as a chao
s
function. Th
e
seq
uen
ce of t
he pr
ocess of
se
curi
ng the
digital im
ag
e can b
e
seen i
n
Figure 1 an
d
pro
c
e
ss to re
gain a
c
cess to the origin
al digital image
can b
e
se
en i
n
Figure 2:
Figure 1. Encryption Pro
c
e
s
s
Figure 2. De
cryption Pro
c
e
s
s
Figure 1
an
d
Figu
re
2
sh
ows the
flow
in securin
g
di
gital imag
es.
Functio
n
key
stream
gene
rato
r is t
he logi
stic m
ap. The in
put
of this
algo
rit
h
m are the o
r
iginal ima
ge
and the
key, the
key
is
and
λ
. The output is an imag
e that has b
een
encrypte
d
or image ha
s b
een safe. To
regai
n a
c
cess to the ori
g
i
nal imag
e, then we
do
the
decryption p
r
ocess a
s
sh
own in Fi
gu
re 2.
Input of the decryption p
r
oce
s
s are the image that
has b
een e
n
crypted
and t
he key. The
key
use
d
in
the
decryption
proce
s
s i
s
the
same
du
ri
n
g
the en
cryptio
n
p
r
ocess. T
he o
u
tput i
s
the
origin
al imag
e. Encryption
algorith
m
is d
e
scrib
ed in th
e step 1 to st
ep 5 [12]:
Step 1 : Insert the
key
,
and original im
ag
e with
siz
e
Step 2: Do
200 time
s iteration th
e l
ogisti
c
map equatio
n
(1
) and we
will get
deci
m
al
frac
tions
.
Step 3 : Check co
ndition.
Step 3a : If yes, then
do 3
times the lo
gi
stic
m
ap itera
t
ion and
we
will obtain
the
re
sults
are de
cim
a
l fraction
s , su
ch
as
.
Step 3b : If not, so the e
n
cyption pro
c
e
s
s is
done fo
r
all part of ima
ge an
d we
wil
l
obtain
encrypted im
age.
Step 4 :
Che
c
k wh
eth
e
r the iteratio
n is the last o
r
not.
Step 4a : If
yes, then do a
real tra
n
sfo
r
mation to an integer, with p
r
ocedu
re
s:
Select th
e first 15
n
u
mbe
r
b
ehin
d
the
de
cimal
fro
m
de
cimal
fraction
that
h
a
s
bee
n
placed before
( for example
), that are
the result of 3
iterations lo
gistic map. T
hen
divide 15 nu
mber to p integer
with ea
ch intege
rnya
has 3 point
s. Then take
as mu
ch
.
,
integer . Do operation mo
d 256 to each integer, so
we get
.
,
byte integer. 1 byte this integer
n
u
mb
er
is call
ed key strea
m
.
Step 4a.1 : Take th
e pixel
value information at e
a
ch
gray
scal
e as m
u
ch a
s
.
,
. Each 1 byte informatio
n of the image is
calle
d P.
Step 4a.2 : Do step 5
.
,
times
.
Ke
y
stream
De
cry
p
tion
Logi
stic
map
,
Original
Image
Enc
r
ypted
Image
Original
image
En
c
r
yp
tion
Logi
stic
map
,
Ke
y
stream
Enc
r
ypted
image
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TELKOM
NIKA
ISSN:
1693-6
930
Perform
a
n
c
e
of Chao
s-B
a
sed Encryption
Algorithm
for Digital Im
age (Suryadi MT
)
677
Step 4.b : If not, then do transfo
rmatio
n
from re
al
to i
n
teger, li
ke in
the step 4
a
, but take
by
p
integer. Then take
p
integer. Do o
peratio
n mod
256 to each
integer, so
we get
p
bytes intege
r numbe
r or
p
KS.
Step 4b.1 : T
a
ke t
he pixel i
n
formatio
n at
each pixel
grayscale by
p .
Each
1 byte
informatio
n of the image is
calle
d P.
Step 4b.2 : Do the step 5 b
y
p times.
Step 5: Do b
i
twise XO
R o
peratio
n on
e
a
ch
byte inte
ger n
u
mb
er
with every by
te image d
a
ta.
Otherwise, do:
⊕
. Back to
Step 3.
3. Results a
nd Analy
s
is
The te
st data
used
are
cat.jpg digital
im
age
gray
scal
e
an
d colo
r, with
different sizes
are
pre
s
ente
d
in Table 1.
Table 1. Te
st Data Image
Test D
a
ta
Image S
h
o
w
Image
T
y
p
e
Pixel Size
Data 1.
Cat.jpg
80
60
Data 2.
320
240
Data 3.
640
480
Data 4.
1280
960
Data 5.
2560
1920
Data 6.
80
60
Data 7.
164
123
Data 8.
8.jpg
178
132
Data 9.
269
200
Data 10.
315
234
Data 11.
96
128
Data 12.
152
203
Data 13.
Birthda
y
.
jpg
211
281
Data 14.
256
341
Data 15.
300
400
All test data in Table 1
will be used in
the encryption proce
ss to be
shown time
encryption and
decryption
of the algorit
h
m. Then it
will be
testing the durabili
ty of the chaos-
based en
cryption algorith
m
. The first test is the test
of resi
stan
ce to
brute force a
ttacks with
ke
y
sen
s
itivity an
alysis an
d d
e
t
erminatio
n of
the
size
of
t
he
key
spa
c
e
.
A
se
co
nd t
e
st
is
t
h
e
t
e
st
of
resi
stan
ce to
kno
w
n
plain
t
ext attack b
y
rando
mne
s
s of key stre
am analy
s
is
and hi
stog
ra
m
analysi
s
.
3.1 Encr
y
p
tion and De
cr
y
p
tion Time
Analy
s
is
Test
s towa
rd
all digital image test data
,
perform
ed
usin
g the sa
me key value
for both
encryption an
d decryption pro
c
e
ss. The
keys that use
d
are
0
.
1
and
4
.
Base
d on the test
results of the cat.jpg grayscale an
d col
o
r digital
imag
e, we obtaine
d an averag
e
process time
o
f
encryption an
d decryption
whi
c
h is
sho
w
n in Figu
re
3, where ea
ch image is d
o
ne by 5 attempts
experim
ent (Data 1 to Dat
a
5).
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 3, September 20
14: 67
5 – 682
678
Figure 3. Encryption and
Decryptio
n
Pro
c
e
ssi
ng Time
for cat.jpg u
s
ing the pro
p
o
s
ed al
gorith
m
Shown
in
Fig
u
re
3 th
at th
e time
betwe
en the
en
cryption a
nd
de
cryption
p
r
o
c
ess i
s
n
o
t
much
differe
nt or rel
a
tively similar. Fo
r co
l
o
r ima
g
e
s ta
ke
s time encryption
and de
crypt
i
on
pro
c
e
ss i
s
lo
nger
whe
n
compa
r
ed to the graysc
ale
image. That
is be
cau
s
e,
the encryption
pro
c
e
ss i
s
do
ne for ea
ch compon
ent of each gray
sca
l
e red, green
and blu
e
, so i
t
takes a lon
g
e
r
pro
c
e
ss tha
n
just doin
g
the
encrypt
io
n proce
s
s on a grayscale imag
e.
Time analysi
s
from this p
r
opo
se
d algo
rithm is bette
r if compare with the algo
rithm by
Gao. et. al [10]. Those
we
re shown in
Figure 4,
Fig
u
re 5, Figu
re
6, and Figu
re
7. The test data
whi
c
h was u
s
ed we
re Data
6 to Data 15 (Tabl
e 1).
Figure 4. Encryption and
Decryptio
n
Pro
c
e
ssi
ng Time
for 8.jpg usin
g the algorith
m
by Gao,et.al.
Figure 5. Encryption and
Decryptio
n
Pro
c
e
ssi
ng Time
for 8.jpg usin
g the prop
ose
d
algorith
m
0
10
20
30
40
50
60
70
Data
1
D
ata
2
D
ata
3
D
ata
4
D
ata
5
Second
Test
Data
average
encryption
time
‐
colour
average
decryption
time
‐
colour
average
encryption
time
‐
grayscale
average
decryption
time
‐
grayscale
0
1
2
3
4
5
Data
6
D
ata
7
D
ata
8
D
ata
9
D
ata
10
Second
Test
Data
average
encryption
time
‐
colour
average
decryption
time
‐
colour
average
encryption
time
‐
grayscale
average
decryption
time
‐
grayscale
0
0.2
0.4
0.6
0.8
1
Data
6
D
ata
7
D
ata
8
D
ata
9
D
ata
10
Second
Test
Data
average
encryption
time
‐
colour
average
decryption
time
‐
colour
average
encryption
time
‐
grayscale
average
decryption
time
‐
grayscale
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Perform
a
n
c
e
of Chao
s-B
a
sed Encryption
Algorithm
for Digital Im
age (Suryadi MT
)
679
Figure 6. Encryption and
Decryptio
n
Pro
c
e
ssi
ng Time
for birthday.j
pg usi
ng
the algorith
m
by Gao, et. al.
Figure 7. Encryption and
Decryptio
n
Pro
c
e
ssi
ng Time
for birthday.j
pg usi
ng
the prop
osed
algorith
m
Based
on th
e Figu
re 4 t
o
Figu
re 7, i
t
is
sh
own that the en
cryption and
d
e
cryptio
n
pro
c
e
ssi
ng ti
me on Fig
u
re
5 and Fig
u
re 7 is b
e
tter
then en
crypti
on and
de
cry
p
tion processing
time on Fi
gu
re 4
an
d Fig
u
re
6. In terms of
en
cry
p
tion an
d d
e
c
ryption
processing tim
e
,
the
algorith
m
in this propo
se
d algorith
m
is b
e
tter t
han alg
o
rithm that was u
s
ed by G
ao H, et. al.[10].
3.2 Ke
y
Sen
s
itivit
y
Analy
s
is
The valu
e of
the key th
at i
s
u
s
ed
is
always
same f
o
r
each digital
i
m
age te
st dat
a in thi
s
pape
r. While
the de
cryptio
n
process
wil
l
be te
sted
wi
th variou
s diff
erent
key val
ue.
The resul
t
s
are p
r
e
s
ente
d
in Figure 8.
(a)
(b)
(c
)
(d)
(e)
Figure 8. The
Results of Cat.jpg. (a) Pla
i
n image;
(b
) Ciph
er ima
g
e
of (a); (c) De
crypted im
ag
e;
(d)
De
crypted
image with Difference
x
1
0
; (e)
De
crypted im
age with
Differen
c
e
x
1
0
0
1
2
3
4
5
6
7
Data
11
Data
12
Data
13
Data
14
Data
15
Second
Test
Data
average
encryption
time
‐
colour
average
decryption
time
‐
colour
average
encryption
time
‐
grayscale
average
decryption
time
‐
grayscale
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Data
11
Data
12
Data
13
Data
14
Data
15
Second
Test
Data
average
encryption
time
‐
colour
average
decryption
time
‐
colour
average
encryption
time
‐
grayscale
average
decryption
time
‐
grayscale
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 3, September 20
14: 67
5 – 682
680
In Figure 8b
and Fig
u
re
8c a
r
e
sho
w
n the
re
sult
s of the encryption and
de
cryption
pro
c
e
ss sim
u
l
a
tion using cat image with the same key that is
0
.
1
,
4
.
Thus seen that the
decryption p
r
oce
s
s su
ccee
ded in op
enin
g
the origin
al data (Fig
ure
8a).
In Figure 8d
are sho
w
n th
at the attempt to decrypt using a key differen
c
e bet
ween the
value
by
10
did not su
cced t
o
get the o
r
igi
nal imag
e.
Th
is is
due to
o
ne of the p
r
o
pertie
s
of
the logi
stic
map i
s
sen
s
itive to initial va
lues. Val
ue of 0.1
a
nd 0.10
000
0
0000
0000
01
still
con
s
id
ere
d
different values by this algorithm
. But in Figure 8e,
when the difference rea
c
hes
10
the de
crypti
on p
r
o
c
cess
got the info
rmation of
o
r
i
g
inal ima
ge. I
t
sho
w
s that the nu
mbe
r
s
0.1 and
0.10
0000
0000
000
0001 i
s
con
s
i
dere
d
to be t
he same n
u
m
ber th
at is
0.1. Previou
s
ly,
have be
en te
sted u
s
in
g th
e differe
nt de
cryption
key for g
r
ayscal
e
and
colo
r ima
ges
ra
nging
from
10
to
10
. So we ge
t the sensitivity of this algorithm is up to
10
.
So we
obtain
that a b
r
ute
force
attack
woul
d be ve
ry difficult to g
e
t the ori
g
ina
l
image
informatio
n,
becau
se th
ese alg
o
rithm
s
are ve
ry
sen
s
itive to
cha
nge
s in th
e v
a
lue
of the
key.
Hist
o
g
ra
m di
splay
f
o
r ea
c
h
colum
n
in a row i
s
just
the compo
n
ents R
ed (R) that shows the
distrib
u
tion of
pixel values (Figure 9).
(
a
)
(
b
)
(
c
)
Figure 9. Hist
ogra
m
of Cat.jpg. (a)
Histo
g
ram
of Figu
re 8a; (b)
Hist
ogra
m
of Figure 8b;
(c) Hi
stogram
of Figure 8
c
3.3 Size of Ke
y
Space
The ran
dom numbe
r gen
e
r
ator
which was used
to
g
enerate
key
stream i
s
l
ogi
stic ma
p.
Keys that are
used o
n
logi
stic map a
r
e
and
, where
and
are rea
l
numbe
r. If
we u
s
e a
higher level of preci
s
ion, for
example 64-bit doubl
e preci
s
ion I
EEE standard, the preci
s
ion level
will reach
10
. So, the total of key sp
ace a
r
e
10
10
1
0
.
Time req
u
ired to exh
a
u
stive
key se
arch [1
4] can be
see
n
in Table 2.
Table 2. Time
Requi
red to
Exhaustive Key Search
Ke
y
Space
Experime
nts/s
e
c
Time Neede
d
Secon
d
Da
y
s
Years
10
10
10
1,157
10
3,215
10
10
10
1,157
10
3,215
10
10
10
1,157
10
3,215
10
10
10
1,157
10
32150
10
10
11574
32,15
It can be co
n
c
lud
ed that, the algo
rithm i
s
very difficult
to be cra
c
ke
d by brute force
attac
k
.
3.4 Rand
omness Ke
y
Str
eam
Analy
s
is
Test of ran
d
o
mne
ss p
e
rf
orme
d usi
n
g
inter
nation
a
l
standa
rd te
sting of the
Nation
al
Institute of Standards
and
Tech
nology
is mon
obits
f
r
equ
en
cy test [15]. With the initial value
0
.
1
dan
4
testing
has be
en
ca
rrie
d
out
on t
he key strea
m
s g
ene
rate
d by the
cha
o
s-
R P
i
xe
l In
t
e
n
s
it
y
V
a
lue
Fr
eque
ncy D
i
s
tr
i
b
uti
o
n
R P
i
xe
l In
t
e
n
s
it
y
Val
u
e
Fr
eque
n
cy D
i
s
tr
i
buti
o
n
R P
i
xe
l In
t
e
n
s
it
y
Val
u
e
Fr
eque
n
cy D
i
s
tr
i
buti
o
n
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Perform
a
n
c
e
of Chao
s-B
a
sed Encryption
Algorithm
for Digital Im
age (Suryadi MT
)
681
based e
n
cryp
tion algo
rithm
.
Key strea
m
test in th
e
key stre
am g
e
nerate
d
by th
e logi
stic
ma
p
are:
,
,
,
…
.,
,
,
,
, so the length of the b
i
nary se
que
n
c
e is 1
320 bit
s
.
The testing p
r
oce
dure is [1
4]:
1.
1320
2.
With the help
of compute
r
calcul
ated
until
and obtain
ed
12.
3.
Then comp
ute
|
|
√
|12|
√
1320
0
.3302891295
4.
After that, get
the
√
.
√
0.7411815059
5.
It can b
e
co
nclu
ded
with
the si
gnifica
nce l
e
vel of
1 % proven
true that th
e
seq
uen
ce
is
rand
om be
ca
use
0
.
0
1
.
Obtaine
d
fro
m
the
ra
ndo
mness an
alysis of
th
e ke
y
stre
am whi
c
h gen
erated
by
thi
s
algorith
m
is completely ran
dom. So that,
the alg
o
r
i
thm is
ver
y
d
i
ffic
u
lt to
be
c
r
ac
ke
d
b
y
k
now
n
plaintext attack that utilizes the statis
ti
cal properties
of the ciphertext.
3.5 Histo
g
ra
m Analy
s
is
The key
s
that we used is
0
.
1
and
4
, performed testing
usin
g Good
n
e
ss of fit
tes
t
[16] on digital image of the enc
r
yption pr
oc
cesss r
e
s
u
lts w
i
th
var
i
ous
s
i
zes. The results
of
test statistic values
towards grayscale
test
data di
gital
ima
ge cat.jpg with
Good
ne
ss
of
fit
method a
r
e shown in Tabl
e 3.
Table 3. Tes
t
Statis
tic
Values
for
Gr
ayscale Image
Test D
a
ta
Pixel Size
Test S
t
atis
tic V
a
lue
Data 1.
80 x 60
287.573333
3333
Data 2.
320 x 2
4
0
255.680000
0000
Data 3.
640 x 4
8
0
292.248333
3333
Data 4.
1280 x
960
265.269583
3333
Data 5.
2560 x
1920
260.445625
0000
While th
e test results for t
he test d
a
ta
of cat.jpg
col
o
r digital i
m
a
ge in vari
ou
s
sizes
are
sho
w
n in Ta
b
l
e 4.
Table 4. Te
st Statistic Valu
e for Colo
r Im
age.
Test
Data
Pixel Size
Test S
t
atis
tic V
a
lue
for Re
d (R
)
Test S
t
atis
tic V
a
lue
for Gr
een
(G
)
Test S
t
atis
tic V
a
lue
for Bl
ue (B
)
Data 1.
80 x 60
222.293333
3333
233.066666
6667
264.213333
3333
Data 2.
320 x 2
4
0
241.406666
6667
271.760000
0000
283.626666
6667
Data 3.
640 x 4
8
0
263.726666
6667
236.366666
6667
201.446666
6667
Data 4.
1280 x
960
226.920833
3333
296.332500
0000
291.493333
3333
Data 5.
2560 x
1920
231.914062
5000
225.101562
5000
231.379687
5000
With d
e
g
r
ee
s of fre
edom
256-1=255,
a
nd 1%
si
gnifican
c
e
level,
the critical v
a
lue i
s
310.45
738
82
199. It wa
s
see
n
fro
m
th
e re
sult
s of t
he expe
rime
nt are
sho
w
n
in Ta
ble 3
and
Table
4, all the test
statist
i
c value
s
le
ss than t
he
criti
c
al valu
e. It can be
co
ncl
u
ded that all
the
tested
data
proved
unifo
rmly distrib
u
te
d. As
se
e
n
i
n
Figu
re
9b
for compo
n
e
n
t R, hi
stog
ram
diagram from
the re
sults o
f
encrypte
d
i
m
age i
s
flat, whi
c
h sho
w
s the distri
bution of en
crypt
e
d
image pixel value, is unifo
rm.
Based
on th
e test results, the di
strib
u
tion
en
crypted ima
ge pi
xel value, using th
i
s
algorith
m
, is
uniform. So t
h
is
ciphe
rtext is very
difficult to be cracked
by kno
w
n plaintext attack
that utilizes th
e statistical propertie
s
of the ciph
ertext.
4. Conclu
sion
Con
c
lu
sion of
this pape
r are :
a.
Perform
a
n
c
e
of chao
s-ba
sed en
cryption
algorithm a
r
e
:
(i).
The time of encryptio
n and
decryptio
n proc
e
s
se
s are relatively similar to each grayscal
e
and color im
a
ge.
(ii).
Time of
col
o
r image
en
cryption a
nd
de
cryption p
r
o
c
e
s
s is lon
ger t
han
gray
scal
e imag
e
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 3, September 20
14: 67
5 – 682
682
becau
se on t
he col
o
r ima
ge , the pro
c
ess
of encry
ption and d
e
c
ryption
we
re
done for
each com
pon
ent grayscal
e
,
they are red
,
green, and
blue.
(iii).
Encryption al
gorithm has
key space for
10
and key sen
s
itivity that reach
e
s
10
, s
o
the algorith
m
is very difficul
t
to
be cra
c
ke
d by brute force attack.
(iv).
This e
n
crypti
on algo
rithm i
s
very difficult
to be cra
c
ke
d by kno
w
n
p
l
aintext attack, due to
the value
di
stribution
of t
he pixel
s
of
the en
crypte
d result is p
r
oved u
n
iform
(all
test
statistic value less th
a
n
the
criti
c
al val
u
e
)
an
d
key
stre
ams th
at were ge
nerated,
prove
d
to be compl
e
tely rando
m with P
va
l
u
e
= 0.74118
> 0.01.
b.
So, it can
be
con
c
lu
ded t
hat, the alg
o
r
ithm is
very
difficult to b
e
cra
c
ked by
brute fo
rce
attack a
nd al
so kno
w
n plai
ntext attack.
Ackn
o
w
l
e
dg
ments
This wo
rk wa
s sup
porte
d by
the Dire
ct
or
ate
of Research
and
Community En
gagem
ent
Universita
s in
done
sia (Initi
al Re
sea
r
ch Gr
ant PUPT
UI, No. 3355/
H2.R12/HKP.
05.00/20
14).
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W.
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