TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.1, Jan
uary 20
14
, pp. 635 ~
643
DOI: http://dx.doi.org/10.11591/telkomni
ka.v12i1.3482
635
Re
cei
v
ed
Jun
e
17, 2013; Revi
sed
Jul
y
1
7
, 2013; Acce
pted Augu
st 13, 2013
Plaintext Related Image Encryption Scheme Using
Chaotic Map
Yong Zhang
Schoo
l of Softw
a
r
e a
nd Com
m
unic
a
tion En
gin
eeri
ng, Jia
n
g
xi Univ
ersit
y
o
f
F
i
nance an
d
Econom
ics
Nanc
han
g, PR Chin
a, Ph./F
ax: +
086-152
70
0
150
09/7
918
38
457
02
e-mail: zh
ang
yong
@j
xufe.e
du
.cn
A
b
st
r
a
ct
A plai
ntext rela
ted imag
e bl
oc
king e
n
cryptio
n
algor
ith
m
is pr
opos
ed i
n
this pap
er, w
h
ich i
n
clu
des
tw
o kinds of op
eratio
ns on
inn
e
r-block c
onfus
ion a
nd i
n
te
r-b
l
o
ck diffusi
on. F
i
rstly, a float-p
oint lo
oku
p
tabl
e
nee
d to be ge
n
e
rated by iter
ating ch
aotic sys
tem w
i
th
the se
cret keys as the initi
a
l val
ues
and p
a
ra
met
e
r
s
;
Secon
d
ly, cho
o
se on
e of the
entries in th
e
look-u
p
tabl
e accord
ing to t
he pix
e
l val
u
e
derive
d
from
the
plai
n-i
m
age
as
initia
l va
lu
e of
chaot
ic syste
m
, and
iterate
it to pro
duc
e
o
ne
secret cod
e
se
que
nce for
in
n
e
r
-
block co
nfusi
o
n; T
h
irdly, by u
s
ing o
ne
pixe
l valu
e of t
he for
m
er
block to l
o
cate an
other e
n
try in the l
ook
-u
p
table, w
h
ich to be e
m
pl
oye
d
a
s
the
new
initia
l value of the c
haotic syste
m
, iterate it to yiel
d anoth
e
r secr
et
code s
e
q
uenc
e for inter-
bl
oc
k diffusio
n
; F
i
n
a
lly, thro
ug
h tw
o rounds
of the b
l
ock-by-
b
l
o
ck proc
esses,
th
e
plai
n-i
m
age
w
ill b
e
tra
n
sfor
med
into
the c
i
pher-i
mag
e
. The s
i
mul
a
tio
n
results s
how
that the
pr
op
o
s
e
d
meth
od
has g
o
od ch
aracters,
such as l
a
rg
e
key spac
e,
fast encryptio
n sp
eed, stro
n
g
ke
y sensitivity, a
n
d
hig
h
security a
gai
nst the brut
e-force a
ttack and the c
hose
n
pla
i
ntext atta
ck, etc.
Ke
y
w
ords
: image e
n
crypti
on
, chaotic map, plai
ntext relat
e
d ciph
er, cryptana
lysis
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
A great de
al
of research
on chaoti
c
sys
tem ba
sed
image e
n
cryption technol
ogy ha
s
sprung
up
sin
c
e 1
989 [1
-9]
and
seve
ral o
f
them
have b
een
chall
eng
ed si
nce 20
0
3
. For
exampl
e,
the encryptio
n algo
rithms
prop
osed in [
4
-6] hav
e b
e
en crypt-an
al
yzed in [7-9] by using
ch
o
s
en
plaintext attack o
r
other
attack meth
o
d
s. In t
hese
resea
r
ch wo
rks, the main
reason for l
o
w
se
curity is th
at the se
cret
cod
e
stream
s us
ed to e
n
crypt the plain-i
m
age a
r
e onl
y relied on th
e
se
cret
key
b
u
t bea
r n
o
relation to th
e plain
-
ima
g
e
. Awa
r
e
of
this d
e
ficie
n
cy, an en
cryp
tion
scheme
whi
c
h uses th
e si
ze of pl
ain-i
m
age a
s
p
a
rt o
f
secret
keys wa
s propo
se
d [10], but this
method
ha
s
defect i
n
aga
inst time
atta
ck;
Anot
he
r
schem
e i
n
trod
uce
d
the
h
a
sh code
of
pla
i
n-
image a
s
part of
the secret keys [11]. It has
high secu
rity but need
s an extra private se
cret
cha
nnel to tra
n
smit the ha
sh cod
e
whi
c
h
increa
se
s the
burde
n of co
mmuni
cation.
Re
cently, Zh
ang et al. propo
sed a
n
image
e
n
cryp
tion method
based on tot
a
l shuffling
scheme [1
2]. This meth
od i
s
ch
aracte
rized in that
the
secret code
strea
m
used i
n
encryption i
s
not only asso
ciated
with the key, but also the plai
n im
age. Ho
weve
r, the first se
cret co
de in [1
2]
is in
dep
ende
nt of plai
n im
age, a
nd th
at ma
ke it i
s
no
t safe
eno
ugh
to resi
st the
cho
s
e
n
pl
aint
ext
attack, this i
s
pointe
d
ou
t and crypt-a
nalyze
d
in [13]. Eslami et al. sugge
ste
d
an improv
ed
algorith
m
[14
]
over these
sho
r
tco
m
ing
s
describ
ed
in
[13]. Two major imp
r
ove
m
ents of it are to
use previous ciph
er
im
age pixels
to
exe
c
ute “ad
d
mo
dulu
s
an
d xor” op
eratio
ns i
n
stea
d of plai
n
image
pixels,
and
to e
n
large the
iteratio
n times of
ch
aotic
syste
m
i
n
every
ro
un
d. That m
ade
the
image en
cry
p
tion schem
e
propo
se
d in [12] was hi
gher
se
curity
against the
cho
s
e
n
plaint
ext
attacks b
u
t sl
owe
r
the e
n
cryption spee
d
as the
co
st. Similar to the
scheme
of [12], some
pl
ain
image relate
d image e
n
cryption metho
d
s
were prop
ose
d
[15-16], in whi
c
h the
information
of
plain imag
e was u
s
ed to de
termine the p
a
ram
e
ters an
d iteration tim
e
s of the ch
a
o
tic map
.
More
recently, Ahmed A.
Abd El
-Latif
et al.
pre
s
e
n
ted a
plai
n-image
rel
a
te
d ima
ge
encryption schem
e called
BES-w/
r/b, where ‘BE
S
’ meant
bl
ock encrypti
on
scheme,
‘w’
rep
r
e
s
ente
d
t
he n
u
mbe
r
of bits i
n
e
a
ch
pixel,
‘r’ in
dicated the
num
ber
of roun
ds, and ‘
b
’
wa
s
the
key le
ngth
(in
bytes) [17]. I
n
this sch
e
m
e
, the
fou
r
o
n
e
-dim
en
siona
l ch
aotic sy
stems
are u
s
e
d
to
encrypt the p
l
ain imag
e, b
l
ock by
blo
c
k. The sh
ortn
ess of this
schem
e is th
a
t
the encryption
speed will
be very slow when the va
lue
of ‘r’ is large.
Interestingl
y, Ahmed A. Abd El-Latif et al
.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 230
2
-
404
6
TELKOM
NIKA
Vol. 12, No
. 1, Janua
ry 2014: 635 – 6
4
3
636
seem
ed to have discovered the defi
c
iency, and on
ly gave the
sim
u
lation results for BES-32/2/16
(r=2). B
u
t even with
r=2, t
he
s
pee
d of
encryption i
s
less optimi
s
ti
c
a
nd slo
w
er comp
ared
to the
other fou
r
en
cryption
sche
mes tabul
ate
d
in [17].
In
2012, we sug
g
e
s
ted
a plain
ima
ge
relat
ed
ima
g
e
encryption method with
two
level
s
of se
cret
key
s
[18]. T
h
is schem
e
can
withdra
w
the
e
x
isting p
a
ssiv
e attacks effe
ctively, but th
e
encryption sp
eed ne
ed to be furthe
r im
proved. O
n
the basi
s
of the
s
e research
e
s
, a new
ch
a
o
tic
system b
a
se
d image e
n
cryption meth
od is p
r
op
osed in this pa
per. Sectio
n 2 describe
s
the
cha
o
tic sy
ste
m
and the de
tailed image
encryption
scheme for thi
s
method. Section 3 provid
es
some si
mulation result
s
by us
ing MA
TLAB to demonst
r
ate the
feasibility of the proposed
method. Se
ct
ion 4
di
scusses th
e
se
cu
rity perfo
rman
ce of
the pro
posed schem
e
center
o
n
t
he
se
cret
key
space, statisti
cal p
r
o
pertie
s
of
the cip
her
im
age, NPCI
a
nd UACI,
informa
t
ion
entropy,
and resi
sting cho
s
en
plaintext a
ttack, etc.
2. Proposed
Encr
y
p
tion
Scheme
2.1. Used
Ch
aotic Sy
stem
The tri
angul
a
r
ma
p of di
screte fo
rm
sho
w
n in
(1) i
s
e
m
ployed i
n
th
e propo
se
d schem
e,
whe
r
ein,
a
a
nd
b
are its para
m
eters.
Whe
n
the values of
a
an
d
b
belon
g to the interval [3.57,
4.00], Eq. (1) has
cha
o
tic a
ttractor, an
d the state valu
es of
x
n
and
y
n
range in (0,1) [19].
1
1
(1)
2.2. Basic Pr
inciple of Encr
y
p
tion
The ba
sic p
r
i
n
cipl
e of the
prop
osed en
cryption sche
me is sho
w
n i
n
Figure 1. Fi
rstly, the
se
cret
key i
s
rega
rd
ed a
s
t
he initial valu
es a
nd the
p
a
ram
e
ters of
the ch
aotic
m
ap. Iterate the
cha
o
tic
syste
m
to o
b
tain
a floating
-
poi
nt form
of lo
ok-up
table
(size of
256
entrie
s
) an
d
two
pse
udo
-rand
om num
bers
whi
c
h
will be
use
d
a
s
the
initial value
s
of the chaotic system. Iterate
the chaoti
c
sy
stem to
ge
ne
rate the
secret
co
de
stream
s fo
r the
first
block
of the
p
l
ain im
age
an
d
yield the first block of the ciph
er imag
e;
Secondly, after obtainin
g
the ciphe
r im
age blo
ck
n
-1,
two n
e
w ra
n
dom n
u
mb
ers a
r
e
gen
era
t
ed by
cont
i
nuing
iteratin
g the
ch
aoti
c
m
ap, a
nd
are
transfo
rme
d
i
n
to intege
rs t
o
locate the p
i
xel in block
n
of the plain i
m
age. Th
e value of the
pi
xel
is used to
search the lo
ok-up
tabl
e for the ent
ry with co
rres
p
ondin
g
value
,
and the en
try’s
conte
n
t se
rves a
s
the n
e
w
initial valu
es of t
he
ch
aotic ma
p which i
s
iterated to gen
era
t
e the
rand
om nu
m
bers for
encry
pt
ing the plai
n image
blo
c
k
n
; Thi
r
dly, the ra
ndom
n
u
mbe
r
s
gene
rated
in
the previo
us step
are employed
to
encrypt the
p
l
ain ima
ge
bl
ock
n
to
pro
duce the
ci
p
her
image bl
ock
n
, whi
c
h
will be cycl
ed by
2 rounds. Finally
, the whol
e encryption
process i
s
cy
cled
by 2 roun
ds f
r
om the pl
ain
image by th
e se
cret
key
transfo
rmin
g
to the ciph
er
image, an
d the
decryption p
r
oce
s
s is the reve
rse of the encryption on
e.
Figure 1. Basic prin
cipl
e di
agra
m
of encryption sche
me
2.3. Encr
y
p
tion Scheme
Encryptio
n
schem
e en
crypts the pl
ain
image into
the noi
se-li
k
e cip
her i
m
a
ge, and
therein th
e pl
ain image
an
d the se
cret key are inp
u
ts,
while the
cip
her ima
ge an
d the en
crypti
on
time are outp
u
ts. The detai
led step
s are as follo
ws:
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Plaintext Rel
a
ted Im
age Encryptio
n
Sc
h
e
m
e
Using
Chaotic Ma
p (Yong Zha
ng)
637
(1)
Giv
en t
h
e
se
cret
key
K
={
k
1
,
k
2
,
k
3
,
k
4
}, 0<
k
i
<1,
i
=1,
2, 3, 4, the param
eters of
Eq. (1)
are
a
=3.5
7+0
.
43×
k
1
,
b
=3.5
7+0.4
3
×
k
2
, and its initial v
a
lues are
x
0
=
k
3
,
y
0
=
k
4
. Then, iterate Eq.
(1)
to gen
erate a
seque
nce
{(
x
i
,
y
i
),
i
=1,2,…,132}, wh
erei
n, {(
x
i
,
y
i
),
i
=1,2,…,128} is u
s
ed a
s
the look-
up table
(na
m
ed by
LT) o
f
size 25
6, in
whi
c
h e
a
ch e
n
try is
noted
by
e
i
,
i
=0,1,2,
…
,255, satisf
ying
e
2
i
-2
=
x
i
,
e
2
i
-1
=
y
i
,
i
=
1
,2,…,128.
(2) Sup
p
o
s
e that the grayscale plai
n image
P
is of
size
m
=
M
×
N
. Divide
P
into
u=
/
1
6
blocks, whe
r
ein
rep
r
e
s
e
n
ts the sm
allest intege
r value of not less than
x
(t
herei
nafter th
e
same m
eani
n
g
). Each
block co
ntain
s
16
pixels, and if
the last blo
c
k ha
s less th
an 16 pixel
s
, the
block sh
ould
be padde
d to 16 pixels wi
th ze
ro
s. Denote ea
ch b
l
ock by
P
i
,
i
=
0
,1,…,
u
-1, and
P
i
=
p
i
,0
p
i
,
1
p
i
,
2
,…,
p
i
,
15
, then
p
ij
rep
r
e
s
e
n
ts the value of
the
j
-th pixel in the
i
-th bl
ock,
i
=
0
,1,…,
u
-1,
j
=0,1,2,…,15.
Therefo
r
e, th
e plain imag
e
P
=
P
0
,
P
1
,…,
P
u
-1
.
(3) Tra
n
sfo
r
m
(
x
129
,
y
129
) into two integers
k
1
and
l
1
by
usin
g
k
1
=
1
0
mod 16
and
l
1
=
1
0
mod 256,
then lo
cate
the
k
1
-th pixe
l in the blo
ck
P
0
, who
s
e v
a
lue i
s
,
. Let
,
mod 256, th
en locate the
d
1
-th ent
ry in the LT, who
s
e value i
s
. And
refresh
x
129
with
x
129
=(f
o
rmer
x
129
+
) mod
1.
(4) Use val
u
e
s
of
(
x
129
,
y
129
) as the
initial v
a
lue
s
of Eq.
(1), an
d iterate the
cha
o
tic
map to
gene
rate 9 p
a
irs of value
s
, denoted by (
,
,
,
),
i
=0,1,2,…
,8, wherei
n the former ei
gh
t pairs of
values are arrang
ed into a vector, deno
ted by
h
0
,
h
1
,
h
2
,...,
h
15
, s
a
ti
s
f
ying
h
0
=
,
,
h
1
=
,
,
h
2
=
,
,
…,
h
15
=
,
. Each
h
i
is
conve
r
ted into the
integer
g
i
with formulatio
n
g
i
=
1
0
mod 2
56,
i
=0,1,2,…,15,
and the later are use
d
to do “ad
d
and
modulu
s
” op
eration
s
with
the 15 pixels
o
f
block
P
0
(ex
c
ept the
k
1
-th position of pixe
l
,
) by using th
e followin
g
formula.
,
,
mod
256
,
,
,
mod 256,
1
1
,
,
,
,
,
mod 256
,
,
,
mod 256,
2
15
(2)
Therefore, th
e so-call
ed bl
ock
Q
0
＝
q
0
,
0
q
0
,
1
q
0
,
2
…
q
0
,
15
is obtaine
d.
(5) Conv
e
r
t
(
x
130
,
y
130
) into
two integers
k
2
and
l
2
by
usin
g
k
2
=
1
0
mod 16 an
d
l
2
=
1
0
mod 2
56.
If
k
1
=
k
2
, then
k
2
=(
k
2
+1)
mo
d 16. Th
en lo
cate the
k
2
-th
pixel in the
b
l
ock
Q
0
, who
s
e va
lue is
,
. Let
d
2
=(
,
+
l
2
) mo
d 2
56, then lo
cat
e
the
d
2
-th en
try in the LT,
who
s
e
value is
. And
refres
h
x
130
with
x
130
=(f
o
rm
er
x
130
+
) mod
1.
(6) T
he valu
es of (
x
130
,
y
130
) are u
s
ed
as the initial
values
of Eq.
(1) an
d, iterate the
cha
o
tic m
ap
to gene
rate
9 pai
rs
of va
lues, d
enote
d
by (
,
,
,
),
i
=0,1,2,…,8, wherein the
former ei
ght pairs of values are arran
ged into a vector, de
note
d
by
w
0
,
w
1
, ...,
w
15
, s
a
tis
f
ying
w
0
=
,
,
w
1
=
,
,
w
2
=
,
, …,
w
15
=
,
. E
a
c
h
w
i
is con
v
erted into the integer
v
i
with formulation
v
i
=
1
0
mod 256,
i
=0,1,2,…,15,
and the l
a
ter
are u
s
e
d
to d
o
“ad
d
an
d m
odulu
s
”
ope
ra
tions
with the 1
5
pixels of blo
c
k
Q
0
(except
the
k
2
-th po
sition of pixel
,
) by usi
ng t
he follo
wing
formula.
,
,
m
o
d
256
,
,
,
mod 256,
14
1
,
,
,
,
,
mod 256
,
,
,
mod 256,
2
0
(3)
Therefore, th
e so-call
ed bl
ock
R
0
＝
r
0
,
0
,
r
0
,
1
,
r
0
,
2
,.
..,
r
0
,
15
is
obtaine
d.
(7) De
rive
int
eger
l
3
from
,
by usin
g
l
3
=
,
1
0
mod 25
6, an
d let
d
3
=(
q
0
,
15
+
l
3
) mod
256, lo
cate th
e
d
3
-th
entry i
n
the LT, wh
ose val
ue is
. Refres
h
,
wit
h
,
=(f
o
rme
r
,
+
) mod 1, the
n
use the values of (
,
,
,
) as the initial value
s
of Eq.
(1), and itera
t
e the
cha
o
tic map
once to gene
rate a pair of state values a
s
ne
w (
x
129
,
y
129
).
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ISSN: 230
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TELKOM
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Vol. 12, No
. 1, Janua
ry 2014: 635 – 6
4
3
638
(8) Derive an
integer
l
4
from
,
by using
l
4
=
,
1
0
mod 256,
and let
d
4
=(
r
0
,
0
+
l
4
)
mod 256, the
n
locate the
d
4
-th entry in the LT, who
s
e
value is
. Refresh
,
with
,
=(f
o
rme
r
,
+
) mod
1, then the
valu
es of
(
,
,
,
)
a
r
e u
s
ed
as
th
e in
itia
l va
lu
es o
f
Eq
. (
1
)
,
an
d
iterate the ch
aotic map o
n
c
e to gen
erat
e a pair of sta
t
e values a
s
new (
x
130
,
y
130
).
(9) Re
pla
c
e
P
0
with
P
1
, a
nd re
peat
ste
p
s
(3-6) to
o
b
tain the e
n
cryption blo
c
k
R
1
of the
plain imag
e block
P
1
. The
n
repe
at step
s (7
-8) to p
r
o
duce ne
w iterative initial value
s
(
x
129
,
y
129
)
and (
x
130
,
y
130
).
(10
)
Rep
eat step
s (7
-9) f
o
r
u
-2 times,
and repl
ace
P
0
with
P
i
(
i
=
2
,3,...,
u
-1) i
n
step (9
)
every time, seque
ntially to
produ
ce the
encryption bl
ock
R
i
(
i
=
2
,3,.
..,
u
-1) for bl
oc
k
P
i
.
(11
)
Let
R
=
R
u
-1
,
R
u-2
,
...,
R
1
,
R
0
, s
ubs
titute
P
with
R
, also repla
c
e (
x
12
9
,
y
129
) and (
x
130
,
y
13
0
)
with (
x
131
,
y
131
) and (
x
132
,
y
132
), re
spe
c
tivel
y
. Then re
pe
at step
s (3
-1
0
)
to get the fi
nal ci
phe
r im
age
C
＝
C
0
,
C
1
,
...
,
C
u
-1
.
De
cryption
scheme is the i
n
verse of the enc
ryption scheme, wh
erei
n the inputs a
r
e the
ciph
er ima
ge
and the ide
n
tical secret key
,
and the outp
u
ts are th
e ori
g
inal plain im
age an
d the
decryption time.
3. Simulate Resul
t
s
A large num
b
e
r of experim
ents are ca
rri
ed su
cc
e
ssful
ly with the propo
sed sch
e
m
e. The
followin
g
s a
r
e the re
sults
of
encrypting
the image
s (Lena a
nd Ba
boon
) as
exa
m
ples, a
s
sh
own
in Fig
u
re
2.
T
he
se
cret keys u
s
e
d
are
{
0
.9767
，，
，
0.883
4
0
.7834
0.3
401},
and
the
co
rrespon
din
g
para
m
eters
a
nd the
initial
values of Eq.
(1
) a
r
e
a
=3.9
8998
1,
b
=3.9
4986
2,
x
0
=0.7
834,
y
0
=0.340
1.
From Fig
u
re
2, we can
se
e that the cipher ima
g
e
s
are visu
ally noise
-like, and
the decrypte
d
image
s are id
entical to the
origin
al imag
es.
(a)
(b)
(c
)
(d)
(e)
(f)
Figure 2. The
result
s of Le
na and Bab
o
on. (a
) Plain i
m
age; (b
) Cip
her ima
ge of (a);
(c) De
crypte
d
image; (d) Pl
ain image; (e) Ci
phe
r imag
e of (d); (f) Decrypte
d ima
ge.
(a)
(b)
(c
)
(d)
Figure 3. Hist
ogra
m
s of Le
na and Bab
o
on. (a)
Histo
g
r
am of Figu
re
2a;
(b)
Histo
g
ra
m
of Figure 2b;
(c)
Histo
g
ra
m
of Figure 2
d
; (d) Hi
stog
ram of Figure
2e.
4. Securit
y
Performa
nce
Analy
s
is
4.1. Ke
y
Spa
c
e
S
e
cr
et
key
s
{
k
1
,
k
2
,
k
3
,
k
4
} range i
n
(0,1
),
whe
r
e,
k
1
,
k
2
and
k
3
a
r
e
correct to 1
4
decim
al
places, while
k
4
is co
rre
ct
to
13
decim
al
place
s
, so t
he si
ze of th
e key spa
c
e
is app
roximat
e
ly
10
55
(equival
ent to the ke
y of 183-bit
binary n
u
mb
ers). Mea
n
while the loo
k
-up table of le
ngth
256
can b
e
regarded
as t
he equival
ent
key agai
nst
di
fferential att
a
ck, and e
a
ch of the entri
es i
s
corre
c
t to
1
4
de
cimal
n
u
mbe
r
s,
so
the
size of t
he e
quivalen
t
key
spa
c
e
is
about
10
3584
.
Therefore the
size of the key spa
c
e is la
rge
en
oug
h to confront the
brute-fo
rce a
ttacks.
0
50
100
150
200
25
0
0
500
1000
1500
2000
2500
3000
0
50
100
150
200
25
0
0
200
400
600
800
1000
1200
0
50
100
150
20
0
25
0
0
500
1000
1500
2000
2500
3000
0
50
100
150
200
25
0
0
200
400
600
800
1000
1200
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Plaintext Rel
a
ted Im
age Encryptio
n
Sc
h
e
m
e
Using
Chaotic Ma
p (Yong Zha
ng)
639
4.2. Histogr
a
m
Take
the
hist
ogra
m
s of th
e imag
es of
Lena
and
Ba
boon
a
s
exa
m
ples,
sh
own in Fi
gure
3. From Figu
re 3, it can be seen that the hist
og
ram
of the cipher image is co
mpletely differen
t
from that of the plain ima
g
e
. Meanwhile
the histogr
a
m
of the ciph
er imag
e is flat and clo
s
e t
o
the
histog
ram of the noi
se-li
k
e i
m
age, whi
c
h
can re
si
st the
statistical att
a
cks effe
ctively.
4.3. Correla
tion Analy
s
is
Take th
e ima
ges of Le
na
and Babo
on
as exampl
es
to calculate the hori
z
o
n
tal, vertical
and dia
gon
al
correlatio
n coeffici
ents [
3
], and tabul
ate them in Table 1. Here illustrate o
n
ly
hori
z
ontal
co
rrelation
s
of L
ena a
nd its
ci
pher i
m
ag
e in
Figure 4 to
save sp
ace. T
=
10
000 i
n
bo
th
Table
1 a
nd
Figure 4. F
r
o
m
Figu
re
4 a
nd Ta
ble
1,
it
can
be
seen t
hat the
adja
c
ent pixel
s
in
p
l
ain
image a
r
e hig
h
ly relevant, while the a
d
ja
cent pi
xel
s
in ciph
er ima
ge
are ne
arly irrelevant.
Table 1. Co
rrelation coefficients
Horizontal
Vertical
Diagonal
Horizontal Vertical
Diagonal
Lena (Fig.2
a-b
)
0.9720
0.9846
0.9624
－
0.0127
0.0024
0.0032
Baboon (
F
ig. 2d-
e)
0.8685
0.7719
0.7235
－
0.0090
－
0.0069
0.0115
(a)
(b)
Figure 4. Hori
zontal
correl
a
t
i
ons of Len
a and its ci
phe
r image.
(a)
Hori
zo
ntal
correlatio
n of Figure 2
a
;
(b
) Ho
riz
ontal c
o
rr
el
ation of
Figure 2b.
4.4. Encr
y
p
tion Speed
The m
a
chine
used i
s
eq
uippe
d
with
Intel I5 M46
0
processo
r,
2GB m
e
mo
ry and
MATLAB 7. 1
000 pi
eces
of image
s
(all o
f
size
51
2×5
1
2
)
were
cho
s
en to exe
c
ute
the propo
se
d
scheme.
Th
e average
e
n
cryptio
n
o
r
de
cryp
tion
spe
e
d
s
a
r
e 0.3776
and
0.3772
se
co
nds
sep
a
rately.
Under the
sa
me conditio
n
s
, the
av
era
ge e
n
cryptio
n
an
d de
cryption
spee
ds are
about 1.5
646
and 0.7
433
seco
nd
s sepa
rately in [2
], which
are
even
faster th
an t
he conventio
nal
AES. So
the proposed is
muc
h
fas
t
er and
c
a
n be used in the practic
a
l c
o
mmunic
a
tion.
4.5. Information Entrop
y
As well kno
w
n, the theore
t
ical value of
information
entropy for 8
-
bit ran
dom i
m
age is
exactly 8. Howeve
r the entropy valu
es of
Len
a a
nd Baboo
n a
r
e abo
ut 7.4451 an
d 7.3
583,
respe
c
tively. The e
n
tro
p
y
values of thei
r
ciphe
r
im
ag
es
ill
ustrated in
Figu
re
2b
and 2d are
a
bout
7.9992 a
nd 7.
9993, respe
c
tively, which a
r
e cl
ose to t
he theoretical
value of 8. Th
erefo
r
e the
r
e
is
no inform
atio
n leakage in t
he cip
her im
a
ge.
4.6. Ke
y
Sen
s
itivit
y
4.6.1. Theore
t
ical Values
of Sensitiv
it
y
Indicators
The three in
dicato
rs
NP
CR,
UACI a
nd NMSE a
r
e u
s
ed to
demon
strate
the key
sen
s
itivity of the propo
sed
scheme [3
]. Suppo
sin
g
that the ciphe
r im
age
s
C
1
and
C
2
(both of si
ze
M
×
N
)
are obt
ained
by en
crypting same
plain im
age
with
two secret key
s
of o
n
l
y
1-bit differe
nt,
or en
crypting
two plain i
m
age
s of only
1-pixel di
ffere
nt with the sa
me key. Intro
duce a mat
r
ix
D
of size
M
×
N
.
If
C
1
(
i
,
j
)
=
C
2
(
i
,
j
)
, then
D
(
i
,
j
)
=0,
el
se
D
(
i
,
j
)
=1. Th
e NPCR, UA
CI
and
NMSE a
r
e
defined a
s
fol
l
ows.
0
50
100
15
0
20
0
25
0
30
0
0
50
10
0
15
0
20
0
25
0
30
0
P
i
xe
l
gr
a
y
v
a
l
u
e
o
n
l
o
c
a
t
i
o
n
(
x
,
y
)
P
i
xe
l
gra
y
va
l
u
e
on l
o
c
a
t
i
on(
x
+1
,
y
)
0
50
100
150
200
250
30
0
0
50
10
0
15
0
20
0
25
0
30
0
P
i
x
e
l g
r
ay
v
a
lu
e o
n
lo
cat
io
n
(
x
,
y
)
P
i
xe
l
gra
y
va
l
u
e
on l
o
c
a
t
i
on(
x
+1
,
y
)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 230
2
-
404
6
TELKOM
NIKA
Vol. 12, No
. 1, Janua
ry 2014: 635 – 6
4
3
640
NPCR
∑∑
,
100%
(4)
UA
C
I
∑∑
|
,
,
|
100%
(5)
NMSE
∑∑
,
,
∑∑
,
100%
(6)
(1) T
heo
retical value of NPCR bet
wee
n
two ran
dom
noise ima
g
e
s
As for two ra
ndom ima
g
e
s
of 8-bit grayscale, the prob
ability distribu
tion is
,
0,
,
,
,
1
/256
1,
,
,
,
1
1
/256
(7)
Therefore the
expected val
ue of NPCR is
E
NPCR
9
9
.
6094%
.
(2) T
heo
retical value of UACI betwee
n
two ran
dom n
o
ise ima
g
e
s
As for two ra
ndom ima
g
e
s
of 8-bit gra
yscale, the exp
e
cted valu
ed
of UACI is
E
UA
C
I
E
∑
|
,
,
|
,
100%
E
∑|
,
,
|
,
(8)
The value
s
a
nd frequ
en
cie
s
of
C
1
(
i,j
)
-C
2
(
i,j
) are tabul
ated in Table 2.
Table 2. Valu
es an
d frequ
e
n
cie
s
of
C
1
(
i
,
j
)-
C
2
(
i
,
j
)
Value
-255
-254
-253
…
-2
-1
0
1
2
… 253
254 255
Freque
nc
y
1
2
3
…
254 255 256
255 254
…
3
2
1
So |
C
1
(
i
,
j
)-
C
2
(
i
,
j
)
| is expected to be [2×(255×1+
254×2+253×3+...+
2×254+1×255) +
0×2
56] / (25
6
×2
56)
= 55
9232
0/655
36.
Theref
o
r
e, E
[
UACI] = 559
2320/6
553
6/2
55 = 25
7/768
≈
33.463
5%.
(3) T
heo
retical value of NMSE betwee
n
two ran
dom
noise ima
g
e
s
As for two ra
ndom ima
g
e
s
C
1
and
C
2
of
8-bit grayscal
e, the
expect
ed valued of
UACI is
E
NMSE
E
C
C
E
C
E
C
E
C
2
E
C
∙C
va
r
C
E
C
2E
C
2
E
C
va
r
C
E
C
2
va
r
C
va
r
C
E
C
2
1
EC
va
r
C
2
1
255
0
/2
255
0
/12
1
2
50%
(4) T
heo
retical value of NPCR bet
wee
n
a rand
om i
m
age an
d a d
e
termini
s
tic i
m
age
As for 8-bit grayscale imag
es, the expected val
ue of
NPCR is the same a
s
the ca
se wit
h
two ran
dom i
m
age
s. Therefore,
E
NPCR
9
9
.
6094%
.
(5) T
heo
retical value of UACI betwee
n
a rand
om ima
ge and a d
e
te
rmini
s
tic imag
e
The value
s
o
f
UACI are
di
fferent for sp
ecif
ic im
age
s.
For exam
ple
s
, the value
of UACI
betwe
en Le
n
a
and rand
o
m
image i
s
2
8
.6242%, wh
i
l
e the value
of UACI between Bab
oon
and
rand
om imag
e is 27.84
72
%.
(6) T
heo
retical value of NMSE betwee
n
a rand
om i
m
age an
d a d
e
termini
s
tic i
m
age
The value
s
of
NMSE are di
fferent for sp
ecific im
age
s.
For exampl
e
s
, the value o
f
NMSE
betwe
en Le
n
a
and rand
o
m
image is
3
5
.6210%, wh
ile the value o
f
NMSE between Bab
oon
and
rand
om imag
e is 33.28
10
%.
4.6.2. Ke
y
Se
nsitivit
y
Anal
y
s
is
Take the images Lena a
nd Baboon of 8-bit grayscale as
exam
ples to calculate the
NPCR, UACI
and NMSE in
dicato
rs
with four situ
ation
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Plaintext Rel
a
ted Im
age Encryptio
n
Sc
h
e
m
e
Using
Chaotic Ma
p (Yong Zha
ng)
641
For
en
cryptio
n
: (1
) Ge
ne
ra
te two
set of
ciph
er im
age
s fro
m
the
sa
me plai
n ima
ge
with
two set of se
cret keys. Fo
r the two set of se
cr
et keys, randomly sele
ct 1000 value
s
ran
ge from
0
to 1 as
k
1
for one set of the se
cret key,
but kee
p
ke
ys {
k
2
,
k
3
,
k
4
}
always
are
{
0
.7329, 0.57
12,
0.8320
}, we
get 1000
se
cret key
s
a
s
o
ne
set of them. Keep the
value of key
s
{
k
2
,
k
3
,
k
4
}, but
cha
nge
ea
ch
k
1
value w
i
th
10
-14
,
we get the
othe
r set of
se
cret
key, then
cal
c
ulat
e the
avera
g
e
,
minimum
an
d maximum
values
of NP
CR,
UACI a
n
d
NMSE b
e
twee
n the o
b
tained t
w
o
se
t of
ciph
er imag
e
s
; (2) Sam
e
as metho
d
1, but keep ke
ys {
k
1
,
k
3
,
k
4
}
as {0.27
89, 0.7904, 0.33
21},
while ma
ke the 1000
k
2
different as the
k
1
in method 1; (3) Same as metho
d
1, but keep ke
ys
{
k
1
,
k
2
,
k
4
} a
s
{0.77
39, 0.3
015, 0.4
848},
while
ma
ke t
he 10
00
k
3
di
fferent a
s
the
k
1
in
me
th
od 1
;
(4) Same
as
method
1, bu
t kee
p
keys
{
k
1
,
k
2
,
k
3
} a
s
{0.490
8, 0.65
83, 0.49
89},
while
ma
ke t
he
1000
k
4
cha
n
ged with 1
0
-13
. These results are ta
bulate
d
in Table 3 a
nd 4.
For d
e
cryptio
n
: (1) Gen
e
ra
te one
set of
ciph
er im
age
s from
a pl
ai
n image
with
a set of
se
cret
keys.
For the
se
cre
t
keys, ran
d
o
m
ly sele
ct 10
00 value
s
ra
n
ge from 0 to
1 as
k
1
, but keep
key
s
{
k
2
,
k
3
,
k
4
} alway
s
are{
0.7329, 0.57
1
2
, 0.8320
} to get
the set of
se
cret
keys.
Keep the valu
e
of keys {
k
2
,
k
3
,
k
4
}, but change e
a
ch
k
1
value with 1
0
-14
, we get the other
set
of secret keys
.
Then
de
crypt
the set of ci
pher
ima
g
e
s
with
the
correct
se
cret ke
ys, and
the
secret
keys in
the
other set of se
cret key
s
. This way, we
get
tw
o set
of de
crypted
image
s. Th
e
n
calculate t
h
e
averag
e, mini
mum and m
a
ximum value
s
of NP
CR, UACI an
d NMSE betwee
n
the obtaine
d two
set of de
cryp
ted image
s; (2) Same
as
method 1, b
u
t
keep
key
s
{
k
1
,
k
3
,
k
4
} a
s
{0.278
9, 0.79
04,
0.3321
}, whil
e ma
ke the
1000
k
2
different as th
e
k
1
in metho
d
1
;
(3) Sa
me a
s
meth
od 1,
but
kee
p
key
s
{
k
1
,
k
2
,
k
4
} as {0.
7739, 0.30
15
, 0.4848}, whi
l
e make th
e 1000
k
3
different as the
k
1
in
method 1; (4
) Same as me
thod 1, but keep key
s
{
k
1
,
k
2
,
k
3
} as {0.4908, 0.658
3
,
0.4989}, whi
l
e
make th
e 10
00
k
4
cha
nge
d with 10
-13
.
These results are tab
u
late
d in Tabl
e 5
and 6, whe
r
e
the
values in b
r
a
c
ket are theo
retical value
s
.
Table 3. Key sen
s
itivity analysis of Le
na
image (for e
n
cryptio
n
)
NPCR(99
.6094
%
)
UACI(33.4
635%
)
NMSE(50%
)
max
mean
min
max
mean
min
max
mean
min
k1
99.6559
99.6092
99.5731
33.6058
33.4638
33.3210
50.7289
50.2989
49.9027
k2
99.6502
99.6090
99.5701
33.6324
33.4614
33.2935
50.7511
50.2985
49.6817
k3
99.6536
99.6092
99.5693
33.5859
33.4617
33.3383
50.7271
50.2911
49.8652
k4
99.6521
99.6093
99.5682
33.6388
33.4636
33.3043
50.7431
50.2938
49.8573
Table 4. Key sen
s
itivity analysis of Bab
oon imag
e (fo
r
encryption
)
NPCR(99
.6094
%
)
UACI(33.4
635%
)
NMSE(50%
)
max
mean
min
max
mean
min
max
mean
min
k1
99.6441
99.6087
99.5644
33.6439
33.4643
33.3170
50.7530
50.2962
49.8735
k2
99.6498
99.6088
99.5476
33.5983
33.4606
33.3212
50.7171
50.2875
49.8189
k3
99.6456
99.6095
99.5701
33.6208
33.4632
33.3295
50.7571
50.2884
49.8407
k4
99.6517
99.6099
99.5686
33.5946
33.4635
33.3216
50.7684
50.2884
49.8407
Table 5. Key sen
s
itivity analysis of Le
na
image (for d
e
cryptio
n
)
NPCR(99
.6094
%
)
UACI(28.6
242
%
)
NMSE(35.621
0
%
)
max
mean
min
max
mean
min
max
mean
min
k1
99.6460
99.6095
99.5674
28.7380
28.6250
28.5041
36.0229
35.7467
35.4594
k2
99.6456
99.6090
99.5701
28.7455
28.6249
28.4778
35.9800
35.7477
35.4769
k3
99.6532
99.6103
99.5762
28.7515
28.6256
28.5164
36.0274
35.7497
35.4211
k4
99.6531
99.6088
99.5674
28.7514
28.6236
28.5075
36.0747
35.7484
35.4883
Table 6. Key sen
s
itivity analysis of Bab
oon imag
e (fo
r
decryption
)
NPCR(99
.6094
%
)
UACI(27.8
472%
)
NMSE(33.281
0
%
)
max
mean
min
max
mean
min
max
mean
min
k1
99.6517
99.6095
99.5708
28.0011
27.8744
27.7123
33.6832
33.4115
33.1236
k2
99.6426
99.6094
99.5693
27.9665
27.8482
27.7419
33.6330
33.4153
33.1394
k3
99.6609
99.6093
99.5716
27.9511
27.8462
27.7343
33.7258
33.4103
33.1756
k4
99.6437
99.6094
99.5724
27.9549
27.8476
27.7488
33.6582
33.4110
33.1457
From
Tabl
es 3-6, it
can
be d
edu
ce
d
that
the m
a
x
i
mum
relativ
e
e
rro
r
of N
P
CR
is
0.0620
4%, the maximum
relative error
of UACI
i
s
0.
5527%, an
d the maximum
relative e
rro
r of
NMSE is 1.53
68%, which d
e
mon
s
trate th
at the
propo
sed schem
e h
a
s hig
h
key sensitivity.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 230
2
-
404
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TELKOM
NIKA
Vol. 12, No
. 1, Janua
ry 2014: 635 – 6
4
3
642
4.7. Plain Image Sensitiv
it
y
and R
esisting
Cho
sen Plaintext Attack
Take
the im
a
ges of Le
na,
Baboon,
all-white and
all-bl
ack of 8
-
bit g
r
ayscale
(of
size 5
12
× 5
12) a
s
exa
m
ples. Exp
e
ri
ment on
the
m
for
10,
00
0
times. In
each expe
rime
nt, ran
domly
sel
e
ct
one pixel fro
m
one plai
n
image, an
d p
l
us 1 to the
same
pixel to get the oth
e
r plai
n imag
e,
encrypt the t
w
o
plain i
m
a
ges with th
e
identi
c
al
se
cret
key to
get two
ci
ph
er im
age
s, t
hen
comp
are the cal
c
ulate
d
NPCR an
d UA
CI indica
tors. The re
sult
s are tabulated in
Table 7.
Table 7. NPCR a
nd UA
CI indicato
rs fo
r cho
s
en pl
ain
t
ext attack
NPCR(99
.6094
%
)
UACI(33.4
635%
)
max mean
min
max
mean
min
Lena
99.6563
99.6096
99.5625
33.6176
33.4595
33.2848
Baboon
99.6521
99.6095
99.5590
33.6166
33.4709
33.3199
All-black
99.6590
99.6093
99.5647
33.6551
33.4629
33.2909
All-w
h
ite
99.6490
99.6090
99.5590
33.6176
33.4483
33.2873
From T
able
7, it can be
calculated t
hat
the max
i
mum rel
a
tiv
e
erro
r of NP
CR i
s
0.0506
0%, and the maxim
u
m relative e
rro
r of UA
CI i
s
0.572
56%, whi
c
h dem
on
strate
s that a
n
y
slightly change in the
plain images
will
make
the produced
cipher image
s com
p
letely
different,
and
ea
ch pix
e
l’s info
rmati
on in
plain
i
m
age
ca
n
sp
read
all
over the
ciphe
r i
m
age. Sin
c
e
the
prop
osed met
hod bei
ng the
plain imag
e related alg
o
ri
t
h
m, i.e. different plain ima
ges
co
rre
sp
o
nd
to different
secret code
st
ream
s, that
make
s th
e propo
sed
sche
me can resi
st
the ch
osen
plain
image attack.
5. Conclusio
n
This pa
per
su
gge
sted the p
l
ain image related image e
n
cryptio
n
method ba
sed o
n
image
blocks. On th
e one ha
nd a
part of the informatio
n
of plain imag
e is used to co
nfuse the
pixels
within e
a
ch b
l
ock, on the
o
t
her ha
nd the
plain
ima
ge i
n
formatio
n is
employed to
make
diffusio
n
betwe
en the
adja
c
ent bl
ock, so a
s
to a
c
hieve th
e
pu
r
p
os
ed
o
f
en
c
r
yp
ting
or
igin
a
l
imag
e
.
Th
e
entire
pro
c
e
s
s do
es not di
sru
p
t the pixe
l locatio
n
s,
a
nd it ju
st scra
mbles an
d dif
f
use
s
the val
ue
of each pixel
.
Simulation result
s confi
r
m that
the propo
sed sch
e
m
e has the chara
c
te
risti
c
s of
high spe
ed, large key sp
ace,
hi
gh ke
y
sen
s
itiv
ity, and
well
re
sistin
g differe
ntial attack a
nd
cho
s
e
n
plain
image atta
ck, et
c. So the pro
p
o
s
ed sche
me
can b
e
u
s
ed in p
r
acti
cal
comm
uni
cati
ons.
Ackn
o
w
l
e
dg
ement
This work wa
s fully suppo
rted by the Natura
l Scie
nce Found
ation
s
of Jiangxi
Province
(Grant Nos: 20122BAB2
01036 and 20114BAB211011).
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