I
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n J
o
urna
l o
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lect
rica
l En
g
ineering
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Co
m
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er
Science
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l.
3
9
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1
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ly
2
0
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5
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700
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:
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ttp
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A nov
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d
p
re
v
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t
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n
a
u
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rize
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a
c
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ss
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is
p
a
p
e
r
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o
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e
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t
(
,
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u
lt
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g
e
sh
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rin
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e
m
e
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t
lev
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g
e
s
ri
b
o
n
u
c
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c
id
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RNA
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c
ry
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to
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ra
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h
y
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n
d
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e
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l
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ro
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p
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lar
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t
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ta
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,
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M
S
IS
sc
h
e
m
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n
c
ry
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g
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t
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re
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n
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o
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lex
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t
k
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y
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e
n
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se
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n
c
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i
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se
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ry
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se
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e
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le
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o
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n
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ri
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d
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k
n
o
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it
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re
v
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c
o
m
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n
d
ro
b
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st
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ss
a
g
a
in
st
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ry
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ra
p
h
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a
tt
a
c
k
s.
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e
p
r
o
p
o
se
d
m
o
d
e
l,
imp
lem
e
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ted
i
n
P
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o
n
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li
d
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ted
t
h
ro
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g
h
e
x
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m
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stra
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g
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ffe
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ffir
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l'
s
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ey
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s
:
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f
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tial a
ttack
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n
tr
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p
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test
Gr
o
u
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ata
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ag
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c
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CC B
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se
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C
o
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r
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s
p
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A
uth
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r
:
Ven
k
atesan
R
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asam
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Dep
ar
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T
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n
s
titu
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n
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en
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ater
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s
r
m
is
t.e
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u
.
in
1.
I
NT
RO
D
UCT
I
O
N
I
n
th
e
m
o
d
e
r
n
d
ig
ital
lan
d
s
c
ap
e,
th
e
s
ec
u
r
e
tr
an
s
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o
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ata
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o
m
e
cr
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cial,
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n
u
m
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s
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ter
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et
ap
p
licatio
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s
f
ac
ilit
atin
g
co
n
f
i
d
en
tial c
o
m
m
u
n
icatio
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o
n
s
eq
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en
tly
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s
af
eg
u
ar
d
in
g
i
n
f
o
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ag
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s
t
u
n
au
th
o
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ized
ac
ce
s
s
h
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cr
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o
b
jec
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T
h
e
r
ap
id
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p
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ter
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et
tech
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lo
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as
u
n
d
e
r
s
co
r
ed
in
f
o
r
m
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n
s
ec
u
r
ity
as
a
p
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n
.
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o
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m
eth
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s
s
u
ch
as
cr
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p
to
g
r
ap
h
y
[
1
]
,
[
2
]
,
s
teg
an
o
g
r
ap
h
y
[
3
]
,
[
4
]
,
a
n
d
wate
r
m
ar
k
in
g
[
5
]
,
[
6
]
h
a
v
e
b
ee
n
p
r
o
p
o
s
ed
an
d
ex
ten
s
iv
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s
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.
Ho
wev
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,
with
th
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p
r
o
life
r
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f
d
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im
ag
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p
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at
o
f
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n
f
o
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m
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Dig
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p
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.
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im
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cr
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f
o
r
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cien
tific
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tech
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o
lo
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v
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n
ce
m
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ts
as
well
as
f
o
r
en
s
u
r
in
g
th
e
p
r
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ac
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co
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tiality
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I
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d
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J
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C
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m
p
Sci
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N:
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-
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ity
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C
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6
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o
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ir
em
en
ts
o
f
C
A
r
en
d
er
k
ey
d
is
co
v
er
y
co
m
p
u
tatio
n
ally
im
p
r
ac
tical
f
o
r
att
ac
k
er
s
,
en
s
u
r
in
g
s
ec
u
r
e
d
ata
tr
an
s
m
is
s
io
n
,
im
ag
e
cr
y
p
to
g
r
ap
h
y
,
p
r
o
ce
s
s
in
g
,
a
n
d
au
th
e
n
ticatio
n
with
lo
w
co
m
p
lex
ity
in
b
o
th
h
ar
d
war
e
an
d
s
o
f
twar
e
im
p
lem
en
tatio
n
s
.
R
NA
b
ased
en
cr
y
p
tio
n
s
ch
em
es
lev
er
ag
e
th
e
d
is
tin
ctiv
e
ch
ar
ac
ter
is
tics
o
f
R
NA
m
o
lecu
les
to
s
to
r
e
d
ata
with
in
n
u
cleo
tid
e
s
eq
u
en
ce
s
,
wh
ich
ar
e
th
en
tr
an
s
lated
in
to
p
ix
el
s
eq
u
en
ce
s
in
im
ag
es.
T
h
is
ap
p
r
o
ac
h
ca
n
p
o
ten
tially
o
v
er
co
m
e
tr
a
d
itio
n
al
en
cr
y
p
tio
n
v
u
ln
er
ab
il
ities
,
in
clu
d
in
g
q
u
an
t
u
m
co
m
p
u
tin
g
attac
k
s
an
d
b
r
u
te
-
f
o
r
ce
attem
p
ts
,
d
u
e
to
th
e
v
ast
n
u
m
b
er
o
f
p
o
s
s
ib
le
R
NA
s
eq
u
en
ce
s
[
7
]
.
Alth
o
u
g
h
s
till
in
ea
r
ly
d
ev
elo
p
m
e
n
t,
cu
r
r
e
n
t
m
eth
o
d
s
co
m
b
in
in
g
R
NA
an
d
DNA
m
o
lecu
les
,
alo
n
g
with
n
o
n
-
co
d
in
g
R
NA
p
atter
n
s
,
r
eq
u
ir
e
f
u
r
th
er
r
esear
ch
a
n
d
r
i
g
o
r
o
u
s
test
in
g
[
8
]
.
Wu
et
a
l.
[
9
]
p
r
o
p
o
s
ed
a
n
e
n
cr
y
p
tio
n
tech
n
iq
u
e
u
tili
zin
g
R
NA
m
o
lecu
les
an
d
g
en
etic
co
d
es
to
en
h
an
ce
s
ec
u
r
ity
a
n
d
s
ca
lab
i
lity
.
A
s
tu
d
y
in
[
1
0
]
co
m
p
a
r
ed
R
NA
b
ased
e
n
cr
y
p
tio
n
s
y
s
tem
s
b
ased
o
n
en
cr
y
p
tio
n
tim
e,
d
ec
r
y
p
tio
n
ti
m
e,
an
d
im
a
g
e
q
u
ality
.
Gilb
er
t
et
a
l.
[
1
1
]
in
v
esti
g
ated
a
DN
A
an
d
R
NA
m
o
tif
-
b
ased
m
eth
o
d
f
o
r
k
ey
g
en
er
atio
n
,
em
p
h
asizin
g
s
ec
u
r
ity
a
n
d
co
m
p
u
tatio
n
al
ef
f
icien
c
y
.
Ab
b
asi
et
a
l.
[
1
2
]
d
ev
elo
p
e
d
th
e
er
r
atic
am
in
o
ac
id
tec
h
n
iq
u
e,
c
o
m
b
in
i
n
g
SHA
-
2
5
6
k
ey
g
e
n
er
atio
n
,
p
ix
el
p
e
r
m
u
tatio
n
,
d
if
f
u
s
io
n
,
a
n
d
o
p
tim
izatio
n
,
b
u
t th
e
p
r
o
ce
s
s
r
em
ain
ed
tim
e
-
c
o
n
s
u
m
in
g
d
esp
ite
its
h
ig
h
r
esi
s
tan
ce
to
attac
k
s
.
Alv
ar
ez
et
a
l.
[
1
3
]
d
ev
elo
p
e
d
an
im
ag
e
en
c
r
y
p
tio
n
tech
n
iq
u
e
u
s
in
g
s
ec
o
n
d
-
o
r
d
er
C
A,
wh
er
e
th
e
s
u
b
s
eq
u
en
t
s
tate
o
f
a
ce
ll
was
b
ased
o
n
its
p
r
io
r
s
tate
an
d
a
d
jace
n
t
ce
lls
,
d
o
u
b
lin
g
th
e
en
cr
y
p
ted
im
a
g
e
s
ize.
Ma
lek
i
et
a
l.
[
1
4
]
ex
ten
d
ed
th
is
to
h
ig
h
er
-
o
r
d
er
C
A,
b
u
t
im
ag
e
q
u
ality
was
co
m
p
r
o
m
is
ed
as
th
e
least
s
ig
n
if
ican
t
b
it
-
p
la
n
e
c
o
u
l
d
n
'
t
b
e
r
ec
o
v
er
ed
.
L
i
et
a
l.
[
1
5
]
p
r
o
p
o
s
ed
co
m
b
in
in
g
a
ch
ao
tic
m
ap
with
C
A
f
o
r
b
etter
s
ec
u
r
ity
,
th
o
u
g
h
im
p
r
o
v
em
en
ts
wer
e
n
ee
d
ed
in
n
o
is
e
attac
k
r
esis
tan
ce
an
d
o
v
e
r
all
ef
f
ec
tiv
en
ess
.
Secr
et
im
ag
e
s
h
ar
in
g
was
f
ir
s
t
p
io
n
ee
r
ed
u
s
in
g
th
e
Sh
am
ir
–
L
ag
r
an
g
e
tech
n
iq
u
e
[
1
6
]
,
f
o
llo
wed
b
y
ad
v
an
ce
m
e
n
ts
in
s
in
g
le
-
s
ec
r
et
im
ag
e
s
h
ar
in
g
[
1
7
]
-
[
1
9
]
.
T
o
en
h
an
ce
ef
f
icien
c
y
f
o
r
m
u
ltip
le
s
ec
r
ets,
m
eth
o
d
s
u
tili
zin
g
ad
d
itio
n
al
s
to
r
ag
e
w
er
e
in
tr
o
d
u
ce
d
[
2
0
]
,
alo
n
g
s
id
e
a
th
eo
r
etica
l
f
r
am
ew
o
r
k
f
o
r
s
h
ar
in
g
two
s
ec
r
et
im
ag
es
[
2
1
]
.
Su
b
s
eq
u
en
t
in
n
o
v
atio
n
s
in
clu
d
ed
th
e
d
u
al
-
r
in
g
m
u
lti
-
s
ec
r
et
im
ag
e
s
h
ar
in
g
(
MSI
S
)
s
ch
em
e
[
2
2
]
an
d
a
n
(
,
)
MSI
S
m
eth
o
d
le
v
e
r
ag
in
g
B
o
o
lean
o
p
er
ati
o
n
s
f
o
r
e
n
co
d
in
g
m
u
ltip
le
s
h
ar
es
[
2
3
]
.
Vis
u
al
cr
y
p
to
g
r
ap
h
y
,
o
r
ig
in
ally
d
ev
is
ed
f
o
r
s
in
g
le
-
im
ag
e
en
cr
y
p
tio
n
,
ev
o
l
v
ed
to
ac
co
m
m
o
d
ate
m
u
ltip
le
im
ag
es,
with
d
ec
r
y
p
tio
n
r
e
q
u
ir
in
g
all
s
h
ar
e
s
[
2
4
]
.
T
h
e
MSI
S
s
ch
em
e
f
o
u
n
d
d
iv
e
r
s
e
a
p
p
licatio
n
s
,
in
cl
u
d
in
g
m
is
s
ile
lau
n
ch
co
d
es,
s
af
ety
d
ep
o
s
it b
o
x
es,
ac
ce
s
s
co
n
tr
o
l,
an
d
e
-
v
o
tin
g
o
r
e
-
au
ctio
n
s
.
T
h
e
ea
r
lier
an
al
y
s
is
h
ig
h
lig
h
ted
th
e
p
r
o
s
an
d
c
o
n
s
o
f
C
A
an
d
R
NA
in
im
ag
e
en
c
r
y
p
tio
n
,
with
ex
is
tin
g
m
eth
o
d
s
f
ac
in
g
c
h
a
llen
g
es
lik
e
s
u
s
ce
p
tib
ilit
y
to
s
tatis
tical
attac
k
s
,
h
ig
h
p
ix
el
co
r
r
elatio
n
,
lo
w
en
tr
o
p
y
,
an
d
lim
ited
r
esis
tan
ce
to
d
if
f
er
en
tial
attac
k
s
.
C
o
n
s
id
er
in
g
th
ese
is
s
u
es
an
d
th
e
b
r
o
ad
ap
p
licatio
n
s
o
f
MSI
S,
th
is
p
ap
er
in
tr
o
d
u
ce
s
a
n
(
,
)
MSI
S
s
ch
em
e
th
at
in
teg
r
ates
GC
A
an
d
R
NA
to
ef
f
ec
tiv
ely
tack
le
th
ese
ch
allen
g
es
an
d
p
r
o
v
id
e
a
r
o
b
u
s
t
s
o
lu
tio
n
.
R
NA
co
d
o
n
s
en
h
an
ce
s
ec
u
r
ity
th
r
o
u
g
h
th
eir
ex
ten
s
iv
e
s
eq
u
en
ce
v
ar
iab
ilit
y
an
d
in
h
er
e
n
t
co
m
p
l
ex
ity
d
u
r
in
g
k
e
y
im
ag
e
g
en
er
atio
n
.
Fu
r
th
er
m
o
r
e,
th
e
d
ep
lo
y
m
en
t
o
f
1
-
D
GC
A
r
u
les
en
s
u
r
es
r
an
d
o
m
n
ess
an
d
r
o
b
u
s
t
im
ag
e
en
c
r
y
p
tio
n
b
y
iter
atin
g
im
a
g
e
p
ix
els,
th
er
eb
y
e
n
h
an
ci
n
g
r
esil
ien
ce
ag
ain
s
t c
r
y
p
to
g
r
ap
h
i
c
attac
k
s
d
u
e
to
th
eir
s
im
p
licity
an
d
e
f
f
ec
tiv
en
ess
in
co
m
p
u
ti
n
g
.
T
h
e
r
em
ain
in
g
s
ec
tio
n
s
o
f
th
e
p
ap
er
ar
e
o
r
g
a
n
ized
in
th
e
f
o
llo
win
g
m
an
n
er
:
s
ec
tio
n
2
d
el
iv
er
s
an
in
-
d
ep
th
ex
p
lo
r
atio
n
o
f
R
NA
cr
y
p
to
g
r
ap
h
y
an
d
C
A.
Sectio
n
3
elu
cid
ates
th
e
p
r
o
p
o
s
ed
im
ag
e
en
cr
y
p
tio
n
tech
n
iq
u
e,
i
n
clu
d
in
g
th
e
r
elev
an
t
alg
o
r
ith
m
s
.
Sectio
n
4
th
o
r
o
u
g
h
ly
ex
am
in
es
th
e
o
b
s
er
v
at
io
n
s
an
d
f
i
n
d
in
g
s
.
Sectio
n
5
co
n
cl
u
d
es th
e
co
n
cise su
m
m
ar
y
o
f
th
e
p
ap
er
.
2.
F
UNDA
M
E
N
T
AL
S O
F
CA
AND
RNA
CRYP
T
O
G
RAP
H
Y
2.
1
.
RNA
c
ry
pt
o
g
ra
ph
y
R
NA
cr
y
p
to
g
r
ap
h
y
h
ar
n
ess
es
th
e
d
is
tin
ctiv
e
tr
aits
o
f
R
NA
s
eq
u
en
ce
s
to
en
h
an
ce
d
ata
s
ec
u
r
ity
.
An
R
NA
s
eq
u
en
ce
co
m
p
r
is
es
f
o
u
r
n
u
cleic
ac
id
b
ases
,
a
d
en
in
e
(
A)
,
g
u
a
n
in
e
(
G)
,
cy
to
s
in
e
(
C
)
,
an
d
u
r
ac
il
(
U)
.
Ad
en
in
e
f
o
r
m
s
a
b
ase
p
air
wi
th
u
r
ac
il
(
A
-
U)
,
an
d
g
u
a
n
in
e
f
o
r
m
s
a
b
ase
p
air
with
c
y
to
s
in
e
(
G
-
C
)
,
m
ir
r
o
r
in
g
th
e
co
m
p
lem
e
n
tar
y
n
atu
r
e
o
f
b
in
ar
y
d
ig
its
(
0
an
d
1
)
.
Usi
n
g
th
e
f
o
u
r
R
NA
b
ases
to
en
co
d
e
b
in
ar
y
p
air
s
(
0
0
,
1
1
,
0
1
,
1
0
)
r
esu
lts
i
n
2
4
p
o
s
s
ib
le
co
d
in
g
s
ch
em
es.
Desp
ite
th
is
,
m
er
ely
eig
h
t
o
f
th
ese
s
ch
em
es
ad
h
er
in
g
to
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
3
9
,
No
.
1
,
Ju
ly
20
25
:
700
-
7
0
9
702
W
atso
n
-
C
r
ick
co
m
p
lem
en
tar
it
y
cr
iter
ia,
as
d
ep
icted
in
T
ab
le
1
.
T
h
e
R
NA
co
d
in
g
tab
le
co
n
v
er
ts
th
e
p
ix
el
v
alu
es
o
f
im
ag
es
in
t
o
R
NA
s
eq
u
en
ce
s
.
T
h
e
R
NA
d
ictio
n
ar
y
,
p
r
esen
ted
in
T
a
b
le
2
,
tr
an
s
lates
th
ese
R
NA
s
eq
u
en
ce
s
in
to
d
ec
im
al
v
alu
es.
I
n
th
e
p
r
o
p
o
s
ed
s
ch
em
e,
th
e
R
NA
en
co
d
in
g
tab
le
an
d
d
ict
io
n
ar
y
ar
e
u
tili
ze
d
to
g
en
er
ate
th
e
k
ey
i
m
ag
e
f
r
o
m
th
e
o
r
ig
i
n
al
im
ag
es,
en
s
u
r
i
n
g
a
s
ec
u
r
e
an
d
r
o
b
u
s
t e
n
cr
y
p
ti
o
n
p
r
o
ce
s
s
.
T
ab
le
1
.
R
NA
en
co
d
i
n
g
tab
le
1
2
3
4
5
6
7
8
A
B
C
D
00
11
01
10
00
11
10
01
01
10
00
11
01
10
11
00
10
01
00
11
10
01
11
00
11
00
01
10
11
00
10
01
T
ab
le
2
.
Dictio
n
ar
y
f
o
r
tr
an
s
la
tin
g
R
NA
s
eq
u
en
ce
s
to
d
ec
im
al
f
o
r
m
D
e
c
.
DNA
D
e
c
.
DNA
D
e
c
.
DNA
D
e
c
.
DNA
D
e
c
.
DNA
D
e
c
.
DNA
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
AAAA
AAAU
AAAG
AAAC
AAUA
AAUU
AAUG
AAUC
AAGA
AAGU
AAGG
AAGC
A
A
C
A
A
A
C
U
A
A
C
G
A
A
C
C
AUAA
AUAU
AUAG
AUAC
AUUA
AUUU
AUUG
AUUC
AUGA
AUGU
AUGG
AUGC
A
U
C
A
A
U
C
U
A
U
C
G
A
G
C
C
AGAA
AGAU
AGAG
AGAC
AGUA
AGUU
AGUG
AGUC
AGGA
AGGU
AGGG
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
AGGC
A
G
C
A
A
G
C
U
A
G
C
G
A
G
C
C
A
C
A
A
A
C
A
U
A
C
A
G
A
C
A
C
A
C
U
A
A
C
U
U
A
C
U
G
A
C
U
C
A
C
G
A
A
C
G
U
A
C
G
G
A
C
G
A
A
C
C
A
A
C
C
U
A
C
C
G
A
C
C
C
UAAA
UAAU
UAAG
UAAC
UAUA
UAUU
UAUG
UAUC
UAGA
UAGU
UAGG
UAGC
U
A
C
A
U
A
C
U
U
A
C
G
U
A
C
C
UUAA
UUAU
UUAG
UUAC
UUUA
UUUU
86
87
88
89
90
91
92
93
94
95
96
97
98
99
1
0
0
1
0
1
1
0
2
1
0
3
1
0
4
1
0
5
1
0
6
1
0
7
1
0
8
1
0
9
1
1
0
1
1
1
1
1
2
1
1
3
1
1
4
1
1
5
1
1
6
1
1
7
1
1
8
1
1
9
1
2
0
1
2
1
1
2
2
1
2
3
1
2
4
1
2
5
1
2
6
1
2
7
1
2
8
UUUG
UUUC
UUGA
UUGU
UUGG
UUGC
U
U
C
A
U
U
C
U
U
U
C
G
U
G
C
C
UGAA
UGAU
UGAG
UGAC
UGUA
UGUU
UGUG
UGUC
UGGA
UGGU
UGGG
UGGC
U
G
C
A
U
G
C
U
U
G
C
G
U
G
C
C
U
C
A
A
U
C
A
U
U
C
A
G
U
C
A
C
U
C
U
A
U
C
U
U
U
C
U
G
U
C
U
C
U
C
G
A
U
C
G
U
U
C
G
G
U
C
G
C
U
C
C
A
U
C
C
U
U
C
C
G
U
C
C
C
GAAA
1
2
9
1
3
0
1
3
1
1
3
2
1
3
3
1
3
4
1
3
5
1
3
6
1
3
7
1
3
8
1
3
9
1
4
0
1
4
1
1
4
2
1
4
3
1
4
4
1
4
5
1
4
6
1
4
7
1
4
8
1
4
9
1
5
0
1
5
1
1
5
2
1
5
3
1
5
4
1
5
5
1
5
6
1
5
7
1
5
8
1
5
9
1
6
0
1
6
1
1
6
2
1
6
3
1
6
4
1
6
5
1
6
6
1
6
7
1
6
8
1
9
0
1
7
0
1
7
1
GAAU
GAAG
GAAC
GAUA
GAUU
GAUG
GAUC
GAGA
GAGU
GAGG
GAGC
G
A
C
A
G
A
C
U
G
A
C
G
G
A
C
C
GUAA
GUAU
GUAG
GUAC
GUUA
GUUU
GUUG
GUUC
GUGA
GUGU
GUGG
GUGC
G
U
C
A
G
U
C
U
G
U
C
G
G
U
C
C
GGAA
GGAU
GGAG
GGAC
GGUA
GGUU
GGUG
GGUC
GGGA
GGGU
GGGG
GGGC
1
7
2
1
7
3
1
7
4
1
7
5
1
7
6
1
7
7
1
7
8
1
7
9
1
8
0
1
8
1
1
8
2
1
8
3
1
8
4
1
8
5
1
8
6
1
8
7
1
8
8
1
8
9
1
9
0
1
9
1
1
9
2
1
9
3
1
9
4
1
9
5
1
9
6
1
9
7
1
9
8
1
9
9
2
0
0
2
0
1
2
0
2
2
0
3
2
0
4
2
0
5
2
0
6
2
0
7
2
0
8
2
0
9
2
1
0
2
1
1
2
1
2
2
1
3
2
1
4
G
G
C
A
G
G
C
U
G
G
C
G
G
G
C
C
G
C
A
A
G
C
A
U
GGAG
G
C
A
C
G
C
U
A
G
C
U
U
G
C
U
G
G
C
U
C
G
C
G
A
G
C
G
U
G
C
G
G
G
C
G
C
G
C
C
A
G
C
C
U
G
C
C
G
G
C
C
C
C
A
A
A
C
A
A
U
C
A
A
G
C
A
A
C
C
A
U
A
C
A
U
U
C
A
U
G
C
A
U
C
C
A
G
A
C
A
G
U
C
A
G
G
C
A
G
C
C
A
C
A
C
A
C
U
C
A
C
G
C
A
C
C
C
U
A
A
C
U
A
U
C
U
A
G
C
U
A
C
C
U
U
A
C
U
U
U
C
U
U
G
2
1
5
2
1
6
2
1
7
2
1
8
2
1
9
2
2
0
2
2
1
2
2
2
2
2
3
2
2
4
2
2
5
2
2
6
2
2
7
2
2
8
2
2
9
2
3
0
2
3
1
2
3
2
2
3
3
2
3
4
2
3
5
2
3
6
2
3
7
2
3
8
2
3
9
2
4
0
2
4
1
2
4
2
2
4
3
2
4
4
2
4
5
2
4
6
2
4
7
2
4
8
2
4
9
2
5
0
2
5
1
2
5
2
2
5
3
2
5
4
2
5
5
C
U
U
C
C
U
G
A
C
U
G
U
C
U
G
G
C
U
G
C
C
U
C
A
C
U
C
U
C
U
C
G
C
G
C
C
C
G
A
A
C
G
A
U
C
G
A
G
C
G
A
C
C
G
U
A
C
G
U
U
C
G
U
G
C
G
U
C
C
G
G
A
C
G
G
U
C
G
G
G
C
G
G
C
C
G
C
A
C
G
C
U
C
G
C
G
C
G
C
C
C
C
A
A
C
C
A
U
C
C
A
G
C
C
A
C
C
C
U
A
C
C
U
U
C
C
U
G
C
C
U
C
C
C
G
A
C
C
G
U
C
C
G
G
C
C
G
C
C
C
C
A
C
C
C
U
C
C
C
G
C
C
C
C
2
.
2
.
Cellula
r
a
uto
m
a
t
a
C
A
ar
e
d
is
cr
ete
m
ath
em
atica
l
s
y
s
tem
s
wh
er
e
tim
e,
s
tate
s
,
an
d
s
p
ac
e
ar
e
all
q
u
an
tize
d
.
C
ells
ar
e
s
y
s
tem
atica
lly
ar
r
an
g
ed
in
a
f
in
ite,
r
eg
u
lar
lattice
s
tr
u
ctu
r
e.
C
A
ca
n
b
e
r
ig
o
r
o
u
s
ly
d
ef
in
e
d
b
y
t
h
e
f
iv
e
-
tu
p
le
(
,
,
,
,
)
wh
er
e
d
en
o
tes
th
e
lattice
o
f
a
r
eg
u
lar
g
r
id
,
is
th
e
f
in
ite
s
et
o
f
s
tates,
r
ep
r
esen
ts
th
e
s
et
o
f
n
eig
h
b
o
r
s
,
is
th
e
tr
an
s
itio
n
s
t
ate
f
u
n
ctio
n
a
n
d
s
ig
n
if
ies
th
e
in
itial
s
tate.
E
lem
en
tar
y
C
A
also
ca
lled
1
-
D
C
A,
co
n
s
is
t
o
f
a
lin
ea
r
s
eq
u
e
n
ce
o
f
ce
lls
.
E
ac
h
ce
ll m
o
d
if
ies
its
s
tate
b
y
a
l
o
ca
l
tr
an
s
itio
n
r
u
le
th
at
d
e
p
en
d
s
o
n
th
e
p
r
esen
t
s
tate
an
d
t
h
e
s
tates
o
f
its
n
eig
h
b
o
r
in
g
ce
lls
.
T
h
e
s
tate
o
f
ea
ch
ce
ll
ca
n
o
n
l
y
b
e
eith
er
0
o
r
1
.
T
h
u
s
,
th
er
e
ar
e
2
×
2
×
2
=
2
3
=
8
p
o
s
s
ib
le
n
eig
h
b
o
u
r
h
o
o
d
co
n
f
ig
u
r
atio
n
s
:
111
,
011
,
101
,
110
,
001
,
010
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
A
n
o
ve
l
(
,
)
mu
lti
-
s
ec
r
et
ima
g
e
s
h
a
r
in
g
s
ch
eme
h
a
r
n
ess
in
g
R
N
A
…
(
Ya
s
min
A
b
d
u
l
)
703
100
,
000
r
esu
ltin
g
in
2
8
=
256
p
o
s
s
ib
le
r
u
les
f
o
r
1
-
D
C
A.
T
h
e
tr
an
s
itio
n
m
atr
i
x
o
f
a
1
-
D
C
A,
s
y
m
b
o
lized
b
y
,
is
an
×
m
atr
ix
en
ca
p
s
u
latin
g
th
e
lo
ca
l
u
p
d
ate
r
u
les
f
o
r
al
l
ce
lls
.
T
h
e
ℎ
r
o
w
co
r
r
esp
o
n
d
s
to
th
e
n
eig
h
b
o
r
h
o
o
d
r
elatio
n
s
o
f
t
h
e
ℎ
ce
ll.
I
f
(
,
)
is
1
,
it
in
d
icate
s
th
at
th
e
s
u
b
s
eq
u
en
t
s
tate
o
f
th
e
ℎ
ce
ll
d
ep
en
d
s
u
p
o
n
th
e
cu
r
r
en
t
s
tate
o
f
th
e
ℎ
ce
ll,
C
o
n
tr
ar
ily
,
th
e
v
alu
e
is
0
.
State
tr
an
s
itio
n
s
ar
e
m
ath
em
atica
lly
r
ep
r
esen
ted
as
:
[
+
1
(
)
]
=
[
]
×
[
(
)
]
wh
er
e
+
1
(
)
r
ep
r
esen
t
th
e
s
tate
o
f
c
ell
at
th
e
n
ex
t
tim
e
s
tep
+
1
.
At
th
e
cu
r
r
e
n
t
tim
e
s
tep
,
th
e
s
tate
o
f
ce
ll
is
d
en
o
ted
b
y
(
)
,
wh
ile
(
−
1
)
an
d
(
+
1
)
in
d
icate
th
e
s
tates
o
f
th
e
lef
t
an
d
r
ig
h
t
n
eig
h
b
o
u
r
in
g
ce
lls
,
r
esp
ec
tiv
ely
.
C
A
is
ca
teg
o
r
ized
as
GC
A
if
t
h
e
d
eter
m
i
n
an
t
o
f
is
1
,
co
n
tr
a
r
y
,
it
is
ca
teg
o
r
ized
as
n
o
n
-
g
r
o
u
p
C
A.
I
n
a
GC
A,
ap
p
ly
in
g
a
s
p
ec
if
i
c
r
u
le
o
r
r
u
le
v
ec
to
r
to
th
e
c
ells
r
eg
en
er
ates
th
eir
in
itial
s
tate
af
ter
a
s
p
ec
if
ic
n
u
m
b
er
o
f
iter
atio
n
s
.
T
h
is
n
u
m
b
er
is
r
ef
er
r
ed
as th
e
o
r
d
er
o
f
th
e
C
A
an
d
ca
n
b
e
m
ath
e
m
atica
lly
ex
p
r
ess
ed
as
:
[
]
=
⇒
[
+
(
)
]
=
×
[
(
)
]
wh
er
e
s
ig
n
if
ies th
e
o
r
d
er
o
f
th
e
g
r
o
u
p
an
d
r
ep
r
esen
ts
th
e
i
d
en
tity
m
atr
ix
.
E
x
am
p
les o
f
GC
As
in
clu
d
e
r
u
les
9
0
,
1
0
2
,
1
0
5
an
d
2
0
4
.
T
h
eir
co
m
p
lem
en
ts
ar
e
r
u
les
1
6
5
,
1
5
3
,
1
5
0
,
an
d
5
1
,
r
esp
ec
tiv
ely
.
Acc
o
r
d
in
g
to
[
2
5
]
,
th
e
co
m
p
lem
e
n
t
o
f
a
C
A
r
u
le
th
at
f
o
r
m
s
a
g
r
o
u
p
is
also
a
GC
A.
T
h
er
ef
o
r
e,
all
th
e
v
ar
io
u
s
lo
g
ical
o
p
er
ato
r
s
o
u
tli
n
ed
in
T
ab
le
3
ar
e
id
en
ti
f
ied
as
GC
A.
T
ab
le
4
d
elin
ea
tes
th
e
n
ex
t
s
tate
o
f
th
ese
r
u
les
u
n
d
er
d
if
f
er
e
n
t
n
eig
h
b
o
r
h
o
o
d
c
o
n
f
ig
u
r
atio
n
s
.
I
n
th
e
p
r
o
p
o
s
ed
m
o
d
el,
th
e
p
ix
el
v
alu
es
o
f
an
im
a
g
e
ar
e
tr
an
s
m
u
ted
b
y
a
k
ey
f
u
n
ctio
n
t
h
r
o
u
g
h
th
e
u
n
iq
u
e
c
h
ar
ac
ter
is
tics
o
f
G
C
A
r
u
les,
iter
atin
g
th
r
o
u
g
h
a
h
alf
-
cy
cle
d
u
r
i
n
g
th
e
en
cr
y
p
tio
n
p
h
ase.
T
h
e
s
u
b
s
eq
u
en
t
h
alf
-
cy
cle
iter
atio
n
is
ex
ec
u
ted
d
u
r
i
n
g
th
e
d
ec
r
y
p
tio
n
p
h
ase,
th
er
eb
y
r
esto
r
in
g
th
e
o
r
i
g
in
al
p
ix
el
v
alu
es.
T
h
is
m
eth
o
d
o
l
o
g
y
e
n
s
u
r
es
a
r
o
b
u
s
t
an
d
e
f
f
icien
t
cr
y
p
to
g
r
ap
h
ic
s
y
s
tem
b
y
ca
p
italizin
g
o
n
th
e
in
h
er
en
t
r
ev
er
s
ib
ilit
y
o
f
GC
A
r
u
les.
T
ab
le
3
.
L
o
g
ical
ex
p
r
ess
io
n
o
f
GC
A
r
u
les
No
R
u
l
e
Lo
g
i
c
a
l
o
p
e
r
a
t
i
o
n
s
1
51
+
1
(
)
=
(
)
̅
̅
̅
̅
̅
̅
̅
2
90
+
1
(
)
=
(
−
1
)
⊕
(
+
1
)
3
1
0
2
+
1
(
)
=
(
−
1
)
⊕
(
)
4
1
0
5
+
1
(
)
=
(
−
1
)
⊕
(
)
⊕
(
+
1
)
5
1
5
0
+
1
(
)
=
(
−
1
)
⊕
(
)
⊕
(
+
1
)
6
1
5
3
+
1
(
)
=
(
−
1
)
⊕
(
)
7
1
6
5
+
1
(
)
=
(
−
1
)
⊕
(
+
1
)
8
2
0
4
+
1
(
)
=
(
)
T
ab
le
4
.
I
llu
s
tr
atio
n
o
f
GC
A
r
u
les f
o
r
n
e
x
t state
R
u
l
e
1
1
1
0
1
1
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
51
90
1
0
2
1
0
5
1
5
0
1
5
3
1
6
5
2
0
4
0
1
0
0
1
1
1
1
0
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
1
0
0
1
0
0
1
0
1
1
0
3.
P
RO
P
O
SE
D
M
E
T
H
O
D
T
h
is
s
ec
tio
n
d
elin
ea
tes
an
i
n
n
o
v
ativ
e
ap
p
r
o
ac
h
to
(
,
)
MSI
S,
u
tili
zin
g
R
NA
an
d
GC
A
to
s
ig
n
if
ican
tly
en
h
an
ce
th
e
en
c
r
y
p
tio
n
an
d
tr
an
s
m
is
s
io
n
o
f
m
u
ltip
le
im
ag
es
s
im
u
ltan
eo
u
s
ly
.
I
n
th
e
p
r
o
p
o
s
ed
m
o
d
el,
all
o
r
ig
in
al
im
ag
es
ar
e
o
f
u
n
if
o
r
m
s
ize
with
d
im
en
s
io
n
×
an
d
co
m
p
r
is
e
f
o
u
r
p
r
im
a
r
y
co
m
p
o
n
en
ts
:
o
r
ig
in
al
im
ag
es,
a
k
ey
im
ag
e,
a
k
ey
f
u
n
ctio
n
,
an
d
en
cr
y
p
ted
im
ag
es.
T
h
e
k
e
y
im
ag
e,
g
en
er
ate
d
f
r
o
m
th
e
o
r
ig
in
al
im
a
g
es
v
ia
an
R
NA
en
co
d
in
g
tab
le
a
n
d
d
ictio
n
ar
y
,
is
u
s
ed
to
en
c
r
y
p
t
t
h
e
o
r
ig
in
al
im
a
g
es
in
th
e
in
itial
p
h
ase.
T
o
f
u
r
th
er
en
h
an
ce
s
ec
u
r
ity
an
d
r
a
n
d
o
m
n
ess
,
th
e
k
ey
f
u
n
ctio
n
,
d
e
r
iv
e
d
f
r
o
m
GC
A
r
u
les,
is
em
p
lo
y
ed
to
iter
ate
th
e
im
ag
e
p
ix
els
d
u
r
in
g
th
e
cu
lm
i
n
atio
n
o
f
th
e
en
cr
y
p
tio
n
p
r
o
ce
s
s
.
T
h
is
d
u
al
-
lay
er
en
cr
y
p
tio
n
s
ch
em
e
en
s
u
r
es
h
eig
h
ten
ed
s
ec
u
r
ity
an
d
y
ield
s
en
cr
y
p
te
d
im
a
g
es
co
r
r
esp
o
n
d
in
g
t
o
t
h
e
o
r
ig
in
al
im
ag
es.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
3
9
,
No
.
1
,
Ju
ly
20
25
:
700
-
7
0
9
704
3
.
1
.
K
ey
g
ener
a
t
io
n pro
ce
s
s
Gen
er
atin
g
th
e
k
e
y
im
ag
e
f
r
o
m
o
r
ig
in
al
im
a
g
es
in
v
o
lv
e
t
h
e
d
ep
lo
y
m
en
t
o
f
an
R
NA
en
c
o
d
in
g
ta
b
le
an
d
R
NA
d
ictio
n
a
r
y
.
I
n
itially
,
th
e
o
r
ig
in
al
im
ag
es
ar
e
i
n
p
u
tted
,
an
d
th
eir
r
ed
,
g
r
ee
n
,
an
d
b
lu
e
(
R
GB
)
co
m
p
o
n
en
ts
ar
e
ex
tr
ac
ted
a
n
d
co
n
v
e
r
ted
in
to
b
in
ar
y
m
at
r
ices.
Seq
u
en
tial
B
o
o
lean
XOR
o
p
er
atio
n
s
ar
e
p
er
f
o
r
m
ed
o
n
th
e
R
,
G,
an
d
B
co
m
p
o
n
en
ts
,
y
ield
in
g
co
n
s
o
lid
ated
R
GB
v
alu
es.
T
h
ese
v
alu
es a
r
e
th
en
en
co
d
ed
in
to
R
NA
co
d
o
n
s
ac
c
o
r
d
in
g
t
o
r
u
les
d
eter
m
in
ed
b
y
t
h
e
n
u
m
b
er
o
f
im
ag
es
u
s
in
g
T
ab
le
1
.
T
h
e
R
NA
co
d
o
n
s
ar
e
s
u
b
s
eq
u
en
tly
tr
an
s
lated
in
to
d
ec
im
al
v
alu
es
an
d
th
en
in
to
b
in
ar
y
v
alu
es
u
s
in
g
T
ab
le
2
.
Fin
ally
,
th
ese
b
in
ar
y
v
alu
es
ar
e
in
ter
p
r
eted
a
s
R
G
B
co
m
p
o
n
en
ts
an
d
r
ec
o
n
s
tr
u
cted
in
to
an
im
ag
e,
s
er
v
in
g
as
th
e
k
ey
im
ag
e
f
o
r
e
n
h
an
ci
n
g
s
ec
u
r
ity
in
th
e
en
cr
y
p
tio
n
p
r
o
ce
s
s
.
T
h
e
wo
r
k
f
lo
w
o
f
k
e
y
g
en
er
atio
n
i
s
d
e
p
icted
in
Fig
u
r
e
1
,
wh
ile
th
e
d
etailed
k
ey
g
en
e
r
atio
n
p
r
o
ce
s
s
is
p
r
esen
ted
in
Alg
o
r
ith
m
1
.
Fig
u
r
e
1
.
W
o
r
k
f
lo
w
o
f
k
ey
im
ag
e
g
en
er
atio
n
p
r
o
ce
s
s
Alg
o
r
ith
m
1
.
Key
im
ag
e
f
o
r
m
atio
n
Input: Original Images
(
,
,
…
,
)
Output: Key Image
1.
Consider
,
,
…
,
as input
2.
Extract the RGB components and transform them into matrices
●
=
,
,
●
=
,
,
●
=
,
,
3.
Perform
XOR
on
the
R,
G,
and
B
components
of
all
images
to
yield
the
consolidated
RGB
matrix
′
=
[
,
,
]
●
=
⊕
⊕
⋯
⊕
●
=
⊕
⊕
⋯
⊕
●
=
⊕
⊕
⋯
⊕
4.
Convert
'
to
′
′
to
en
co
de
bi
na
ry
va
lu
es
in
to
RN
A
se
qu
en
ce
us
in
g
RN
A
ru
le
s
ba
se
d
on
image count
●
′′
=
[
′
]
●
RNA
=
,
where
=
number of images
5.
Convert
the
RNA
sequence
′′
in
to
de
ci
ma
l
va
lu
es
us
in
g
an
RN
A
di
ct
io
na
ry
to
ge
ne
ra
te
key matrix
•
= Decimal values
[
′′
]
6.
Transform
into its equivalent binary values
•
′
=
[
]
7.
The values in
′
act as RGB components, constructing key image
3
.
2
.
E
ncry
ptio
n
a
nd
decr
y
ptio
n pro
ce
s
s
I
n
th
e
p
r
o
p
o
s
ed
im
ag
e
en
c
r
y
p
tio
n
tech
n
iq
u
e,
a
s
er
ies
o
f
s
o
p
h
is
ticated
tr
an
s
f
o
r
m
atio
n
s
ar
e
ap
p
lied
to
s
ec
u
r
e
o
r
ig
in
al
im
ag
es
1
,
2
,
…
,
,
ea
ch
with
d
im
en
s
io
n
s
×
.
I
n
itially
,
ea
ch
o
r
i
g
in
al
im
ag
e
u
n
d
er
g
o
es
an
XOR
o
p
e
r
atio
n
with
a
k
ey
im
ag
e
o
f
th
e
s
am
e
s
ize
to
d
if
f
u
s
e
th
e
p
ix
el
v
alu
es,
g
e
n
er
atin
g
p
r
im
ar
y
en
cr
y
p
ted
s
h
a
r
es
1
′
,
2
′
,
…
,
′
.
Su
b
s
eq
u
en
tly
,
t
h
ese
p
r
im
ar
y
s
h
ar
es
ar
e
c
o
n
v
er
te
d
in
to
2
-
D
m
atr
ices
1
,
2
,
…
,
.
Fo
llo
win
g
th
is
s
tep
,
th
e
r
o
ws
an
d
co
lu
m
n
s
o
f
th
e
s
e
m
atr
ices
a
r
e
s
h
u
f
f
led
t
o
d
is
r
u
p
t
s
p
atial
co
r
r
elatio
n
s
,
p
r
o
d
u
ci
n
g
p
er
m
u
ted
m
atr
ices
1
′
,
2
′
,
…
,
′
.
T
h
e
p
r
o
ce
s
s
co
n
tin
u
es
with
f
u
r
th
er
m
o
d
if
icatio
n
o
f
p
ix
el
v
alu
es
th
r
o
u
g
h
ar
ith
m
etic
o
p
e
r
atio
n
s
,
lead
in
g
to
m
at
r
ices
1
′′
,
2
′′
,
…
,
′′
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
A
n
o
ve
l
(
,
)
mu
lti
-
s
ec
r
et
ima
g
e
s
h
a
r
in
g
s
ch
eme
h
a
r
n
ess
in
g
R
N
A
…
(
Ya
s
min
A
b
d
u
l
)
705
Su
b
s
eq
u
en
tly
,
a
k
ey
f
u
n
ctio
n
p
r
o
ce
s
s
es
th
e
p
ix
el
v
alu
es
ac
co
r
d
in
g
to
th
e
GC
A
r
u
les,
d
eter
m
in
ed
b
y
,
s
y
s
tem
atica
lly
iter
atin
g
th
e
f
in
al
2
-
D
m
atr
ices
o
v
er
h
al
f
o
f
th
e
cy
cle
len
g
th
.
T
h
is
iter
ativ
e
p
r
o
ce
s
s
s
ig
n
if
ican
tly
in
cr
ea
s
es
r
an
d
o
m
n
ess
,
r
esu
ltin
g
in
m
atr
ices
1
′′
′
,
2
′′
′
,
…
,
′′
′
.
T
h
ese
f
in
al
tr
an
s
f
o
r
m
ed
m
atr
i
ce
s
ar
e
th
en
co
n
v
er
ted
b
ac
k
in
t
o
im
ag
e
f
o
r
m
,
y
ield
in
g
th
e
en
c
r
y
p
ted
im
ag
es
1
,
2
,
…
,
,
wh
ich
co
r
r
esp
o
n
d
to
th
e
o
r
ig
in
al
im
ag
es.
T
h
is
en
cr
y
p
tio
n
m
et
h
o
d
o
lo
g
y
r
o
b
u
s
tly
o
b
s
cu
r
es
th
e
p
ix
el
v
a
lu
es
b
y
em
p
lo
y
i
n
g
ad
v
an
ce
d
tech
n
iq
u
es
s
u
c
h
as
d
if
f
u
s
io
n
,
p
er
m
u
tatio
n
,
tr
an
s
f
o
r
m
atio
n
,
an
d
iter
ativ
e
p
r
o
ce
s
s
es
g
o
v
er
n
e
d
b
y
th
e
GC
A
r
u
les.
C
o
n
v
er
s
ely
,
im
p
lem
en
tin
g
th
e
r
ev
er
s
e
tech
n
i
q
u
e
allo
ws
f
o
r
th
e
p
r
ec
is
e
r
esto
r
atio
n
o
f
t
h
e
o
r
ig
i
n
al
p
ix
els,
th
er
eb
y
r
eg
en
e
r
atin
g
th
e
d
ec
r
y
p
ted
im
ag
es
1
,
2
,
…
,
,
e
n
s
u
r
in
g
th
e
d
ec
r
y
p
tio
n
p
r
o
c
ess
ac
cu
r
ately
r
ec
o
n
s
tr
u
cts
th
e
o
r
ig
in
al
im
a
g
es.
T
h
e
wo
r
k
f
lo
w
o
f
th
e
p
r
o
p
o
s
ed
tech
n
iq
u
e
is
m
eticu
lo
u
s
ly
elu
cid
ated
in
Fig
u
r
e
2
,
wh
ile
th
e
en
cr
y
p
tio
n
an
d
d
ec
r
y
p
ti
o
n
p
r
o
ce
d
u
r
es
ar
e
d
escr
ib
ed
in
Alg
o
r
ith
m
2
an
d
Alg
o
r
ith
m
3
,
r
esp
ec
tiv
ely
.
Alg
o
r
ith
m
2
.
E
n
cr
y
p
tio
n
p
r
o
c
ed
u
r
e
Input: Original Images
(
,
,
…
,
)
Output: Encrypted Images
(
,
,
…
,
)
1.
Read
,
,
…
,
as input
2.
Perform XOR operation between
original images and key image
●
′
=
⊕
;
′
=
⊕
⋯
′
=
⊕
3.
Convert
′
,
′
,
…
,
′
into 2
-
D matrices
,
,
…
,
4.
Permute
,
,
…
,
to
′
,
′
,
…
,
′
●
For each
′
(
=
)
interchange rows
↔
columns
5.
Modify the pixel value of matrix
′
′′
●
′′
=
(
(
×
′
)
times, where
is an integer
6.
Apply key function to iterate each matrix
′′
to obtain
the final encrypted matri
x
′′′
•
′′′
=
(
′′
)
7.
Transform
matrix
′′
′
(
=
)
in
to
im
ag
es
an
d
st
or
e
th
em
as
en
cr
yp
te
d
im
ag
es
,
,
…
,
Alg
o
r
ith
m
3
.
Dec
r
y
p
tio
n
p
r
o
c
ed
u
r
e
Input: Encrypted Images
(
,
,
…
,
)
Output: Original Images (
,
,
…
,
)
1.
Input the encrypted images
,
,
…
,
2.
Convert each encrypted image
into its corresponding 2
-
D matrix form
′′
′
for
=
3.
Apply key function on
′′
, where
′′
denotes the decrypted 2
-
D matrix
•
′′
=
(
′′′
)
4.
Transform each matrix
′′
to obtain
′
for modifying the pixel values
•
′
=
(
(
′
×
′′
)
)
, where
′
is a multiplicative integer of
∀
=
5.
Revert the permutation of
′
to derive matrices
(
=
)
•
=
interchange rows
↔
columns
(
′
)
6.
Perform the XOR operation amid
and
′
to retrieve the original pixel values
•
Calculate
=
⊕
for each matrix
,
∀
=
7.
Obtain decrypted images
,
,
…
,
from restored pixel values
,
,
…
Fig
u
r
e
2
.
Flo
wch
ar
t
o
f
th
e
p
r
o
p
o
s
ed
(
,
)
MSI
S sch
em
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
3
9
,
No
.
1
,
Ju
ly
20
25
:
700
-
7
0
9
706
3
.
3
.
F
o
rma
t
io
n o
f
k
e
y
f
un
ct
io
n
T
h
e
k
e
y
f
u
n
ctio
n
is
i
n
v
o
k
ed
d
u
r
in
g
b
o
th
th
e
e
n
cr
y
p
tio
n
a
n
d
d
ec
r
y
p
tio
n
p
r
o
ce
s
s
es,
u
tili
zin
g
a
2
-
D
m
atr
ix
as in
p
u
t.
E
ac
h
R
GB
v
alu
e
is
tr
ea
ted
as a
b
lo
ck
a
n
d
is
en
cr
y
p
ted
o
r
d
ec
r
y
p
ted
u
s
in
g
a
GC
A
r
u
le
v
ec
to
r
.
T
h
e
r
u
les
ar
e
s
elec
ted
b
ased
o
n
8
,
wh
er
e
b
e
t
h
e
n
u
m
b
er
o
f
i
m
ag
es.
T
h
is
k
ey
f
u
n
ctio
n
s
ig
n
if
ican
tly
en
h
an
ce
s
r
an
d
o
m
n
ess
b
y
iter
atin
g
o
v
er
th
e
m
atr
ix
,
th
er
e
b
y
f
o
r
tify
in
g
co
n
f
id
en
tiality
,
en
s
u
r
in
g
d
ata
in
teg
r
ity
,
an
d
b
o
ls
ter
in
g
d
ef
e
n
s
e
ag
ain
s
t secu
r
ity
v
u
ln
e
r
ab
ilit
ies.
T
h
e
k
ey
f
u
n
ctio
n
g
e
n
er
atio
n
is
s
h
o
w
n
in
Alg
o
r
ith
m
4
.
Alg
o
r
ith
m
4
.
Gen
er
atio
n
o
f
k
e
y
f
u
n
ctio
n
Input: 2
-
D matrix, GCA rule vector
Output: Iterated matrix (encryption/ decryption)
1.
Load a block from the 2
-
D matrices into an array of length 8
2.
Initialize the array with a designated GCA rule set
3.
Iterate the array using a specific GCA rule
4.
The final output array signifies the encrypted or decrypted value of the original block
5.
Execute Steps 1 through 4 for each RGB value to encrypt or decrypt the entire matrix.
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
cu
r
r
en
t
s
ec
tio
n
co
m
p
r
is
es
a
s
er
ie
s
o
f
r
ig
o
r
o
u
s
ex
p
er
im
en
ts
d
esig
n
ed
to
ass
es
s
an
d
v
alid
ate
th
e
ef
f
ec
tiv
en
ess
an
d
s
u
p
er
io
r
ity
o
f
th
e
p
r
o
p
o
s
ed
(
,
)
MSI
S
m
o
d
e
l.
R
GB
im
ag
es,
s
p
ec
if
ically
a)
B
ab
o
o
n
,
b
)
L
en
a,
an
d
c)
Pep
p
er
,
ea
c
h
s
ized
5
1
2
×
5
1
2
,
we
r
e
s
o
u
r
ce
d
f
r
o
m
th
e
Un
iv
er
s
ity
o
f
W
ater
lo
o
I
m
ag
e
R
ep
o
s
ito
r
y
f
o
r
s
tan
d
ar
d
an
aly
s
is
an
d
c
o
m
p
ar
is
o
n
[
2
6
]
.
T
h
ese
ex
p
er
im
e
n
ts
wer
e
m
eticu
lo
u
s
ly
c
o
n
d
u
c
ted
o
n
an
HP
lap
t
o
p
eq
u
ip
p
e
d
with
a
1
2
th
-
g
en
er
atio
n
I
n
tel
C
o
r
e
i5
p
r
o
ce
s
s
o
r
an
d
a
5
1
2
GB
SS
D.
Py
th
o
n
s
o
f
twar
e
was
u
tili
z
ed
to
r
u
n
th
e
a
n
aly
s
is
,
an
d
th
e
r
esu
lts
will b
e
p
r
esen
ted
in
th
e
f
o
llo
win
g
s
ec
tio
n
s
.
1)
Statis
t
ical
an
aly
s
is
:
th
e
ev
alu
atio
n
o
f
s
ec
u
r
ity
in
en
c
r
y
p
ted
im
ag
es
is
ac
h
iev
ed
th
r
o
u
g
h
h
is
to
g
r
am
an
d
co
r
r
elatio
n
an
al
y
s
is
.
His
to
g
r
am
an
aly
s
is
ass
e
s
s
e
s
p
ix
el
in
ten
s
ity
d
i
s
tr
ib
u
tio
n
s
f
o
r
u
n
i
f
o
r
m
ity
,
wh
ile
th
e
co
r
r
elatio
n
co
ef
f
icien
t
m
ea
s
u
r
es
th
e
r
esem
b
lan
ce
b
etwe
en
n
eig
h
b
o
r
i
n
g
p
ix
els
(
h
o
r
izo
n
tal,
v
er
tical,
an
d
d
iag
o
n
al
)
,
aim
in
g
f
o
r
v
al
u
es
clo
s
e
to
ze
r
o
.
T
ab
le
5
d
is
p
lay
s
s
m
o
o
th
er
,
f
latter
h
is
to
g
r
am
d
i
s
tr
ib
u
tio
n
s
f
o
r
th
e
en
cr
y
p
ted
im
a
g
es,
an
d
T
a
b
le
6
r
ev
ea
ls
a
n
eg
lig
ib
le
ass
o
ciatio
n
b
etwe
en
th
e
o
r
ig
in
al
an
d
en
cr
y
p
ted
im
ag
es,
co
n
f
ir
m
i
n
g
th
e
p
r
o
p
o
s
ed
m
o
d
el'
s
r
esis
tan
ce
to
s
tatis
t
ical
attac
k
s
.
T
ab
le
5
.
His
to
g
r
am
a
n
aly
s
is
o
f
th
e
p
r
o
p
o
s
ed
(
,
)
MSI
S sch
em
e
O
r
i
g
i
n
a
l
i
ma
g
e
s
En
c
r
y
p
t
e
d
i
ma
g
e
s
H
i
st
o
g
r
a
m
o
f
o
r
i
g
i
n
a
l
i
m
a
g
e
s
H
i
st
o
g
r
a
m
o
f
e
n
c
r
y
p
t
e
d
i
ma
g
e
s
2)
I
n
f
o
r
m
atio
n
en
tr
o
p
y
an
aly
s
is
:
e
n
tr
o
p
y
q
u
an
tifie
s
th
e
u
n
p
r
ed
ictab
ilit
y
an
d
r
an
d
o
m
n
ess
o
f
d
ata,
with
v
alu
es
clo
s
e
to
8
in
d
icatin
g
a
u
n
if
o
r
m
p
ix
el
v
alu
e
d
is
tr
ib
u
ti
o
n
.
T
h
is
s
ig
n
if
ies
a
r
o
b
u
s
t
cip
h
er
th
at
is
les
s
s
u
s
ce
p
tib
le
to
s
ec
u
r
ity
b
r
ea
ch
e
s
.
3)
Dif
f
er
en
tial
attac
k
an
aly
s
is
:
d
i
f
f
er
en
tial
attac
k
s
ass
er
t
th
at
e
v
en
m
in
o
r
m
o
d
if
icatio
n
s
to
th
e
p
ix
els
o
f
a
n
o
r
ig
in
al
im
a
g
e
s
h
o
u
ld
r
esu
lt
in
s
ig
n
if
ican
t
c
h
an
g
es
in
th
e
co
r
r
esp
o
n
d
in
g
cip
h
er
im
ag
e.
T
h
is
ca
n
b
e
ev
alu
ated
u
s
in
g
th
e
n
u
m
b
e
r
o
f
p
ix
els
ch
an
g
e
r
ate
(
NPC
R
)
an
d
th
e
u
n
if
ied
av
er
a
g
e
ch
a
n
g
in
g
in
ten
s
ity
(
UACI)
,
wh
ich
p
r
o
v
id
e
b
o
t
h
q
u
an
titativ
e
an
d
q
u
alitativ
e
ass
ess
m
en
ts
o
f
th
e
cip
h
er
im
ag
es.
Gen
er
ally
,
h
ig
h
er
NPC
R
an
d
UACI
s
co
r
es si
g
n
if
y
g
r
ea
ter
r
esis
tan
ce
to
th
ese
attac
k
s
.
4)
Pix
el
d
is
p
ar
ity
an
aly
s
is
:
p
ix
el
d
is
p
ar
ity
ev
alu
ates
th
e
r
elatio
n
s
h
ip
am
id
p
lain
an
d
cip
h
er
im
ag
es.
T
h
e
p
ea
k
s
ig
n
al
-
to
-
n
o
is
e
r
atio
(
PS
NR
)
an
d
m
ea
n
s
q
u
ar
e
e
r
r
o
r
(
MSE
)
ar
e
wid
ely
r
ec
o
g
n
ize
d
m
eth
o
d
s
u
s
ed
t
o
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
A
n
o
ve
l
(
,
)
mu
lti
-
s
ec
r
et
ima
g
e
s
h
a
r
in
g
s
ch
eme
h
a
r
n
ess
in
g
R
N
A
…
(
Ya
s
min
A
b
d
u
l
)
707
g
au
g
e
th
is
r
elatio
n
s
h
ip
.
T
h
e
PS
NR
v
alu
e
r
ef
lects
im
ag
e
d
is
to
r
tio
n
,
wh
er
e
a
lo
wer
PS
N
R
an
d
g
r
ea
ter
MSE
s
ig
n
if
y
b
etter
en
c
r
y
p
tio
n
ef
f
ec
tiv
en
ess
d
u
r
in
g
th
e
ass
ess
m
en
ts
.
T
h
e
r
esu
lts
f
o
r
test
s
2
to
4
,
en
co
m
p
ass
in
g
en
tr
o
p
y
,
NPC
R
,
UACI,
MSE
,
an
d
PS
N
R
f
o
r
th
e
p
r
o
p
o
s
ed
m
o
d
el,
h
av
e
b
ee
n
r
ig
o
r
o
u
s
ly
c
o
m
p
ar
ed
with
ex
is
tin
g
im
ag
e
en
cr
y
p
tio
n
tech
n
iq
u
es.
T
ab
le
7
d
em
o
n
s
tr
ates
th
at
th
e
p
r
o
p
o
s
ed
m
o
d
el
s
u
r
p
ass
es
all
o
th
er
s
ac
r
o
s
s
th
ese
m
etr
ics
an
d
ex
h
ib
its
ex
ce
p
tio
n
ally
h
i
g
h
e
n
tr
o
p
y
,
n
ea
r
in
g
7
.
9
9
8
6
,
in
d
icativ
e
o
f
s
tr
o
n
g
e
n
cr
y
p
tio
n
r
an
d
o
m
n
ess
.
Ad
d
itio
n
ally
,
it
ac
h
ie
v
es
an
a
v
er
ag
e
UACI
o
f
3
4
.
3
0
3
7
an
d
an
NPC
R
o
f
9
9
.
9
2
3
6
,
r
ef
l
ec
tin
g
r
o
b
u
s
t
r
esis
tan
ce
to
d
if
f
er
en
tial
attac
k
s
.
Fu
r
th
er
m
o
r
e,
th
e
m
o
d
el
ac
h
ie
v
es
an
av
er
a
g
e
MSE
o
f
7
4
.
5
2
3
3
an
d
PS
NR
o
f
2
4
.
6
0
3
3
,
s
ig
n
if
y
in
g
c
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