I
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Jou
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Com
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g
(
I
JE
CE
)
Vol.
1
4
,
No.
5
,
Oc
tober
20
2
4
,
pp
.
5330
~
5343
I
S
S
N:
2088
-
8708
,
DO
I
:
10
.
11591/i
jec
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.
v
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i
5
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pp
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330
-
5343
5330
Jou
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:
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c
ipher
C
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map
R
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Af
f
ine
tr
a
ns
f
o
r
mation
E
nc
r
ypti
on
Th
i
s
i
s
a
n
o
p
en
a
c
ces
s
a
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t
i
c
l
e
u
n
d
e
r
t
h
e
CC
B
Y
-
SA
l
i
ce
n
s
e.
C
or
r
e
s
pon
din
g
A
u
th
or
:
Hic
ha
m
R
r
ghout
M
AT
S
I
L
a
bor
a
tor
y,
High
S
c
hool
of
T
e
c
hnology,
M
oha
mm
e
d
F
ir
s
t
Unive
r
s
it
y
Oujda
,
M
or
oc
c
o
E
mail:
h
.
r
r
ghou
t@um
p.
a
c
.
ma
1.
I
NT
RODU
C
T
I
ON
W
it
h
the
inc
r
e
a
s
ing
c
onne
c
ti
vit
y
a
nd
int
e
r
ope
r
a
bil
it
y
of
de
vice
s
a
nd
onl
ine
platf
o
r
ms
,
da
ta
ha
s
be
c
ome
incr
e
a
s
ingl
y
e
xpos
e
d
to
e
xter
na
l
th
r
e
a
ts
s
uc
h
a
s
ha
c
king,
da
ta
int
e
r
c
e
pti
on
,
a
nd
malwa
r
e
a
tt
a
c
ks
.
T
he
r
e
f
or
e
,
it
ha
s
be
c
ome
e
s
s
e
nti
a
l
to
im
pleme
nt
r
obus
t
s
e
c
ur
it
y
mea
s
ur
e
s
to
e
ns
ur
e
that
da
ta,
i
nc
ludi
ng
digi
tal
im
a
ge
s
,
r
e
mains
c
onf
idential
a
nd
s
e
c
ur
e
thr
oughout
it
s
tr
a
ns
f
e
r
ove
r
ne
two
r
ks
.
T
o
a
dd
r
e
s
s
thi
s
pr
oblem,
s
e
ve
r
a
l
s
e
c
ur
it
y
mea
s
ur
e
s
ha
ve
be
e
n
e
s
tablis
he
d,
a
mong
whic
h
c
r
yptogr
a
phy
[
1]
–
[
4]
holds
a
pr
omi
ne
nt
plac
e
.
I
mage
e
nc
r
ypti
on
f
inds
it
s
uti
l
it
y
in
va
r
ious
domains
,
including
I
nter
ne
t
c
omm
un
ica
ti
ons
,
medic
a
l
im
a
ging,
a
nd
mi
li
tar
y
c
omm
unica
ti
ons
.
E
nc
r
ypti
on
c
a
n
be
c
a
tegor
ize
d
int
o
two
main
types
:
s
ymm
e
tr
ic
a
nd
a
s
ymm
e
tr
ic
[
5]
,
[
6]
.
I
n
s
ymm
e
tr
ic
e
nc
r
ypti
on,
the
s
e
nde
r
a
nd
the
r
e
c
e
iver
s
ha
r
e
the
s
a
me
ke
y,
jus
t
li
ke
in
the
Hill
c
ipher
a
nd
the
Vige
nè
r
e
c
ipher
[
7]
,
[
8]
,
while
in
a
s
ymm
e
tr
ic
e
nc
r
ypti
on,
two
dis
ti
nc
t
ke
ys
a
r
e
us
e
d.
T
he
f
i
r
s
t
ke
y
c
a
ll
e
d
the
publi
c
ke
y,
is
us
e
d
by
the
s
e
nde
r
to
e
nc
r
ypt
the
me
s
s
a
ge
,
while
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s
e
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ond
ke
y
,
c
a
ll
e
d
the
pr
ivate
ke
y,
is
us
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d
by
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r
e
c
e
iver
to
de
c
r
ypt
the
mes
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a
ge
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s
in
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he
R
ives
t
–
S
ha
mi
r
–
Adle
man
(
R
S
A)
e
nc
r
ypti
on
[
9]
,
[
10
]
.
R
e
c
e
ntl
y,
s
e
ve
r
a
l
tec
hniques
ha
ve
s
hown
their
e
f
f
e
c
ti
ve
ne
s
s
in
inf
or
mation
t
r
a
ns
f
e
r
,
a
mong
whic
h
a
r
e
c
ha
os
-
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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J
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&
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omp
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I
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N:
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8708
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e
w
image
e
nc
r
y
pti
on
appr
oac
h
us
ing
a
dy
namic
-
c
haoti
c
v
ar
iant
of
Hill
c
ipher
in
…
(
Hic
ham
R
r
gho
ut
)
5331
ba
s
e
d
tec
hniques
[
11]
–
[
14]
.
C
ha
os
,
a
s
a
c
ompl
e
x
a
nd
unpr
e
dicta
ble
phe
nomenon
inher
e
nt
in
nonli
ne
a
r
dyna
mi
c
a
l
s
ys
tems
,
ha
s
ge
ne
r
a
ted
incr
e
a
s
ing
int
e
r
e
s
t
in
the
f
ield
of
e
nc
r
ypti
on
.
T
he
a
ppli
c
a
ti
on
of
c
ha
os
in
e
nc
r
ypti
on
p
r
ovides
f
e
r
ti
le
gr
ound
f
or
e
xplor
ing
ne
w
s
e
c
ur
e
a
ppr
oa
c
he
s
in
the
f
ield
of
c
r
yp
togr
a
phy.
On
the
o
ther
ha
nd,
s
e
ve
r
a
l
e
nc
r
ypti
on
tec
hniques
ha
ve
be
e
n
de
ve
loped
,
a
mong
whic
h
is
the
Hill
c
ipher
[
15
]
,
[
16]
,
whic
h
is
a
c
las
s
ica
l
tec
hnique
ge
ne
r
a
ll
y
a
ppli
e
d
to
text
.
I
t
is
ba
s
e
d
on
two
s
teps
:
the
f
ir
s
t
is
the
de
c
ompos
it
ion
of
the
p
laintext
int
o
b
locks
of
s
ize
n
,
whe
r
e
(
n
,
n)
r
e
p
r
e
s
e
nts
the
s
ize
of
the
f
ixed
inver
ti
b
le
mat
r
ix
in
a
c
a
r
e
f
ul
ly
s
e
lec
ted
r
ing.
T
his
matr
ix
is
c
ons
ider
e
d
the
e
nc
r
ypti
on
ke
y.
T
he
n,
e
a
c
h
block
is
tr
a
ns
f
or
med
us
ing
the
ke
y
mat
r
ix
to
obtain
the
e
nc
r
ypted
i
mage
.
Although
the
Hi
ll
c
ipher
of
f
e
r
s
a
dva
ntage
s
,
l
ike
other
c
las
s
ica
l
c
r
yptogr
a
phic
tec
hniques
,
it
ha
s
c
e
r
tain
li
mi
tations
that
r
e
qui
r
e
s
pe
c
ial
a
tt
e
nti
on.
T
he
r
e
f
or
e
,
many
r
e
s
e
a
r
c
he
r
s
ha
ve
r
e
li
e
d
on
c
omb
ini
ng
the
Hill
c
ipher
a
nd
c
ha
os
to
e
nha
nc
e
da
ta
s
e
c
ur
it
y.
Qobbi
e
t
al.
[
17]
pr
opos
e
d
a
nove
l
method
f
or
e
nc
r
ypti
ng
c
olor
im
a
ge
s
.
T
he
y
e
mpl
oye
d
a
n
a
f
f
ine
tr
a
ns
f
or
m
a
ti
on
with
a
n
inver
ti
ble
matr
ix
a
nd
a
dyna
mi
c
tr
a
ns
lation
ve
c
tor
to
pr
oc
e
s
s
im
a
ge
blocks
.
A
s
ub
s
ti
tut
ion
matr
ix
c
ontr
oll
e
d
by
c
ha
oti
c
maps
wa
s
us
e
d
f
or
pr
e
li
mi
na
r
y
c
onf
us
ion.
I
n
thei
r
a
r
ti
c
le
,
J
a
r
jar
e
t
al
.
[
18
]
pr
o
pos
e
d
a
ne
w
e
nc
r
ypti
on
s
ys
tem
f
or
a
r
bit
r
a
r
y
-
s
ize
d
c
olor
im
a
ge
s
.
T
his
a
ppr
oa
c
h
e
nha
nc
e
s
the
c
la
s
s
ic
a
l
Hill
method
by
us
ing
a
(
3×
3)
inver
ti
ble
mat
r
ix
in
the
r
ing
Z
/256Z
.
S
im
ulat
ions
c
onduc
ted
on
a
wide
r
a
nge
of
im
a
ge
s
de
mons
tr
a
te
that
thi
s
a
ppr
oa
c
h
c
a
n
withs
tand
va
r
ious
known
a
tt
a
c
ks
.
Almaia
h
e
t
al.
[
19
]
pr
opo
s
e
d
a
ne
w
hybr
id
e
nc
r
ypti
on
a
ppr
oa
c
h
be
twe
e
n
the
e
ll
ipt
ic
c
ur
ve
c
r
yptos
ys
tem
a
nd
Hill
c
ipher
(
E
C
C
HC
)
t
o
c
onve
r
t
Hill
c
ipher
f
r
om
a
s
ymm
e
tr
ic
tec
hniq
ue
to
a
n
a
s
ymm
e
tr
ic
one
,
ther
e
by
e
nha
nc
ing
it
s
s
e
c
ur
it
y
a
nd
e
f
f
icie
nc
y
a
nd
r
e
s
is
ti
ng
a
tt
a
c
ks
.
S
a
ntos
o
[
20
]
uti
li
z
e
d
hybr
id
e
nc
r
ypti
on
by
c
ombi
ning
Hill
c
ipher
with
a
3×
3
matr
ix
ke
y
a
nd
R
S
A
c
r
yptogr
a
phy
with
a
512
-
bit
ke
y.
T
he
de
mons
tr
a
ti
on
indi
c
a
tes
that
thi
s
a
ppr
oa
c
h
ove
r
c
omes
s
e
c
ur
it
y
is
s
u
e
s
dur
ing
da
ta
e
xc
ha
ng
e
,
e
ns
ur
ing
that
s
e
nt
mes
s
a
g
e
s
c
a
nnot
be
r
e
a
d
by
una
uthor
ize
d
in
divi
dua
ls
.
Ve
r
ma
a
nd
Aga
r
wa
l
[
21]
p
r
opos
e
d
a
n
a
dva
nc
e
d
a
nd
hybr
id
c
r
yptos
ys
tem
in
whic
h
a
62×
62
table
i
s
e
mpl
oye
d
ins
tea
d
of
26,
a
nd
the
Hill
c
ipher
is
c
ombi
ne
d
with
it
to
bols
ter
s
e
c
ur
it
y
.
I
n
thi
s
a
r
ti
c
le,
we
pr
opos
e
the
us
e
of
a
n
inver
ti
bl
e
matr
ix
of
dim
e
ns
ion
(
4×
4)
ope
r
a
ti
ng
withi
n
the
r
ing
Z/
2
12
Z
.
T
his
c
ombi
na
ti
on
a
dds
e
xtr
a
c
ompl
e
xit
y,
making
the
tas
k
of
potential
a
tt
a
c
ke
r
s
mor
e
c
ha
ll
e
nging.
T
h
is
manus
c
r
ipt
is
s
tr
uc
tur
e
d
a
s
f
oll
o
ws
:
s
e
c
ti
on
1
pr
ovides
the
int
r
oduc
ti
on,
whe
r
e
we
a
ddr
e
s
s
the
is
s
ue
of
im
a
ge
tr
a
ns
f
e
r
s
e
c
ur
it
y
a
nd
va
r
ious
t
e
c
hniques
to
tac
kle
thi
s
p
r
oblem.
I
n
s
e
c
ti
on
2,
w
e
pr
e
s
e
nt
s
ome
pr
e
vious
r
e
s
e
a
r
c
h.
T
he
n,
in
the
thi
r
d
s
e
c
ti
on,
we
de
s
c
r
ibe
our
pr
opos
e
d
method
.
S
e
c
ti
on
4
f
oc
us
e
s
on
pr
e
s
e
nti
ng
the
r
e
s
ult
s
obtaine
d
a
nd
thei
r
c
ompar
is
o
n
with
pr
e
vious
wo
r
ks
.
F
inal
ly,
we
c
onc
lude
our
s
tudy.
2.
P
ROP
OS
E
D
M
E
T
HO
D
I
n
thi
s
wo
r
k,
we
p
r
opos
e
a
c
ombi
na
ti
on
of
c
ha
o
s
a
nd
the
Hil
l
c
ipher
,
whe
r
e
the
e
leme
nts
of
a
n
inver
ti
ble
matr
ix
of
s
ize
(
4×
4)
ope
r
a
te
withi
n
th
e
r
ing
Z/
2
12
Z
.
T
his
innovative
a
ppr
oa
c
h
a
im
s
to
lev
e
r
a
ge
c
ha
oti
c
c
ha
r
a
c
ter
is
ti
c
s
to
e
nha
nc
e
r
e
s
is
tanc
e
a
ga
ins
t
va
r
ious
c
r
yptogr
a
phic
a
tt
a
c
ks
.
T
he
int
e
gr
a
ti
on
of
c
ha
os
a
nd
the
Hill
c
ipher
pa
ve
s
the
wa
y
f
or
s
igni
f
ica
nt
a
dva
nc
e
ments
in
de
s
igni
ng
r
obus
t
e
nc
r
ypti
on
s
ys
tem
s
tailor
e
d
to
c
u
r
r
e
nt
in
f
or
mation
s
e
c
ur
it
y
c
ha
ll
e
nge
s
.
Our
s
tudy
is
s
tr
uc
tur
e
d
a
s
f
ol
lows
:
S
tep
1:
Ge
ne
r
a
ti
on
of
c
ha
oti
c
s
e
que
nc
e
s
S
tep
2:
P
r
e
pa
r
a
ti
on
o
f
the
or
igi
na
l
im
a
ge
of
s
ize
1×
3NM
.
−
Ve
c
tor
iza
ti
on
of
the
or
igi
na
l
im
a
ge
−
T
r
a
ns
it
ion
f
r
om
the
r
ing
Z
/
2
8
Z
to
the
r
ing
Z
/
2
12
Z
S
tep
3:
C
r
e
a
ti
on
of
the
c
onf
us
ion
matr
ix
S
tep
4:
C
r
e
a
ti
on
of
the
dif
f
us
ion
matr
ix
S
tep
5:
E
nc
r
ypti
on
pr
oc
e
s
s
on
the
r
ing
Z
/
2
12
Z
S
tep
6:
T
r
a
ns
it
ion
f
r
om
the
r
ing
Z
/
2
12
Z
to
Z
/
2
8
Z
2.
1.
Gener
at
ion
of
c
h
aot
ic
s
e
q
u
e
n
c
e
s
B
a
s
e
d
on
the
c
on
c
e
pt
of
c
ha
os
,
thi
s
s
tudy
e
mpl
oy
s
two
of
the
mos
t
r
e
nowne
d
c
ha
oti
c
maps
in
the
f
ield
of
c
r
yptog
r
a
phy.
T
he
s
e
maps
a
r
e
s
e
lec
ted
f
or
thei
r
e
f
f
e
c
ti
ve
ne
s
s
a
nd
wide
s
pr
e
a
d
r
e
c
ognit
ion.
T
he
ir
uti
li
z
a
ti
on
a
im
s
to
e
nha
nc
e
the
s
e
c
ur
it
y
a
nd
c
ompl
e
xit
y
of
ou
r
c
r
yptog
r
a
phic
methods
.
2.
1.
1.
T
h
e
s
in
e
m
ap
I
n
thi
s
s
tudy,
we
f
oc
us
on
the
one
-
dim
e
ns
ional
c
ha
oti
c
s
ine
map
[
22
]
.
I
t
is
a
we
ll
-
known
c
ha
oti
c
map
us
e
d
in
c
r
yptogr
a
phy
.
T
he
e
xpr
e
s
s
ion
f
or
thi
s
map
is
given
by
(
1)
.
+
1
=
(
)
(
1)
W
it
h
∈
[
0,
1
]
a
s
the
c
ont
r
ol
pa
r
a
mete
r
e
xhibi
ti
ng
c
h
a
oti
c
be
ha
vior
f
o
r
∈
[
0.
87
,
1
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8708
I
nt
J
E
lec
&
C
omp
E
ng
,
Vol
.
1
4
,
No.
5
,
Oc
tober
2
02
4
:
5330
-
5343
5332
2.
1.
2.
T
h
e
P
WL
CM
m
ap
P
iec
e
wis
e
li
ne
a
r
c
ha
oti
c
map
(
P
W
L
C
M
)
[
23]
a
r
e
uti
li
z
e
d
to
ge
ne
r
a
te
ps
e
udo
-
r
a
ndom
s
e
que
nc
e
s
f
or
c
r
yptogr
a
phic
a
ppli
c
a
ti
ons
.
T
he
s
e
maps
a
r
e
e
f
f
e
c
ti
ve
in
e
nha
nc
ing
s
e
c
ur
it
y.
T
he
mathe
matica
l
de
f
i
nit
ion
is
pr
ovided
in
(
2)
.
y
n
=
F
(
y
n
−
1
,
d
)
=
{
−
1
,
0
≤
−
1
≤
−
1
−
0
.
5
−
,
≤
−
1
≤
0
.
5
(
1
−
−
1
,
)
,
≤
−
1
≤
1
2)
T
he
P
W
L
C
M
is
known
to
e
xhibi
t
c
ha
oti
c
be
ha
vio
r
whe
n
it
s
c
hos
e
n
ini
ti
a
l
c
ondit
ion
li
e
s
withi
n
the
int
e
r
va
l:
0
∈
[
0;
1
]
a
nd
it
s
pa
r
a
mete
r
d
∈
[
0;
0
.
5
]
.
2.
2.
P
r
e
p
ar
in
g
t
h
e
or
igi
n
al
im
age
o
f
s
ize
N×
M
Af
ter
loading
the
or
igi
na
l
im
a
ge
of
s
ize
N×
M
a
nd
e
xtr
a
c
ti
ng
thr
e
e
c
olor
c
ha
nne
ls
,
the
im
a
ge
unde
r
goe
s
the
f
oll
owing
tr
a
ns
f
or
mations
:
−
T
he
2
-
dim
e
ns
ional
a
r
r
a
y
r
e
pr
e
s
e
nti
ng
the
im
a
ge
i
s
tr
a
ns
f
or
med
int
o
a
one
-
dim
e
ns
ional
a
r
r
a
y
U
of
s
ize
(
1×
3NM
)
.
−
T
he
e
leme
nts
of
a
r
r
a
y
U
a
r
e
c
onve
r
ted
to
the
r
ing
2
12
Z.
2.
2.
1.
Gener
at
in
g
p
s
e
u
d
o
-
r
an
d
o
m
ve
c
t
or
s
L
an
d
C
T
o
int
r
oduc
e
a
ps
e
udo
-
r
a
ndom
a
s
pe
c
t
to
the
i
mage
pr
e
pa
r
a
ti
on
pha
s
e
,
we
will
us
e
a
ps
e
udo
-
r
a
ndom
ve
c
tor
L
of
s
ize
1×
3NM
ge
ne
r
a
ted
f
r
om
c
ha
oti
c
m
a
ps
us
ing
Algor
it
hm
1:
Algor
it
hm
1
.
Ge
ne
r
a
ti
on
of
a
ps
e
udo
-
r
a
ndom
ve
c
tor
For i=0 to 3NM
-
1
L
[
i
]
=
in
t
(
(
x[i]
)
*
10
9
)
%50
T
he
ps
e
udo
-
r
a
ndom
ve
c
tor
L
wi
ll
be
us
e
d
to
ge
n
e
r
a
te
a
nother
ps
e
udo
-
r
a
ndom
ve
c
tor
C
in
the
r
ing
Z
/3Z
of
s
ize
1×
3NM
,
s
ubdivi
de
d
in
to
blocks
of
th
r
e
e
e
lem
e
nts
,
with
e
a
c
h
block
c
ontaining
dis
ti
nc
t
va
lues
of
0,
1
,
a
nd
2.
T
he
us
e
o
f
ve
c
tor
C
a
ll
ows
f
or
the
c
r
e
a
ti
on
of
a
r
a
ndom
dis
tr
ibut
ion
of
e
leme
nts
f
r
om
the
thr
e
e
ve
c
tor
s
r
e
pr
e
s
e
nti
ng
the
thr
e
e
c
ha
nne
ls
(
R
,
G,
B
)
,
a
s
we
l
l
a
s
the
c
r
e
a
ti
on
o
f
c
ontr
oll
e
d
ps
e
udo
-
r
a
ndom
s
e
que
nc
e
s
.
T
his
is
a
c
c
ompl
is
he
d
a
c
c
or
ding
to
Algo
r
it
hm
2
a
s
:
Algor
it
hm
2
.
P
s
e
udo
-
r
a
ndom
ve
c
tor
C
For i=0 to NM
-
1
d=0
For j=0 to 3NM
-
1
For k=0 to 2
If L[3i+k]==j
C[3i+k]=d
d=d+1
2.
2.
2.
Ve
c
t
or
izat
ion
of
t
h
e
or
igi
n
al
i
m
age
T
he
thr
e
e
c
ha
nne
ls
(
R
,
G
,
B
)
a
r
e
c
onve
r
ted
int
o
th
r
e
e
ve
c
tor
s
VR
,
VG
,
a
nd
VB
,
e
a
c
h
of
s
ize
1×
NM
.
T
he
s
e
thr
e
e
ve
c
tor
s
a
r
e
c
onc
a
tena
ted
to
ge
ne
r
a
te
the
one
-
dim
e
ns
ional
ve
c
tor
U
of
s
ize
1×
3NM
,
us
ing
the
ps
e
udo
-
r
a
ndom
ve
c
tor
C
.
T
he
a
s
s
ignm
e
nt
of
e
leme
nts
to
the
ve
c
tor
U
of
r
a
nk
i
is
a
s
f
oll
ows
:
−
If
(
)
=
0
,
the
e
leme
nt
c
omes
f
r
om
ve
c
tor
VR
−
If
(
)
=
1
,
the
e
leme
nt
c
omes
f
r
om
ve
c
tor
VG
−
If
(
)
=
2
,
the
e
leme
nt
c
omes
f
r
om
ve
c
tor
VB
T
his
is
a
c
hieve
d
us
ing
Algor
it
hm
3:
Algor
it
hm
3
.
Ve
c
tor
iza
ti
on
of
the
or
igi
na
l
im
a
ge
For i =0 to NM
-
1
For k=0 to 2:
if C[3i+k]==0 then
U[3i+k]=VR[i]
else if C[3i+k]==1 then
U[3i+k]=VG[i]
else:
U[3i+k]=VB[i]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
E
lec
&
C
omp
E
ng
I
S
S
N:
2088
-
8708
N
e
w
image
e
nc
r
y
pti
on
appr
oac
h
us
ing
a
dy
namic
-
c
haoti
c
v
ar
iant
of
Hill
c
ipher
in
…
(
Hic
ham
R
r
gho
ut
)
5333
F
igur
e
1
pr
ovides
a
de
tailed
br
e
a
kdown
o
f
the
va
r
ious
s
tage
s
of
the
ve
c
tor
iza
ti
on
pr
oc
e
s
s
.
T
his
pr
oc
e
s
s
e
f
f
e
c
ti
ve
ly
r
e
duc
e
s
the
int
e
ns
e
c
or
r
e
lation
be
twe
e
n
a
djac
e
nt
pixels
.
W
e
c
a
n
thi
nk
of
thi
s
f
i
r
s
t
s
tep
a
s
a
moder
a
te
f
or
m
of
e
nc
r
ypti
on
of
the
o
r
igi
na
l
im
a
ge
.
A
s
e
c
ond
c
yc
le
is
ne
c
e
s
s
a
r
y
to
incr
e
a
s
e
the
c
omp
lexity
of
our
method,
thus
making
dif
f
e
r
e
nti
a
l
a
tt
a
c
ks
mor
e
dif
f
icult
to
pe
r
f
or
m
.
F
igur
e
1.
P
s
e
udo
-
r
a
ndom
ve
c
tor
iza
ti
on
pr
oc
e
s
s
of
t
he
im
a
ge
2.
2.
3.
T
r
an
s
it
ion
f
r
om
t
h
e
r
in
g
Z
/
Z
t
o
t
h
e
r
in
g
Z
/
Z
T
he
tr
a
ns
it
ion
f
r
om
the
r
ing
Z
/
2
8
Z
to
the
r
ing
Z
/
2
12
Z
a
im
s
to
e
nha
nc
e
the
r
obus
tne
s
s
a
nd
s
e
c
ur
it
y
of
the
e
nc
r
ypti
on
p
r
oc
e
s
s
.
Af
ter
ve
c
tor
izing
the
or
ig
inal
im
a
ge
,
a
l
l
e
leme
nts
of
U
a
r
e
c
onve
r
ted
int
o
a
n
8
-
bit
binar
y
f
or
m
,
a
nd
a
f
ter
c
onc
a
tena
ti
ng
a
ll
the
bit
s
,
e
a
c
h
block
of
12
bit
s
of
the
r
e
s
ult
ing
ve
c
tor
is
c
onve
r
ted
int
o
a
de
c
im
a
l
va
lue
(
V
i
)
in
the
r
ing
Z
/
2
12
Z.
F
igu
r
e
2
il
lus
tr
a
tes
the
va
r
ious
s
teps
ne
c
e
s
s
a
r
y
to
obtain
the
ve
c
tor
V
of
s
ize
1×
2NM
in
the
r
ing
Z
/
2
12
Z.
F
igur
e
2.
Ada
pti
ng
the
im
a
ge
to
a
ve
c
tor
of
s
ize
(
1
×
2NM
)
2.
2.
4.
Adap
t
at
ion
of
t
h
e
ve
c
t
or
V
s
ize
As
we
will
be
us
ing
Hil
l
matr
ice
s
of
or
de
r
(
4×
4
)
,
we
divi
de
the
ve
c
tor
V
int
o
two
s
ub
-
ve
c
tor
s
:
−
Ve
c
tor
W
of
s
ize
(
1×
4t)
,
whe
r
e
t
is
the
number
o
f
blocks
of
s
ize
4
.
−
Ve
c
tor
Z
o
f
s
ize
(
1×
r
)
,
whe
r
e
r
r
e
pr
e
s
e
nts
the
s
ize
of
the
ve
c
tor
to
be
tr
unc
a
ted.
T
he
s
ize
s
of
W
a
nd
Z
a
r
e
de
ter
mi
ne
d
ba
s
e
d
on
the
f
oll
owing
e
xpr
e
s
s
ions
:
2
[
4]
0
≤
≤
3
=
2
N
M
-
r
4
W
i
th
:
is
th
e
s
i
z
e
o
f
i
f
≠
0
;
i
s
the
nu
m
be
r
o
f
bl
oc
ks
o
f
s
ize
4
.
T
h
is
d
iv
is
io
n
is
i
ll
us
t
r
a
te
d
b
y
A
lg
o
r
i
t
hm
4:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8708
I
nt
J
E
lec
&
C
omp
E
ng
,
Vol
.
1
4
,
No.
5
,
Oc
tober
2
02
4
:
5330
-
5343
5334
Algor
it
hm
4
.
Adjus
tm
e
nt
o
f
the
im
a
ge
s
ize
/
/
Construction de W
For i=0 to 4t
-
1
W(i)=V(i)
Next i
/
/
Construction de Z
For i=4t to 2
N
M
-
1
Z(i)=V(i)
Next i
T
his
a
da
ptation
is
il
lus
tr
a
ted
by
F
igu
r
e
3
.
F
igur
e
3.
Ada
ptation
o
f
the
im
a
ge
ve
c
tor
d
im
e
ns
ion
2.
3.
I
m
p
r
ove
m
e
n
t
of
Hi
ll
c
ip
h
e
r
Hill
c
ipher
is
a
n
e
nc
r
ypti
on
tec
hnique
that
r
e
li
e
s
on
matr
ix
manipulation
a
nd
mat
r
ix
c
a
lcula
ti
ons
to
e
nc
r
ypt
da
ta.
I
n
our
s
ys
tem,
we
ha
ve
incor
por
a
ted
two
matr
ice
s
:
−
T
he
f
i
r
s
t
matr
ix
C
H
1
,
is
of
s
ize
4×
4,
whic
h
is
inver
ti
ble
a
nd
us
e
d
f
or
the
c
on
f
us
ion
pr
oc
e
s
s
.
−
T
he
s
e
c
ond
matr
ix
C
H
2
,
a
ls
o
of
s
ize
4×
4,
whic
h
is
not
ne
c
e
s
s
a
r
il
y
inver
ti
ble
a
nd
us
e
d
f
o
r
di
f
f
us
ion.
T
o
ove
r
c
ome
the
li
ne
a
r
it
y
is
s
ue
a
s
s
oc
iate
d
with
Hill
c
ipher
,
we
incor
po
r
a
te
two
ps
e
udo
-
r
a
ndom
ve
c
tor
s
,
de
noted
by
K
a
nd
T
,
of
s
ize
1
2NM
,
de
f
ined
by
Algor
it
hm
5
a
s
f
oll
ows
:
Algor
it
hm
5
.
Ge
ne
r
a
ti
on
of
two
c
ha
oti
c
ve
c
tor
s
F
or i =
0 to 2NM
-
1
K[i]=int
(
(
max
(
x
[
i
]
,y
[
i
]
)
*
10
9
)
)
%
2
12
T[i]=int
(
(
min
(
x
[
i
]
,y
[
i
]
)
*
10
9
)
)
%
2
12
2.
3.
1.
Cons
t
r
u
c
t
ion
of
t
h
e
c
on
f
u
s
ion
m
at
r
ix
I
n
our
a
pp
r
oa
c
h,
the
im
pr
ove
ment
o
f
the
Hil
l
c
i
phe
r
invol
ve
s
ge
ne
r
a
ti
ng
a
n
inver
t
ibl
e
matr
ix
of
or
de
r
(
4×
4)
by
us
ing
the
pr
oduc
t
of
two
matr
i
c
e
s
A
a
nd
B
,
one
uppe
r
t
r
iangula
r
a
nd
the
oth
e
r
lowe
r
tr
iangula
r
,
whe
r
e
a
ll
e
leme
nts
of
thes
e
matr
ice
s
a
r
e
of
ps
e
udo
-
r
a
ndom
na
tur
e
,
inj
e
c
ted
int
o
the
r
ing
Z
/
2
12
Z.
A
=
(
a1
a2
a3
a4
0
a5
a6
a7
0
0
a8
a9
0
0
0
a10
)
a
nd
=
(
b1
0
0
0
b2
b5
0
0
b3
b6
b8
0
b4
b7
b9
b
10
)
T
he
two
matr
ice
s
A
a
nd
B
a
r
e
inver
ti
ble
if
a
nd
o
nly
if
a
ll
diagona
l
e
leme
nts
of
A
a
nd
B
a
r
e
odd.
T
he
n,
the
inver
s
e
of
C
H
1
is
de
noted
by
C
H
1
-
1
a
nd
is
obtaine
d
by
c
a
lcula
ti
ng
the
pr
oduc
t
o
f
the
inver
s
e
s
of
B
a
nd
A.
−
1
=
∗
−
CH
1
−
1
=
−
1
∗
−
1
2.
3.
2.
Cons
t
r
u
c
t
ion
of
t
h
e
d
if
f
u
s
ion
m
at
r
ix
T
o
e
nha
nc
e
s
e
c
ur
it
y
a
ga
ins
t
br
ute
f
o
r
c
e
a
tt
a
c
ks
a
nd
im
pleme
nt
the
di
f
f
us
ion
pr
oc
e
s
s
,
we
us
e
a
matr
ix
C
H2
of
or
de
r
(
4×
4)
.
T
h
is
matr
ix
is
not
ne
c
e
s
s
a
r
il
y
inver
ti
ble
a
nd
it
s
e
leme
nts
be
long
to
the
r
ing
Z/
2
12
Z
.
T
he
c
omponents
of
C
H2
a
r
e
de
r
ived
f
r
om
c
ha
oti
c
maps
,
uti
li
z
ing
Algor
it
h
m
6
a
s
f
oll
ows
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
E
lec
&
C
omp
E
ng
I
S
S
N:
2088
-
8708
N
e
w
image
e
nc
r
y
pti
on
appr
oac
h
us
ing
a
dy
namic
-
c
haoti
c
v
ar
iant
of
Hill
c
ipher
in
…
(
Hic
ham
R
r
gho
ut
)
5335
Algor
it
hm
6
.
T
he
e
leme
nts
of
matr
ix
C
H
2
For K=0 to 3
:
For j=0 to 3:
CH
2
[k,j]=K[2*N+3*k+j]
2.
4.
E
n
c
r
yp
t
ion
p
r
oc
e
s
s
of
ve
c
t
or
W
ove
r
t
h
e
r
i
n
g
Z
/
Z
2.
4.
1.
I
n
s
t
all
in
g
t
h
e
d
if
f
u
s
ion
p
h
as
e
T
o
s
e
t
up
thi
s
pha
s
e
,
a
n
ini
ti
a
li
z
a
ti
on
ve
c
tor
I
S
of
s
ize
(
1×
4)
is
int
r
oduc
e
d.
T
he
e
leme
nt
of
ve
c
tor
I
S
a
r
e
obtaine
d
thr
ough
Algor
it
hm
7.
I
n
thi
s
c
ontext,
t
r
e
pr
e
s
e
nts
the
number
o
f
blocks
o
f
s
ize
4
in
ve
c
tor
W
.
Algor
it
hm
7
.
I
nit
ializa
ti
on
ve
c
tor
ge
ne
r
a
ti
on
IS[0]=0
For i=1 to 4t
-
1
IS[0]=IS[0]
W[i]
Next i
IS[1]=IS[0]
W[1]
IS[2]=IS[0]
W[2]
IS[3]=IS[0]
W[3]
2.
4.
2.
M
od
if
icat
ion
of
t
h
e
f
irs
t
b
lock
V
0
T
he
e
leme
nts
of
the
ini
ti
a
li
z
a
ti
on
ve
c
tor
a
r
e
us
e
d
t
o
ini
ti
a
te
a
di
f
f
us
ion
s
tep.
T
his
s
tep
is
e
s
s
e
nti
a
l
f
or
e
nha
nc
ing
s
e
c
ur
it
y.
T
he
ope
r
a
ti
on
is
e
xe
c
uted
us
in
g
the
s
ubs
e
que
nt
e
xpr
e
s
s
ions
.
W
[
0
]
=
W
[
0]
⊕
I
S
[
0]
W
[
1
]
=
W
[
1]
⊕
I
S
[
1]
W
[
2
]
=
W
[
2]
⊕
I
S
[
2]
W
[
3
]
=
W
[
3]
⊕
I
S
[
3]
2.
4.
3.
Conf
u
s
ion
p
h
as
e
C
onf
us
ion
is
the
ini
ti
a
l
s
tep
of
our
e
nc
r
ypti
on
s
ys
tem.
I
n
thi
s
s
tep,
we
us
e
the
matr
ix
C
H
1
in
a
s
pe
c
if
ied
a
f
f
ine
tr
a
ns
f
or
mation.
Ve
c
tor
Y
r
e
pr
e
s
e
nts
the
e
nc
r
ypted
im
a
ge
.
(
Y
[4
i
]
Y
[4
i
+
1
]
Y
[4
i
+
2
]
Y
[4
i
+
3
]
)
=
CH
1
×
(
W
[
4i
]
W
[
4
i
+
1
]
W
[
4
i
+
2
]
W
[
4
i
+
3
]
)
(mo
d
2
12
)
⊕
(
K
[4
i
]
K
[4
i
+
1
]
K
[4
i
+
2
]
K
[4
i
+
3
]
)
2.
4.
4.
Dif
f
u
s
ion
p
h
as
e
T
o
bols
ter
s
e
c
ur
it
y
a
ga
ins
t
potential
dif
f
e
r
e
nti
a
l
a
tt
a
c
ks
,
we
a
dopt
c
ipher
block
c
ha
ini
ng
(
C
B
C
)
mode.
T
his
mode
e
nha
nc
e
s
e
nc
r
ypti
on
by
incor
po
r
a
ti
ng
the
pr
e
vious
c
ipher
text
block
int
o
the
e
nc
r
y
pti
on
of
the
c
ur
r
e
nt
block
.
I
ts
im
pleme
ntation
he
lps
f
or
ti
f
y
our
e
nc
r
ypti
on
method.
(
W
[
4
(i
+
1
)
]
W
[
4
(
i
+
1
)
+1
]
W
[
4
(i
+
1
)+
2
]
W
[
4
(i
+
1
)+
3
]
)
=
CH
2
×
(
Y
[
4i
]
Y
[
4
i
+
1
]
Y
[
4
i
+
2
]
Y
[
4
i
+
3
]
)
(mo
d
2
12
)
⊕
(
T
[4
i
]
T
[4
i
+
1
]
T
[4
i
+
2
]
T
[4
i
+
3
]
)
2.
5.
E
n
c
r
yp
t
ion
p
r
oc
e
s
s
of
v
e
c
t
or
Z
ove
r
t
h
e
r
in
g
Z
/
Z
L
e
t
X(
1×
r
)
be
the
e
nc
r
ypted
ve
c
tor
of
ve
c
tor
Z
(
1
×
r
)
.
T
he
e
nc
r
ypti
on
pr
oc
e
s
s
of
Z
va
r
ies
de
pe
nding
on
the
va
lue
of
r
,
a
ll
owing
the
de
ter
m
ination
of
the
e
leme
nts
of
Z
to
be
e
nc
r
ypted
a
s
:
I
f
r
=
1
I
f
r
=
2
If
r
=
3
X
[0
]=
Z
[0
]
⊕
K
[N
]
X
[
0
]
=
Z
[
1
]
⊕
K
[
N
]
[
1
]
=
[
2
]
⊕
[
+
1
]
[
0
]
=
[
0
]
⊕
[
]
[
1
]
=
[
1
]
⊕
[
+
1
]
[
2
]
=
[
2
]
⊕
[
+
2
]
L
e
t
Y
c
be
t
he
f
i
na
l
o
u
tp
ut
ve
c
to
r
o
f
s
i
z
e
(
1×
2
NM
)
r
e
p
r
e
s
e
nt
i
ng
th
e
e
n
c
r
y
pt
e
d
im
a
ge
,
o
bta
i
ne
d
by
c
o
nc
a
te
na
ti
ng
v
e
c
to
r
Y
wi
th
ve
c
to
r
X
,
a
c
c
or
d
in
g
t
o
Al
go
r
it
h
m
8
.
F
ig
ur
e
4
p
r
ov
id
e
s
a
d
e
ta
i
led
i
ll
us
t
r
a
t
io
n
o
f
t
he
p
r
op
os
e
d
e
nc
r
y
p
ti
on
p
r
oc
e
s
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8708
I
nt
J
E
lec
&
C
omp
E
ng
,
Vol
.
1
4
,
No.
5
,
Oc
tober
2
02
4
:
5330
-
5343
5336
Algor
it
hm
8
.
E
nc
r
ypted
im
a
ge
For i=0 to 4t
-
1
Yc[i]=Y[i]
Next i
For i= 0 to r
-
1
Yc[i+4t]=X[i]
Next i
F
igur
e
4.
E
nc
r
ypti
on
p
r
oc
e
s
s
2.
6
.
De
c
r
yp
t
ion
T
he
de
c
r
ypti
on
pr
oc
e
s
s
is
the
r
e
ve
r
s
e
ope
r
a
ti
on
of
the
ini
ti
a
l
mec
ha
nis
m,
us
ing
the
s
a
me
e
nc
r
ypti
on
ke
ys
.
Our
method
r
e
li
e
s
on
a
s
ymm
e
tr
ic
e
nc
r
ypti
on
s
ys
tem
with
dif
f
us
ion
im
pleme
ntation.
T
h
is
p
r
oc
e
s
s
is
c
a
r
r
ied
out
by
f
oll
owing
the
s
teps
be
low:
Axis
1:
T
r
a
ns
f
o
r
mation
of
the
e
nc
r
ypted
im
a
ge
int
o
a
one
-
dim
e
ns
ional
a
r
r
a
y.
Axis
2:
C
onve
r
t
e
a
c
h
12
-
bit
block
int
o
a
de
c
im
a
l
v
a
lue.
Axi
s
3:
Ge
ne
r
a
ti
on
of
c
ha
oti
c
s
e
que
nc
e
s
.
Axis
4:
C
r
e
a
ti
on
of
the
inve
r
ti
ble
mat
r
ix
C
H
-
1
us
in
g
the
f
oll
owing
mathe
matica
l
f
or
m:
CH
1
-
1
=
B
-
1
*A
-
1
Axis
5:
Ada
ptation
of
the
e
nc
r
ypted
im
a
ge
ve
c
tor
.
T
he
ve
c
tor
of
the
e
nc
r
ypted
im
a
ge
is
s
ubdivi
de
d
int
o
two
s
ub
-
ve
c
tor
s
:
i)
T
he
ve
c
tor
Y
of
s
ize
(
1×
4t)
,
whe
r
e
r
e
pr
e
s
e
nts
the
number
of
blocks
of
s
ize
4
;
ii
)
T
he
ve
c
tor
X
of
s
ize
(
1×
r
)
,
whe
r
e
r
r
e
p
r
e
s
e
nts
the
s
ize
of
ve
c
tor
X
to
be
tr
unc
a
ted,
with
1
<
≤
3.
Axis
6:
De
c
r
ypti
on
o
f
ve
c
tor
X(
1×
).
L
e
t
Z
o
f
s
ize
(
1×
r
)
be
the
de
c
r
ypted
ve
c
tor
of
v
e
c
tor
X
of
s
ize
(
1×
r
)
.
T
he
de
c
r
ypti
on
pr
oc
e
s
s
of
ve
c
tor
X
is
de
ter
m
ined
by
the
f
oll
owing
e
xpr
e
s
s
ion,
whic
h
va
r
ies
a
c
c
or
ding
to
the
va
lue
o
f
,
t
he
r
e
by
de
duc
ing
the
e
leme
nts
of
X
to
de
c
r
ypt:
If
r
=
1
If
r
=
2
If
r
=
3
Z
[
0
]
=
X
[
0
]
⊕
K
[
N
]
Z
[
0
]
=
X
[
0
]
⊕
K
[
N
]
Z
[
1
]
=
X
[
1
]
⊕
K
[
N
+
1
]
Z
[
0
]
=
X
[
0
]
⊕
K
[
N
]
Z
[
1
]
=
X
[
1
]
⊕
K
[
N
+
1
]
Z
[
2
]
=
X
[
2
]
⊕
K
[
N
+
2
]
Axis
7:
I
nve
r
s
e
c
onf
us
ion
pha
s
e
a
nd
inve
r
s
e
dif
f
us
ion
of
ve
c
to
r
Y(
1×
4t
)
.
L
e
t
r
e
pr
e
s
e
nts
the
e
nc
r
ypted
block
of
the
im
a
ge
a
nd
r
e
pr
e
s
e
nt
the
de
c
r
ypted
block
of
the
im
a
ge
,
we
ha
ve
:
Y
i
=
CH
1
(
W
i
)
K
(
i
)
a
nd
W
i
=
W
i
(
CH
2
(
Y
i
−
1
)
T
(
i
−
1
)
)
So
Y
i
=
CH
1
(
W
i
(
CH
2
(
Y
i
−
1
)
T
(
i
−
1
)
)
)
K
(
i
)
W
i
=
CH
1
−
1
[
Y
i
K
(
i
)
]
[
CH
2
(
Y
i
−
1
)
T
(
i
−
1
)
]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
E
lec
&
C
omp
E
ng
I
S
S
N:
2088
-
8708
N
e
w
image
e
nc
r
y
pti
on
appr
oac
h
us
ing
a
dy
namic
-
c
haoti
c
v
ar
iant
of
Hill
c
ipher
in
…
(
Hic
ham
R
r
gho
ut
)
5337
T
he
ve
c
tor
of
s
ize
(
1×
3NM
)
r
e
p
r
e
s
e
nti
ng
the
or
igi
na
l
im
a
ge
is
obtaine
d
by
c
onc
a
tena
ti
ng
the
ve
c
tor
with
the
ve
c
tor
,
a
s
de
s
c
r
ibed
in
A
lgor
i
thm
9
.
T
he
va
r
ious
e
nc
r
ypti
on
s
teps
a
r
e
il
lus
tr
a
ted
in
F
igu
r
e
5
.
Algor
it
hm
9
.
Or
igi
na
l
i
mage
For i=0 to 4t
-
1
V[i]=W(i)
Next i
For i=0 to r
-
1
V[i+4t]=Z(i)
Next i
F
igur
e
5.
De
c
r
ypti
on
p
r
oc
e
s
s
3.
RE
S
UL
T
S
AN
D
DI
S
CU
S
S
I
ON
T
o
a
s
s
e
s
s
the
s
e
c
ur
it
y
of
a
c
r
yptos
ys
tem,
it
mus
t
unde
r
go
va
r
ious
e
f
f
icie
nc
y
tes
ts
a
ga
ins
t
a
ll
known
a
tt
a
c
ks
,
including
e
xha
us
ti
ve
,
s
tatis
ti
c
a
l,
a
nd
dif
f
e
r
e
nti
a
l
a
tt
a
c
ks
.
Our
a
pp
r
oa
c
h
is
thus
tes
ted
on
a
div
e
r
s
e
s
e
t
of
c
olo
r
a
nd
medic
a
l
im
a
ge
s
us
ing
P
ython
on
a
W
indows
10
ope
r
a
ti
ng
s
ys
tem.
T
he
ha
r
dwa
r
e
s
e
tup
i
nc
ludes
a
n
I
ntel(
R
)
C
or
e
(
T
M
)
i5
-
6300U
C
P
U
@
2.
40
GH
z
pr
oc
e
s
s
or
with
a
s
pe
e
d
of
2.
50
GH
z
a
nd
8
GB
of
R
AM
.
3.
1.
Vis
u
al
t
e
s
t
in
g
T
he
e
nc
r
ypti
on
s
c
he
me
we
pr
opos
e
d
wa
s
e
va
luat
e
d
us
ing
va
r
ious
s
tanda
r
d
im
a
ge
s
c
omm
only
us
e
d
f
or
im
a
ge
pr
oc
e
s
s
ing
tes
ts
.
W
e
pa
r
ti
c
ular
ly
highl
ig
hted
the
r
e
s
ult
s
obtaine
d
f
or
thr
e
e
s
pe
c
if
ic
im
a
ge
s
:
B
a
boon
(
512
512)
,
Hous
e
(
256
256)
a
nd
P
e
ppe
r
s
(
512
5
12)
.
F
igur
e
6
pr
e
s
e
nts
the
or
igi
na
l
im
a
ge
s
a
long
with
their
e
nc
r
ypted
ve
r
s
ions
.
T
he
r
e
s
ult
s
c
onf
ir
m
that
the
e
nc
r
ypted
im
a
ge
c
ontains
no
inf
o
r
mation
f
r
om
the
or
igi
na
l
im
a
ge
.
3.
2.
Anal
ys
is
of
b
r
u
t
e
f
or
c
e
at
t
ac
k
s
3.
2.
1.
Key
s
p
ac
e
F
or
a
r
obus
t
e
nc
r
ypti
on
a
lgor
it
hm
,
it
i
s
c
r
uc
ial
th
a
t
the
ke
y
s
pa
c
e
is
e
xtens
ive,
idea
ll
y
s
ur
pa
s
s
ing
2
1
0
0
.
I
n
our
a
lgor
it
hm,
we
leve
r
a
ge
two
c
ha
oti
c
ma
ps
de
r
ived
f
r
om
f
ou
r
r
e
a
l
pa
r
a
mete
r
s
,
with
e
a
c
h
pa
r
a
mete
r
e
nc
ode
d
in
32
bit
s
.
T
his
c
onf
igur
a
ti
on
r
e
s
ult
s
in
a
n
ove
r
a
ll
ke
y
s
pa
c
e
of
2
1
2
8
,
s
igni
f
ica
ntl
y
e
xc
e
e
ding
the
de
s
ir
e
d
thr
e
s
hold
of
2
100
.
3.
2.
2.
Num
b
e
r
of
p
os
s
ib
le
m
at
r
ice
s
T
he
e
leme
nts
a
2,
a
3,
a
4,
a
6
,
a
7,
a
nd
a
9
of
matr
ix
A
c
a
n
take
va
lues
f
r
om
0
to
4095,
thus
of
f
e
r
ing
4096
pos
s
ibi
li
ti
e
s
f
or
e
a
c
h
e
leme
nt.
T
he
r
e
f
o
r
e
,
the
tot
a
l
number
of
pos
s
ibi
li
ti
e
s
to
c
hoos
e
the
va
lues
of
a
2,
a
3,
a
4,
a
6,
a
7
,
a
nd
a
9
is
(
4096
)
6
=
(
2
12
)
6
=2
72
.
B
y
im
po
s
ing
the
c
ondit
ion
that
the
diagona
l
e
leme
nts
mus
t
be
odd
,
e
a
c
h
e
leme
nt
of
a
1,
a
5,
a
8,
a
nd
a
10
ha
s
2
11
pos
s
ib
il
it
ies
,
or
(
2
11
)
4
=2
44
.
T
hus
,
the
tot
a
l
number
of
c
hoice
s
f
or
the
e
leme
nts
of
A
is
2
72
×2
44
=2
1
1
6
.
S
im
il
a
r
ly,
f
o
r
B
,
we
ge
t
2
1
1
6
pos
s
ibi
li
ti
e
s
.
T
he
r
e
f
o
r
e
,
the
nu
mber
of
pos
s
ibi
li
ti
e
s
f
or
matr
ix
C
H
1
is
(
2
116
)
2
=2
2
3
2
.
On
t
he
other
ha
nd,
e
a
c
h
e
leme
nt
of
matr
ix
C
H
2
c
a
n
take
2
12
va
lues
.
T
hus
,
the
tot
a
l
numbe
r
o
f
pos
s
ibi
li
ti
e
s
to
c
hoos
e
matr
ix
C
H
2
is
(
2
12
)
16
=2
1
9
2
.
C
ons
e
que
ntl
y,
the
tot
a
l
number
of
pos
s
ibl
e
matr
ice
s
is
2
232
×2
192
=2
4
2
4
,
whic
h
is
s
igni
f
ica
ntl
y
ve
r
y
lar
ge
.
I
t
is
de
duc
e
d
that
our
a
ppr
oa
c
h
is
im
mune
to
br
ute
f
or
c
e
a
tt
a
c
ks
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8708
I
nt
J
E
lec
&
C
omp
E
ng
,
Vol
.
1
4
,
No.
5
,
Oc
tober
2
02
4
:
5330
-
5343
5338
3.
2.
3.
Key
s
e
n
s
it
ivi
t
y
Our
s
ys
tem
uti
li
z
e
s
two
we
ll
-
e
s
tablis
he
d
c
ha
oti
c
maps
c
omm
only
us
e
d
in
c
r
yptogr
a
phy
due
to
their
e
xc
e
pti
ona
l
s
e
ns
it
ivi
ty
to
ini
ti
a
l
c
ondit
ions
.
T
his
s
e
ns
it
ivi
ty
gua
r
a
ntee
s
a
h
igh
de
g
r
e
e
of
r
e
s
pons
ivene
s
s
to
ou
r
e
nc
r
ypti
on
ke
y.
T
his
is
de
mons
tr
a
ted
in
F
igu
r
e
7.
T
his
e
ns
ur
e
s
that
the
or
igi
na
l
im
a
ge
c
a
nnot
be
r
e
c
ove
r
e
d
without
knowing
the
ge
nuine
e
nc
r
ypti
on
s
e
c
r
e
t
ke
y.
I
n
other
wor
ds
,
the
s
e
c
ur
it
y
of
the
e
nc
r
ypti
on
pr
oc
e
s
s
r
e
li
e
s
on
the
c
onf
identialit
y
of
t
his
ke
y.
W
it
hout
it
,
r
e
tr
ieving
the
o
r
igi
na
l
i
mage
f
r
o
m
the
e
nc
r
ypted
one
is
im
pos
s
ibl
e
.
F
igur
e
6.
Vis
ua
l
tes
t
of
s
e
lec
ted
im
a
ge
s
F
igur
e
7.
Ke
y
s
e
ns
it
ivi
ty
3.
3.
Robu
s
t
n
e
s
s
t
o
s
t
at
is
t
ical
a
t
t
ac
k
s
3.
3.
1.
Cor
r
e
lat
ion
an
alys
is
T
he
e
nc
r
ypti
on
ope
r
a
ti
on
a
im
s
to
r
e
duc
e
the
c
or
r
e
lation
be
twe
e
n
a
djac
e
nt
pixels
to
a
lm
os
t
z
e
r
o
in
or
de
r
to
c
ounter
s
tatis
ti
c
a
l
a
tt
a
c
ks
.
T
he
c
or
r
e
lation
c
oe
f
f
icie
nt
[
24]
is
c
a
lcula
ted
us
ing
(
3
)
,
(
4
)
,
a
nd
(
5
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
E
lec
&
C
omp
E
ng
I
S
S
N:
2088
-
8708
N
e
w
image
e
nc
r
y
pti
on
appr
oac
h
us
ing
a
dy
namic
-
c
haoti
c
v
ar
iant
of
Hill
c
ipher
in
…
(
Hic
ham
R
r
gho
ut
)
5339
co
r
r
x
y
=
c
ov
(
x
,
y
)
√
D
(
x
)
x
D
(
y
)
(
3)
co
r
r
x
y
=
c
ov
(
x
,
y
)
√
D
(
x
)
x
D
(
y
)
(
4)
(
)
=
1
N
∑
(
x
i
–
E
(
x
)
)
2
N
1
(
)
=
1
∑
(
–
(
)
)
2
1
(
5)
w
he
r
e
a
nd
r
e
pr
e
s
e
nt
the
c
olor
c
omponent
va
lues
of
a
djac
e
nt
pixels
in
the
im
a
ge
,
is
the
to
tal
numbe
r
of
s
e
lec
ted
a
djac
e
nt
pixels
in
the
im
a
ge
,
a
nd
is
th
e
c
or
r
e
lation
c
oe
f
f
icie
nt
.
T
he
c
o
r
r
e
lation
c
oe
f
f
ici
e
nt
is
pr
e
s
e
nted
in
T
a
ble
1
.
Our
method
ha
s
de
mons
tr
a
ted
that
a
ll
e
va
luate
d
im
a
ge
metr
ics
e
xhibi
ted
va
lues
e
xtr
e
mely
c
los
e
to
z
e
r
o.
T
h
is
c
onf
ir
ms
the
r
obus
tn
e
s
s
of
our
a
lgor
i
thm
a
ga
ins
t
a
ny
s
tatis
ti
c
a
l
a
tt
a
c
k.
T
a
ble
1.
C
or
r
e
lation
c
oe
f
f
icie
nts
I
ma
ge
s
V
H
D
R
G
B
R
G
B
R
G
B
B
a
boon
0.0020
0.0013
0.0017
-
0.0038
0.0010
-
0.0019
0.0022
-
0.0020
0.0009
H
ous
e
0.0044
0.0070
0.0059
-
0.0024
0.0015
-
0.0051
0.0043
-
0.0036
-
0.0006
P
e
ppe
r
s
-
0.00005
0.0003
-
0.0033
0.0024
-
0.0012
-
0.0036
-
0.0015
-
0.0003
-
0.0047
3.
3.
2.
Hi
s
t
ogr
am
a
n
alys
is
I
de
a
ll
y,
a
r
obus
t
e
nc
r
ypti
on
a
lgor
it
hm
[
24]
s
hould
dis
tr
ibut
e
va
lues
in
a
r
a
ndom
o
r
ps
e
udo
-
r
a
ndom
manne
r
.
F
igu
r
e
8
pr
ovides
a
n
i
ll
us
tr
a
ti
on
o
f
the
hi
s
togr
a
ms
of
the
e
nc
r
ypted
im
a
ge
.
T
he
h
is
togr
a
m
o
utcome
s
of
im
a
ge
s
e
nc
r
ypted
by
our
a
lgo
r
it
hm
r
e
ve
a
ls
a
uni
f
or
m
dis
tr
ibut
ion.
F
igur
e
8.
His
togr
a
ms
of
e
nc
r
ypted
im
a
ge
s
3.
3.
3.
E
n
t
r
op
y
an
alys
is
E
ntr
opy
mea
s
ur
e
s
the
a
mount
of
r
a
ndom
inf
o
r
mat
ion
pr
e
s
e
nt
in
the
e
nc
r
ypti
on.
I
t
is
e
xpr
e
s
s
e
d
[
25]
by
(
6)
:
(
)
=
−
∑
p(m
i
255
i
=
0
)
log
2
(p(m
i
)
)
(
6)
T
he
theor
e
ti
c
a
l
e
ntr
opy
is
e
qua
l
to
8.
T
a
ble
2
il
lus
tr
a
tes
the
e
nt
r
opy
va
lues
of
the
thr
e
e
im
a
ge
s
e
nc
r
ypted
by
our
s
ys
tem.
E
a
c
h
of
the
im
a
ge
s
e
va
luate
d
by
our
method
e
xhibi
ts
e
ntr
opy
c
los
e
to
8
.
T
his
e
ns
ur
e
s
the
r
e
s
il
ienc
e
of
our
s
ys
tem
a
ga
ins
t
e
ntr
opy
-
ba
s
e
d
a
tt
a
c
ks
.
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