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946
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m
e
s
s
a
g
es.
On
l
y
t
h
e
h
o
ld
er
s
o
f
s
te
g
o
k
e
y
s
ca
n
co
r
r
ec
tl
y
r
etr
iev
e
h
id
d
en
s
ec
r
et
m
es
s
ag
e
s
.
Steg
a
n
o
g
r
ap
h
y
ca
n
b
e
d
escr
i
b
ed
w
it
h
t
h
e
f
o
llo
w
in
g
f
o
r
m
u
la:
s
teg
o
m
ed
ia
=
co
v
er
m
ed
ia
+
e
m
b
ed
d
ed
m
es
s
ag
e
+
s
teg
o
k
e
y
.
Steg
a
n
o
g
r
ap
h
y
is
cla
s
s
i
f
ie
d
in
to
lin
g
u
i
s
tic
s
te
g
a
n
o
g
r
ap
h
y
an
d
tech
n
ical
s
teg
a
n
o
g
r
ap
h
y
.
L
i
n
g
u
i
s
tic
s
te
g
a
n
o
g
r
ap
h
y
in
v
o
lv
e
s
th
e
u
s
e
o
f
n
at
u
r
al
lan
g
u
a
g
e
as
a
ca
r
r
ier
f
o
r
h
id
in
g
s
ec
r
et
d
ata.
T
ec
h
n
ical
s
te
g
an
o
g
r
ap
h
y
e
m
p
lo
y
s
a
m
u
lti
m
ed
ia
ca
r
r
ier
.
Mo
s
t
d
ig
ita
l
f
ile
f
o
r
m
ats
ar
e
c
h
ar
ac
ter
is
ed
b
y
a
h
i
g
h
d
eg
r
ee
o
f
r
ed
u
n
d
an
c
y
t
h
at
b
en
ef
its
s
teg
a
n
o
g
r
ap
h
ic
tec
h
n
i
q
u
es.
C
o
m
m
o
n
s
te
g
an
o
g
r
ap
h
ic
tech
n
iq
u
es
ar
e
s
teg
a
n
o
g
r
ap
h
y
i
n
te
x
ts
,
i
m
a
g
e
s
,
au
d
io
an
d
v
id
eo
s
.
Am
o
n
g
t
h
ese
v
ar
ieties
o
f
f
ile
f
o
r
m
a
ts
,
d
ig
ital
i
m
a
g
es
ar
e
th
e
m
o
s
t
p
o
p
u
lar
b
ec
au
s
e
o
f
th
eir
f
r
eq
u
en
c
y
o
n
t
h
e
i
n
ter
n
et
an
d
h
i
g
h
ca
p
ac
it
y
f
o
r
d
ata
tr
an
s
m
is
s
io
n
w
h
i
le
m
i
n
i
m
is
i
n
g
i
m
ag
e
q
u
alit
y
d
eg
r
ad
atio
n
[
6
-
1
0
]
.
Steg
an
o
g
r
ap
h
ic
m
et
h
o
d
s
m
a
y
b
e
i
n
th
e
f
o
r
m
o
f
s
p
atial
d
o
m
ai
n
e
m
b
ed
d
in
g
o
r
f
r
eq
u
e
n
c
y
d
o
m
ain
e
m
b
ed
d
i
n
g
.
Fre
q
u
en
c
y
d
o
m
ai
n
e
m
b
ed
d
in
g
i
n
v
o
lv
e
s
t
h
e
tr
an
s
f
o
r
m
atio
n
o
f
i
m
a
g
es
in
to
f
r
eq
u
en
c
y
co
m
p
o
n
en
t
s
th
r
o
u
g
h
d
is
cr
ete
co
s
i
n
e
tr
an
s
f
o
r
m
,
f
ast
Fo
u
r
ier
tr
an
s
f
o
r
m
a
n
d
d
is
cr
ete
w
a
v
elet
tr
an
s
f
o
r
m
(
DW
T
)
.
M
ess
a
g
es
ar
e
e
m
b
ed
d
ed
a
t
th
e
b
it
o
r
b
lo
ck
lev
el.
I
n
s
p
atial
d
o
m
ai
n
e
m
b
ed
d
in
g
,
in
f
o
r
m
atio
n
i
s
d
ir
ec
tl
y
h
id
d
en
d
ep
en
d
in
g
o
n
th
e
i
n
te
n
s
it
y
o
f
p
ix
els.
Fre
q
u
en
c
y
d
o
m
ai
n
p
r
o
ce
d
u
r
es
ar
e
r
o
b
u
s
t
an
d
ar
e
co
m
m
o
n
l
y
u
s
ed
f
o
r
w
ater
m
ar
k
i
n
g
,
w
h
er
ea
s
s
p
atia
l
d
o
m
ain
m
eth
o
d
s
p
r
o
v
id
e
h
i
g
h
ca
p
ac
it
y
an
d
ar
e
w
id
el
y
u
s
ed
i
n
s
te
g
an
o
g
r
ap
h
y
.
Ste
g
a
n
o
g
r
ap
h
y
a
n
d
it
s
u
s
e
f
u
ln
e
s
s
ar
e
in
f
l
u
e
n
ce
d
b
y
t
h
r
ee
asp
ec
ts
,
n
a
m
el
y
,
1
)
ca
p
ac
ity
,
w
h
ich
r
e
f
er
s
to
t
h
e
n
u
m
b
er
o
f
d
ata
b
its
th
a
t
ca
n
b
e
h
id
d
en
i
n
co
v
er
m
ed
ia;
2
)
v
is
u
al
q
u
alit
y
o
f
s
teg
o
i
m
a
g
es,
w
h
ic
h
m
u
s
t
r
e
m
ain
u
n
c
h
an
g
ed
(
i
m
p
er
ce
p
tib
ilit
y
)
;
a
n
d
3
)
r
o
b
u
s
tn
e
s
s
,
w
h
ic
h
r
e
f
er
s
to
th
e
r
esis
tan
ce
to
m
o
d
i
f
icatio
n
o
r
d
estru
ctio
n
[
3
,
9
,
1
1
]
.
A
w
id
el
y
u
s
ed
s
p
atial
d
o
m
ai
n
m
e
th
o
d
is
th
e
leas
t
s
ig
n
i
f
ica
n
t
b
it
(
L
SB
)
s
u
b
s
tit
u
tio
n
i
n
w
h
ich
lo
w
er
o
r
d
er
im
a
g
e
b
its
(
t
h
o
s
e
t
h
at
d
o
n
o
t
p
o
s
s
ess
u
s
e
f
u
l
i
m
a
g
e
in
f
o
r
m
atio
n
)
ar
e
r
ep
lace
d
w
ith
s
ec
r
et
m
e
s
s
a
g
e
b
its
[
9
,
1
2
]
.
T
h
e
u
s
e
o
f
L
SB
s
u
b
s
titu
t
io
n
p
r
eser
v
es
i
m
a
g
e
q
u
a
lit
y
w
it
h
o
u
t
en
tail
in
g
co
m
p
le
x
o
p
er
atio
n
s
.
I
n
th
is
m
et
h
o
d
,
th
e
b
its
o
f
s
ec
r
et
d
ata
ar
e
h
id
d
en
in
t
h
e
K
-
L
SB
p
lan
e
i
n
ea
ch
p
ix
e
l
o
f
a
co
v
er
i
m
a
g
e.
T
h
e
m
o
s
t
w
id
el
y
k
n
o
w
n
L
SB
m
eth
o
d
s
ar
e
L
SB
m
atc
h
i
n
g
(
L
SB
M)
,
L
SB
M
r
ev
is
ed
(
L
SB
M
R
)
an
d
ed
g
e
ad
ap
tiv
e
-
b
ased
L
SB
M
R
s
te
g
an
o
g
r
ap
h
y
.
Ho
w
ev
er
,
m
o
s
t o
f
t
h
ese
tec
h
n
iq
u
es
ar
e
m
o
s
t o
f
th
e
s
e
tech
n
iq
u
es
ar
e
p
r
o
b
a
b
ly
ea
s
y
t
o
b
e
b
r
o
k
en
.
T
h
er
ef
o
r
e
th
ese
m
e
th
o
d
s
h
a
v
e
u
n
d
er
g
o
n
e
i
m
p
r
o
v
e
m
e
n
t
s
i
n
v
ar
io
u
s
a
s
p
ec
ts
[
1
,
2
,
7
,
8
,
10
,
1
3
]
.
I
n
p
ar
ticu
lar
,
r
esear
c
h
er
s
h
a
v
e
u
s
ed
c
h
ao
s
th
eo
r
y
.
Un
lik
e
t
r
ad
itio
n
al
m
e
th
o
d
s
,
c
h
ao
tic
m
eth
o
d
s
ar
e
s
e
n
s
iti
v
e
to
p
r
im
ar
y
co
n
d
itio
n
s
a
n
d
n
o
n
p
er
io
d
ic,
n
o
n
co
n
v
er
g
e
n
ce
an
d
co
n
tr
o
llin
g
p
ar
a
m
eter
s
.
He
n
ce
,
th
e
y
h
a
v
e
b
ee
n
u
tili
s
ed
b
y
m
an
y
r
e
s
ea
r
ch
er
s
as
a
v
ita
l
s
o
l
u
tio
n
i
n
th
eir
wo
r
k
[
9
]
.
A
l
th
o
u
g
h
a
1
D
c
h
ao
t
ic
s
y
s
te
m
is
h
ig
h
l
y
ef
f
icien
t,
it
h
as
s
o
m
e
i
n
h
er
e
n
t
d
is
ad
v
a
n
ta
g
es,
s
u
ch
a
s
s
m
all
k
e
y
a
s
s
i
g
n
m
e
n
t
a
n
d
in
ad
eq
u
ate
s
ec
u
r
it
y
t
h
at
r
ed
u
ce
s
its
e
f
f
icien
c
y
a
n
d
p
er
f
o
r
m
a
n
ce
.
Nu
m
er
o
u
s
s
y
s
te
m
s
e
n
co
m
p
as
s
in
g
o
n
e
-
,
t
w
o
-
o
r
h
ig
h
er
-
d
i
m
e
n
s
io
n
al
s
y
s
te
m
s
w
it
h
c
h
ao
tic
m
ap
s
h
av
e
b
ee
n
in
tr
o
d
u
ce
d
in
r
ec
e
n
t
y
ea
r
s
.
3
D
m
ap
s
p
r
o
v
id
e
h
ig
h
er
s
ec
u
r
it
y
a
n
d
r
an
d
o
m
n
es
s
th
an
1
D
a
n
d
2
D
m
ap
s
[
1
4
-
1
7
]
.
C
h
ao
s
-
b
a
s
ed
s
teg
a
n
o
g
r
ap
h
y
al
g
o
r
it
h
m
s
h
a
v
e
attr
ac
ted
m
u
ch
atte
n
tio
n
in
e
x
is
tin
g
s
t
u
d
ies
b
ec
au
s
e
o
f
t
h
eir
ef
f
icie
n
c
y
an
d
ap
p
licab
ilit
y
to
s
te
g
a
n
o
g
r
ap
h
y
f
o
r
p
r
o
v
id
in
g
s
ec
u
r
e
co
m
m
u
n
icatio
n
.
B
an
d
y
o
p
ad
h
y
a
y
,
Da
s
g
u
p
ta,
Ma
n
d
al
an
d
Du
tta
[
2
]
p
u
t
f
o
r
w
ar
d
a
n
e
w
ap
p
r
o
ac
h
s
ec
u
r
e
d
ata
ar
e
b
u
i
lt
in
to
d
ig
ital
i
m
a
g
es
b
y
u
s
in
g
a
1
D
lo
g
i
s
tic
m
ap
.
T
h
is
lo
g
i
s
tic
m
ap
i
s
u
s
ed
to
en
cr
y
p
t
s
ec
r
et
m
e
s
s
a
g
es
b
ef
o
r
e
e
m
b
ed
d
in
g
.
R
aj
en
d
r
an
a
n
d
D
o
r
aip
an
d
ian
[
5
]
p
u
t
f
o
r
w
ar
d
a
n
o
v
el
m
et
h
o
d
f
o
r
h
id
in
g
s
ec
r
et
i
m
a
g
es
u
s
in
g
1
D
lo
g
is
tic
m
ap
s
.
T
h
ese
1
D
lo
g
is
tic
m
ap
s
ar
e
u
tili
s
ed
to
g
en
er
ate
p
s
eu
d
o
r
an
d
o
m
k
e
y
s
.
T
h
ese
k
e
y
s
ar
e
u
s
ed
to
r
an
d
o
m
l
y
s
elec
t
t
h
e
p
i
x
el
p
o
s
itio
n
s
o
f
co
v
er
i
m
a
g
es
f
o
r
h
id
in
g
s
ec
r
et
i
m
a
g
es.
Sh
ar
if
,
Mo
llaee
f
ar
a
n
d
Naz
ar
i
[
6
]
also
p
r
o
p
o
s
ed
a
n
o
v
el
al
g
o
r
ith
m
f
o
r
i
m
a
g
e
s
teg
an
o
g
r
ap
h
y
b
ased
o
n
c
h
ao
s
th
eo
r
y
.
T
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
i
n
v
o
l
v
es a
n
o
v
el
3
D
ch
ao
tic
m
ap
(
L
C
A
m
ap
)
w
i
th
a
m
ax
i
m
u
m
L
y
ap
u
n
o
v
ex
p
o
n
e
n
t o
f
2
0
.
5
8
,
w
h
ic
h
is
ad
o
p
ted
to
g
en
er
ate
t
h
r
ee
c
h
ao
tic
s
eq
u
en
ce
s
.
Mis
h
r
a,
R
o
u
tr
a
y
a
n
d
K
u
m
ar
[
9
]
p
r
o
p
o
s
ed
th
e
e
m
b
ed
d
i
n
g
o
f
s
ec
r
et
in
f
o
r
m
at
io
n
i
n
a
d
i
g
ital
i
m
a
g
e
i
n
t
h
e
s
p
atial
d
o
m
ain
th
r
o
u
g
h
L
SB
an
d
A
r
n
o
ld
’
s
tr
an
s
f
o
r
m
.
A
r
n
o
ld
’
s
tr
an
s
f
o
r
m
is
ap
p
lied
t
w
o
ti
m
es
in
t
w
o
d
if
f
er
en
t
p
h
ases
.
T
h
en
m
o
zh
i
an
d
C
h
an
d
r
ase
k
a
r
an
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1
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[
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f
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p
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as
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2
p
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it
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.
S
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3
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Sectio
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4
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n
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th
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s
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alg
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r
ith
m
.
Sectio
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5
d
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th
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s
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ith
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ased
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v
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f
ac
to
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.
Sectio
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6
p
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th
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m
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.
2.
CH
AO
T
I
C
M
AP
C
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ao
s
r
ef
er
s
to
a
s
tate
o
f
d
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o
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.
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n
th
e
f
ie
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o
f
m
at
h
e
m
atics,
ch
ao
tic
b
eh
a
v
io
u
r
i
s
r
e
v
ea
led
b
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m
ap
s
s
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v
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n
g
an
ev
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l
u
tio
n
f
u
n
ctio
n
.
Di
s
cr
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-
t
i
m
e
d
y
n
a
m
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y
s
te
m
s
ar
e
also
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e
f
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r
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to
as
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s
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th
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m
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a
n
d
DW
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is
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s
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to
h
id
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in
f
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m
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tio
n
[
5
,
1
3
]
.
T
h
is
th
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y
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n
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n
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a
n
d
n
atu
r
al
r
ea
l
s
y
s
te
m
s
.
Nu
m
er
o
u
s
s
te
g
an
o
g
r
ap
h
ic
m
et
h
o
d
s
b
ased
o
n
ch
ao
s
t
h
eo
r
y
h
av
e
b
ee
n
p
r
o
p
o
s
ed
an
d
d
is
cu
s
s
ed
in
t
h
e
p
ast
f
e
w
d
ec
ad
es
[
2
]
.
I
n
th
ese
m
eth
o
d
s
,
s
e
cr
et
k
e
y
s
ar
e
g
e
n
er
ated
u
s
in
g
3
D
lo
g
is
tic
a
n
d
3
D
C
h
eb
y
s
h
ev
m
ap
s
.
2
.
1
.
3D
lo
g
is
t
ic
m
a
p
A
lo
g
i
s
tic
m
ap
is
a
s
i
m
p
le
ch
ao
tic
m
ap
w
h
ic
h
b
elo
n
g
s
to
th
e
f
a
m
il
y
o
f
f
ir
s
t
-
o
r
d
er
d
if
f
er
e
n
ce
eq
u
atio
n
s
.
I
t c
an
b
e
m
ath
e
m
at
i
ca
ll
y
r
ep
r
esen
ted
as
f
o
llo
w
s
:
X
n
+
1
=
RX
n
(
1
−
Xn
),
(
1
)
w
h
er
e
th
e
s
y
s
te
m
p
ar
a
m
eter
i
s
μ
∈
[
0
,
4
]
an
d
th
e
in
itial
co
n
d
itio
n
i
s
X
0
∈
(
0
,
1
)
.
A
lo
g
is
t
ic
m
ap
ch
ao
ticall
y
b
eh
av
es
w
i
th
R
∈
(
3
.
5
6
9
9
4
5
6
,
4
]
[
1
9
,
20
].
A
1
D
lo
g
is
ti
c
m
ap
ca
n
b
e
ex
ten
d
ed
to
th
e
3
D,
as
d
ef
in
ed
in
(
2
)
to
(
4
)
.
X
n+
1
= R
X
n
(
1
−X
n
)
+
β
X
n
+
α
,
(
2
)
Y
n+
1
= R
Y
n
(
1
−
Y
n
)
+β
Y
n
+α
,
(
3
)
Z
n+
1
= R
Z
n
(
1
− Z
n
)
+β
Z
n
+α
.
(
4
)
T
h
e
p
ar
am
eter
s
o
f
a
n
o
n
l
in
ea
r
s
y
s
te
m
ar
e
v
a
lu
ed
i
n
th
e
r
a
n
g
e
o
f
0
.
5
3
<
R
<
3
.
8
1
,
0
<
β
<
0
.
0
2
2
,
0
<
α
<
0
.
0
1
5
,
w
h
er
e
X
0
,
Y
0
an
d
Z
0
ar
e
d
ef
i
n
e
d
in
[
1
,
1
6
,
1
7
,
26
].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
10
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
0
:
9
3
5
-
946
938
2
.
2
.
3
D
cheby
s
hev
m
a
p
C
h
eb
y
s
h
ev
p
o
l
y
n
o
m
ials
ar
e
u
tili
s
ed
to
g
en
er
ate
th
e
s
ec
r
et
k
e
y
s
r
eq
u
ir
ed
to
h
id
e
in
f
o
r
m
at
io
n
.
C
h
eb
y
s
h
ev
p
o
l
y
n
o
m
ials
ar
e
c
h
ar
ac
ter
is
ed
as
F
n
(
x
)
o
f
t
h
e
f
i
r
s
t
t
y
p
e
w
h
ich
i
s
a
p
o
ly
n
o
m
ial
o
f
x
w
it
h
d
eg
r
ee
n
.
T
h
ey
co
m
p
r
is
e
t
h
e
p
r
o
to
ty
p
e
o
f
a
ch
ao
tic
m
ap
an
d
ar
e
d
ef
in
ed
as
Fn
(
x
)
=
co
s
n
θ,
w
h
er
e
x
=
co
s
θ.
B
y
lettin
g
n
=
0
,
1
,
2
,
3
,
4
,
w
e
ca
n
o
b
ta
in
co
s
0
θ
=
1
,
co
s
1
θ
=
co
s
θ,
c
o
s
2
θ
=
2
co
s
2
θ
−
1
,
co
s
3
θ
=
4
co
s
3
θ
−
3
co
s
θ
an
d
co
s
4
θ
=
8
co
s
4
θ
−
8
co
s
2
θ
+
1
.
W
ith
co
s
θ
=
x
,
w
e
o
b
tain
F0
(
x
)
=
1
,
F1
(
x
)
=
x
,
F2
(
x
)
=
2
x
2
−
1
,
F3
(
x
)
=
4
x
3
−3
x
an
d
F4
(
x
)
=
8
x
4
−8
x
2
+
1
.
T
h
e
tr
an
s
f
o
r
m
atio
n
s
ar
e
ex
p
r
ess
ed
as
F
2(
x
)
=
2
x
2
–
1,
(
5
)
F
3(
y
)
=
4
y
3
−3
y
,
(
6
)
F
4(
z
)
=
8
z
4
−8
z
2
+1
.
(
7
)
T
h
e
C
h
eb
y
s
h
ev
p
o
l
y
n
o
m
ial
m
ap
is
Fp
:
[
−1
,
1
]
[
−1
,
1
]
o
f
d
eg
r
ee
p
,
w
h
e
n
p
>
1
[
1
6
,
17]
.
T
h
e
(
5
)
to
(
7
)
ar
e
u
s
ed
to
g
e
n
er
ate
s
ec
r
et
k
e
y
s
wh
ich
ar
e
t
h
en
u
s
ed
as a
s
ec
r
et
m
ap
o
f
i
m
ag
e
p
i
x
els i
n
th
e
h
id
in
g
p
r
o
ce
s
s
.
3.
P
RO
P
O
SE
D
AL
G
O
R
I
T
H
M
T
h
is
s
ec
tio
n
is
co
m
p
o
s
ed
o
f
t
w
o
p
h
ases
(
e
m
b
ed
d
in
g
an
d
ex
tr
ac
ti
n
g
p
h
ase
s
)
th
at
ar
e
ex
p
lain
ed
i
n
th
e
f
o
llo
w
i
n
g
s
u
b
s
ec
tio
n
s
.
3
.
1
.
E
m
bed
din
g
ph
a
s
e
T
h
e
em
b
ed
d
in
g
p
h
ase
i
n
cl
u
d
es sev
er
al
s
tep
s
,
in
cl
u
d
i
n
g
t
h
e
f
o
llo
w
i
n
g
:
1.
Select
th
e
s
ec
r
et
m
e
s
s
a
g
e
an
d
h
o
s
t i
m
ag
e.
2.
Set th
e
le
n
g
th
o
f
th
e
s
ec
r
et
m
e
s
s
a
g
e
in
t
h
e
f
ir
s
t t
w
o
p
ix
el
s
o
f
th
e
h
o
s
t i
m
a
g
e.
3.
C
o
n
v
er
t
th
e
s
ec
r
et
m
e
s
s
a
g
e
to
A
SC
I
I
v
al
u
es
a
n
d
th
e
n
to
b
in
ar
y
n
u
m
b
er
s
.
Fo
r
ex
a
m
p
le,
S
=
8
3
,
0
1
0
1
0
0
1
1
.
4.
I
n
itiali
s
e
th
e
s
ec
r
et
p
ar
am
e
ter
s
o
f
th
e
3
D
C
h
eb
y
s
h
e
v
m
ap
to
g
en
er
ate
s
ec
r
et
k
e
y
s
X
,
Y
an
d
Z
.
= (
*
1
0
4
th
e
le
n
g
th
o
f
th
e
b
in
ar
y
s
ec
r
et
m
e
s
s
a
g
e)
,
(
8
)
Y
=
(
Y
*
1
0
4
od
3
)
,
(
9
)
Z
= (
Z
*
1
0
4
3
)
.
(
1
0
)
5.
P
er
m
u
te
th
e
s
ec
r
et
m
e
s
s
a
g
e
o
n
th
e
b
asis
o
f
th
e
s
ec
r
et
k
e
y
s
g
e
n
er
ated
f
r
o
m
(
8
)
b
ef
o
r
e
h
id
in
g
it in
t
h
e
h
o
s
t
i
m
a
g
e.
Fo
r
e
x
a
m
p
le,
let
th
e
s
e
cr
et
m
e
s
s
a
g
e
b
e
0
1
0
1
0
0
1
1
w
it
h
a
len
g
t
h
o
f
8
.
S
u
p
p
o
s
e
t
h
at
t
h
e
s
ec
r
et
k
e
y
s
o
f
X
ar
e
ex
p
r
ess
ed
as 1
,
5
,
6
,
4
,
0
,
2
,
3
,
7
.
T
h
en
,
th
e
s
ec
r
et
m
ess
a
g
e
is
lab
elled
as 1
0
1
0
0
0
1
1
.
6.
Dec
o
m
p
o
s
e
th
e
b
in
ar
y
n
u
m
b
e
r
s
in
to
th
r
ee
s
ep
ar
ate
g
r
o
u
p
s
as f
o
llo
w
s
:
1
0
,
1
0
0
,
0
1
1
(
0
,
1
,
2
)
.
7.
Select
th
e
g
r
o
u
p
th
a
t
w
ill b
e
h
i
d
d
en
f
ir
s
t o
n
t
h
e
b
asi
s
o
f
t
h
e
s
ec
r
et
k
e
y
s
g
e
n
er
ated
f
r
o
m
(
9
)
.
Fo
r
ex
a
m
p
le,
let
th
e
g
e
n
er
ated
s
ec
r
et
k
e
y
s
b
e
{1
,
2
,
0
}.
I
n
th
is
ca
s
e,
s
elec
t
1
0
0
f
ir
s
t,
f
o
llo
w
ed
b
y
0
1
1
an
d
1
0
.
8.
B
r
ea
k
d
o
w
n
t
h
e
r
ed
(
R
)
,
g
r
ee
n
(
G)
an
d
b
lu
e
(
B
)
co
m
p
o
n
en
ts
o
f
t
h
e
i
m
a
g
e.
Sto
r
e
th
e
co
m
p
o
n
e
n
t
s
in
th
r
ee
N
×
M
ar
r
a
y
s
,
w
h
er
e
N
an
d
M
ar
e
th
e
n
u
m
b
er
o
f
ar
r
a
y
r
o
w
s
a
n
d
co
lu
m
n
s
,
r
esp
ec
tiv
el
y
.
9.
L
ab
el
th
e
co
m
p
o
n
en
ts
as
f
o
llo
w
s
:
R
GB
0
1
2
10.
Select
w
h
ic
h
co
m
p
o
n
e
n
t
(
R
,
G
o
r
B
)
w
ill
b
e
h
id
d
en
f
ir
s
t
o
n
th
e
b
asis
o
f
t
h
e
s
ec
r
et
k
e
y
s
g
en
er
ated
f
r
o
m
(
10
)
.
Fo
r
ex
a
m
p
le,
le
t t
h
e
g
e
n
er
ated
s
ec
r
et
k
e
y
s
b
e
{2
,
0
,
1
}.
I
n
t
h
is
ca
s
e,
t
h
e
s
ec
r
et
m
es
s
ag
e
1
0
0
is
h
id
d
en
in
t
h
e
B
co
m
p
o
n
e
n
t,
f
o
ll
o
w
ed
b
y
0
1
1
in
th
e
R
co
m
p
o
n
en
t a
n
d
1
0
in
th
e
G
co
m
p
o
n
e
n
t.
11.
Dec
o
m
p
o
s
e
ea
ch
co
m
p
o
n
e
n
t
(
ar
r
ay
)
in
to
n
o
n
o
v
er
lap
p
in
g
b
lo
ck
s
b
y
d
i
v
id
in
g
N
a
n
d
M
b
y
8
.
T
h
e
r
esu
lt
r
ep
r
esen
ts
t
h
e
n
u
m
b
er
o
f
b
lo
c
k
s
i
n
ea
ch
co
m
p
o
n
en
t.
Fo
r
ex
am
p
le,
th
e
r
es
u
lt i
s
1
2
8
b
lo
ck
s
o
f
4
×4
w
h
e
n
N
an
d
M
ar
e
5
1
2
.
12.
I
n
itiali
s
e
th
e
s
ec
r
et
p
ar
am
e
ter
s
o
f
th
e
3
D
lo
g
i
s
tic
m
ap
.
13.
Gen
er
ate
th
e
s
ec
r
et
k
e
y
s
f
o
r
ea
ch
b
lo
ck
in
to
R
,
G
an
d
B
co
m
p
o
n
en
ts
.
14.
C
o
n
v
er
t th
e
s
ec
r
et
k
e
y
s
i
n
to
d
ec
i
m
al
n
u
m
b
er
s
b
y
u
s
i
n
g
th
e
f
o
llo
w
i
n
g
eq
u
a
tio
n
s
:
=
o
r
(
*
1
0
4
d
1
6
)
,
(
1
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
I
ma
g
e
s
teg
a
n
o
g
r
a
p
h
y
u
s
in
g
le
a
s
t sig
n
ifica
n
t b
it a
n
d
s
ec
r
et
ma
p
tech
n
iq
u
es
(
A
s
h
w
a
k
A
La
b
a
ich
i
)
939
Y
=
(
Y
*
1
0
4
1
6
)
,
(
1
2
)
Z
=
o
r
(
Z
*
1
0
4
1
6
)
,
(
1
3
)
W
h
er
e
X
,
Y
an
d
Z
r
ep
r
esen
t th
e
s
ec
r
et
k
e
y
s
f
o
r
b
lo
ck
s
R
,
G
an
d
B
,
r
esp
ec
tiv
el
y
.
15.
Sto
r
e
th
e
s
e
s
ec
r
et
k
e
y
s
i
n
a
n
8
×8
ar
r
ay
w
it
h
a
r
an
g
e
o
f
0
–
6
3
.
T
h
e
v
al
u
es
i
n
t
h
e
ar
r
a
y
s
h
o
u
ld
s
ati
s
f
y
th
e
co
n
d
itio
n
w
i
th
o
u
t r
ep
ea
tin
g
th
e
v
al
u
es i
n
th
e
r
o
w
s
a
n
d
co
lu
m
n
s
.
16.
Ma
p
th
e
v
al
u
es
o
f
t
h
e
b
lo
ck
s
w
ith
t
h
e
v
alu
e
s
i
n
Step
1
4
an
d
h
id
e
th
eir
in
f
o
r
m
at
io
n
.
He
n
ce
,
t
h
e
h
o
s
t
i
m
a
g
e
p
ix
els
ar
e
r
an
d
o
m
l
y
s
el
ec
ted
o
n
th
e
b
asis
o
f
th
e
g
e
n
e
r
ated
s
ec
r
et
k
ey
s
in
ea
ch
b
lo
ck
in
Step
1
4
.
Fo
r
s
i
m
p
li
f
icatio
n
,
w
e
ta
k
e
t
h
e
f
o
llo
w
in
g
:
Secr
et
k
e
y
s
(
X
)
Secr
et
k
e
y
s
(
Y
)
Secr
et
k
e
y
s
(
Z
)
5
6
3
2
4
0
1
7
8
2
5
6
3
4
1
0
8
7
3
1
0
6
5
8
4
7
2
Ho
s
t i
m
a
g
e
(
R
)
Ho
s
t i
m
a
g
e
(
G)
Ho
s
t i
m
a
g
e
(
B
)
0
1
2
3
4
5
6
7
8
0
1
2
3
4
5
6
7
8
0
1
2
3
4
5
6
7
8
W
e
ch
o
o
s
e
t
h
e
s
i
x
t
h
(
5
)
p
ix
el
in
th
e
b
lo
ck
o
f
h
o
s
t
i
m
a
g
e
(
R
)
an
d
co
n
v
er
t
it
i
n
to
b
i
n
ar
y
f
o
r
m
to
e
m
b
ed
0
1
1
in
to
3
L
SB
.
T
h
en
,
w
e
ch
o
o
s
e
th
e
th
ir
d
(
2
)
p
ix
el
in
th
e
b
lo
ck
o
f
h
o
s
t
i
m
ag
e
(
G)
an
d
co
n
v
er
t
it
i
n
to
b
in
ar
y
f
o
r
m
to
e
m
b
ed
1
0
in
to
2
L
SB
.
Su
b
s
eq
u
e
n
tl
y
,
w
e
c
h
o
o
s
e
t
h
e
f
o
u
r
th
(
3
)
p
ix
el
i
n
t
h
e
b
lo
ck
o
f
h
o
s
t i
m
a
g
e
(
B
)
an
d
co
n
v
er
t it
i
n
to
b
in
ar
y
f
o
r
m
to
e
m
b
ed
1
0
0
in
to
3
L
SB
.
17.
C
o
n
v
er
t t
h
e
b
in
ar
y
v
al
u
es to
d
ec
i
m
al
v
al
u
e
s
.
18.
R
ep
ea
t Step
s
1
3
to
1
6
to
em
b
ed
all
b
y
te
s
o
f
th
e
s
ec
r
et
m
e
s
s
ag
e
in
all
co
m
p
o
n
en
ts
o
f
t
h
e
h
o
s
t i
m
a
g
e.
19.
Ob
tain
th
e
s
teg
o
i
m
a
g
e.
Fig
u
r
e
1
p
r
esen
ts
t
h
e
d
iag
r
a
m
o
f
t
h
e
e
m
b
ed
d
in
g
p
h
a
s
e.
Fig
u
r
e
1
.
Diag
r
a
m
o
f
e
m
b
ed
d
in
g
p
h
ase
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
10
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
0
:
9
3
5
-
946
940
3
.
2
.
E
x
t
ra
ct
io
n pha
s
e
I
n
th
is
p
h
a
s
e,
t
h
e
s
ec
r
et
m
e
s
s
a
g
e
is
r
etr
iev
ed
f
r
o
m
t
h
e
s
teg
o
i
m
a
g
e.
T
h
is
p
r
o
ce
d
u
r
e
is
t
h
e
o
p
p
o
s
ite
o
f
th
e
e
m
b
ed
d
in
g
p
r
o
ce
s
s
.
I
n
t
h
e
ex
tr
ac
tio
n
p
h
a
s
e,
t
h
e
r
ec
ei
v
in
g
p
ar
t
y
m
u
s
t
b
e
a
w
ar
e
o
f
t
h
e
i
n
itial
v
a
lu
e
s
o
f
th
e
3
D,
C
h
eb
y
s
h
e
v
an
d
3
D
lo
g
is
t
ic
m
ap
s
to
p
r
o
d
u
ce
s
ec
r
et
k
e
y
s
X
,
Y
an
d
Z
.
T
h
e
s
teg
o
i
m
ag
e
is
u
s
ed
as
i
n
p
u
t
in
th
is
p
h
a
s
e.
Su
b
s
eq
u
en
tl
y
,
t
h
e
s
teg
o
i
m
ag
e
i
s
b
lo
ck
ed
in
to
n
o
n
o
v
er
lap
p
in
g
4
×4
b
lo
ck
s
,
an
d
th
e
i
m
ag
e
p
i
x
els
ar
e
s
elec
ted
in
th
e
b
lo
ck
s
o
n
th
e
b
asis
o
f
th
e
s
ec
r
et
k
e
y
s
f
o
r
ea
ch
b
lo
ck
o
f
th
e
3
D
lo
g
is
tic
m
ap
,
w
h
ich
ar
e
X
f
o
r
R
,
Y
f
o
r
G
a
n
d
Z
f
o
r
B
.
T
h
e
p
r
o
ce
d
u
r
e
i
m
p
le
m
e
n
ted
i
n
t
h
e
e
m
b
ed
d
in
g
p
h
a
s
e
i
s
t
h
e
n
r
u
n
.
Z
o
f
t
h
e
3
D
C
h
eb
y
s
h
ev
m
ap
is
o
b
tai
n
ed
b
y
u
s
i
n
g
ch
ao
tic
s
eq
u
e
n
ce
s
.
T
h
e
o
r
d
er
o
f
th
e
co
m
p
o
n
en
ts
i
s
s
elec
ted
i
n
th
e
e
m
b
ed
d
in
g
p
r
o
ce
s
s
,
w
h
er
ea
s
th
e
ch
ao
tic
s
eq
u
e
n
ce
s
o
f
Y
d
eter
m
in
e
t
h
e
o
r
d
er
o
f
th
e
g
r
o
u
p
s
o
f
b
its
th
at
ar
e
h
id
d
en
.
T
h
e
o
r
ig
in
al
o
r
d
er
o
f
ch
ar
ac
ter
s
in
t
h
e
s
ec
r
et
m
es
s
ag
e
is
k
n
o
w
n
t
h
r
o
u
g
h
t
h
e
X
v
al
u
es.
4.
E
XP
E
R
I
M
E
NT
A
L
RE
SUL
T
S
T
h
e
em
b
ed
d
in
g
an
d
ex
tr
ac
tio
n
p
h
ase
s
o
f
m
o
r
e
t
h
an
3
0
i
m
ag
es
w
er
e
r
u
n
o
n
M
A
T
L
A
B
R
2
0
1
8
a
o
n
a
co
m
p
u
ter
w
it
h
W
in
d
o
w
s
1
0
6
4
b
it,
I
n
tel
C
o
r
e
i7
-
7
5
0
0
U
p
r
o
ce
s
s
o
r
,
8
GB
C
P
U
an
d
2
4
0
0
MH
z
R
A
M.
I
n
th
i
s
s
ec
tio
n
,
f
o
u
r
s
tan
d
ar
d
w
ell
-
k
n
o
w
n
i
m
a
g
es,
n
a
m
el
y
,
L
e
n
a
,
P
ep
p
e
r
,
B
ab
o
o
n
an
d
B
ar
b
ar
a,
ar
e
p
r
esen
ted
.
Fig
u
r
e
2
(
a
–
d
)
illu
s
tr
ates
t
h
e
h
o
s
t
an
d
s
teg
o
i
m
a
g
e
s
.
As
s
h
o
w
n
in
t
h
e
f
i
g
u
r
e,
th
e
h
o
s
t
a
n
d
s
teg
o
i
m
ag
e
s
d
o
n
o
t
p
r
esen
t
s
i
g
n
i
f
ica
n
t
d
if
f
er
e
n
ce
s
.
Hen
ce
,
th
e
p
r
o
p
o
s
ed
alg
o
r
it
h
m
ca
n
s
u
cc
ess
f
u
ll
y
h
id
e
s
ec
r
et
m
es
s
ag
e
s
in
h
o
s
t
i
m
a
g
es
w
i
th
o
u
t
a
n
y
d
i
s
to
r
tio
n
.
T
h
e
co
r
r
ec
t
s
ec
r
et
m
e
s
s
a
g
es
ca
n
b
e
ea
s
il
y
a
n
d
co
r
r
ec
tl
y
e
x
tr
ac
ted
f
r
o
m
s
teg
o
i
m
a
g
es
w
it
h
v
a
lid
s
teg
o
k
e
y
s
w
h
en
s
teg
o
i
m
ag
e
s
ar
e
tr
an
s
m
i
tted
to
au
th
o
r
is
ed
r
ec
eiv
e
r
s
,
as
ex
p
lain
ed
i
n
th
e
n
e
x
t
s
ec
tio
n
.
T
h
e
f
o
llo
w
i
n
g
i
n
itial
v
a
lu
e
s
w
er
e
u
s
ed
i
n
t
h
e
3
D
lo
g
i
s
tic
an
d
3
D
C
h
eb
y
s
h
e
v
m
ap
s
i
n
all
ex
p
er
i
m
e
n
ts
:
Fo
r
th
e
3
D
lo
g
i
s
tic
m
ap
,
x
0
=
0
.
9
7
6
,
y
0
=
0
.
6
7
7
,
z
0
=
0
.
9
7
3
,
R
=
3
.
7
9
,
β
=
0
.
0
2
0
,
α
=
0
.
0
1
4
,
w
h
er
e
x
d
en
o
te
s
R
,
y
d
en
o
tes
G
an
d
z
d
en
o
tes
B
.
Fo
r
th
e
3
D
C
h
eb
y
s
h
ev
m
ap
,
x
0
=
0
.
2
3
4
,
y
0
=
−0
.
3
9
8
,
z
0
=
−0
.
8
8
.
Fig
u
r
e
2
.
(
A
)
h
o
s
t i
m
a
g
es,
(
B
)
s
teg
o
i
m
ag
e
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
I
ma
g
e
s
teg
a
n
o
g
r
a
p
h
y
u
s
in
g
le
a
s
t sig
n
ifica
n
t b
it a
n
d
s
ec
r
et
ma
p
tech
n
iq
u
es
(
A
s
h
w
a
k
A
La
b
a
ich
i
)
941
5.
SE
CUR
I
T
Y
ANA
L
YS
I
S
I
n
th
is
s
ec
tio
n
,
s
ev
er
al
s
tatis
ti
ca
l
an
al
y
s
e
s
ar
e
p
r
esen
ted
to
v
er
if
y
t
h
e
e
f
f
ec
tiv
e
n
e
s
s
a
n
d
ef
f
icie
n
c
y
o
f
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
a
g
ain
s
t statis
t
ical
attac
k
s
.
5
.
1
.
Co
rr
el
a
t
io
n c
o
e
f
f
icient
C
o
r
r
elatio
n
co
ef
f
ic
ien
t
r
is
u
s
ed
to
m
ea
s
u
r
e
th
e
ex
te
n
t
an
d
d
ir
ec
tio
n
o
f
th
e
lin
ea
r
co
r
r
elatio
n
o
f
t
w
o
r
an
d
o
m
v
ar
iab
les.
A
co
r
r
elatio
n
co
ef
f
ic
ien
t
clo
s
e
to
1
in
d
ic
ates
th
at
t
w
o
r
an
d
o
m
v
ar
iab
le
s
ar
e
clo
s
el
y
r
elate
d
;
th
e
o
p
p
o
s
ite
is
tr
u
e
w
h
e
n
t
h
e
co
r
r
elatio
n
co
ef
f
ic
ien
t
is
clo
s
e
to
0
.
C
o
ef
f
icie
n
t
r
ca
n
b
e
ca
lc
u
lated
a
s
f
o
llo
w
s
[
1
8
]
:
r=
∑
∑
√
∑
√
∑
,
(
1
4
)
W
h
er
e
X
i
is
th
e
p
i
x
el
i
n
te
n
s
it
y
o
f
th
e
o
r
ig
in
al
i
m
a
g
e,
X
m
is
th
e
m
ea
n
v
al
u
e
o
f
t
h
e
o
r
ig
i
n
al
i
m
ag
e
in
te
n
s
it
y
,
Y
i
i
s
th
e
p
ix
el
i
n
te
n
s
it
y
o
f
t
h
e
s
te
g
o
im
a
g
e
a
n
d
Y
m
is
t
h
e
m
ea
n
v
alu
e
o
f
th
e
s
teg
o
i
m
a
g
e
in
te
n
s
it
y
.
T
h
e
r
esu
lt
s
o
f
th
is
te
s
t
ar
e
s
h
o
w
n
i
n
T
ab
le
1
.
A
ll
v
a
lu
e
s
in
T
ab
le
1
ar
e
clo
s
e
to
1
,
in
d
icatin
g
th
a
t
th
e
h
o
s
t
an
d
s
teg
o
i
m
a
g
e
s
ar
e
clo
s
el
y
r
elate
d
.
T
ab
le
1
C
o
r
r
elatio
n
co
ef
f
icie
n
t r
esu
lt
s
I
mag
e
C
o
r
r
e
l
a
t
i
o
n
c
o
e
f
f
i
c
i
e
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2
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nfo
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T
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it
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teg
a
n
o
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r
a
p
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te
m
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s
m
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s
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er
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s
o
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n
tr
o
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L
et
,
,...,
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p
o
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s
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le
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m
e
n
ts
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th
p
r
o
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ab
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ies P
(
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,
P
(
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,
.
.
.
,
P(
)
.
T
h
e
en
tr
o
p
y
is
g
i
v
en
a
s
∑
.
(
1
5
)
T
h
is
eq
u
atio
n
y
ie
ld
s
an
esti
m
ate
o
f
t
h
e
av
er
a
g
e
m
i
n
i
m
u
m
n
u
m
b
er
o
f
b
it
s
t
h
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is
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ee
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ed
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d
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a
s
tr
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f
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its
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t
h
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asi
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o
f
th
e
f
r
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u
e
n
c
y
o
f
t
h
e
s
y
m
b
o
l [
2
7
]
.
5
.
3
.
H
o
m
o
g
eneit
y
T
h
e
v
alu
e
r
etu
r
n
ed
in
h
o
m
o
g
e
n
eit
y
an
al
y
s
is
i
s
u
s
ed
to
d
eter
m
i
n
e
h
o
w
clo
s
e
t
h
e
ele
m
en
t
d
is
tr
ib
u
tio
n
in
th
e
g
r
e
y
-
le
v
el
co
-
o
cc
u
r
r
en
c
e
m
atr
ix
(
G
L
C
M)
is
to
th
e
G
L
C
M
d
iag
o
n
al.
I
m
ag
e
h
o
m
o
g
en
eit
y
is
ca
lc
u
lated
as
Ho
m
=
∑
,
(
1
6
)
w
h
er
e
p
(
i
,
j
)
d
en
o
te
th
e
p
ix
el
v
alu
e
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at
t
h
e
i
th
r
o
w
a
n
d
j
th
co
lu
m
n
a
n
d
(
i
,
j
)
r
ep
r
esen
t
th
e
i
n
d
ices
o
f
r
o
w
an
d
co
lu
m
n
n
u
m
b
er
s
,
r
esp
ec
tiv
el
y
[
6
]
.
5
.
4
.
Co
ntr
a
s
t
C
o
n
tr
ast
a
n
al
y
s
i
s
p
r
o
d
u
ce
s
a
m
ea
s
u
r
e
o
f
t
h
e
i
n
te
n
s
it
y
co
n
tr
ast
b
et
w
ee
n
a
p
i
x
el
a
n
d
its
n
e
ig
h
b
o
u
r
in
an
en
tire
i
m
a
g
e.
Fo
r
v
ie
w
er
s
,
co
n
tr
ast
an
al
y
s
i
s
h
elp
s
t
h
e
m
r
ec
o
g
n
is
e
o
b
j
ec
ts
in
th
e
t
ex
tu
r
e
o
f
a
n
i
m
ag
e.
C
o
n
tr
ast a
n
al
y
s
i
s
is
w
r
itte
n
as
[
6
]
C=
∑
.
(
1
7
)
T
ab
le
2
p
r
esen
ts
t
h
e
r
esu
lts
o
f
th
e
test
s
o
n
t
h
e
f
o
u
r
s
tan
d
ar
d
im
ag
e
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
10
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
0
:
9
3
5
-
946
942
T
ab
le
2
.
Statis
tical
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al
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.
5
.
I
m
a
g
e
his
t
o
g
ra
m
A
h
is
to
g
r
a
m
s
h
o
w
s
th
e
e
x
ac
t
o
cc
u
r
r
en
ce
o
f
ea
ch
p
ix
el
i
n
th
e
i
m
ag
e.
T
h
e
h
i
g
h
s
i
m
ilar
it
y
b
et
w
ee
n
th
e
h
o
s
t
a
n
d
s
teg
o
i
m
a
g
e
h
is
to
g
r
a
m
s
in
d
icate
s
t
h
e
o
cc
u
r
r
en
ce
o
f
m
i
n
i
m
al
d
i
s
to
r
tio
n
af
ter
e
m
b
ed
d
in
g
th
e
s
ec
r
et
i
m
ag
e
i
n
to
th
e
h
o
s
t
i
m
a
g
e
[
5
,
1
0
]
.
T
h
is
test
is
p
er
f
o
r
m
ed
o
n
m
a
n
y
i
m
ag
e
s
.
T
h
e
h
is
to
g
r
a
m
o
f
th
e
L
e
n
a
i
m
ag
e
is
p
r
ese
n
ted
.
Fig
u
r
e
3
s
h
o
w
s
t
h
e
h
i
s
to
g
r
a
m
o
f
th
e
h
o
s
t
an
d
s
te
g
o
i
m
a
g
es
o
f
th
r
ee
co
m
p
o
n
en
t
s
.
Fro
m
F
i
g
u
r
e
3
ca
n
b
e
s
h
o
w
n
t
h
at
t
h
e
h
is
to
g
r
a
m
o
f
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
h
i
g
h
lig
h
t
s
s
li
g
h
t
ch
a
n
g
e
s
b
et
w
ee
n
th
e
h
o
s
t a
n
d
s
te
g
o
i
m
a
g
es.
Fig
u
r
e
3
.
His
to
g
r
a
m
o
f
h
o
s
t a
n
d
s
teg
o
i
m
a
g
es o
f
th
r
ee
co
m
p
o
n
en
t
s
5
.
6
.
K
ey
s
ens
it
iv
it
y
C
h
ao
tic
m
ap
s
ar
e
ex
tr
e
m
el
y
s
e
n
s
iti
v
e
to
i
n
itia
l
co
n
d
i
tio
n
s
a
n
d
s
y
s
te
m
co
n
tr
o
l
p
ar
a
m
eter
s
.
T
h
e
s
lig
h
test
ch
a
n
g
e
ca
n
ca
u
s
e
d
if
f
icu
l
ties
i
n
t
h
e
e
x
tr
ac
tio
n
o
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h
id
d
en
m
e
s
s
a
g
es
f
r
o
m
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te
g
o
i
m
a
g
e
s
[
6
,
1
8
]
.
T
h
e
k
e
y
s
e
n
s
iti
v
it
y
te
s
t
co
n
d
u
cted
in
t
h
is
w
o
r
k
is
ai
m
e
d
at
estab
li
s
h
in
g
th
e
s
e
n
s
i
tiv
it
y
o
f
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
to
s
lig
h
t
m
o
d
i
f
icati
o
n
s
in
s
ec
r
et
k
e
y
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.
3
D
lo
g
is
ti
c
an
d
C
h
eb
y
s
h
e
v
m
ap
s
ar
e
u
s
ed
in
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
a
n
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ar
e
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ig
o
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o
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l
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al
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ated
.
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h
e
s
en
s
iti
v
it
y
o
f
t
h
e
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r
o
p
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s
ed
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o
r
ith
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n
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itio
n
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h
o
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in
g
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T
h
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P
ep
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ed
as
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s
t.
T
h
e
f
ir
s
t
ch
a
n
g
e
i
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ap
p
lied
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e
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itial
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o
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3
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lo
g
is
tic
m
ap
.
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h
e
s
u
b
s
eq
u
en
t
ch
a
n
g
e
i
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ap
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lied
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h
e
i
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itial
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al
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o
f
th
e
3
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h
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y
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e
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m
ap
.
S
u
p
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o
s
e
th
at
t
h
e
s
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ted
k
e
y
s
f
o
r
th
e
3
D
lo
g
i
s
tic
m
ap
ar
e
α
=
0
.
0
1
4
,
β
=
0
.
0
2
0
an
d
R
=
3
.
7
9
w
h
ile
t
h
e
s
li
g
h
tl
y
d
if
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er
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n
t
k
e
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e
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=
0
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0
1
4
0
0
0
0
1
,
β
=
0
.
0
2
0
an
d
R
=
3
.
7
9
;
α
=
0
.
0
1
4
,
β
=
0
.
0
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0
0
0
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0
1
an
d
R
=
3
.
7
9
;
an
d
α
=
0
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0
1
4
,
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.
0
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0
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d
R
=
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7
9
0
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0
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.
Fig
u
r
e
4
s
h
o
w
s
th
at
th
e
h
id
d
en
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
I
ma
g
e
s
teg
a
n
o
g
r
a
p
h
y
u
s
in
g
le
a
s
t sig
n
ifica
n
t b
it a
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(
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(
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[
5
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7
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.
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P
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m
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[
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