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1457
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Evaluation Warning : The document was created with Spire.PDF for Python.
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Vo
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22
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No
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3
,
J
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n
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2
0
2
1
:
1
4
5
7
-
1466
1458
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[
1
7
]
,
th
e
h
ig
h
s
ec
u
r
it
y
p
r
o
p
er
ty
d
u
e
to
th
e
u
n
n
e
ce
s
s
it
y
to
s
h
ar
e
t
h
e
k
e
y
s
p
er
io
d
icall
y
(
d
ail
y
,
w
ee
k
l
y
,
an
d
m
o
n
t
h
l
y
)
i
n
a
v
er
y
v
er
y
s
ec
u
r
e
w
a
y
.
T
h
e
d
if
f
er
en
ce
s
ar
e
also
in
th
e
g
e
n
er
al
s
tr
u
ct
u
r
e
o
f
th
e
al
g
o
r
ith
m
s
o
f
th
e
s
y
s
te
m
b
ec
au
s
e
o
f
t
h
e
n
u
m
b
er
o
f
k
e
y
s
,
i
n
ad
d
itio
n
to
t
h
e
ea
s
e
o
f
co
n
n
ec
ti
n
g
f
o
r
an
y
o
n
e
b
y
k
n
o
w
in
g
its
p
u
b
lic
k
e
y
w
it
h
th
e
as
y
m
m
etr
ic
k
e
y
s
y
s
te
m
.
T
h
is
p
ap
er
p
r
o
p
o
s
ed
t
w
o
n
e
w
p
u
b
li
c
k
e
y
cr
y
p
to
s
y
s
te
m
s
f
o
r
i
m
ag
e
en
cr
y
p
tio
n
b
ased
o
n
m
u
ltip
le
ch
ao
tic
m
ap
s
(
to
m
a
k
e
th
e
c
r
y
p
to
s
y
s
te
m
s
m
o
r
e
co
m
p
lica
ted
ag
i
n
s
t
t
h
e
v
ar
io
u
s
attac
k
s
)
,
w
h
er
e
b
o
th
s
y
s
te
m
s
d
ep
en
d
o
n
g
en
er
ati
n
g
a
c
h
ao
tic
m
a
tr
ix
u
s
i
n
g
m
u
ltip
le
ch
ao
tic
m
ap
s
.
T
h
e
p
a
r
a
m
eter
s
f
o
r
th
ese
m
ap
s
ar
e
d
e
r
iv
ed
f
r
o
m
th
e
s
h
ar
ed
s
ec
r
et
k
e
y
s
g
e
n
er
ated
f
r
o
m
th
e
C
h
eb
y
s
h
ev
m
ap
.
T
h
e
p
ap
er
is
ar
r
an
g
ed
a
s
f
o
llo
w
s
:
T
h
e
s
ec
tio
n
2
i
n
tr
o
d
u
ce
s
s
o
m
e
w
ell
-
k
n
o
w
n
c
h
ao
tic
m
ap
s
.
T
h
e
s
ec
tio
n
3
ex
p
lain
s
h
o
w
to
r
ec
r
u
it
ch
ao
tic
m
ap
s
i
n
th
e
t
w
o
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
an
d
in
tr
o
d
u
ce
s
th
e
t
w
o
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
i
n
d
etails.
Sectio
n
4
g
i
v
es
s
o
m
e
s
t
atis
tical
a
n
al
y
s
i
s
f
o
r
th
e
t
w
o
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
an
d
co
m
p
ar
is
o
n
s
th
e
r
es
u
lt
w
it
h
s
o
m
e
ch
ao
tic
-
b
ased
s
y
s
te
m
s
an
d
co
m
p
u
te
s
k
e
y
s
p
ac
e
an
d
s
en
s
iti
v
it
y
.
F
in
all
y
,
in
s
ec
tio
n
5
,
a
co
n
clu
s
io
n
is
g
i
v
en
.
2.
SO
M
E
WE
L
L
-
K
NO
WN
CH
AO
T
I
C
M
AP
S
T
h
e
p
r
o
p
o
s
ed
cr
y
p
to
s
y
s
te
m
s
e
m
p
lo
y
f
o
u
r
ch
ao
tic
m
ap
s
in
t
h
is
p
ap
er
,
l
o
g
is
tic
m
ap
[
2
]
,
ten
t
m
ap
[
11
]
,
q
u
ad
r
atic
m
ap
an
d
C
h
eb
y
s
h
e
v
m
ap
[
10
].
a.
L
o
g
i
s
tic
m
ap
Th
is
m
ap
i
s
o
n
e
o
f
t
h
e
m
o
s
t
co
m
m
o
n
c
h
ao
tic
m
ap
s
.
I
t
is
d
ef
i
n
ed
b
y
t
h
e
f
o
llo
w
in
g
d
i
f
f
er
e
n
c
e
eq
u
atio
n
,
w
h
er
e
th
e
c
h
ao
tic
b
eh
a
v
io
r
o
f
th
e
m
ap
i
s
o
b
tain
ed
w
h
e
n
∈
[
3
.
57
,
4
]
an
d
th
e
ch
ao
tic
s
eq
u
e
n
ce
∈
[
0
,
1
]
:
+
1
=
(
1
−
)
(
1
)
b.
T
en
t m
ap
Th
is
is
d
ef
i
n
ed
b
y
t
h
e
f
o
llo
w
i
n
g
d
i
f
f
er
en
ce
eq
u
atio
n
:
+
1
=
(
,
1
−
)
(
2
)
c.
Qu
ad
r
atic
m
ap
T
h
is
is
d
ef
in
ed
b
y
t
h
e
f
o
llo
w
in
g
d
if
f
er
e
n
ce
eq
u
atio
n
,
w
h
er
e
th
e
ch
ao
tic
b
eh
av
io
r
o
f
th
e
m
ap
is
o
b
tain
ed
w
h
e
n
μ
∈
[
1
.
5
,
2
]
w
it
h
ch
ao
tic
s
eq
u
en
ce
∈
[
-
2
,
2
]
.
+
1
=
−
(
2
)
(
3
)
d.
C
h
eb
y
s
h
ev
m
ap
C
h
eb
y
s
h
ev
p
o
l
y
n
o
m
ial
m
ap
i
s
d
ef
in
ed
as
(
4
)
,
(
)
=
2
−
1
(
)
−
−
2
(
)
(
4
)
w
h
er
e
(
)
is
th
e
o
r
d
er
f
o
r
th
e
p
o
ly
n
o
m
ial
an
d
(
)
is
th
e
v
ar
iab
l
e,
w
ith
i
n
itial
s
0
(
)
=
1
an
d
1
(
)
=
,
s
o
m
e
n
ex
t
o
r
d
er
s
ar
e:
=
2
,
2
(
)
=
2
2
−
1
,
=
3
,
3
(
)
=
4
3
−
3
an
d
s
o
o
n
.
I
n
o
r
d
er
to
d
ea
l
w
it
h
in
te
g
er
s
,
a
s
i
m
p
le
m
o
d
i
f
icatio
n
o
f
th
e
b
asic
m
ap
is
m
ad
e
b
y
ad
d
in
g
m
o
d
N
to
h
an
d
le
a
s
p
ec
if
ic
f
ield
w
h
er
e
th
e
d
ef
in
i
tio
n
o
f
t
h
e
m
o
d
u
lar
m
ap
b
ec
o
m
e
s
:
=
(
)
(
5
)
3.
T
H
E
P
RO
P
O
SE
D
AL
G
O
RI
T
H
M
S
T
h
is
s
ec
tio
n
d
escr
ib
es
h
o
w
to
r
ec
r
u
it
ch
ao
tic
m
ap
s
i
n
th
e
t
wo
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
b
y
ex
p
l
ain
i
n
g
t
h
e
p
u
r
p
o
s
e
o
f
u
s
in
g
t
h
e
m
an
d
t
h
e
m
et
h
o
d
o
f
g
e
n
e
r
atio
n
c
h
ao
tic
m
atr
i
x
(
)
th
e
n
d
escr
ib
es
t
h
e
s
tr
u
ctu
r
e
o
f
t
h
e
t
w
o
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
in
d
etail
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4752
P
u
b
lic
ke
y
cryp
to
s
ystem
b
a
s
ed
o
n
mu
ltip
le
ch
a
o
tic
ma
p
s
fo
r
i
ma
g
e
en
cryp
tio
n
(
Yo
u
s
if S
.
N
a
ja
f
)
1459
3
.
1
.
R
ec
ruit
cha
o
t
ic
m
a
ps
i
n
t
he
pro
po
s
ed
a
lg
o
rit
h
m
s
T
w
o
r
ea
s
o
n
s
ar
e
b
eh
in
d
t
h
e
u
s
e
o
f
ch
ao
tic
m
ap
s
in
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
.
T
h
e
f
ir
s
t o
n
e
is
to
u
s
e
t
h
e
C
h
eb
y
s
h
ev
m
ap
s
p
ec
if
icall
y
i
n
o
r
d
er
to
g
en
er
ate
s
ec
r
et
s
h
ar
ed
k
ey
s
b
et
w
ee
n
A
lice
an
d
B
o
b
,
th
e
s
ec
o
n
d
o
n
e
is
to
u
s
e
o
th
er
ch
ao
tic
m
ap
s
i
n
o
r
d
er
to
g
en
er
ate
a
ch
ao
tic
m
atr
i
x
b
y
u
s
i
n
g
t
h
ese
s
ec
r
et
s
h
ar
ed
k
e
y
s
.
3
.
1
.
1
.
Secr
et
s
ha
re
d k
ey
s
g
en
er
a
t
ed
by
us
ing
c
h
eby
s
hev
ma
p
T
h
e
C
h
eb
y
s
h
ev
m
ap
u
s
ed
s
p
ec
if
icall
y
in
o
r
d
er
to
g
en
er
ate
s
ec
r
et
s
h
ar
ed
k
e
y
s
b
et
w
ee
n
A
lic
e
an
d
B
o
b
,
w
h
er
e
th
e
g
e
n
er
atio
n
o
f
t
h
e
s
e
cr
et
s
h
ar
ed
k
e
y
s
d
ep
en
d
s
o
n
t
h
e
m
o
d
if
ied
alg
o
r
it
h
m
i
n
tr
o
d
u
ce
d
b
y
[
2
5
]
in
o
r
d
e
r
to
s
o
lv
e
th
e
m
u
lti
-
k
e
y
s
p
r
o
b
lem
.
3
.
1
.2
.
Cha
o
t
ic
m
a
t
ri
x
g
ener
a
t
ed
by
us
ing
cha
o
t
ic
m
a
p
T
h
is
s
u
b
s
ec
tio
n
e
x
p
lain
s
th
e
g
en
er
at
io
n
o
f
th
e
ch
ao
tic
m
atr
i
x
f
r
o
m
s
ec
r
et
s
h
ar
ed
k
e
y
s
an
d
th
e
m
at
h
e
m
a
tical
f
o
r
m
u
la
u
s
ed
f
o
r
th
e
ch
ao
tic
m
atr
ix
i
n
ex
p
r
es
s
iv
e
f
o
r
m
.
a.
Gen
er
atio
n
o
f
t
h
e
c
h
ao
tic
m
atr
ix
I
n
m
o
s
t
e
n
cr
y
p
tio
n
al
g
o
r
ith
m
s
,
i
m
a
g
e
en
cr
y
p
tio
n
d
ep
en
d
s
o
n
g
e
n
er
atin
g
a
r
an
d
o
m
m
atr
i
x
,
as
ea
c
h
p
ix
el
in
th
i
s
r
an
d
o
m
m
atr
i
x
is
u
s
ed
to
en
cr
y
p
t
th
e
co
r
r
esp
o
n
d
in
g
p
ix
el
in
t
h
e
o
r
ig
in
al
i
m
ag
e.
T
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
is
b
ased
o
n
g
en
er
at
i
n
g
a
c
h
ao
tic
m
atr
i
x
f
r
o
m
t
h
e
ch
ao
tic
m
ap
s
.
T
h
e
s
ize
o
f
t
h
e
c
h
ao
tic
m
atr
i
x
is
t
h
e
s
a
m
e
as
t
h
e
s
ize
o
f
th
e
o
r
ig
i
n
a
l
i
m
a
g
e.
L
et
’
s
g
en
er
ate
t
h
e
ch
ao
tic
m
atr
ix
(
)
b
y
u
s
i
n
g
s
a
y
lo
g
i
s
tic
ch
ao
tic
m
ap
f
o
r
ex
a
m
p
le,
a
f
ter
ch
o
o
s
i
n
g
(
,
)
th
e
f
ir
s
t
v
a
lu
e
in
c
h
ao
tic
m
atr
i
x
c
o
m
p
u
ted
f
r
o
m
t
h
e
l
o
g
is
t
ic
m
ap
is
(
1
,
1
)
=
(
1
−
)
th
e
s
ec
o
n
d
v
alu
e
in
th
e
m
atr
i
x
is
(
1
,
2
)
=
+
1
(
1
−
+
1
)
an
d
th
e
n
ex
t
v
al
u
e
in
th
e
m
atr
i
x
is
(
1
,
3
)
=
+
2
(
1
−
+
2
)
an
d
s
o
o
n
.
T
o
m
ak
e
th
e
g
e
n
er
atio
n
p
r
o
ce
s
s
m
o
r
e
co
m
p
lica
ted
,
a
n
e
w
p
ar
a
m
eter
(
)
is
ad
d
ed
th
at
r
ep
r
esen
ts
a
m
u
ltip
licit
y
n
u
m
b
er
to
th
e
m
ap
b
ef
o
r
e
p
r
o
d
u
cin
g
th
e
o
u
tp
u
t.
Fo
r
ex
am
p
le,
if
=
2
th
en
t
h
e
f
ir
s
t
v
al
u
e
in
ch
a
o
tic
m
a
tr
ix
co
m
p
u
ted
f
r
o
m
l
o
g
is
tic
m
ap
is
is
(
1
,
1
)
=
+
2
=
+
1
(
1
−
+
1
)
th
e
s
ec
o
n
d
v
al
u
e
i
n
m
atr
ix
is
(
1
,
2
)
=
+
4
=
+
3
(
1
−
+
3
)
an
d
t
h
e
n
ex
t
v
a
lu
e
in
m
a
tr
ix
is
(
1
,
3
)
=
+
6
=
+
5
(
1
−
+
5
)
an
d
s
o
o
n
.
T
h
e
s
a
m
e
ap
p
lies
if
=
100
w
h
er
e
th
e
f
ir
s
t
v
al
u
e
in
c
h
a
o
tic
m
atr
i
x
co
m
p
u
ted
f
r
o
m
lo
g
i
s
ti
c
m
ap
is
(
1
,
1
)
=
+
100
=
+
99
(
1
−
+
99
)
th
e
s
ec
o
n
d
v
alu
e
in
m
atr
i
x
is
(
1
,
2
)
=
+
200
=
+
1
99
(
1
−
+
1
99
)
an
d
th
e
n
e
x
t
v
al
u
e
i
n
m
atr
ix
is
(
1
,
3
)
=
+
300
=
+
2
99
(
1
−
+
2
99
)
an
d
s
o
o
n
.
b.
C
r
ea
tin
g
t
h
e
ch
ao
tic
m
atr
ix
i
n
ex
p
r
e
s
s
i
v
e
f
o
r
m
u
la
T
h
e
ex
p
r
ess
iv
e
f
o
r
m
u
la
th
a
t
will b
e
u
s
ed
f
o
r
th
e
c
h
ao
tic
m
atr
ix
cr
ea
tio
n
p
r
o
ce
s
s
w
ill b
e
as
(
6
)
,
=
[
ℎ
]
(
6
)
w
h
er
e
(
R
e)
r
ep
r
esen
ts
th
e
r
ep
etitio
n
o
f
t
h
e
m
ap
K
ti
m
e
s
.
I
t
s
h
o
u
ld
b
e
n
o
ted
th
at
th
e
b
est
r
esu
lts
f
r
o
m
th
e
s
e
ch
ao
tic
m
ap
s
ar
e
o
b
tain
ed
i
f
t
h
e
b
if
u
r
ca
tio
n
d
ia
g
r
a
m
o
f
th
e
ch
ao
tic
m
ap
i
s
k
n
o
w
n
.
Fo
r
ex
a
m
p
le,
th
e
lo
g
is
t
ic
m
ap
h
as
t
h
e
b
est
r
esu
lt w
h
e
n
is
clo
s
er
to
4
ten
t
an
d
q
u
ad
r
atic
m
ap
s
h
a
v
e
th
e
b
est
r
esu
lts
w
h
en
is
clo
s
e
to
2
.
Hen
ce
=
3
.
99
is
c
h
o
s
e
n
f
o
r
lo
g
is
tic
a
n
d
=
1
.
99
f
o
r
ten
t
a
n
d
q
u
ad
r
atic
m
ap
s
.
T
h
e
t
y
p
e
o
f
ch
ao
tic
m
ap
u
s
e
d
d
o
es n
o
t a
f
f
ec
t th
e
r
es
u
lt
s
an
d
th
at
g
iv
e
s
m
a
n
y
ch
o
ices a
v
aila
b
le.
3
.1
.
3
.
Sca
lin
g
do
w
n a
nd
s
ca
lin
g
up
I
n
g
en
er
al,
t
h
e
s
ec
r
et
s
h
ar
ed
k
e
y
s
g
e
n
er
ated
f
r
o
m
t
h
e
C
h
eb
y
s
h
e
v
m
ap
ar
e
in
teg
er
s
.
So
in
o
r
d
er
to
u
s
e
s
o
m
e
o
f
t
h
e
m
i
n
a
n
y
s
elec
ted
c
h
ao
tic
m
ap
s
a
s
i
n
itial
p
ar
a
m
ete
r
s
,
th
e
y
m
u
s
t
b
e
s
ca
led
to
t
h
e
r
an
g
e
o
f
m
ap
s
u
s
ed
.
T
h
is
is
ca
lled
“
s
ca
lin
g
d
o
w
n
”
.
A
ls
o
,
th
e
o
u
tp
u
t
s
o
f
th
e
s
elec
t
ed
ch
ao
tic
m
ap
s
m
u
s
t
b
e
s
ca
led
ag
ain
f
o
r
in
teg
er
v
a
lu
es
o
f
th
e
ch
a
o
t
i
c
m
a
t
r
i
x
in
te
g
e
r
s
.
T
h
i
s
i
s
c
al
l
e
d
“
s
ca
l
in
g
u
p
”
.
F
o
r
e
x
am
p
l
e
,
if
t
h
e
l
o
g
is
t
ic
m
a
p
i
s
s
e
l
e
ct
e
d
,
t
h
e
n
i
t'
s
r
an
g
e
i
s
(
=
0
,
ℎ
ℎ
=
1
)
s
o
t
h
e
s
c
a
li
n
g
d
o
w
n
f
o
r
s
e
c
r
e
t
s
h
a
r
e
d
k
ey
Q
w
il
l
b
e
[
(
ℎ
ℎ
−
)
(
)
(
)
+
]
a
n
d
th
e
o
u
tp
u
t
w
ill b
e
s
ca
led
u
p
as
[
(
−
)
(
)
(
ℎ
ℎ
−
)
+
]
.
3
.
2
.
T
he
g
ener
a
l st
ruct
ure
o
f
t
wo
pro
po
s
ed
a
lg
o
ri
t
h
m
s
T
w
o
alg
o
r
it
h
m
s
ar
e
s
u
g
g
ested
,
th
e
s
ec
o
n
d
alg
o
r
ith
m
d
i
f
f
er
s
f
r
o
m
th
e
f
ir
s
t
al
g
o
r
ith
m
i
n
s
o
m
e
p
o
in
t
s
o
n
l
y
,
b
u
t i
n
t
h
e
g
e
n
er
al
s
tr
u
ctu
r
e
th
e
y
ar
e
v
er
y
s
i
m
ilar
an
d
co
n
s
i
s
t o
f
t
h
r
ee
b
asic sta
g
es:
a.
T
h
e
f
ir
s
t
s
ta
g
e
is
t
h
e
k
e
y
s
g
en
e
r
atio
n
s
ta
g
e,
w
h
er
e
A
lice
g
e
n
e
r
ates
h
er
p
r
i
v
ate
k
e
y
s
i
n
ad
d
iti
o
n
to
g
e
n
er
ati
n
g
th
e
p
u
b
lic
k
e
y
s
,
b.
T
h
e
s
ec
o
n
d
s
tag
e
is
th
e
g
en
er
atio
n
o
f
s
h
ar
ed
s
ec
r
et
k
e
y
s
an
d
en
cr
y
p
tio
n
,
w
h
er
e
B
o
b
g
en
er
ates
h
is
s
ec
r
et
k
e
y
s
h
e
w
ill
u
s
e
i
n
ad
d
itio
n
to
th
e
p
u
b
lic
k
e
y
s
f
o
r
A
lice
f
o
r
th
e
p
u
r
p
o
s
e
o
f
g
e
n
er
ati
n
g
s
h
ar
ed
s
ec
r
et
k
e
y
s
,
an
d
th
e
n
u
s
es t
h
e
s
h
ar
ed
k
e
y
s
f
o
r
th
e
p
u
r
p
o
s
e
o
f
en
cr
y
p
tio
n
t
h
e
i
m
a
g
e.
c.
T
h
e
th
ir
d
s
tag
e
is
th
e
g
en
er
ati
o
n
o
f
s
h
ar
ed
s
ec
r
et
k
e
y
s
an
d
d
ec
r
y
p
tio
n
,
w
h
er
e
A
l
ice
g
e
n
e
r
ates
th
e
s
h
ar
ed
s
ec
r
et
k
e
y
s
u
s
i
n
g
h
er
p
r
iv
ate
k
e
y
s
an
d
th
e
cip
h
er
p
ar
am
eter
s
ar
e
s
en
t
f
r
o
m
B
o
b
af
ter
th
at,
A
lice
d
ec
r
y
p
t
s
th
e
cip
h
er
i
m
ag
e
.
F
ig
u
r
es
1
an
d
2
illu
s
tr
ate
th
e
s
e
s
ta
g
es i
n
b
o
th
alg
o
r
it
h
m
s
r
esp
ec
ti
v
el
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2502
-
4752
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
22
,
No
.
3
,
J
u
n
e
2
0
2
1
:
1
4
5
7
-
1466
1460
Fig
u
r
e
1
.
Gen
er
atio
n
o
f
c
h
ao
ti
c
m
atr
ix
(
I
)
in
f
ir
s
t a
l
g
o
r
ith
m
w
h
e
n
B
o
b
s
en
d
s
a
m
es
s
ag
e
to
A
lice
Fig
u
r
e
2
.
Gen
er
atio
n
o
f
c
h
ao
ti
c
m
atr
ix
(
I
)
in
s
ec
o
n
d
alg
o
r
ith
m
w
h
en
B
o
b
s
en
d
s
a
m
e
s
s
a
g
e
to
A
lice
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4752
P
u
b
lic
ke
y
cryp
to
s
ystem
b
a
s
ed
o
n
mu
ltip
le
ch
a
o
tic
ma
p
s
fo
r
i
ma
g
e
en
cryp
tio
n
(
Yo
u
s
if S
.
N
a
ja
f
)
1461
3
.
2
.1
.
Descript
io
n o
f
t
he
f
irst
pro
po
s
ed
a
lg
o
rit
h
m
a.
A
lice
p
er
f
o
r
m
s
t
h
e
f
o
llo
w
i
n
g
s
tep
s
f
o
r
s
tag
e
1
:
1)
C
h
o
o
s
e
a
lar
g
e
i
n
te
g
er
n
u
m
b
er
N
an
d
an
ap
p
r
o
p
r
iate
in
teg
er
n
u
m
b
er
x
<
N
.
2)
C
h
o
o
s
e
a
lar
g
e
p
r
i
m
e
n
u
m
b
er
P
>
>
N
.
3)
C
h
o
o
s
e
r
an
d
o
m
i
n
te
g
er
n
u
m
b
er
s
(
s
1
,
s
2
,
s
3
,
…
,
s
n
)
,
less
th
a
n
N
,
w
h
er
e
n
r
ep
r
ese
n
ts
t
h
e
n
u
m
b
er
o
f
s
ec
r
et
k
e
y
s
to
b
e
ch
o
s
en
a
s
an
ev
en
n
u
m
b
er
.
4)
C
o
m
p
u
te
A
n
=
T
s
n
(
x
)
modP
.
5)
T
h
e
p
u
b
lic
k
e
y
s
f
o
r
A
l
ice
ar
e
(
x
,
N
,
P
,
A
1
,
A
2
,
A
3
,
…
,
A
n
)
,
an
d
th
e
p
r
iv
ate
k
e
y
s
ar
e
(
s
1
,
s
2
,
s
3
,
…
,
s
n
)
.
b.
B
o
b
p
er
f
o
r
m
s
th
e
f
o
llo
w
i
n
g
s
t
ep
s
f
o
r
s
tag
e
2
:
1)
Use th
e
p
u
b
lic
k
e
y
f
o
r
A
lice
(
,
,
,
1
,
2
,
3
,
…
,
)
.
2)
C
h
o
o
s
e
a
r
an
d
o
m
i
n
te
g
er
s
(
1
,
2
,
3
,
…
,
)
,
le
s
s
t
h
an
.
3)
C
alcu
late
=
(
)
an
d
=
(
)
.
4)
C
alcu
late
=
f
o
r
ev
en
v
al
u
e
o
f
,
w
h
er
e
=
/
2
.
5)
C
alcu
late
f
r
o
m
s
ca
li
n
g
d
o
w
n
f
o
r
th
e
o
d
d
v
alu
e
o
f
,
w
h
er
e
th
is
s
ca
li
n
g
d
ep
en
d
s
o
n
th
e
ch
ao
tic
m
ap
s
u
s
ed
i
n
th
e
n
ex
t step
.
6)
Gen
er
ate
ch
ao
tic
m
atr
i
x
ele
m
e
n
ts
=
(
[
ℎ
]
)
.
7)
C
alcu
late
=
∑
=
1
.
8)
C
alcu
late
=
(
+
1
)
256
w
h
er
e
is
th
e
o
r
ig
i
n
al
i
m
a
g
e
an
d
is
th
e
cip
h
er
i
m
a
g
e.
9)
Sen
d
th
e
cip
h
er
p
ar
am
e
ter
s
to
A
lice
(
1
,
2
,
3
,
…
,
)
,
w
h
er
e
th
e
s
e
p
ar
a
m
eter
s
ar
e
s
en
t o
n
l
y
o
n
ce
an
d
n
o
t r
elate
d
to
th
e
p
lain
i
m
ag
e.
10)
Sen
d
th
e
cip
h
er
ed
i
m
a
g
e
to
A
l
ice
(
)
.
c.
A
lice
p
er
f
o
r
m
s
t
h
e
f
o
llo
w
i
n
g
s
tep
s
f
o
r
s
tag
e
3
:
1)
Use c
ip
h
er
p
ar
a
m
eter
s
s
e
n
t
f
r
o
m
B
o
b
(
1
,
2
,
3
,
…
,
)
an
d
h
er
p
r
iv
ate
k
e
y
s
(
1
,
2
,
3
,
…
,
)
to
ca
lcu
late
=
(
)
.
2)
R
ep
ea
t step
s
4
-
7
as i
n
th
e
s
ec
o
n
d
s
tag
e
u
n
til all
ele
m
e
n
ts
o
f
(
)
ar
e
ca
lcu
lated
.
3)
Fin
all
y
co
m
p
u
te
t
h
e
o
r
ig
i
n
al
i
m
ag
e
M
=
(
C
-
I
)
mod256
.
3
.
2
.2
.
Descript
io
n o
f
t
he
s
ec
o
nd
pro
po
s
ed
a
lg
o
rit
h
m
a.
A
lice
p
er
f
o
r
m
s
t
h
e
f
o
llo
w
i
n
g
s
tep
s
f
o
r
s
tag
e
(
1
)
:
1)
C
h
o
o
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m
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d
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.
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C
h
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lar
g
e
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m
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n
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m
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>
.
3)
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r
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d
o
m
i
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g
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m
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(
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2
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…
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e
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n
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5)
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p
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(
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6)
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A
l
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,
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,
,
1
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2
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d
th
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p
r
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b.
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s
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,
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(
[
ℎ
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[
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late
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r
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d
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,
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,
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10)
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alcu
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(
+
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2
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).
c.
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2
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to
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ad
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th
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k
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1
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4
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,
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d
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4
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as sh
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ap
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s
ed
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f
ir
s
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lg
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r
ith
m
=
120
=
149
=
29803
A
1
=
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r
1
=
25
B
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=
4930
s
2
=
47
A
2
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4
r
2
=
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2
=
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s
3
=
55
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3
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r
3
=
37
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3
=
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s
4
=
75
A
4
=
22135
r
4
=
67
B
4
=
27390
1
=
506
.
15709827
8697
−
003
K
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2
=
467
.
134181122706
−
003
K
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T
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s
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ed
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d
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o
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ith
m
=
4
=
120
=
149
=
29803
R
a
n
d
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m
i
n
t
e
g
e
r
s
P
u
b
l
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k
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R
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S
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d
se
c
r
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t
k
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y
s
s
1
=
54
A
1
=
21202
r
1
=
48
B
1
=
11954
QB
4
=
Q
1
=
5430
s
2
=
110
A
2
=
50
63
r
2
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B
2
=
18975
QB
1
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Q
2
=
202
s
3
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59
A
3
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18296
r
3
=
14
B
3
=
4110
QB
2
=
Q
3
=
3674
s
4
=
102
A
4
=
25943
r
4
=
17
B
4
=
5295
QA
3
=
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4
=
29187
s
5
=
105
A
5
=
18687
r
5
=
21
B
5
=
18230
Q
5
=
19810
s
6
=
66
A
6
=
6217
r
6
=
100
B
6
=
2625
Q
6
=
11772
s
7
=
3
A
7
=
27147
r
7
=
74
B
7
=
1422
Q
7
=
5963
s
8
=
50
A
8
=
1106
r
8
=
22
B
8
=
21080
Q
8
=
14811
s
9
=
64
A
9
=
22801
r
9
=
9
B
9
=
18571
Q
9
=
24621
s
10
=
41
A
10
=
22025
r
10
=
127
B
10
=
950
Q
10
=
8338
s
11
=
30
A
11
=
17377
r
11
=
44
B
11
=
7339
Q
11
=
10419
s
12
=
123
A
12
=
816
r
12
=
139
B
12
=
24282
Q
12
=
7534
s
13
=
65
A
13
=
4343
r
13
=
87
B
13
=
4135
Q
13
=
22047
s
14
=
133
A
14
=
8259
r
14
=
25
B
14
=
4930
QA
2
=
Q
14
=
28862
s
15
=
59
A
15
=
18296
r
15
=
120
B
15
=
1404
Q
15
=
11855
s
16
=
115
A
16
=
20623
r
16
=
96
B
16
=
15264
QB
3
=
Q
16
=
4088
s
17
=
60
A
17
=
22068
r
17
=
136
B
17
=
5509
QA
4
=
Q
17
=
29556
s
18
=
121
A
18
=
9276
r
18
=
32
B
18
=
18700
QA
1
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Q
18
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24640
s
19
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113
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19
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23300
r
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77
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27684
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17220
s
20
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57
A
20
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5838
r
20
=
18
B
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3449
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12259
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826
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762406469147
−
003
KA
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28862
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33
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57
KB
2
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Evaluation Warning : The document was created with Spire.PDF for Python.
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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4
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8
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9
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ials
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0
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K.
P
ra
sa
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h
,
K.
Ra
m
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r
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a
n
d
R
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n
a
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je
y
a
ra
m
a
n
,
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u
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m
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sh
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v
p
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ly
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ials
,
”
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.
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1
]
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.
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c
a
re
v
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d
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.
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se
v
,
“
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u
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o
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h
e
b
y
sh
e
v
m
a
p
s
,
”
IEE
E
I
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ter
n
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ti
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siu
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irc
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it
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4
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.
[2
2
]
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.
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a
re
v
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J
.
M
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k
ra
d
u
l
i
,
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n
d
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.
Am
a
to
,
“
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u
b
li
c
-
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h
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e
v
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ly
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ials
,
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Pr
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2
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5
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p
p
.
4
9
7
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1
7
,
2
0
0
5
.
[2
3
]
D.
Yo
sh
io
k
a
,
“
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ro
p
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f
c
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y
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v
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ly
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ials
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k
,
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c
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Circ
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II:
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ss
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v
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l.
6
5
,
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o
.
3
,
p
p
.
3
8
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-
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0
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2
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1
8
.
[2
4
]
X
.
L
iao
,
F
.
C
h
e
n
,
a
n
d
K
.
-
W
.
W
o
n
g
,
“
On
t
h
e
se
c
u
rit
y
o
f
p
u
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li
c
-
k
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y
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s
b
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se
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h
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y
sh
e
v
p
o
ly
n
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m
ials
o
v
e
r
th
e
f
in
it
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f
ield
Z
N
,
”
IEE
E
T
ra
n
sa
c
ti
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.
[2
5
]
Y.
S
.
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jaf
,
a
n
d
M
.
K.
M
a
h
m
o
o
d
,
“
A
n
im
p
ro
v
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d
p
u
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to
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se
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e
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ti
c
m
a
p
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f
in
it
e
f
ield
,
”
S
c
ien
ti
fi
c
Co
n
fer
e
n
c
e
fo
r Gr
a
d
u
a
te
En
g
in
e
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rin
g
S
tu
d
e
n
ts,
2
0
2
0
,
p
p
.
3
1
4
-
3
2
4
.
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