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Rec
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r
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Da
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l Sha
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Co
m
p
u
ters
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m
s E
n
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p
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rtme
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t,
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AZHR Un
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rsity
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y
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nfo
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ticle
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Cry
p
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so
m
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a
lg
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rit
h
m
s
fo
r
e
n
c
ry
p
ti
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f
d
a
ta.
M
o
st
o
f
a
v
a
il
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b
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p
ti
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n
tec
h
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i
q
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re
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tex
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a
l
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t
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fe
w
o
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n
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ti
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th
o
d
s
a
re
u
se
d
fo
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m
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d
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a
ta;
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o
we
v
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r,
Th
is
Alg
o
rit
h
m
s
th
a
t
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l
d
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n
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e
ff
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t
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m
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e
c
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se
it
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is
g
re
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ter
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a
n
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tex
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e
re
fo
re
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p
t
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sy
ste
m
s
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e
d
t
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fi
n
d
a
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d
d
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v
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p
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p
ti
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sc
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e
m
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s
fo
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su
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h
d
a
ta.
Th
e
m
o
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p
o
p
u
lar
sy
m
m
e
tri
c
k
e
y
a
l
g
o
ri
th
m
s
a
re
Da
ta
En
c
ry
p
t
io
n
S
tan
d
a
rd
(DE
S
).
Ho
we
v
e
r,
DE
S
is
m
a
y
b
e
n
o
t
su
it
a
b
le
fo
r
m
u
lt
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d
ia
b
e
c
a
u
se
it
c
o
n
su
m
e
s
ti
m
e
s.
En
c
r
y
p
ti
o
n
a
n
d
d
e
c
ry
p
ti
o
n
o
f
t
h
e
se
d
a
ta
re
q
u
ire
d
iffere
n
t
m
e
th
o
d
s.
In
th
is
p
a
p
e
r
a
m
e
th
o
d
fo
r
e
n
c
ry
p
ti
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n
/
d
e
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ti
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d
a
ta
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y
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sin
g
t
h
e
n
a
tu
re
o
f
F
rF
T
in
si
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a
ls
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n
a
ly
sis,
b
a
se
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n
m
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l
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r
F
ra
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ti
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n
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l
F
o
u
rier
Tran
sfo
rm
h
a
s
b
e
e
n
in
tr
o
d
u
c
e
d
.
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e
se
c
u
rit
y
o
f
th
e
m
e
th
o
d
u
se
d
in
th
e
e
n
c
ry
p
ti
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n
wo
rk
wa
s
tak
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n
i
n
to
a
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u
n
t
t
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i
d
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n
ti
fy
th
e
d
iffere
n
t
in
d
ica
to
rs
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o
m
e
a
su
re
t
h
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se
c
u
r
it
y
o
f
th
e
e
n
c
ry
p
ti
o
n
Tec
h
n
iq
u
e
s.
Th
e
se
in
d
ica
to
rs
a
re
:
se
n
siti
v
it
y
p
ro
p
o
s
e
d
Tec
h
n
i
q
u
e
s
fo
r
th
e
k
e
y
,
t
h
e
c
o
m
p
lex
it
y
o
f
t
h
e
p
ro
c
e
ss
e
s,
a
n
d
sta
ti
stica
l
a
n
a
ly
sis.
Th
e
k
e
y
is
fo
rm
e
d
b
y
c
o
m
b
in
a
ti
o
n
o
f
o
rd
e
r
o
f
F
ra
c
ti
o
n
a
l
F
o
u
rier
Tr
a
n
sfo
rm
.
T
h
e
e
n
c
r
y
p
ted
d
a
ta
is
o
b
tain
e
d
b
y
th
e
su
m
m
a
ti
o
n
o
f
d
iffere
n
t
o
r
d
e
rs.
Nu
m
e
rica
l
sim
u
lati
o
n
re
su
lt
s
a
re
g
iv
e
n
t
o
d
e
m
o
n
stra
te t
h
is
p
r
o
p
o
se
d
m
e
th
o
d
.
K
ey
w
o
r
d
s
:
Data
en
cr
y
p
tio
n
s
tan
d
ar
d
Field
-
p
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m
m
ab
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Fo
u
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m
Fra
ctio
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r
tr
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s
f
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m
s
Sy
m
m
etr
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k
ey
c
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p
to
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T
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s
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p
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c
c
e
ss
a
rticle
u
n
d
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r th
e
CC B
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SA
li
c
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n
se
.
C
o
r
r
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s
p
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ing
A
uth
o
r
:
A.
R
ab
ie
,
C
o
m
p
u
ter
s
&
s
y
s
tem
s
en
g
in
ee
r
in
g
d
e
p
ar
tm
en
t
,
E
L
AZ
HR
Un
iv
er
s
ity
,
C
air
o
,
E
g
y
p
t
.
E
m
ail:
en
g
ah
m
e
d
_
r
ab
ie
2
0
1
0
@
y
ah
o
o
.
co
m
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
s
cien
ce
o
f
p
r
o
tectin
g
th
e
in
f
o
r
m
atio
n
b
y
co
n
v
er
ti
n
g
it
in
to
u
n
r
ea
d
ab
le
wh
il
e
s
to
r
ed
an
d
tr
an
s
m
itted
is
C
r
y
p
to
g
r
ap
h
y
[
1
]
.
T
h
e
en
c
r
y
p
tio
n
is
p
lay
s
a
m
ajo
r
r
o
le
in
s
ec
u
r
in
g
th
e
d
ata
in
tr
an
s
m
is
s
io
n
.
Dif
f
er
en
t
en
cr
y
p
tio
n
tech
n
iq
u
es
ar
e
u
s
ed
to
p
r
o
tect
co
n
f
id
e
n
tial
d
ata
f
r
o
m
u
n
au
th
o
r
ized
u
s
es.
C
r
y
p
to
g
r
ap
h
y
tech
n
iq
u
e
n
ee
d
s
s
o
m
e
alg
o
r
ith
m
s
f
o
r
en
c
r
y
p
tio
n
o
f
d
ata
[
2
]
.
On
e
o
f
th
e
m
o
s
t
p
o
p
u
lar
s
y
m
m
etr
ic
k
ey
alg
o
r
ith
m
s
ar
e
Data
E
n
cr
y
p
tio
n
Stan
d
ar
d
(
D
E
S).
A
6
4
-
b
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k
ey
a
r
e
u
s
ed
with
DE
S,
wh
ile
1
2
8
,
1
9
2
,
2
5
6
b
its
k
ey
s
u
s
es
f
o
r
AE
S
[
3
]
.
DE
S,
AE
S
o
f
f
e
r
th
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g
r
ea
test
s
ec
u
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ity
to
s
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iti
v
e
d
ata
co
m
p
a
r
ed
to
o
t
h
er
cr
y
p
to
g
r
ap
h
ic
alg
o
r
ith
m
s
.
T
h
e
A
E
S
was
ac
ce
p
ted
as
a
s
tan
d
ar
d
in
No
v
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b
e
r
2
0
0
1
[
4
]
.
On
e
o
f
th
e
m
o
s
t
p
o
p
u
lar
to
o
ls
u
s
ed
in
s
ig
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p
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s
s
in
g
an
d
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s
is
ar
e
T
h
e
Fo
u
r
ier
tr
a
n
s
f
o
r
m
(
FT)
[
5
]
.
T
h
e
i
d
ea
o
f
f
r
ac
tio
n
al
p
o
wer
s
o
f
th
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Fo
u
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ier
o
p
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r
ap
p
ea
r
s
in
th
e
m
at
h
em
atica
l
l
iter
atu
r
e
as
ea
r
ly
as
1
9
2
9
[
6
-
8
]
.
I
t
h
as
b
ee
n
r
ed
is
co
v
er
ed
in
q
u
a
n
tu
m
m
ec
h
a
n
i
cs
[
9
,
1
0
]
,
o
p
tics
[
1
1
-
1
3
]
,
an
d
s
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p
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s
s
in
g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
0
8
9
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I
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t J Reco
n
f
ig
u
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a
b
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&
E
m
b
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d
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Sy
s
t,
Vo
l.
9
,
No
.
2
,
J
u
ly
2
0
2
0
:
141
–
1
5
2
142
[
1
4
]
.
T
h
e
f
r
ac
tio
n
al
Fo
u
r
ier
tr
an
s
f
o
r
m
(
FrFT
)
was
m
ath
em
a
tically
in
tr
o
d
u
ce
d
b
y
Nam
ias
in
1
9
8
0
.
R
ec
en
tly
,
Me
n
d
lo
v
ic
an
d
Oza
k
tas in
tr
o
d
u
ce
d
a
n
ew
t
o
o
l f
o
r
im
ag
e
a
n
a
ly
s
is
i
n
o
p
tics
[
1
5
,
1
6
]
.
T
h
e
r
em
ain
in
g
s
ec
tio
n
s
ar
e:
B
ac
k
g
r
o
u
n
d
in
tr
o
d
u
ce
d
h
as
b
ee
n
in
tr
o
d
u
ce
d
in
s
ec
tio
n
2
,
th
e
p
r
o
p
o
s
ed
d
ata
en
cr
y
p
tio
n
Me
th
o
d
s
h
as
b
ee
n
in
tr
o
d
u
ce
d
in
Sectio
n
3
,
co
m
p
ar
ativ
e
s
tu
d
y
b
etwe
en
DE
S
alg
o
r
ith
m
s
an
d
FrFT
h
as
b
ee
n
in
tr
o
d
u
ce
d
in
s
ec
tio
n
4
,
in
s
ec
tio
n
5
im
p
lem
en
tatio
n
o
f
DE
S
u
s
in
g
FP
GA
ar
e
p
er
f
o
r
m
ed
.
A
b
r
ief
co
n
clu
s
io
n
h
as b
ee
n
in
tr
o
d
u
ce
d
in
Sectio
n
6
.
2.
B
ACK
G
RO
UND
Data
E
n
cr
y
p
tio
n
Stan
d
ar
d
(
DE
S),
T
r
ip
le
DE
S,
an
d
Ad
v
an
ce
E
n
cr
y
p
tio
n
Stan
d
ar
d
(
AE
S)
ar
e
th
e
m
o
s
t p
o
p
u
lar
s
y
m
m
etr
ic
k
ey
alg
o
r
ith
m
s
.
2
.
1
.
Da
t
a
encr
y
ptio
n sta
nd
a
rd
(
DE
S)
T
h
e
DE
S
is
u
s
ed
f
o
r
en
cr
y
p
tio
n
.
T
h
e
DE
S
is
a
b
lo
ck
cip
h
er
Dev
elo
p
ed
b
y
I
B
M
an
d
NI
ST
(
Nat
io
n
al
I
n
s
titu
te
Stan
d
ar
d
T
ec
h
n
o
lo
g
y
)
in
th
e
1
9
7
0
s
as
a
m
o
d
if
icatio
n
o
f
th
e
p
r
ev
io
u
s
s
y
s
tem
was
ca
lled
L
UC
I
FER,
DE
S
o
p
er
ates
o
n
b
lo
ck
s
o
f
6
4
-
b
its
at
a
tim
e,
th
e
in
p
u
t
k
ey
is
6
4
b
its
.
E
v
er
y
8
th
b
it
in
th
e
in
p
u
t
k
ey
is
a
p
ar
ity
ch
ec
k
b
it
wh
ich
m
ea
n
s
th
at
in
f
ac
t
th
e
k
ey
s
ize
is
ef
f
ec
tiv
ely
r
ed
u
ce
d
to
5
6
b
its
.
DE
S
co
n
s
is
ts
o
f
a
1
6
-
r
o
u
n
d
s
o
f
s
u
b
s
titu
tio
n
an
d
p
er
m
u
tatio
n
as sh
o
wn
in
Fig
u
r
e
1
an
d
Fig
u
r
e
2.
Fig
u
r
e
1
.
DE
S e
n
c
r
y
p
tio
n
an
d
d
ec
r
y
p
tio
n
p
r
o
ce
s
s
Fig
u
r
e
2
.
DE
S a
lg
o
r
ith
m
2
.
2
.
T
heo
ry
o
f
f
ra
ct
io
na
l f
o
urier
t
ra
ns
f
o
rm
T
h
e
Fo
u
r
ier
tr
an
s
f
o
r
m
is
a
r
o
tatio
n
b
y
an
g
le
/2
in
th
e
tim
e
-
f
r
eq
u
en
cy
p
lan
e,
th
e
f
r
ac
tio
n
al
Fo
u
r
ier
tr
an
s
f
o
r
m
in
ter
p
r
eted
as
th
e
co
u
n
ter
clo
ck
wis
e
r
o
tatio
n
b
y
an
an
g
le
α
in
th
e
tim
e
-
f
r
eq
u
en
cy
p
lan
e.
FR
FT
is
th
e
g
en
er
aliza
tio
n
o
f
th
e
class
ical
FT.
C
o
n
v
en
tio
n
ally
,
F
r
F
T
o
f
α
o
r
d
er
o
f
in
p
u
t f
u
n
ctio
n
x(
t)
ca
n
b
e
d
ef
in
ed
as f
o
llo
ws [
1
7
]
:
(
)
(
)
(
,
)
X
u
x
t
K
t
u
dt
−
=
(1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Reco
n
f
ig
u
r
a
b
le
&
E
m
b
ed
d
ed
Sy
s
t
I
SS
N:
2089
-
4
8
6
4
Da
ta
ec
r
yp
tio
n
b
a
s
ed
o
n
m
u
lti
-
o
r
d
er F
r
F
T,
a
n
d
F
P
GA
imp
le
men
ta
tio
n
o
f D
E
S
a
lg
o
r
ith
(
A.
R
a
b
ie
)
143
W
h
er
e
k
α
(
t,u
)
o
f
tr
an
s
f
o
r
m
is
:
22
(
)
c
o
t
s
in
2
(
,
)
u
t
i
i
t
u
K
t
u
C
e
−
+
+
=
(
2
)
An
d
1
c
ot
2
sin
2
i
ie
i
C
−−
==
,
22
(
(
)
c
o
t
c
s
c
)
2
1
c
o
t
(
,
)
2
i
t
u
i
u
t
i
K
t
u
e
+−
−
=
(
3
)
x(
t)
s
ig
n
al
r
ec
o
v
er
ed
b
y
FrFT
o
p
er
atio
n
with
b
ac
k
war
d
an
g
els
–
α
:
(
)
(
)
(
,
)
x
t
X
u
K
t
u
d
u
−
−
=
(
4
)
T
h
e
2
-
D
FrFT
o
f
a
f
u
n
ctio
n
f(
x,
y)
is
:
[
]
;
xy
xy
f
F
rF
T[f(
x
,
y
)
]
(
u,
v
)
f(
x
,
y
)
K
(
x
,
y
u,
v
)
dx
dy
−
−
=
(
5
)
W
h
er
e
22
/
2
[
]
c
o
t
c
s
c
(
,
)
xx
x
i
x
u
ix
u
Ce
K
x
u
+−
=
(
6
)
An
d
,
b
y
s
u
b
s
titu
tin
g
y
f
o
r
x
an
d
v
f
o
r
u,
y
-
a
xis,
)
,
(
v
y
K
y
ca
n
b
e
o
b
tain
ed
.
T
h
e
s
ig
n
al
f(
x,
y)
ca
n
b
e
r
ec
o
v
er
ed
b
y
FrFT
o
p
er
atio
n
with
b
ac
k
war
d
an
g
les(
-
α
x
,
-
α
y
):
(
,
)
(
,
)
;
xy
f
x
y
f
u
v
K
(
x
,
y
u
,
v
)
d
u
d
v
−−
−
−
=
(
7)
(
;
)
(
,
)
(
,
)
x
y
x
y
K
x
,
y
u,
v
K
x
u
K
y
v
−
−
−
−
=
(
8
)
3.
P
RO
P
O
SE
D
AP
P
RO
ACH
T
h
e
p
r
o
p
o
s
ed
en
cr
y
p
tio
n
tech
n
iq
u
e
is
s
h
o
wn
in
Fig
u
r
e
3
.
L
et
o
r
ig
in
al
d
ata
S
r
ep
r
esen
ts
th
e
in
p
u
t
d
ata
to
b
e
en
cr
y
p
ted
Usi
n
g
FrFT
.
I
n
E
n
cr
y
p
tio
n
s
tep
s
b
ased
o
n
FrFT
,
we
u
s
e
o
n
e
–
d
im
en
s
io
n
al
an
aly
s
is
to
d
esc
r
ib
e
o
u
r
m
eth
o
d
s
,
th
en
we
ca
n
ex
ten
d
all
f
o
r
m
u
lae
to
T
wo
-
d
im
en
s
io
n
s
.
T
o
o
b
tain
en
cr
y
p
ted
d
ata,
f
ir
s
tly
,
in
p
u
t
d
ata
is
m
u
ltip
lied
b
y
m
atr
ix
R
,
an
d
th
eir
r
esu
lts
ar
e
tr
an
s
f
o
r
m
ed
th
r
o
u
g
h
f
ir
s
t
FrFT
s
y
s
tem
with
f
ir
s
t
o
r
d
er
o
f
tr
an
s
f
o
r
m
a
1
to
g
et
d
ata,
th
e
r
esu
lt
f
r
o
m
th
is
s
tag
e
is
tr
an
s
f
o
r
m
ed
th
r
o
u
g
h
s
ec
o
n
d
o
r
d
er
o
f
tr
an
s
f
o
r
m
a
2
b
y
tak
in
g
s
ec
o
n
d
FrFT
,
th
en
it
p
ass
es
th
e
r
esu
lt
b
y
tak
in
g
FrFT
with
th
ir
d
o
r
d
er
o
f
tr
an
s
f
o
r
m
a
3
to
g
et
en
cr
y
p
ted
d
ata
'
L
'
,
T
h
e
en
cr
y
p
ted
d
ata
is
o
b
tain
b
y
s
u
m
m
atio
n
s
o
f
d
if
f
er
en
t
o
r
d
er
s
,
an
d
th
e
k
ey
f
o
r
en
cr
y
p
tio
n
/d
ec
r
y
p
tio
n
p
r
o
ce
s
s
is
a
co
m
b
in
atio
n
o
f
o
r
d
er
o
f
Fra
ctio
n
al
Fo
u
r
ier
T
r
an
s
f
o
r
m
[
1
8
]
an
d
m
atr
ix
R
.
E
n
cr
y
p
tio
n
m
o
d
el
as
s
h
o
wn
in
Fig
u
r
e
3
.
is
s
ec
u
r
e
an
d
m
o
r
e
r
o
b
u
s
t
to
war
d
s
b
r
u
te
f
o
r
ce
attac
k
,
b
u
t
th
e
co
m
p
lex
ity
o
f
th
e
s
y
s
tem
is
in
cr
ea
s
ed
.
I
n
d
ec
r
y
p
tio
n
p
r
o
ce
s
s
,
th
e
r
ev
er
s
e
f
o
r
en
cr
y
p
tio
n
p
r
o
ce
s
s
,
is
ap
p
lied
as
s
h
o
wn
in
Fig
u
r
e
4
.
Firstl
y
,
tr
an
s
f
o
r
m
ed
en
cr
y
p
ted
d
ata
'
L
'
th
r
o
u
g
h
f
ir
s
t
FrFT
with
o
r
d
er
o
f
tr
an
s
f
o
r
m
-
a
3,
an
d
p
ass
es
th
e
r
esu
lt
ag
ain
th
r
o
u
g
h
s
ec
o
n
d
FrFT
with
o
r
d
er
o
f
tr
an
s
f
o
r
m
-
a
2
,
th
en
th
e
r
esu
lt
f
r
o
m
last
s
tag
e
p
ass
es
th
r
o
u
g
h
last
FrFT
with
o
r
d
er
o
f
tr
an
s
f
o
r
m
-
a
1
,
f
in
ally
,
th
e
r
esu
lt
is
m
u
ltip
lied
with
m
atr
ix
co
n
ju
g
ate
o
f
th
e
m
atr
ix
R*
to
g
et
in
p
u
t d
ata
S
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4
8
6
4
I
n
t J Reco
n
f
ig
u
r
a
b
le
&
E
m
b
ed
d
ed
Sy
s
t,
Vo
l.
9
,
No
.
2
,
J
u
ly
2
0
2
0
:
141
–
1
5
2
144
Fig
u
r
e
3.
Pro
p
o
s
ed
e
n
cr
y
p
tio
n
s
y
s
tem
Fig
u
r
e
4
.
Pro
p
o
s
ed
d
ec
r
y
p
tio
n
s
y
s
tem
3
.
1
.
E
x
a
m
ple 1
:
E
nc/Dec
pro
po
s
ed
m
et
ho
d f
o
r
a
n i
m
a
g
e
:
Ma
th
em
atica
lly
,
th
e
en
cr
y
p
tio
n
p
r
o
ce
s
s
in
Fig
u
r
e
4
,
Su
m
m
ar
ized
as:
in
p
u
t
d
ata
S
(x
,
y)
is
m
u
ltip
lied
with
m
atr
ix
R
an
d
p
ass
es th
r
o
u
g
h
F
r
F
T
with
o
r
d
er
a
1
till
a
k
; a
s
in
eq
u
atio
n
s
b
ello
w:
(
,
)
'
xy
L
S
R
=
(9
)
1
(
,
)
'
'
[
]
xy
L
F
S
R
a
=
(
1
0
)
21
(
,
)
'
'
'
[
[
]
]
xy
L
F
F
S
R
aa
=
(
1
1
)
E
n
cr
y
p
te
d
d
ata
is
g
iv
en
b
y
:
21
3
(
,
)
1
'
'
'
'
[
[
[
]
]
]
k
k
xy
k
L
F
F
F
S
R
a
a
a
=
=
=
(
1
2
)
T
h
e
d
ec
r
y
p
tio
n
p
r
o
ce
s
s
is
in
f
ig
u
r
e
1
4
an
d
m
ath
em
atica
lly
is
g
iv
en
as:
21
(
,
)
'
'
'
'
[
[
[
]
]
]
k
xy
L
F
F
F
S
R
a
a
a
=
,
21
(
,
)
'
'
'
[
[
[
[
]
]
]
]
kk
xy
L
F
F
F
F
S
R
a
a
a
a
=
−
(
1
3
)
2
2
1
(
,
)
'
'
[
[
[
[
[
]
]
]
]
]
kk
xy
L
F
F
F
F
F
S
R
a
a
a
a
a
=
−−
(
1
4
)
1
2
2
1
(
,
)
'
[
[
[
[
[
[
]
]
]
]
]
]
kk
xy
L
F
F
F
F
F
F
S
R
a
a
a
a
a
a
=
−
−
−
(
1
5
)
Fin
ally
;
d
ec
r
y
p
ted
im
ag
e
is
g
iv
en
b
y
:
1
2
2
1
(
,
)
[
[
[
[
[
[
]
]
]
]
]
]
kk
xy
L
F
F
F
F
F
F
S
R
R
a
a
a
a
a
a
=
−
−
−
(
1
6
)
T
h
e
tim
e
in
s
ec
o
n
d
s
f
o
r
e
n
cr
y
p
tio
n
a
n
d
d
ec
r
y
p
tio
n
o
p
er
atio
n
s
o
f
a
n
I
m
ag
e
,
an
d
au
d
i
o
s
ig
n
als
ar
e
s
h
o
wn
in
T
ab
le
1
an
d
T
ab
le
2
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Reco
n
f
ig
u
r
a
b
le
&
E
m
b
ed
d
ed
Sy
s
t
I
SS
N:
2089
-
4
8
6
4
Da
ta
ec
r
yp
tio
n
b
a
s
ed
o
n
m
u
lti
-
o
r
d
er F
r
F
T,
a
n
d
F
P
GA
imp
le
men
ta
tio
n
o
f D
E
S
a
lg
o
r
ith
(
A.
R
a
b
ie
)
145
T
ab
le
1
.
C
o
m
p
le
x
ity
o
f
p
r
o
p
o
s
ed
m
eth
o
d
f
o
r
a
n
im
ag
e
En
c
r
y
p
t
i
o
n
/
D
e
c
r
y
p
t
i
o
n
Ti
m
e
(
i
n
sec
)
I
mag
e
N
a
m
e
S
i
z
e
o
f
I
mag
e
P
r
o
p
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se
d
E
n
c
/
D
e
c
s
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m
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r
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c
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s
e
d
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h
r
e
e
F
r
F
T
I
mag
e
1
2
2
.
9
K
B
0
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6
2
5
0
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0
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4
8
4
0
3
.
7
5
4
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3
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1
3
9
6
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3
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5
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9
0
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mag
e
2
2
3
.
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0
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2
2
1
6
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8
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3
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4
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8
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5
8
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mag
e
4
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4
8
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5
5
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6
4
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4
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mag
e
5
2
0
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5
K
B
0
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6
2
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0
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5
0
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3
.
7
6
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7
1
1
7
6
.
6
5
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6
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1
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A
v
e
r
a
g
e
Ti
m
e
0
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6
2
8
2
/
0
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4
8
7
4
4
.
0
3
3
3
/
3
.
0
3
0
1
8
6
.
8
7
2
6
/
5
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8
4
0
3
2
T
ab
le
2
.
C
o
m
p
le
x
ity
o
f
p
r
o
p
o
s
ed
m
eth
o
d
f
o
r
a
n
Au
d
io
En
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r
y
p
t
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o
n
/
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20
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er
r
o
r
s
in
th
e
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r
y
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ted
f
r
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tio
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al
o
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s
.
L
et
o
(
i,j)
an
d
r
(
i,j)
is
v
alu
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o
f
th
e
o
r
ig
in
al
an
d
th
e
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ec
o
v
er
ed
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e
p
ix
el
(
i
,
j)
,
wh
er
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M
an
d
N
in
d
icted
th
e
s
ize.
th
e
MSE
d
ef
in
ed
as
f
o
llo
ws in
(
1
7
)
[
1
9
]
:
22
11
1
(
,
)
(
,
)
MN
ij
M
S
E
r
o
r
i
j
o
i
j
MN
==
=
−
=
−
(
1
7
)
T
o
ev
alu
ate
an
en
cr
y
p
tio
n
s
ch
em
e
an
d
en
cr
y
p
tio
n
q
u
ality
Peak
s
ig
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al
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to
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e
r
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NR
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n
b
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s
ed
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NR
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s
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ally
ex
p
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d
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ib
els.
Ma
th
em
atica
lly
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PS
NR
ca
n
b
e
d
escr
ib
ed
in
(
1
8
)
[
2
0
]
:
2
10
255
1
0
l
o
g
P
S
N
R
M
S
E
=
(
1
8
)
T
h
e
ex
p
er
im
en
tal
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esu
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th
at
s
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o
w
th
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d
PS
NR
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o
r
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m
ag
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s
h
o
wn
in
T
ab
le
2
,
T
ab
le
3
,
an
d
T
ab
le
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s
h
o
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ig
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n
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d
b
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e
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p
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im
en
tal
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w
th
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d
PS
NR
fo
r
an
Au
d
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e
s
h
o
wn
in
T
ab
le
5
an
d
T
ab
le
6
.
T
ab
le
3
.
Me
an
s
q
u
ar
e
er
r
or
I
mag
e
P
r
o
p
o
se
d
E
n
c
/
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e
c
s
y
st
e
m
b
a
s
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d
o
n
O
n
e
F
r
F
T
P
r
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se
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E
n
c
/
D
e
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st
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m
b
a
s
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o
n
Tw
o
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r
F
T
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se
d
E
n
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s
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st
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m
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o
n
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r
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r
F
T
A
v
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S
E
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0
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4
3
6
0
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0
2
5
3
0
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1
0
3
7
2
T
ab
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4
.
Peak
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ig
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al
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n
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r
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d
b
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I
mag
e
P
r
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E
n
c
/
D
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s
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st
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m
b
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d
o
n
O
n
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r
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r
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o
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T
h
r
e
e
F
r
F
T
A
v
e
r
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g
e
P
S
N
R
6
6
.
8
1
6
4
.
3
1
2
5
5
8
.
2
0
2
1
4
T
ab
le
5
.
Me
an
s
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u
ar
e
e
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r
A
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d
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o
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E
n
c
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c
s
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st
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m
b
a
s
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d
o
n
O
n
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r
F
T
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se
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E
n
c
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c
s
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st
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m
b
a
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o
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Tw
o
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r
F
T
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se
d
E
n
c
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D
e
c
s
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st
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m
b
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s
e
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o
n
T
h
r
e
e
F
r
F
T
A
v
e
r
a
g
e
0
.
0
0
0
9
2
3
9
6
8
0
.
0
0
1
4
6
6
5
1
4
0
.
0
2
0
8
2
T
ab
le
6
.
Peak
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ig
n
al
t
o
n
o
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atio
A
u
d
i
o
P
r
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p
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d
E
n
c
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c
s
y
st
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o
n
O
n
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r
F
T
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se
d
E
n
c
/
D
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c
s
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st
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m
b
a
s
e
d
o
n
Tw
o
F
r
F
T
P
r
o
p
o
se
d
E
n
c
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c
s
y
st
e
m
b
a
s
e
d
o
n
T
h
r
e
e
F
r
F
T
A
v
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a
g
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1
1
4
.
9
8
3
4
9
9
.
0
7
4
8
4
8
0
.
9
5
3
2
4
4
.
4
.
Dif
f
er
ent
ia
l
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na
ly
s
is
I
n
im
ag
e
en
cr
y
p
tio
n
,
th
e
cip
h
er
r
esis
tan
ce
to
d
if
f
er
en
tial
attac
k
s
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co
m
m
o
n
ly
an
aly
ze
d
v
ia
th
e
NPC
R
an
d
UACI
test
s
[
1
9
]
.
n
u
m
b
er
o
f
p
ix
els
ch
an
g
e
r
ate
wh
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n
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p
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im
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is
ch
an
g
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is
r
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s
to
Nu
m
b
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o
f
Pix
els
C
h
an
g
e
R
ate
(
NPC
R
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.
T
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d
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m
in
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s
th
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av
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ag
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in
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s
ity
o
f
d
if
f
er
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ce
s
b
etwe
en
th
e
p
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d
cip
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Un
if
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Av
er
ag
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C
h
an
g
in
g
I
n
ten
s
ity
(
UACI)
is
u
s
in
g
.
T
h
e
NPC
R
an
d
th
e
UACI
ar
e
d
ef
in
ed
in
(
1
9
)
an
d
(
2
1
)
:
,
(
,
)
100%
ij
D
i
j
NP
CR
MN
=
(
1
9
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wh
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C
1
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d
C
2
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lain
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d
if
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er
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t
b
y
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n
ly
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n
e
b
it.
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h
e
g
r
ay
v
alu
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at
g
r
id
(
i; j)
in
C
1
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d
C
2
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b
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C
1
(
i;
j)
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d
C
2
(
i;
j)
.
D
ar
r
ay
is
d
eter
m
in
ed
b
y
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1
(
i;
j)
an
d
C
2
(
i;
j)
,
if
C
1
(
i;
j)
=
C
2
(
i;
j)
th
en
D(
i; j)
=
0
; o
th
er
wis
e,
D(
i; j)
=
1
.
D
(
i,
j)
is
d
e
f
in
ed
as in
(
2
0
)
[
2
1
]
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J Reco
n
f
ig
u
r
a
b
le
&
E
m
b
ed
d
ed
Sy
s
t
I
SS
N:
2089
-
4
8
6
4
Da
ta
ec
r
yp
tio
n
b
a
s
ed
o
n
m
u
lti
-
o
r
d
er F
r
F
T,
a
n
d
F
P
GA
imp
le
men
ta
tio
n
o
f D
E
S
a
lg
o
r
ith
(
A.
R
a
b
ie
)
149
12
12
0
,
.
(
,
)
(
,
)
(
,
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1
,
.
(
,
)
(
,
)
if
C
i
j
C
i
j
D
i
j
if
C
i
j
C
i
j
=
=
(
2
0
)
UACI
Ma
th
em
atica
lly
ca
n
d
ef
in
e
in
(
2
1
)
[
2
1
]
:
12
,
(
,
)
(
,
)
1
[
]
1
0
0
%
255
ij
C
i
j
C
i
j
U
A
C
I
MN
−
=
(
2
1
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T
ab
le
7
.
NPC
R
v
alu
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f
o
r
p
r
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p
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s
ed
m
eth
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d
N
PC
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mag
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P
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se
d
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n
c
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s
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m
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O
n
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r
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n
c
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D
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c
s
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m
b
a
s
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d
o
n
Tw
o
F
r
F
T
P
r
o
p
o
se
d
E
n
c
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D
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c
s
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st
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m
b
a
s
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T
h
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e
F
r
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T
A
v
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g
e
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.
0
7
2
9
6
.
3
3
5
9
7
.
4
9
3
T
ab
le
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.
UACI
v
alu
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f
o
r
p
r
o
p
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s
ed
m
eth
o
d
U
AC
I
%
I
mag
e
P
r
o
p
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se
d
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n
c
/
D
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c
s
y
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b
a
s
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d
o
n
O
n
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F
r
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P
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g
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3
3
.
7
9
3
4
.
5
5
3
4
.
1
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4
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5
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Co
rr
ela
t
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co
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f
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a
na
ly
s
is
T
h
e
r
elatio
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s
h
ip
an
d
s
im
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ity
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etwe
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r
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C
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1
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11
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1
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1
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1
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0
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1
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T
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9
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C
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Evaluation Warning : The document was created with Spire.PDF for Python.