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i
ed
in
f
o
r
m
atio
n
an
d
d
o
cu
m
en
ts
a
g
ai
n
s
t
d
an
g
er
s
l
i
k
e
r
o
b
b
e
r
y
an
d
il
leg
al
ac
ce
s
s
es
[
2
]
.
Mu
ltip
le
Secr
et
I
m
a
g
e
Sh
ar
i
n
g
o
r
s
i
m
p
l
y
(
MSI
S)
is
a
s
ec
r
et
i
m
a
g
e
s
h
ar
i
n
g
s
ch
e
m
e
t
h
at
p
r
o
tect
m
o
r
e
t
h
an
o
n
e
s
ec
r
et
i
m
a
g
es
at
a
ti
m
e.
C
o
n
v
e
n
tio
n
a
ll
y
,
tr
an
s
m
is
s
io
n
o
f
a
s
in
g
le
s
ec
r
et
i
m
a
g
e
i
s
p
o
s
s
ib
le
o
v
er
a
c
h
a
n
n
el
at
a
ti
m
e.
B
u
t
a
s
lo
n
g
a
s
tech
n
o
lo
g
y
g
r
o
w
s
,
th
er
e
is
an
e
n
o
r
m
o
u
s
n
ee
d
to
s
h
ar
e
m
o
r
e
th
a
n
o
n
e
s
ec
r
et
i
m
a
g
e
at
a
ti
m
e
[
3
]
.
2.
RE
L
AT
E
D
WO
RK
S
I
n
1
9
7
9
,
Sh
a
m
ir
[
4
]
in
tr
o
d
u
ce
d
th
e
co
n
ce
p
ts
an
d
th
eo
r
y
o
f
s
ec
r
et
s
h
ar
in
g
.
Sh
a
m
ir
’
s
s
ec
r
et
s
h
ar
in
g
s
ch
e
m
e
w
as
b
a
s
ed
o
n
a
n
-
d
eg
r
ee
p
o
ly
n
o
m
ial,
a
n
d
s
h
ar
e
s
wer
e
th
e
p
o
in
ts
o
n
th
at
p
o
l
y
n
o
m
ial.
I
n
2
0
0
2
,
T
h
ien
an
d
L
i
n
[
5
]
p
r
o
p
o
s
ed
an
ex
ten
s
io
n
o
f
S
h
a
m
ir
’
s
s
c
h
e
m
e
w
h
er
e
th
e
s
ec
r
et
i
m
ag
e
i
s
s
h
ar
ed
b
y
n
s
h
ar
es,
a
n
d
an
y
r
(
r
<n
)
s
h
ar
es
ca
n
b
e
u
s
ed
to
r
ec
o
n
s
tr
u
ct
th
e
s
ec
r
et.
T
h
is
s
ch
e
m
e
is
s
tar
ted
w
it
h
a
p
er
m
u
tatio
n
tec
h
n
iq
u
e
to
s
h
u
f
f
le
t
h
e
i
m
ag
e
’
s
p
ix
els
a
n
d
d
e
-
co
r
r
elate
it,
th
en
s
h
ar
e
s
w
er
e
m
ad
e
b
y
p
r
o
ce
s
s
i
n
g
t
h
e
i
m
a
g
e
p
ix
e
ls
o
r
p
atter
n
s
i
n
t
h
e
s
p
atial
d
o
m
ai
n
,
ea
ch
p
ar
ticip
a
n
t
r
ec
eiv
e
in
g
h
is
o
w
n
s
h
ar
e
a
s
a
s
h
ad
o
w
i
m
a
g
e
lo
o
k
s
lik
e
a
r
an
d
o
m
n
o
is
e
i
m
ag
e
h
o
ld
in
g
p
ar
tial
in
f
o
r
m
at
io
n
o
f
th
e
s
ec
r
et.
Sh
ar
e
s
ize
is
j
u
s
t
1
/r
o
f
th
e
s
ec
r
et
i
m
a
g
e.
I
n
2
0
0
7
,
C
h
in
an
d
C
h
i
n
g
[
6
]
,
in
tr
o
d
u
ce
d
a
w
a
y
o
f
s
h
ar
e
i
m
a
g
e
s
b
ased
o
n
th
e
r
ev
er
s
ib
le
in
teg
er
-
to
-
i
n
teg
er
(
I
T
I
)
w
a
v
elet
tr
a
n
s
f
o
r
m
.
T
h
is
m
e
th
o
d
p
r
o
ce
s
s
es
th
e
tr
an
s
f
o
r
m
co
ef
f
icien
ts
in
ea
c
h
s
u
b
b
an
d
,
an
d
ea
ch
o
f
th
e
r
esu
ltin
g
co
m
b
i
n
atio
n
co
ef
f
icie
n
ts
w
er
e
d
iv
id
ed
in
to
n
s
h
ar
es.
I
t
was
allo
w
i
n
g
t
h
e
r
ec
o
v
er
y
o
f
t
h
e
co
m
p
lete
s
ec
r
et
i
m
a
g
e
u
s
i
n
g
a
n
y
r
o
r
m
o
r
e
s
h
ar
es
(
r
≤
n
)
.
T
h
is
m
eth
o
d
h
as
lar
g
er
s
h
ad
o
w
i
m
a
g
es
w
it
h
o
u
t
co
d
in
g
t
h
an
t
h
o
s
e
b
elo
n
g
to
th
e
m
et
h
o
d
s
th
at
ap
p
ly
in
g
co
d
in
g
a
s
a
p
r
ep
r
o
ce
s
s
in
g
f
o
r
th
e
in
p
u
tti
n
g
to
th
e
s
h
a
r
in
g
p
h
a
s
e.
A
l
s
o
,
in
t
h
is
m
et
h
o
d
,
th
e
d
ata
is
en
co
d
ed
eith
er
b
y
H
u
f
f
m
a
n
co
d
in
g
o
r
b
y
ar
ith
m
etic
co
d
in
g
b
ef
o
r
e
th
e
d
ata
is
s
en
t
to
th
e
s
h
ar
in
g
p
h
a
s
e.
A
l
s
o
,
in
t
h
is
m
e
th
o
d
th
e
Hu
f
f
m
an
co
d
in
g
o
r
ar
ith
m
etic
co
d
in
g
h
a
v
e
b
ee
n
u
s
ed
to
en
co
d
e
d
ata
b
ef
o
r
e
it
is
s
en
t
to
th
e
s
h
ar
in
g
p
h
ase
.
I
n
2
0
0
7
,
J
u
n
et
al
[
7
]
,
p
r
o
p
o
s
ed
a
s
ca
lab
le
s
ec
u
r
e
ap
p
r
o
ac
h
to
s
h
ar
e
an
d
h
id
e
s
ec
r
et
i
m
ag
e.
T
h
e
s
ec
r
et
i
m
ag
e
g
i
v
en
f
ir
s
t is d
iv
id
ed
in
to
n
u
m
er
o
u
s
n
o
n
o
v
er
lap
p
in
g
b
lo
ck
s
,
a
n
d
ea
ch
b
lo
ck
is
th
en
tr
an
s
f
o
r
m
ed
in
to
o
n
e
-
lev
e
l
d
is
cr
ete
w
a
v
elet
tr
an
s
f
o
r
m
.
T
h
en
,
t
h
e
w
av
e
let
co
ef
f
icien
ts
h
a
v
e
b
ee
n
q
u
an
tized
in
to
2
5
6
g
r
ay
lev
el
s
.
Af
ter
th
at
t
h
e
g
r
a
y
v
al
u
e
in
f
o
r
m
atio
n
o
f
th
e
q
u
a
n
tized
i
m
ag
e
w
a
s
r
ea
r
r
an
g
e
d
b
y
u
s
i
n
g
a
b
it
-
p
lan
e
s
ca
n
n
in
g
m
et
h
o
d
.
Fin
all
y
,
t
h
e
i
m
a
g
e
d
ata
is
r
ea
r
r
an
g
ed
in
to
n
s
h
ad
o
w
s
b
y
u
s
i
n
g
m
u
ltip
le
th
r
es
h
o
ld
s
.
Fin
a
ll
y
,
ea
c
h
s
h
ad
o
w
i
m
ag
e
o
f
R
,
G,
an
d
B
ch
an
n
els i
s
h
id
d
en
i
n
t
h
e
co
v
er
i
m
a
g
e.
T
h
e
r
esu
lts
o
f
t
h
e
test
in
d
icate
d
th
at
th
e
in
cr
ea
s
in
g
o
f
t
h
e
n
u
m
b
er
o
f
s
h
ad
o
w
s
ca
n
lead
to
r
ec
o
v
er
y
o
f
th
e
s
ec
r
et
i
m
ag
e
w
it
h
b
etter
q
u
alit
y
.
I
n
2
0
1
1
,
Yan
g
et
al
[
8
]
,
s
u
g
g
ested
a
f
a
s
t
s
ec
r
et
i
m
a
g
e
s
h
ar
i
n
g
m
et
h
o
d
b
ased
o
n
Haa
r
w
av
e
let
tr
a
n
s
f
o
r
m
an
d
Sh
a
m
ir
’
s
m
et
h
o
d
.
Firs
tl
y
,
t
h
e
y
u
s
ed
d
is
cr
ete
Haa
r
wav
elet
tr
a
n
s
f
o
r
m
t
o
r
ed
u
ce
th
e
s
ec
r
et
i
m
a
g
e
to
it
s
q
u
ar
ter
s
ize
(
i.e
.
,
1
-
lev
e
l
L
L
s
u
b
b
an
d
)
.
T
h
en
,
th
e
m
o
d
if
ied
Sh
a
m
ir
’
s
al
g
o
r
ith
m
h
as
b
ee
n
ap
p
lied
to
o
n
l
y
th
is
L
L
s
u
b
b
an
d
f
o
r
g
e
n
er
atin
g
t
h
e
s
h
ad
o
w
i
m
a
g
es.
I
n
2
0
1
1
,
T
.
Ho
an
g
a
n
d
et
al
[
9
]
,
p
r
o
p
o
s
ed
a
(
2
,
n
)
g
r
a
y
i
m
a
g
e
s
ec
r
et
s
h
ar
in
g
s
ch
e
m
e.
T
h
e
p
r
o
p
o
s
ed
s
ch
e
m
e
i
s
b
asi
s
o
n
th
r
ee
e
x
is
tin
g
ap
p
r
o
ac
h
es: b
lo
ck
tr
u
n
ca
tio
n
c
o
d
in
g
(
B
T
C
)
,
v
ec
to
r
q
u
an
tizat
io
n
(
VQ)
an
d
d
is
cr
ete
w
av
ele
t
tr
an
s
f
o
r
m
(
DW
T
)
.
I
n
th
is
s
ch
e
m
e,
t
h
e
s
et
o
f
g
e
n
er
ated
s
h
ar
es
h
a
v
e
b
ee
n
m
u
c
h
s
m
a
ller
t
h
an
th
e
o
r
ig
i
n
al
i
m
a
g
e.
An
y
g
r
a
y
i
m
ag
e
ca
n
b
e
r
ec
o
n
s
tr
u
cted
b
y
co
m
b
i
n
in
g
at
lea
s
t t
w
o
s
h
ad
o
w
s
.
T
h
e
q
u
alit
y
o
f
t
h
e
r
ec
o
n
s
tr
u
ct
ed
im
a
g
e
r
an
g
ed
f
r
o
m
2
9
.
5
b
ea
r
s
to
3
6
.
5
d
B
.
I
n
2
0
1
2
,
Sag
ar
et
al.
[
1
0
]
p
r
o
p
o
s
ed
a
n
e
w
m
et
h
o
d
to
p
er
f
o
r
m
co
lo
r
v
is
u
al
cr
y
p
to
g
r
ap
h
y
b
ased
o
n
w
a
v
elet
tr
an
s
f
o
r
m
.
W
av
elet
tr
an
s
f
o
r
m
h
as
b
ee
n
u
tili
ze
d
to
o
b
tain
a
g
r
a
y
i
m
a
g
e
f
r
o
m
a
co
lo
r
i
m
a
g
e
w
h
er
e
th
e
i
n
te
n
s
it
y
i
m
a
g
e
(
Y)
f
o
r
m
ed
f
r
o
m
t
h
e
YC
b
C
r
co
lo
r
tr
an
s
f
o
r
m
.
T
h
en
,
E
r
r
o
r
-
Dif
f
u
s
io
n
Fil
ter
h
as
b
ee
n
ap
p
lied
o
n
th
e
o
b
tain
ed
g
r
e
y
i
m
a
g
e.
Af
ter
th
at
th
e
v
is
u
al
cr
y
p
to
g
r
ap
h
y
s
y
s
te
m
(
V
C
S)
m
o
d
el
w
a
s
ap
p
lied
o
n
t
h
e
g
en
er
ated
h
alf
to
n
e
i
m
a
g
e.
I
n
2
0
1
4
,
A
s
h
w
aq
an
d
L
o
a
y
[
2
]
in
tr
o
d
u
ce
a
s
ec
u
r
it
y
s
ec
r
et
co
lo
r
i
m
ag
e
s
h
ar
i
n
g
b
ased
o
n
tr
an
s
f
o
r
m
co
d
in
g
,
u
s
i
n
g
w
a
v
elet
o
r
co
s
in
e
tr
an
s
f
o
r
m
a
tio
n
to
p
r
o
d
u
ce
s
ec
u
r
e
s
ec
r
et
s
h
ar
e
s
b
y
f
ir
s
t
co
m
p
r
ess
th
e
i
m
ag
e
u
s
i
n
g
o
n
e
o
f
th
e
tr
an
s
f
o
r
m
co
d
in
g
tech
n
iq
u
es
m
en
t
io
n
ed
ea
r
lier
.
T
h
e
co
m
p
r
es
s
ed
s
tr
ea
m
is
t
h
en
s
u
b
j
ec
t
to
a
d
ata
d
if
f
u
s
er
f
o
llo
w
ed
b
y
a
r
an
d
o
m
g
e
n
er
ato
r
to
s
h
u
f
f
le
t
h
e
i
m
ag
e
i
n
to
s
h
ar
es;
a
s
ec
r
et
s
h
ar
es
g
e
n
er
ato
r
s
y
s
te
m
i
s
t
h
en
ap
p
lied
o
n
t
h
ese
s
h
ar
es to
p
r
o
d
u
ce
th
e
s
ec
r
et
s
h
ar
es.
3.
T
H
E
T
I
NY
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I
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1
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Ste
p 4
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1
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m
4
.
1
.
P
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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
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ac
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ed
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esig
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o
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A
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er
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en
o
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d
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h
e
C
ip
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as
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n
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ed
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ck
cip
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er
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h
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n
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V,
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ter
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en
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ted
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s
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d
o
r
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u
r
e
2
s
h
o
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t
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e
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lo
ck
d
iag
r
a
m
o
f
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Fig
u
r
e
2
.
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h
e
p
r
o
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s
ed
k
ey
s
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ea
m
g
e
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er
ato
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KSG
As
n
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tice
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e
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h
e
in
p
u
t
to
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e
f
ir
s
t
C
ascad
ed
T
E
A
,
an
d
th
e
m
i
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in
ter
m
ed
iate.
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h
en
th
e
o
u
tp
u
t
o
f
th
e
KS
G
is
y
i
.
T
h
e
d
etail
o
f
C
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ed
T
E
A
h
as b
ee
n
s
h
o
wed
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F
ig
u
r
e
s
3
an
d
4
.
Fig
u
r
e
3
.
T
h
e
p
r
o
p
o
s
ed
o
f
C
as
ca
d
ed
T
E
A
Fig
u
r
e
4
.
T
h
e
p
r
o
p
o
s
ed
o
f
Feis
tel
T
E
A
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
6
,
Dec
em
b
er
2
0
1
8
:
5
0
0
4
-
5
0
1
3
5008
AL
G
O
RI
T
H
M
3
:
P
RO
P
O
S
E
D
P
SE
UDO
RAND
O
M
G
E
NE
RA
T
O
R
I
np
ut:
T
// C
o
m
b
in
ed
t
h
e
LL
1
,
L
L
2
,
…,
LL
m
s
u
b
b
an
d
s
n
// L
e
n
g
t
h
o
f
T
r
// T
h
r
esh
o
ld
v
alu
e
K,
K'
// M
aster
k
e
y
s
ea
ch
o
f
w
h
ich
6
4
b
its
O
utput
:
S
Bk
// Ge
n
er
ated
r
s
u
b
b
lo
ck
s
Ste
p1
:
T
h
e
n
e
w
i
n
p
u
t
f
o
r
th
e
f
ir
s
t
C
as
ca
d
ed
T
E
A
is
:
x
i
=
I
V
(
3
)
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p2
:
T
h
e
m
i
is
co
m
p
u
ted
as in
ter
m
e
d
iate
v
alu
e:
m
i
=
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ascad
ed
T
E
A
ki
(
x
i
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(
4
)
Ste
p3
:
T
h
e
KSG
o
u
tp
u
t
y
i
is
co
m
p
u
te
d
as:
y
i
=
C
ascad
ed
T
E
A
k
’i
(
m
i
)
(
5
)
Ste
p4
:
T
h
e
n
e
w
i
n
p
u
t
f
o
r
th
e
n
ex
t
C
a
s
ca
d
ed
T
E
A
is
:
x
i+
1
=
I
V
⊕
y
i
.
(
6
)
Ste
p5
:
I
n
th
e
K
SG
d
esig
n
,
t
h
e
in
ter
n
al
s
tate
at
ea
c
h
s
tep
h
as
b
e
en
u
s
ed
to
u
p
d
ate
r
u
n
n
in
g
k
e
y
s
s
u
c
h
as
f
o
llo
w
in
g
k
i+
1
= k
i
⊕
m
i
(
7)
an
d
k
’
i+
1
= k
’
i
⊕
m
i
(
8
)
T
h
e
k
an
d
k’
r
e
p
r
esen
ted
th
e
m
aster
k
e
y
s
an
d
t
h
e
k
i
an
d
k’
i
th
e
r
u
n
n
i
n
g
k
e
y
s
.
Ste
p6
:
R
ep
ea
t step
2
to
s
tep
5
u
n
til
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e
n
er
ate
y
i
w
h
er
e
i=1
.
.
n
Ste
p7
:
Fo
r
ea
ch
y
i
co
m
p
o
n
e
n
t
s
(
i.e
.
,
C
1
, C
2
,
an
d
C
3
)
w
h
er
e
i=1
.
.
n
,
Do
th
e
f
o
llo
w
i
n
g
:
Ste
p7
-
1:
L
et
K
=
C
1
,
I
=n
-
1
Ste
p7
-
2:
W
h
ile
1
>1
K
←
(
2
×
K
+
3
)
m
o
d
u
lar
I
S
w
a
p
b
[
I
]
,
b
[
K
]
E
n
d
l
o
o
p
I
Ste
p8
:
F
o
r
I
=1
⇾
n
X
←
b
[
I
]
I
F
(
X
<> 0
)
X
←
X
× n
/ r
E
N
DI
F
no
←
co
u
n
t[
X
]
+
1
w
←
X
+ n
o
S
Bk
[
w
]
=S
[
I
]
en
d
lo
o
p
I
4
.
2
.
M
ultiple Sec
re
t
I
m
a
g
e
S
ha
ring
B
a
s
ed
o
n L
inea
r
Sy
s
t
e
m
T
h
e
in
p
u
t
I
1
,
I
2
,
…,
I
m
im
ag
e
s
h
av
e
b
ee
n
r
ed
u
ce
d
(
i.e
.
,
to
its
q
u
ar
ter
s
ize)
an
d
s
h
u
f
f
led
r
an
d
o
m
l
y
i
n
to
r
s
u
b
b
lo
ck
s
.
I
n
th
e
m
u
ltip
le
s
ec
r
et
im
a
g
es
s
h
ar
in
g
,
th
e
in
p
u
t
co
n
ten
t
is
co
m
p
o
s
ed
b
y
a
s
et
o
f
eq
u
al
s
ized
b
lo
ck
s
(
i.e
.
,
S
Bk1
,
S
Bk2
,…,
S
Bkr
)
.
E
ac
h
o
f
t
h
e
b
lo
ck
s
ca
n
b
e
an
y
t
y
p
e
o
f
co
n
te
n
t.
Fo
r
a
b
lo
ck
o
f
d
ata
{Q
j
|
j=1
.
.
r
}
(
i.e
.
,
ea
ch
Q
j
is
a
b
y
te
f
r
o
m
j
th
b
lo
ck
)
,
th
e
i
th
s
h
ar
e
is
ca
lc
u
lat
ed
b
y
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s
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n
g
th
e
l
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ea
r
eq
u
at
io
n
s
ad
ap
ted
f
r
o
m
[
2
]
an
d
s
h
o
w
n
in
(
9
)
:
Sh
i
= c
ij
Q
j
+ c
ij
Q
j
+ .
.
.
.
.
+c
ij
Q
j
mo
d
2
5
5
,
i=1
,
…,
n
,
j=1
,
.
.
,
r
(
9
)
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
R
ev
ers
ib
le
Mu
ltip
le
I
ma
g
e
S
ec
r
et
S
h
a
r
in
g
u
s
in
g
Dis
crete
Ha
a
r
W
a
ve
let
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r
a
n
s
fo
r
m
(
S
u
h
a
d
A
.
A
h
med
)
5009
W
h
e
r
e,
Sh
i
is
th
e
i
th
s
h
ar
e
w
h
i
ch
is
g
e
n
er
ated
f
o
r
th
e
s
u
b
b
lo
ck
Q
(
)
,
c
ij
is
t
h
e
j
th
co
ef
f
icien
t
b
elo
n
g
to
th
e
lin
ea
r
eq
u
atio
n
d
en
o
ted
th
e
i
th
s
h
ar
e.
5.
E
XP
E
R
I
M
E
NT
A
L
RE
SUL
T
S AN
D
D
I
SC
USS
I
O
N
Dif
f
er
en
t
te
s
ts
w
er
e
i
m
p
le
m
e
n
ted
to
ev
alu
ate
th
e
p
r
o
p
o
s
ed
s
y
s
te
m
al
g
o
r
ith
m
p
er
f
o
r
m
a
n
ce
.
Six
g
r
a
y
s
o
f
s
ize
5
1
2
×5
1
2
im
a
g
es
(
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e
n
a”
,
“
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et
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p
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e”
,
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Sp
las
h
”,
“
P
ep
p
er
s
”
an
d
“
Sailb
o
at”
an
d
“
Ho
u
s
e
”
)
h
a
v
e
b
ee
n
u
s
ed
.
T
h
e
test
i
m
a
g
es
h
av
e
d
i
f
f
er
en
t
v
is
u
al
p
r
o
p
er
ties
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e
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n
atu
r
al
s
ce
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e,
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v
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n
g
lo
t
o
f
ed
g
es
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d
h
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v
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n
g
h
ig
h
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r
r
elate
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s
ec
tio
n
s
.
T
h
es
e
s
ix
tes
t i
m
a
g
e
s
ar
e
s
h
o
w
n
in
Fig
u
r
e
5
.
Fig
u
r
e
5.
T
est im
a
g
es
T
ab
le
1
lis
ts
th
e
P
SN
R
af
ter
ap
p
ly
i
n
g
h
aa
r
DW
T
;
th
e
o
n
l
y
d
is
to
r
tio
n
o
f
t
h
e
p
r
o
p
o
s
ed
m
u
lti
p
le
s
ec
r
et
i
m
a
g
e
s
h
ar
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g
w
a
s
d
u
e
to
t
h
e
u
s
e
o
f
th
is
s
tep
,
n
o
f
u
r
t
h
er
lo
s
s
w
a
s
ca
u
s
ed
b
y
t
h
e
r
est o
p
er
ati
o
n
s
o
r
f
u
n
c
tio
n
s
o
f
th
e
p
r
o
p
o
s
ed
s
y
s
te
m
.
T
ab
le
1
.
T
h
e
C
R
,
Nu
m
b
er
o
f
b
y
tes a
n
d
P
SNR
o
f
ea
ch
i
m
a
g
e
w
h
e
n
a
p
p
l
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g
p
r
o
p
o
s
ed
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m
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ess
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n
s
c
h
e
m
e
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mag
e
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S
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R
L
e
n
a
3
4
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t
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l
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n
e
3
0
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1
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l
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3
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3
5
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e
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p
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o
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h
e
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in
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ab
le
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o
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at
t
h
e
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ize
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ea
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a
s
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ee
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r
ed
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ce
d
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1
/4
o
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th
e
s
ize
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f
t
h
e
o
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ig
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n
al
s
ec
r
et
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m
a
g
e
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d
t
h
e
q
u
alit
ies
o
f
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m
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g
es
w
er
e
at
ac
ce
p
tab
le
lev
el
(
i.e
.
,
g
r
ea
ter
th
an
3
0
d
B
)
.
So
th
at
th
e
to
tal
s
ize
f
o
r
all
in
p
u
t
i
m
ag
e
s
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av
e
b
ee
n
r
ed
u
ce
d
to
1
/4
r
af
ter
ap
p
ly
i
n
g
a
(
r
,
n
)
th
r
es
h
o
ld
m
u
ltip
le
s
ec
r
et
i
m
ag
e
s
h
ar
i
n
g
.
T
h
e
p
r
o
p
o
s
ed
P
s
eu
d
o
-
r
an
d
o
m
n
u
m
b
er
g
en
er
ato
r
d
ep
en
d
s
o
n
t
w
o
m
a
s
ter
k
e
y
s
a
n
d
an
in
i
tia
l
v
ec
to
r
to
g
en
er
ate
a
n
d
m
an
y
r
an
d
o
m
n
u
m
b
er
s
a
s
n
ee
d
ed
.
Ma
n
y
s
tatis
tical
te
s
ts
h
a
v
e
b
ee
n
ap
p
lied
to
test
th
e
r
an
d
o
m
n
e
s
s
o
f
a
s
eq
u
e
n
ce
,
in
g
en
er
al
m
a
n
y
s
eq
u
e
n
ce
s
t
h
at
c
o
n
s
id
er
ed
r
an
d
o
m
m
a
y
b
e
ea
s
y
to
p
r
ed
ict.
So
it'
s
i
m
p
o
r
tan
t
to
test
t
h
e
g
en
er
ato
r
s
to
p
r
o
v
e
its
ef
f
icie
n
c
y
.
T
ab
le
2
s
h
o
w
s
f
ir
s
t
t
h
r
ee
s
a
m
p
le
s
g
en
er
ated
u
s
i
n
g
t
h
e
s
p
ec
if
ied
i
n
itia
l
v
ec
to
r
an
d
k
e
y
s
.
T
ab
le
3
s
h
o
w
s
t
h
e
d
i
f
f
e
r
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.
RE
F
E
R
E
NC
E
S
[1
]
A
l
f
re
d
J.
M
e
n
e
z
e
s,
P
a
u
l
C.
v
a
n
Oo
rsc
h
o
t
a
n
d
S
c
o
tt
A
.
V
a
n
sto
n
e
,
“
Ha
n
d
b
o
o
k
o
f
A
p
p
li
e
d
Cry
p
t
o
g
ra
p
h
y
”
,
CRC
P
re
ss
,
Oc
t
1
6
,
1
9
9
6
.
[2
]
A
sh
w
a
q
T
.
Ha
sh
i
m
a
n
d
L
o
a
y
E
.
G
e
o
rg
e
;
"
S
e
c
re
t
I
m
a
g
e
S
h
a
rin
g
Ba
se
d
o
n
W
a
v
e
let
T
ra
n
s
f
o
r
m
"
,
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
In
f
o
rm
a
ti
o
n
T
e
c
h
n
o
lo
g
y
in
S
i
g
n
a
l
a
n
d
Ima
g
e
Pro
c
e
ss
in
g
(
IT
S
IP
-
2
0
1
3
)
,
Oc
t
1
8
-
1
9
,
2
0
1
3
,
M
u
m
b
a
i.
[3
]
M
o
h
i
t
Ra
jp
u
ta
a
n
d
M
a
r
o
ti
De
sh
m
u
k
h
b
,
"
A
T
e
c
h
n
iq
u
e
to
S
h
a
re
M
u
lt
i
p
le
S
e
c
re
t
Im
a
g
e
s"
,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
In
fo
rm
a
t
io
n
Pro
c
e
ss
in
g
,
V
o
l.
1
0
,
No
.
3
,
P
p
.
3
5
-
4
4
,
2
0
1
6
.
[4
]
A
.
S
h
a
m
ir,
"
Ho
w
to
S
h
a
re
a
S
e
c
re
t"
,
Co
m
m
u
n
ica
ti
o
n
s o
f
th
e
A
CM
,
Vo
l.
2
2
,
No
.
1
1
,
P
P
.
6
1
2
-
6
1
3
,
1
9
7
9
.
[5
]
C.
T
h
ien
,
J.
L
in
,
"
S
e
c
re
t
Im
a
g
e
S
h
a
rin
g
"
,
Co
mp
u
ter
s
&
Gr
a
p
h
ics
,
V
o
l
.
2
6
,
P
P
.
7
6
5
-
7
7
0
,
2
0
0
2
.
[6
]
C.
Ya
n
g
,
Y.
Hu
a
n
g
a
n
d
J
.
S
y
u
e
,
"
Re
v
e
rsib
le
S
e
c
re
t
Im
a
g
e
S
h
a
rin
g
Ba
se
d
o
n
S
h
a
m
ir’s
S
c
h
e
m
e
w
it
h
Disc
re
te
Ha
a
r
W
a
v
e
let
T
r
a
n
sf
o
r
m
"
,
El
e
c
trica
l
a
n
d
C
o
n
tr
o
l
E
n
g
i
n
e
e
rin
g
(
ICECE
),
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
,
Yic
h
a
n
g
,
P
P
.
1
2
5
0
-
1
2
5
3
,
2
0
1
1
.
[7
]
C.
Hu
a
n
g
a
n
d
C.
L
i,
"
A
S
e
c
re
t
Im
a
g
e
S
h
a
rin
g
M
e
th
o
d
Us
in
g
I
n
teg
e
r
Wav
e
l
e
t
T
ra
n
s
f
o
r
m
"
,
Eu
ra
sip
J
o
u
rn
a
l
o
n
Ad
v
a
n
c
e
s i
n
S
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g
n
a
l
Pro
c
e
ss
in
g
,
Vo
l.
2
0
0
7
,
No
.
2
,
P
P
.
1
-
1
3
,
2
0
0
7
.
[8
]
J.
Ko
n
g
,
Y.
Z
h
a
n
g
,
X
.
M
e
n
g
,
Y
.
Zh
e
n
g
,
Y.
L
u
,
"
A
S
c
a
lab
le
S
e
c
re
t
I
m
a
g
e
S
h
a
rin
g
M
e
th
o
d
Ba
s
e
d
o
n
Disc
re
te
W
a
v
e
let
T
r
a
n
sf
o
r
m
"
,
L
e
c
tu
re
No
tes
in
Co
mp
u
ter
S
c
ien
c
e
,
S
p
ri
n
g
e
r,
Be
rli
n
,
Vo
l.
4
6
8
8
,
P
P
.
7
3
6
-
7
4
5
,
2
0
0
7
.
[9
]
C.
Hu
a
n
g
a
n
d
C.
L
i,
"
S
e
c
re
t
I
m
a
g
e
S
h
a
rin
g
Us
in
g
M
u
lt
iw
a
v
e
let
T
ra
n
s
f
o
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.
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