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Fig
u
r
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P
r
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ce
s
s
I
n
1
9
9
9
,
P
o
p
escu
[
4
]
p
r
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ted
b
lin
d
m
u
lt
i
-
s
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g
n
at
u
r
es
b
ased
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n
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tic
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r
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s
.
I
n
2
0
0
5
,
C
h
o
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e
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al.
p
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p
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t
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o
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li
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ar
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ased
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ilin
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r
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air
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g
s
[
5
]
.
I
n
2
0
1
1
,
Mo
ld
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[
6
]
p
r
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ted
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b
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n
2
0
1
2
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e
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n
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Dan
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[
7
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p
r
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ed
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h
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n
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f
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ter
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S
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Ver
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also
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P
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y
B
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ased
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Facto
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Di
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s
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8
]
.
I
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0
1
3
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P
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r
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lin
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n
elec
tr
o
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v
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g
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ce
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es
[
9
]
.
I
n
2
0
1
4
,
Hu
a
Su
n
et
al.
p
r
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p
o
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ed
New
C
er
ti
f
icate
le
s
s
B
lin
d
R
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g
n
at
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r
e
Sch
e
m
e
[
1
0
]
.
I
n
2
0
1
6
,
Sh
ilb
ay
e
h
et
al.
p
r
o
p
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ed
s
ec
u
r
it
y
s
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e
m
e
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f
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elec
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es
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1
1
]
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I
n
2
0
1
7
,
Min
h
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lin
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S
ig
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ased
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n
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Ne
w
Har
d
P
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o
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l
e
m
[
1
2
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;
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m
e
J
a
m
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p
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p
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ed
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d
en
tit
y
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B
ased
B
lin
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Sig
n
a
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e
Sc
h
e
m
e
w
it
h
Me
s
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e
R
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v
er
y
[
1
3
]
.
I
n
t
h
e
n
ex
t
s
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t
io
n
,
d
etail
s
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n
th
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m
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ased
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s
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h
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p
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f
o
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ed
.
2.
B
ACK
G
RO
UND
T
h
e
f
o
llo
w
i
n
g
n
o
tatio
n
s
ar
e
u
s
ed
:
Z
: set o
f
all
i
n
te
g
er
s
p
: p
r
im
e
n
u
m
b
er
,
p
> 3
a
,
b
: e
llip
tic
cu
r
v
e
co
ef
f
ic
ien
t
s
m
: p
o
in
ts
o
f
t
h
e
ellip
tic
c
u
r
v
e
g
r
o
u
p
o
r
d
er
q
: su
b
g
r
o
u
p
o
r
d
er
o
f
g
r
o
u
p
o
f
p
o
in
ts
o
f
t
h
e
ellip
tic
cu
r
v
e
O
: z
er
o
p
o
in
t o
f
th
e
ellip
tic
cu
r
v
e
P
: e
llip
tic
cu
r
v
e
p
o
in
t o
f
o
r
d
er
q
d
: in
teg
er
-
a
s
i
g
n
at
u
r
e
k
e
y
G
: e
llip
tic
cu
r
v
e
p
o
in
t
-
a
v
er
if
icatio
n
k
e
y
An
ellip
tic
c
u
r
v
e
w
it
h
t
h
e
f
o
ll
o
w
i
n
g
f
o
r
m
i
s
s
t
u
d
ied
in
t
h
is
w
o
r
k
:
23
m
o
d
.
y
x
a
x
b
p
(
1
)
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I
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w
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y,
a
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b
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d
32
4
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7
0
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o
d
.
a
b
p
I
n
ad
d
itio
n
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J
(
E
)
ca
n
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e
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to
ca
lcu
late
E
as f
o
llo
w
s
:
3
32
4
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)
1
7
2
8
m
o
d
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4
2
7
a
J
E
p
ab
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h
e
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t
s
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ca
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e
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eter
m
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ed
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J
(
E
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as f
o
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s
:
m
o
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m
o
d
.
2
;
3
a
k
b
k
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()
m
o
d
;
(
)
0
;
(
)
1
7
2
8
.
1
7
2
8
(
)
JE
k
p
J
E
J
E
JE
Def
i
n
itio
n
1
(
B
MS)
: A
b
lin
d
m
u
lti
-
s
i
g
n
atu
r
e
s
c
h
e
m
e
ca
n
b
e
d
escr
ib
ed
b
y
f
o
llo
w
i
n
g
f
i
v
e
al
g
o
r
ith
m
s
:
s
etu
p
,
b
lin
d
,
s
i
g
n
,
u
n
b
lin
d
,
an
d
v
er
if
icatio
n
.
A
t
h
ir
d
tr
u
s
t p
ar
t
y
(
T
T
P
)
is
u
s
ed
,
an
d
th
e
p
r
o
ce
s
s
is
d
etailed
as f
o
llo
w
s
.
a.
Setu
p
:
C
r
ea
te
p
u
b
lic
ar
g
u
m
e
n
ts
b
ased
o
n
th
e
GF(
p
)
f
ield
a
n
d
o
p
en
th
e
ar
g
u
m
e
n
t
(
p
,
q
,
G,
P)
to
th
e
p
u
b
lic.
E
ac
h
u
s
er
in
th
e
g
r
o
u
p
ca
n
u
s
e
th
eir
p
r
iv
ate
k
e
y
as
i
d
en
tific
atio
n
an
d
ca
lcu
late
th
e
v
alu
e
o
f
th
e
p
u
b
lic
k
e
y
.
b.
B
lin
d
:
User
s
c
h
o
s
e
t
w
o
r
a
n
d
o
m
ar
g
u
m
e
n
t
s
an
d
co
m
b
in
e
t
h
e
m
w
it
h
t
h
e
h
a
s
h
o
f
m
es
s
ag
e
M
to
m
ak
e
th
e
co
n
te
n
t
o
f
M
b
lin
d
.
T
h
e
f
ir
s
t
p
ar
t
o
f
t
h
e
s
ig
n
at
u
r
e
v
alu
e
(
r
)
is
s
i
m
u
lta
n
eo
u
s
l
y
b
li
n
d
ed
in
th
is
p
ar
t a
n
d
s
e
n
t to
th
e
s
ig
n
i
n
g
g
r
o
u
p
.
c.
Sig
n
:
E
ac
h
u
s
er
i
n
t
h
e
s
ig
n
i
n
g
g
r
o
u
p
ca
lcu
lates
t
h
eir
o
w
n
s
ig
n
at
u
r
e,
an
d
t
h
e
T
T
P
ca
lcu
l
ates
t
h
e
s
ig
n
at
u
r
e
o
f
th
e
g
r
o
u
p
an
d
s
e
n
d
s
it b
ac
k
to
th
e
r
eq
u
esti
n
g
u
s
er
.
d.
Un
b
li
n
d
:
T
h
e
r
eq
u
esti
n
g
u
s
er
u
n
b
li
n
d
s
t
h
e
s
i
g
n
atu
r
e.
T
h
e
r
esu
lt
i
s
t
h
e
s
et
(
r
,
s
)
,
w
h
ic
h
is
th
e
b
lin
d
m
u
lti
-
s
i
g
n
atu
r
e
o
n
m
es
s
a
g
e
M.
e.
Ver
if
y
:
th
e
ch
ec
k
i
n
g
u
s
er
v
er
i
f
ies
t
h
e
s
i
g
n
at
u
r
e,
w
h
ic
h
is
o
n
l
y
ac
ce
p
ted
if
t
h
e
v
er
i
f
icatio
n
p
r
o
ce
s
s
is
s
ati
s
f
ied
; o
t
h
er
w
is
e,
t
h
e
s
i
g
n
atu
r
e
i
s
n
o
t a
cc
ep
ted
.
T
h
e
d
ig
ital sig
n
at
u
r
e
p
ar
a
m
ete
r
s
ar
e:
a.
p
is
a
lar
g
e
p
r
i
m
e
n
u
m
b
er
,
w
h
i
ch
co
m
p
o
s
es t
h
e
f
ield
GF
(
p
)
o
f
EC
.
b.
EC
is
d
eter
m
i
n
ed
b
y
th
e
d
escr
ip
tio
n
in
P
ar
t 2
.
c.
in
te
g
er
m
is
an
ell
ip
tic
cu
r
v
e
EC
p
o
in
ts
g
r
o
u
p
o
r
d
er
:
m
=
nq
,
n
b
elo
n
g
s
to
Z
,
1.
n
d.
q
is
a
p
r
im
e
n
u
m
b
er
th
at
i
n
d
ic
ates th
e
n
u
m
b
er
o
f
EC
p
o
in
t
g
r
o
u
p
s
an
d
is
d
eter
m
i
n
ed
as f
o
l
lo
w
s
:
2
5
4
2
5
6
22
q
o
r
5
0
8
5
1
2
2
2
.
q
e.
G
is
a
p
o
in
t th
at
d
o
es n
o
t c
o
i
n
cid
e
w
it
h
th
e
o
r
i
g
in
O
o
f
EC
a
n
d
h
as t
h
e
co
o
r
d
in
ate
(
,
)
,
GG
xy
w
h
ic
h
s
atis
f
ies t
h
e
f
o
llo
w
in
g
co
n
d
iti
o
n
:
q
G
O
f.
H
(
M
)
is
th
e
v
al
u
e
o
f
th
e
h
as
h
f
u
n
ct
io
n
w
it
h
an
l
-
b
it le
n
g
th
s
at
is
f
ie
s
t
h
e
f
o
llo
w
i
n
g
co
n
d
itio
n
:
I
f
2
5
4
2
5
6
22
q
th
e
n
l
=
2
5
6
;
I
f
5
0
8
5
1
2
22
q
th
e
n
l
=
5
1
2
.
g.
d
is
a
p
r
iv
ate
k
e
y
o
f
u
s
er
(
0
<d
< q
)
.
2
.
1
.
G
O
S
T
R
3
4
-
10
-
2
0
1
2
Sta
nd
a
rd
[
3
]
a.
Setu
p
: Ca
lcu
la
te
th
e
p
u
b
lic
k
e
y
p
o
in
t a
s
f
o
llo
w
s
: P
=
d
×
G.
T
h
e
s
ig
n
i
n
g
p
ar
t
y
ch
o
s
e
s
a
r
an
d
o
m
n
u
m
b
er
k
t
h
at
s
ati
s
f
ies (
0
<
k
<
q
)
an
d
ca
lcu
lates
C
=
k
×
G.
b.
Sig
n
:
C
a
lcu
la
te
th
e
h
as
h
v
al
u
e
o
f
m
es
s
ag
e
M.
Dete
r
m
i
n
e
t
h
e
f
ir
s
t
p
ar
t
o
f
s
ig
n
at
u
r
e
r
as
f
o
llo
w
s
:
m
o
d
,
C
r
x
q
w
h
er
e
C
x
is
th
e
ab
s
ciss
a
o
f
p
o
in
t
C
.
I
f
r
=
0
,
th
en
an
o
t
h
er
v
al
u
e
o
f
k
n
ee
d
s
to
b
e
ch
o
s
en
.
C
alcu
la
te
(
)
m
o
d
.
e
H
M
q
C
alcu
la
te
th
e
s
ec
o
n
d
p
ar
t
o
f
th
e
s
ig
n
at
u
r
ea
s
m
o
d
.
s
r
d
k
e
q
I
f
s
=
0
,
th
en
c
h
o
o
s
e
an
o
th
er
v
alu
e
o
f
k
.
T
h
e
o
u
tp
u
t o
f
th
e
al
g
o
r
ith
m
i
s
th
e
s
et
(
r
,
s
)
,
w
h
ic
h
is
s
et
as t
h
e
d
ig
ital si
g
n
atu
r
e
o
n
m
es
s
ag
e
M.
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
N
ew B
lin
d
Mu
ti
-
s
ig
n
a
tu
r
e
S
ch
eme
s
B
a
s
ed
o
n
E
C
DLP
(
Du
c
N
g
u
ye
n
Ta
n
)
1077
c.
Ver
if
y
:
C
a
lcu
la
te
-
1
-
1
(
m
o
d
)
-
(
m
o
d
)
;
m
o
d
.
C'
C
s
e
q
G
r
e
q
P
r
'
x
q
C
o
m
p
ar
e
rʹ
w
it
h
r
.
I
f
rʹ
=
r
,
th
e
n
th
e
d
i
g
ital si
g
n
at
u
r
e
is
ac
ce
p
ted
; o
th
er
w
is
e,
t
h
e
d
ig
i
ta
l sig
n
at
u
r
e
is
n
o
t a
cc
ep
ted
.
2
.
2
.
EC
-
Sch
no
rr
s
che
m
e
[
1
4
]
a.
Setu
p
:
C
alc
u
late
th
e
p
u
b
lic
k
e
y
p
o
in
t
:
P
=
d
×
G.
T
h
e
s
i
g
n
i
n
g
p
ar
t
y
c
h
o
s
e
s
a
r
an
d
o
m
n
u
m
b
er
k
th
at
s
at
is
f
ies (
0
<
k
<
q
)
an
d
ca
lcu
lates
C
= k
× G
.
b.
Sig
n
:
C
alc
u
late
t
h
e
f
ir
s
t
p
a
r
t
o
f
t
h
e
s
ig
n
at
u
r
e.
Dete
r
m
in
e
t
h
e
f
ir
s
t
p
ar
t
o
f
s
i
g
n
a
t
u
r
e
as
(
,
)
m
o
d
.
C
r
H
M
x
q
W
h
er
e
C
x
is
th
e
ab
s
ci
s
s
a
o
f
p
o
i
n
t
C
.
I
f
r
=
0
,
th
e
n
an
o
t
h
er
v
a
lu
e
o
f
k
is
ch
o
s
en
.
C
alcu
late
m
o
d
.
s
k
r
d
q
I
f
s
=
0
,
th
en
th
e
p
r
o
ce
s
s
i
s
s
tar
ted
ag
ai
n
.
T
h
e
o
u
tp
u
t o
f
th
e
al
g
o
r
ith
m
i
s
th
e
s
et
(
r
,
s
)
,
w
h
ic
h
is
u
s
ed
as t
h
e
d
ig
ital
s
i
g
n
at
u
r
e
o
n
m
ess
a
g
e
M.
c.
Ver
if
y
:
C
alcu
late
C
s
G
r
P
an
d
(
,
)
.
C
r
H
M
x
C
o
m
p
ar
e
rʹ
w
it
h
r
.
I
f
rʹ
=
r
,
th
e
n
t
h
e
d
ig
ital si
g
n
at
u
r
e
is
ac
ce
p
ted
; o
th
er
w
is
e,
t
h
e
d
ig
ita
l si
g
n
a
tu
r
e
is
n
o
t a
cc
ep
ted
.
2
.
3
.
B
lin
d
M
ulti
-
s
ig
na
t
ure
Ass
u
m
e
th
at
u
s
er
U
as
k
s
t
h
e
en
tire
g
r
o
u
p
S
w
h
o
h
as
t
h
e
au
th
o
r
it
y
to
in
cl
u
d
e
n
s
ig
n
e
r
s
to
s
ig
n
d
o
cu
m
en
t
M
;
h
o
w
e
v
er
,
th
is
u
s
er
d
o
es n
o
t
w
an
t th
i
s
au
t
h
o
r
ize
d
g
r
o
u
p
to
k
n
o
w
th
e
co
n
ten
t o
f
M
.
Firs
t,
th
i
s
u
s
er
b
lin
d
s
t
h
e
d
o
cu
m
en
t
M
,
w
h
ic
h
b
ec
o
m
es
d
o
cu
m
e
n
t
Mʹ.
Th
en
,
Mʹ
is
s
e
n
t
to
t
h
e
au
t
h
o
r
ized
s
ig
n
i
n
g
g
r
o
u
p
.
T
h
is
g
r
o
u
p
s
ig
n
s
Mʹ
an
d
s
e
n
d
s
it
b
ac
k
to
th
e
r
eq
u
esti
n
g
u
s
er
.
T
h
en
,
th
e
u
s
er
u
n
b
li
n
d
s
Mʹ
t
o
M
an
d
ch
ec
k
s
th
e
r
ec
eiv
ed
s
ig
n
at
u
r
e.
I
f
th
e
s
ig
n
atu
r
e
is
v
a
lid
,
th
e
n
th
e
u
s
er
h
a
s
a
v
alid
s
i
g
n
a
tu
r
e
o
n
d
o
cu
m
e
n
t
M
.
2
.
4
.
Ra
nd
o
m
O
ra
cle
M
o
del
I
n
1
9
9
3
,
B
ellar
e
an
d
R
o
g
a
w
a
y
[
1
5
]
g
en
er
alize
d
a
m
o
d
el
t
h
at
allo
w
ed
f
o
r
th
e
s
ec
u
r
it
y
o
f
d
i
f
f
er
e
n
t
co
d
in
g
s
c
h
e
m
e
s
.
A
b
lin
d
d
ig
it
al
s
ig
n
at
u
r
e
s
ch
e
m
e
is
co
n
s
id
e
r
ed
s
af
e
w
h
e
n
its
ch
ar
ac
ter
i
s
ti
cs
o
f
b
lin
d
n
e
s
s
a
n
d
an
ti
-
f
o
r
g
er
y
ca
n
b
e
en
s
u
r
ed
in
a
r
an
d
o
m
p
r
ed
ictiv
e
m
o
d
el.
Def
i
n
itio
n
3
:
(
B
lin
d
n
es
s
)
.
W
it
h
all
p
o
l
y
n
o
m
ial
ti
m
e
al
g
o
r
ith
m
s
o
f
a
ttack
er
A
ac
ti
n
g
a
s
t
h
e
s
ig
n
er
,
t
h
e
p
r
o
b
a
b
ilit
y
o
f
s
u
cc
es
s
o
f
t
h
e
ex
p
er
i
m
e
n
t b
elo
w
i
s
a
n
e
g
li
g
ib
l
y
s
m
all
f
u
n
ctio
n
.
T
h
er
e
ar
e
tw
o
tr
u
s
ted
u
s
er
s
U
0
,
U
1
,
w
h
ic
h
j
o
in
th
e
b
lin
d
m
u
l
ti
-
s
ig
n
at
u
r
e
s
i
g
n
at
u
r
e
s
c
h
e
m
e
w
it
h
A
o
n
th
e
m
ess
a
g
e
1
,,
bb
MM
an
d
th
e
o
u
tp
u
t
t
h
e
s
i
g
n
atu
r
e
1
,
bb
ss
co
r
r
esp
o
n
d
in
g
to
{
0
,
1
}
b
is
r
an
d
o
m
l
y
s
elec
ted
.
11
(
,
,
,
)
b
b
b
b
M
M
s
s
is
th
e
n
s
en
t
to
A
,
an
d
th
e
o
u
tp
u
t
is
{
0
,
1
}
.
b
Fo
r
all
A
,
U
0
,
U
1
,
w
h
en
an
y
co
n
s
tan
t
p
r
i
m
e
n
u
m
b
er
p
is
lar
g
e
en
o
u
g
h
,
t
h
e
p
r
o
b
a
b
ilit
y
o
f
s
u
cc
es
s
o
f
t
h
e
ex
p
er
i
m
e
n
t is
n
eg
lig
ib
le:
11
|
P
r
[
]
|
.
2
c
bb
p
Def
i
n
itio
n
4
:
(
Ass
u
m
ed
E
C
DL
P
P
r
o
b
lem
)
T
ak
in
g
a
s
et
o
f
p
o
in
ts
P
t
h
at
h
a
v
e
a
f
i
eld
p
Z
an
d
ele
m
e
n
tar
y
G
so
,
d
G
P
w
h
er
e
d
i
s
a
r
an
d
o
m
n
u
m
b
er
c
h
o
s
e
n
i
n
t
h
e
f
ield
*
,
q
Z
th
e
ass
u
m
ed
E
C
D
L
P
o
f
P
is
th
e
ca
lc
u
lated
v
alu
e
o
f
d
.
(
,
)
t
-
i
s
ass
u
m
ed
i
n
t
h
e
p
o
in
t
P
g
r
o
u
p
if
it
ca
n
s
o
l
v
e
w
i
th
i
n
t
i
m
e
t
th
e
d
if
f
ic
u
lt
E
C
D
L
P
o
f
g
r
o
u
p
P
w
i
th
t
h
e
s
m
alle
s
t p
r
o
b
ab
ilit
y
.
3.
P
RO
P
O
SE
D
B
L
I
N
D
M
UL
T
I
SI
G
NA
T
UR
E
SCH
E
M
E
S
3
.
1
.
B
M
S ba
s
ed
o
n t
he
G
O
ST
R3
4
-
10
-
2
0
1
2
s
t
a
nd
a
rd
a.
Setu
p
:
Fo
r
ea
ch
s
i
g
n
er
w
it
h
th
e
au
th
o
r
it
y
to
s
i
g
n
S,
ca
lcu
late
th
e
v
al
u
e
o
f
th
e
p
u
b
lic
k
e
y
an
d
s
en
d
it
to
th
e
T
T
P
to
ca
lcu
late
th
e
p
u
b
lic
k
e
y
v
al
u
e:
ii
P
d
G
an
d
12
1
.
.
.
.
n
ni
i
P
P
P
P
d
G
E
ac
h
s
i
g
n
er
w
i
th
th
e
a
u
t
h
o
r
it
y
to
s
ig
n
s
elec
t
s
t
h
e
r
an
d
o
m
n
u
m
b
er
s
()
i
i
q
k
k
Z
an
d
ca
lcu
lates
,
i
C
w
h
ic
h
is
s
en
t
to
th
e
T
T
P
to
ca
lcu
late
C
w
it
h
,
ii
C
k
G
w
h
er
e
i
=
1
,
2
,
.
.
.
n
an
d
11
.
nn
ii
ii
C
C
k
G
S sen
d
s
C
to
U.
b.
B
lin
d
:
U
s
elec
ts
t
w
o
r
an
d
o
m
n
u
m
b
er
s
,
,
{
1
,
2
,
.
.
.
,
-
1
}
,
q
an
d
th
e
f
o
llo
w
i
n
g
v
ar
ia
n
ts
ar
e
ca
lcu
lated
.
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.
8
,
No
.
2
,
A
p
r
il 2
0
1
8
:
1
0
7
4
–
1083
1078
V
a
r
i
a
n
t
1
V
a
r
i
a
n
t
2
-1
;
m
od
;
m
od
;
;
m
od
;
(
)
m
od
.
C
h
H
M
e
h
q
e
e
q
C
C
G
r
x
q
r
r
q
1
;
m
od
;
m
od
;
;
m
od
;
(
m
od
)
(
)
m
od
.
C
h
H
M
e
h
q
e
e
q
CG
r
x
q
C
q
P
r
r
e
q
U
s
en
d
s
r
an
d
e
to
th
e
g
r
o
u
p
w
it
h
th
e
a
u
t
h
o
r
it
y
to
s
i
g
n
S.
c.
Sig
n
b
lin
d
:
E
ac
h
s
i
g
n
er
ca
lcu
l
ates
,
i
s
s
en
d
s
it
to
th
e
T
T
P
to
ca
l
cu
late
s
,
an
d
th
en
s
en
d
s
s
to
th
e
u
s
er
as
f
o
llo
w
s
:
1
m
o
d
;
m
o
d
.
n
i
i
i
i
i
s
k
e
d
r
q
s
s
q
d.
Un
b
li
n
d
:
T
h
e
u
s
er
ca
lcu
la
tes
s
.
A
p
air
(
r
,
s
)
is
th
e
b
lin
d
m
u
lt
i
-
s
i
g
n
at
u
r
e
o
f
a
s
i
g
n
er
co
llecti
v
e
f
o
r
m
es
s
ag
e
M.
V
a
r
i
a
n
t
1
V
a
r
i
a
n
t
2
1
(
)
m
o
d
.
s
s
e
q
11
(
)
m
o
d
.
s
s
e
q
e.
Ver
if
y
:
C
alcu
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4.
ANALY
SI
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ef
f
icie
n
c
y
t
h
a
n
an
o
th
er
s
c
h
e
m
e
[
6
]
,
an
d
t
h
e
p
r
o
p
o
s
ed
s
ch
e
m
e
b
ased
o
n
th
e
E
C
-
Sc
h
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o
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r
s
ch
e
m
e
h
a
s
lo
w
er
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m
p
u
tat
io
n
al
ef
f
icie
n
c
y
th
a
n
t
h
e
o
th
er
s
ch
e
m
e
[
6
]
,
[
4
]
.
W
h
en
co
m
p
ar
in
g
t
h
e
p
er
f
o
r
m
an
ce
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p
er
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s
ta
n
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ar
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d
ig
ita
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s
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g
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atu
r
e
s
c
h
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m
e,
t
h
e
p
er
f
o
r
m
an
ce
o
f
th
e
p
r
o
p
o
s
ed
b
lin
d
m
u
lti
-
s
i
g
n
a
tu
r
e
h
as b
etter
co
m
p
u
tatio
n
a
l e
f
f
icien
c
y
.
5.
CO
NCLU
SI
O
N
I
n
th
i
s
p
ap
er
,
w
e
p
r
ese
n
ted
o
p
tio
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s
f
o
r
b
u
ild
i
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li
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d
m
u
lt
i
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s
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g
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at
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r
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s
ig
n
at
u
r
e
s
c
h
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m
e
s
b
ased
o
n
th
e
GO
ST
R
3
4
.
1
0
-
2
0
1
2
d
ig
ital
s
i
g
n
a
tu
r
e
s
tan
d
ar
d
a
n
d
th
e
E
C
-
Sch
n
o
r
r
d
ig
ital
s
i
g
n
atu
r
e
s
ch
e
m
e.
T
h
e
b
li
n
d
m
u
lti
-
s
i
g
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atu
r
e
s
i
g
n
at
u
r
e
s
c
h
e
m
es
w
er
e
d
ev
elo
p
ed
th
at
i
n
h
er
its
t
h
e
s
ec
u
r
it
y
a
n
d
th
e
p
r
o
p
er
ties
o
f
d
ig
it
al
s
ig
n
at
u
r
e
s
tan
d
ar
d
s
i
n
p
r
ac
tice.
T
h
e
p
r
o
o
f
s
o
f
th
e
p
r
o
p
o
s
ed
s
ch
e
m
e
s
w
er
e
f
u
ll
b
lin
d
n
es
s
an
d
u
n
f
o
r
g
ea
b
ilit
y
i
n
th
e
R
OM
.
T
h
e
r
esu
lts
s
h
o
w
t
h
at
th
e
p
r
o
p
o
s
ed
b
lin
d
m
u
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ti
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s
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n
at
u
r
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s
ig
n
at
u
r
e
s
ch
e
m
es
a
r
e
s
af
e
an
d
p
r
esen
t
h
ig
h
p
er
f
o
r
m
a
n
ce
; t
h
er
ef
o
r
e,
t
h
e
y
ca
n
b
e
ap
p
lied
in
p
r
ac
tice.
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
N
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lin
d
Mu
ti
-
s
ig
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a
tu
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S
ch
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s
B
a
s
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n
E
C
DLP
(
Du
c
N
g
u
ye
n
Ta
n
)
1083
RE
F
E
R
E
NC
E
S
[1
]
Ch
a
u
m
D,
“
Bli
n
d
sig
n
a
tu
re
s
f
o
r
u
n
trac
e
a
b
le
p
a
y
m
e
n
ts”
,
A
d
v
a
n
c
e
s
in
Cr
y
p
to
lo
g
y
,
Cr
y
p
to
’8
2
,
P
le
n
u
m
(1
9
8
3
)
199
-
2
0
3
[2
]
N.
Ko
b
li
tz (1
9
8
7
),
“
El
l
ip
ti
c
c
u
rv
e
c
r
y
p
to
sy
ste
m
s”
,
M
a
th
e
ma
ti
c
s o
f
Co
mp
u
t
a
ti
o
n
,
V
o
l
.
4
8
,
p
p
.
2
0
3
-
2
0
9
.
[3
]
G
OS
T
R
3
4
.
1
0
-
2
0
1
2
,
“
Dig
it
a
l
S
i
g
n
a
tu
re
A
lg
o
rit
h
m
d
ra
f
t
-
d
o
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g
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st3
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1
0
2
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1
2
-
0
0
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V
.
D
o
lm
a
to
v
,
Ed
,
(2
0
1
3
).
[4
]
P
o
p
e
sc
u
C,
“
Bli
n
d
S
ig
n
a
t
u
re
a
n
d
BM
S
Us
in
g
El
li
p
t
ic
Cu
rv
e
”
s.
S
tu
d
ia
u
n
iv
.
“
b
a
b
e
s¸
–
b
o
ly
a
i”,
In
f
o
rm
a
ti
c
a
.
(1
9
9
9
)
43
-
49
[5
]
S
.
S
.
Ch
o
w
e
t
a
l.
(2
0
0
5
),
“
T
w
o
Im
p
ro
v
e
d
P
a
rti
a
ll
y
Bli
n
d
S
ig
n
a
tu
r
e
S
c
h
e
m
e
s
f
ro
m
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in
e
a
r
P
a
iri
n
g
s”
,
In
fo
rm
a
ti
o
n
S
e
c
u
rity a
n
d
Priv
a
c
y
,
3
5
4
7
,
p
p
.
3
1
6
–
3
2
8
.
[6
]
M
o
ld
o
v
y
a
n
,
N.
A
.
,
“
Bli
n
d
S
ig
n
a
tu
re
P
r
o
to
c
o
ls
f
ro
m
Di
g
it
a
l
S
ig
n
a
tu
re
S
tan
d
a
rd
s”
,
I
n
ter
n
a
t
io
n
a
l
J
o
u
r
n
a
l
o
f
Ne
two
rk
S
e
c
u
rity
(2
0
1
1
)
2
2
-
30
[7
]
T
.
A
.
T
.
N
g
u
y
e
n
a
n
d
T
.
K.
Da
n
g
(2
0
1
3
),
“
En
h
a
n
c
e
d
se
c
u
rit
y
in
in
tern
e
t
v
o
ti
n
g
p
ro
t
o
c
o
l
u
si
n
g
b
li
n
d
sig
n
a
tu
re
a
n
d
d
y
n
a
m
ic b
a
ll
o
ts”
,
El
e
c
tro
n
ic Co
m
me
rc
e
Res
e
a
rc
h
,
1
3
.
[8
]
S
w
a
ti
V
e
rm
a
,
Biren
d
ra
Ku
m
a
r
S
h
a
rm
a
l
(2
0
1
2
),
“
Ne
w
P
ro
x
y
Bli
n
d
M
u
lt
i
S
ig
n
a
tu
re
b
a
se
d
o
n
I
n
teg
e
r
F
a
c
to
riza
ti
o
n
a
n
d
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re
te
-
L
o
g
a
rit
h
m
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r
o
b
lem
s
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h
tt
p
:/
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o
u
r
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a
l.
p
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rtalg
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ru
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a
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x
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p
h
p
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o
l
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1
,
p
p
1
8
5
~
1
9
0
.
[9
]
S
.
P
a
n
d
a
e
t
a
l.
(2
0
1
3
),
“
A
n
A
p
p
li
c
a
ti
o
n
o
f
ti
m
e
sta
m
p
e
d
p
ro
x
y
b
li
n
d
sig
n
a
tu
re
in
e
-
v
o
ti
n
g
”
,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
on
C
o
mp
u
ter
S
c
ien
c
e
a
n
d
En
g
in
e
e
rin
g
,
5
(6
)
,
p
p
.
5
4
7
–
5
5
2
.
[1
0
]
Hu
a
S
u
n
,
Ya
n
q
ian
g
G
e
(2
0
1
4
),
“
Ne
w
Ce
rti
f
ica
tele
ss
Bli
n
d
Rin
g
S
ig
n
a
tu
re
S
c
h
e
m
e
”
,
T
EL
KOM
NIKA
(
T
e
lec
o
mm
u
n
ica
t
io
n
Co
mp
u
ti
n
g
El
e
c
tro
n
ics
a
n
d
C
o
n
tro
l)
,
Vo
l.
1
2
,
No
.
1
,
p
p
7
7
8
-
7
8
3
[1
1
]
S
h
il
b
a
y
e
h
,
N.F
.
,
Al
-
S
a
id
i,
R.
A
.
,
A
lss
we
y
,
A
.
H.,
“
Ev
a
lu
a
ti
o
n
a
n
d
A
n
a
l
y
si
s
o
f
th
e
S
e
c
u
re
E
-
V
o
ti
n
g
A
u
th
e
n
ti
c
a
ti
o
n
P
re
p
a
ra
ti
o
n
S
c
h
e
m
e
”
,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
C
o
mp
u
ter
,
El
e
c
trica
l,
Au
to
m
a
ti
o
n
,
Co
n
tro
l
a
n
d
In
f
o
rm
a
ti
o
n
En
g
i
n
e
e
rin
g
,
(2
0
1
6
)
5
6
0
-
5
6
8
.
[1
2
]
M
in
h
,
H.,
Ha
i,
N.,
M
o
l
d
o
v
y
a
n
,
N.,
G
ian
g
,
T
.
,
“
N
e
w
Bli
n
d
S
ig
n
a
tu
re
P
r
o
t
o
c
o
ls
Ba
se
d
o
n
a
Ne
w
Ha
rd
P
r
o
b
lem
”,
T
h
e
In
ter
n
a
ti
o
n
a
l
Ar
a
b
J
o
u
rn
a
l
o
f
In
f
o
rm
a
ti
o
n
T
e
c
h
n
o
lo
g
y
,
V
o
l
.
1
4
,
No
.
3
,
M
a
y
2
0
1
7
.
[1
3
]
S
a
lo
m
e
J
a
m
e
s,
T
.
G
o
w
ri,
G
.
V
.
Ra
m
e
sh
Ba
b
u
,
P
.
V
a
su
d
e
v
a
Re
d
d
y
(2
0
1
7
),
“
Id
e
n
ti
ty
-
Ba
se
d
Bli
n
d
S
ig
n
a
tu
re
S
c
h
e
m
e
w
it
h
M
e
ss
a
g
e
R
e
c
o
v
e
r
y
”
,
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
a
n
d
Co
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
)
,
Vo
l.
7
,
N
o
.
5
,
pp
2
6
7
4
-
2
6
8
2
.
[1
4
]
Da
rre
l
Ha
n
k
e
rso
n
,
A
l
f
re
d
M
e
n
e
z
e
,
S
c
o
tt
V
a
n
sto
n
e
(2
0
0
4
),
G
u
id
e
t
o
E
ll
ip
t
icCu
rv
e
Cry
p
to
g
ra
p
h
y
,
S
p
rin
g
e
r,
Ne
w
Yo
rk
,
USA
.
[1
5
]
Be
ll
a
re
,
M
.
,
Ro
g
a
w
a
y
,
P
.
,
“
Ra
n
d
o
m
o
ra
c
les
a
re
p
ra
c
ti
c
a
l:
a
p
a
ra
d
ig
m
f
o
r
d
e
sig
n
i
n
g
e
ff
ici
e
n
t
p
ro
t
o
c
o
ls”
,
P
r
o
c
e
e
d
in
g
s o
f
th
e
1
st A
CM
c
o
n
f
e
re
n
c
e
o
n
Co
m
p
u
ter an
d
c
o
m
m
u
n
ica
ti
o
n
s se
c
u
rit
y
.
(1
9
9
3
)
6
2
–
73
[1
6
]
L
iu
,
J.K.,
Ba
e
k
,
J,
Zh
o
u
,
J.,
Ya
n
g
,
Y.,
W
o
n
g
,
J.
W
.
,
“
E
f
fi
c
ien
t
o
n
li
n
e
/o
f
fl
in
e
id
e
n
ti
ty
-
ba
se
d
sig
n
a
t
u
re
f
o
r
w
irele
s
s
se
n
so
r
n
e
tw
o
rk
”
,
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
In
f
o
rm
a
ti
o
n
S
e
c
u
rity
,
(
2
0
1
0
)
2
8
7
-
2
9
6
[1
7
]
Ch
u
n
-
I
F
a
n
,
W
e
i
-
Zh
e
S
u
n
,
V
i
n
c
e
n
t
S
h
i
-
M
in
g
H
u
a
n
g
(2
0
1
0
),
“
P
ro
v
a
b
l
y
se
c
u
re
ra
n
d
o
m
ize
d
b
li
n
d
si
g
n
a
tu
re
sc
h
e
m
e
b
a
se
d
o
n
b
i
li
n
e
a
r
p
a
iri
n
g
”
.
[1
8
]
D.
S
c
h
ro
d
e
r
(2
0
1
0
),
O
n
t
h
e
Co
m
p
lex
it
y
o
f
Bli
n
d
S
ig
n
a
t
u
re
s
,
T
e
c
h
n
isc
h
e
n
Un
iv
e
rsitat
Da
rm
sta
d
t
g
e
n
e
h
m
ig
te.
Evaluation Warning : The document was created with Spire.PDF for Python.