I
nte
rna
t
io
na
l J
o
urna
l o
f
E
lect
rica
l a
nd
Co
m
pu
t
er
E
ng
ineering
(
I
J
E
CE
)
Vo
l.
16
,
No
.
4
,
A
u
g
u
s
t
20
26
,
p
p
.
1
976
~
1
9
8
4
I
SS
N:
2088
-
8
7
0
8
,
DOI
: 1
0
.
1
1
5
9
1
/ijece.
v
16
i
4
.
pp
1
9
7
6
-
1
9
8
4
1976
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
ec
e.
ia
esco
r
e.
co
m
A non
-
in
teractive
la
tt
ice
-
ba
sed
sch
eme suppo
rti
ng
multiple
blindnes
s mo
des
Dinh
H
a
i Le
1
,
L
uo
ng
Vu N
g
o
c
B
ui
2
1
C
l
a
ss
K
1
0
C
o
m
p
u
t
e
r
S
c
i
e
n
c
e
,
H
o
n
g
D
u
c
U
n
i
v
e
r
s
i
t
y
,
Th
a
n
h
H
o
a
,
V
i
e
t
n
a
m
2
Th
a
n
h
H
o
a
C
a
mp
u
s,
H
a
n
o
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M
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d
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c
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U
n
i
v
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si
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y
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D
o
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D
a
D
i
s
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r
i
c
t
,
H
a
n
o
i
,
V
i
e
t
n
a
m
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Au
g
8
,
2
0
2
5
R
ev
is
ed
Ma
y
8
,
2
0
2
6
Acc
ep
ted
J
u
l 2
2
,
2
0
2
6
Th
is
p
a
p
e
r
p
ro
p
o
se
s
a
latti
c
e
b
a
se
d
m
u
lt
i
-
m
o
d
e
b
li
n
d
sig
n
a
tu
re
f
ra
m
e
wo
rk
th
a
t
u
n
if
o
rm
ly
su
p
p
o
rts
th
re
e
o
p
e
ra
ti
n
g
m
o
d
e
s:
f
u
ll
b
li
n
d
n
e
s
s,
p
a
rti
a
l
b
li
n
d
n
e
ss
,
a
n
d
n
o
n
-
b
l
in
d
n
e
ss
.
T
h
e
d
e
sig
n
e
m
p
l
o
y
s
p
u
b
li
c
m
a
tr
ice
s
with
trap
d
o
o
rs,
c
o
m
b
in
e
d
wit
h
h
a
sh
f
u
n
c
ti
o
n
s
m
a
p
p
in
g
i
n
to
ℤ
,
sh
o
rt
p
r
e
ima
g
e
sa
m
p
li
n
g
m
e
c
h
a
n
ism
s,
a
n
d
a
n
id
e
n
ti
t
y
e
n
c
ry
p
ti
o
n
c
o
m
p
o
n
e
n
t
to
e
n
su
re
fa
irn
e
ss
a
n
d
e
n
a
b
le t
ra
c
e
a
b
il
it
y
in
c
a
se
o
f
m
isu
se
.
Ba
se
d
o
n
th
is co
n
stru
c
ti
o
n
,
th
e
u
se
r
g
e
n
e
ra
tes
a
b
li
n
d
e
d
re
q
u
e
st,
th
e
sig
n
e
r
p
r
o
d
u
c
e
s
a
sh
o
rt
re
sp
o
n
se
b
o
u
n
d
to
t
h
e
e
n
c
ry
p
te
d
id
e
n
t
it
y
,
a
n
d
th
e
u
se
r
p
e
rf
o
rm
s
a
n
u
n
b
li
n
d
in
g
ste
p
t
o
o
b
tai
n
th
e
fin
a
l
si
g
n
a
t
u
re
.
Th
e
p
a
p
e
r
a
lso
p
re
se
n
ts
th
e
sy
ste
m
m
o
d
e
l,
re
se
a
rc
h
m
e
th
o
d
o
l
o
g
y
,
se
c
u
ri
ty
c
laim
s,
a
n
d
p
a
ra
m
e
ter
d
isc
u
ss
i
o
n
s
in
th
e
p
o
st
-
q
u
a
n
t
u
m
se
tt
i
n
g
.
T
h
e
m
a
in
p
r
o
p
e
rti
e
s
a
n
a
ly
z
e
d
in
c
lu
d
e
c
o
rre
c
tn
e
ss
,
b
li
n
d
n
e
ss
,
p
a
rti
a
l
b
li
n
d
n
e
ss
,
e
x
isten
ti
a
l
u
n
fo
r
g
e
a
b
il
it
y
,
o
n
e
m
o
re
u
n
f
o
rg
e
a
b
il
i
ty
,
fa
ir
n
e
ss
,
a
n
d
trac
e
a
b
il
it
y
u
n
d
e
r
th
e
sh
o
rt
in
teg
e
r
so
lu
ti
o
n
(S
IS
)
a
n
d
o
n
e
m
o
re
S
I
S
a
ss
u
m
p
ti
o
n
s.
Th
e
re
su
lt
s
in
d
ica
te
th
a
t
t
h
e
p
ro
p
o
se
d
a
p
p
ro
a
c
h
p
r
o
v
i
d
e
s
a
flex
ib
le
s
o
l
u
ti
o
n
f
o
r
a
p
p
li
c
a
ti
o
n
s
re
q
u
ir
in
g
a
b
a
lan
c
e
b
e
twe
e
n
a
n
o
n
y
m
it
y
,
a
c
c
o
u
n
tab
il
it
y
,
a
n
d
p
o
st
-
q
u
a
n
t
u
m
se
c
u
rit
y
.
K
ey
w
o
r
d
s
:
B
lin
d
s
ig
n
atu
r
e
L
attice
No
n
-
in
ter
ac
tiv
e
b
lin
d
s
ig
n
atu
r
es
Par
tially
b
lin
d
SIS
an
d
o
n
e
m
o
r
e
SIS
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
L
u
o
n
g
Vu
Ng
o
c
B
u
i
T
h
an
h
Ho
a
C
am
p
u
s
,
Han
o
i M
ed
ical
Un
iv
er
s
ity
1
T
o
n
T
h
at
T
u
n
g
Stre
et,
Kim
L
ien
W
ar
d
,
Do
n
g
Da
Dis
tr
ict,
Han
o
i,
Vietn
am
E
m
ail:
Ng
o
cb
lv
@
h
m
u
.
e
d
u
.
v
n
1.
I
NT
RO
D
UCT
I
O
N
B
lin
d
s
ig
n
atu
r
es,
o
r
ig
i
n
ally
p
r
o
p
o
s
ed
b
y
C
h
au
m
,
allo
w
a
u
s
er
to
o
b
tain
a
v
alid
s
ig
n
atu
r
e
o
n
a
m
ess
ag
e
o
f
th
eir
ch
o
ice
with
o
u
t
r
ev
ea
lin
g
its
co
n
ten
t
to
t
h
e
s
ig
n
er
;
th
e
ce
n
tr
al
p
r
o
p
er
t
y
o
f
th
is
m
o
d
el
is
b
lin
d
n
ess
[
1
]
.
Ho
wev
e
r
,
m
o
s
t
class
ical
b
lin
d
s
ig
n
atu
r
e
s
ch
e
m
es
s
till
r
eq
u
ir
e
in
ter
ac
tio
n
b
etwe
en
th
e
u
s
er
an
d
th
e
s
ig
n
er
,
ty
p
ically
at
least
t
wo
r
o
u
n
d
s
to
p
er
f
o
r
m
b
lin
d
in
g
,
s
ig
n
in
g
,
a
n
d
u
n
b
lin
d
in
g
[
2
]
,
[
3
]
,
wh
ich
lim
its
th
eir
ap
p
licab
ilit
y
in
asy
n
ch
r
o
n
o
u
s
en
v
ir
o
n
m
en
ts
o
r
in
s
ettin
g
s
r
eq
u
ir
in
g
p
r
e
is
s
u
ed
s
ig
n
atu
r
es.
T
o
r
ed
u
ce
r
elian
ce
o
n
o
n
lin
e
i
n
ter
ac
tio
n
,
Han
zlik
in
tr
o
d
u
ce
d
th
e
n
o
ti
o
n
o
f
n
o
n
-
in
te
r
ac
tiv
e
b
lin
d
s
ig
n
atu
r
es
(
NI
B
S),
wh
er
e
th
e
s
ig
n
er
p
r
e
is
s
u
es
a
p
r
e
-
s
ig
n
atu
r
e
,
an
d
th
e
r
ec
eiv
e
r
u
s
es
co
r
r
esp
o
n
d
in
g
s
ec
r
et
in
f
o
r
m
atio
n
to
d
e
r
iv
e
th
e
f
in
al
s
ig
n
at
u
r
e
with
o
u
t
a
n
y
f
u
r
th
er
in
ter
ac
tio
n
[
4
]
.
E
a
r
ly
NI
B
S
co
n
s
tr
u
ctio
n
s
a
r
e
p
r
im
ar
ily
b
ased
o
n
b
ilin
ea
r
p
air
in
g
s
[
4
]
,
[
5
]
,
an
d
m
o
r
e
r
ec
e
n
t w
o
r
k
s
h
a
v
e
b
e
g
u
n
to
ex
p
lo
r
e
p
o
s
t q
u
an
tu
m
s
ec
u
r
ity
[
6
]
.
I
n
th
e
p
o
s
t
q
u
an
tu
m
s
ettin
g
,
lattices
p
r
o
v
id
e
a
h
i
g
h
ly
p
r
o
m
is
in
g
f
o
u
n
d
atio
n
f
o
r
q
u
an
t
u
m
s
ec
u
r
e
s
ig
n
atu
r
e
an
d
e
n
cr
y
p
tio
n
p
r
im
itiv
es.
No
tab
le
r
esu
lts
in
clu
d
e
tr
ap
d
o
o
r
lattices
an
d
t
h
e
GP
V
s
ig
n
atu
r
e
[
7
]
,
an
ef
f
icien
t
ID
-
b
ased
d
ir
ec
ted
s
ig
n
atu
r
e
s
ch
em
e
f
r
o
m
b
ilin
ea
r
p
air
in
g
s
[
8
]
,
lattice
-
b
ased
I
B
E
/HI
B
E
s
y
s
tem
s
[
9
]
,
ef
f
icien
t
s
ig
n
atu
r
es
[
1
0
]
,
a
n
d
m
o
r
e
r
ec
en
tly
,
r
o
u
n
d
o
p
ti
m
al
lattice
b
ased
b
lin
d
s
ig
n
atu
r
es
[
1
1
]
.
T
h
ese
ad
v
an
ce
s
s
u
g
g
est
th
at
c
o
n
s
tr
u
ctin
g
a
lattice
-
b
ased
NI
B
S
s
ch
em
e,
s
u
p
p
o
r
tin
g
m
u
ltip
le
b
lin
d
in
g
m
o
d
es
a
n
d
in
teg
r
atin
g
f
air
n
ess
an
d
tr
ac
ea
b
ilit
y
,
is
a
n
atu
r
al
an
d
p
r
ac
tica
lly
m
ea
n
in
g
f
u
l r
esear
ch
d
ir
ec
ti
o
n
.
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:
2088
-
8
7
0
8
A
n
o
n
-
in
tera
ctive
la
ttice
-
b
a
s
e
d
s
ch
eme
s
u
p
p
o
r
tin
g
m
u
ltip
le
b
lin
d
n
ess
mo
d
es
(
Din
h
Ha
i Le
)
1977
T
h
e
m
ain
co
n
tr
i
b
u
tio
n
s
o
f
t
h
is
p
ap
er
ca
n
b
e
s
u
m
m
a
r
ized
a
s
f
o
llo
ws:
i
)
we
p
r
o
p
o
s
e
a
lattice
b
ased
non
-
in
te
r
ac
tiv
e
b
lin
d
s
ig
n
atu
r
e
s
ch
em
e
tar
g
etin
g
p
o
s
t
q
u
an
tu
m
s
ec
u
r
ity
;
ii
)
we
d
esig
n
a
m
u
lti
-
mode
ar
ch
itectu
r
e
t
h
at
u
n
if
o
r
m
l
y
s
u
p
p
o
r
ts
th
r
ee
s
ettin
g
s
:
f
u
ll
b
lin
d
n
ess
,
p
ar
tial b
lin
d
n
ess
,
a
n
d
n
o
n
-
b
lin
d
n
ess
;
iii
)
we
in
teg
r
ate
a
f
air
n
ess
an
d
tr
ac
ea
b
ilit
y
m
ec
h
an
is
m
,
allo
win
g
a
d
esig
n
ated
au
th
o
r
ity
t
o
r
ec
o
v
e
r
en
cr
y
p
ted
id
e
n
tity
in
f
o
r
m
atio
n
in
ca
s
e
o
f
ab
u
s
e;
an
d
iv
)
we
co
m
b
in
e
th
e
co
n
ce
p
tu
al
NI
B
S
f
r
am
ewo
r
k
[
4
]
with
lattice
b
ased
b
lin
d
s
ig
n
at
u
r
e
tec
h
n
iq
u
es
[
1
1
]
t
o
p
r
o
v
i
d
e
a
m
o
r
e
f
le
x
i
b
le
p
o
s
t
q
u
an
t
u
m
c
o
n
s
tr
u
cti
o
n
ac
c
o
m
m
o
d
atin
g
d
if
f
er
en
t le
v
els o
f
m
ess
ag
e
ex
p
o
s
u
r
e.
T
ec
h
n
ically
,
o
u
r
s
ch
em
e
is
b
u
ilt u
p
o
n
a
p
u
b
lic
m
atr
ix
∈
ℤ
×
to
g
eth
er
with
a
tr
ap
d
o
o
r
h
eld
b
y
th
e
s
ig
n
er
.
T
h
e
u
s
er
en
co
d
es
th
e
h
id
d
en
m
ess
ag
e
co
m
p
o
n
en
t
an
d
o
p
tio
n
al
p
u
b
lic
in
f
o
r
m
atio
n
in
to
a
b
lin
d
ed
r
e
q
u
est
=
+
1
(
∥
)
,
wh
er
e
is
a
s
h
o
r
t
r
an
d
o
m
v
ec
to
r
u
s
ed
to
h
id
e
th
e
d
ata
f
r
o
m
th
e
s
ig
n
er
.
T
o
e
n
ab
le
tr
ac
ea
b
ilit
y
,
th
e
s
ig
n
e
r
ad
d
itio
n
ally
g
e
n
er
ates
an
id
e
n
tity
cip
h
er
tex
t
=
(
;
)
,
an
d
u
s
es
th
e
tr
a
p
d
o
o
r
to
p
r
o
d
u
ce
a
s
h
o
r
t
r
esp
o
n
s
e
s
ati
s
f
y
in
g
=
+
2
(
)
.
T
h
e
u
s
er
th
e
n
u
n
b
lin
d
s
b
y
c
o
m
p
u
tin
g
=
−
,
th
er
eb
y
o
b
tain
in
g
th
e
f
in
al
s
ig
n
atu
r
e
=
(
,
,
)
,
wh
ich
s
atis
f
ies
th
e
v
er
if
icatio
n
co
n
d
itio
n
=
1
(
∥
)
+
2
(
)
.
T
h
is
f
r
am
ewo
r
k
n
atu
r
ally
u
n
if
ies
th
r
ee
o
p
er
atio
n
al
m
o
d
es,
in
clu
d
in
g
f
u
ll
b
lin
d
n
ess
,
p
ar
tial
b
lin
d
n
ess
,
an
d
n
o
n
b
lin
d
n
ess
,
wh
ile
s
im
u
ltan
eo
u
s
ly
ac
h
iev
in
g
b
lin
d
n
ess
,
u
n
f
o
r
g
ea
b
ilit
y
b
ased
o
n
lattice
ass
u
m
p
tio
n
s
s
u
ch
as
s
h
o
r
t
i
n
teg
er
s
o
lu
tio
n
(
SIS)
,
an
d
f
air
n
ess
an
d
tr
ac
ea
b
ilit
y
v
ia
th
e
id
en
tity
en
cr
y
p
tio
n
co
m
p
o
n
e
n
t.
T
h
e
p
ap
er
clea
r
l
y
d
elin
ea
tes
th
e
s
co
p
e
o
f
its
s
ec
u
r
ity
claim
s
,
f
o
cu
s
in
g
o
n
co
n
ce
p
tu
al
d
esig
n
an
d
p
r
o
o
f
s
k
etch
lev
el
an
aly
s
is
b
ased
o
n
SIS
an
d
o
n
e
m
o
r
e
SIS
ass
u
m
p
tio
n
s
,
to
g
eth
er
with
s
tan
d
ar
d
ass
u
m
p
tio
n
s
o
n
h
ash
f
u
n
ctio
n
s
an
d
p
u
b
lic
k
ey
en
cr
y
p
tio
n
.
P
r
o
p
e
r
ties
s
u
ch
as
co
r
r
ec
tn
ess
,
b
lin
d
n
ess
,
p
ar
tial
b
lin
d
n
ess
,
ex
is
ten
tial
u
n
f
o
r
g
ea
b
ilit
y
,
o
n
e
m
o
r
e
u
n
f
o
r
g
ea
b
ilit
y
,
f
air
n
e
s
s
,
an
d
tr
ac
ea
b
ilit
y
ar
e
an
aly
ze
d
in
th
e
r
an
d
o
m
o
r
ac
le
m
o
d
el
f
o
llo
win
g
th
e
s
c
h
em
e
s
tr
u
ctu
r
e.
Ho
wev
er
,
th
e
wo
r
k
d
o
es
n
o
t
aim
at
p
ar
am
eter
o
p
tim
izatio
n
o
r
tig
h
t
r
ed
u
ctio
n
s
f
o
r
all
ex
ten
d
ed
v
ar
ia
n
ts
.
T
h
e
cip
h
er
tex
t
r
e
r
an
d
o
m
izatio
n
a
f
ter
is
s
u
an
ce
is
tr
ea
ted
as
an
o
p
tio
n
al
p
r
iv
ac
y
e
n
h
an
cin
g
e
x
ten
s
io
n
an
d
is
n
o
t
p
ar
t
o
f
th
e
co
r
e
c
o
n
s
tr
u
ctio
n
.
I
n
th
e
b
ase
s
ch
em
e,
s
ig
n
atu
r
es
ar
e
v
er
if
ied
with
th
e
cip
h
er
tex
t
b
o
u
n
d
at
is
s
u
an
ce
tim
e,
th
er
eb
y
clea
r
ly
s
ep
ar
atin
g
th
e
m
ai
n
an
aly
tical
m
o
d
el
f
r
o
m
p
o
ten
tial f
u
tu
r
e
ex
ten
s
io
n
s
.
2.
M
E
T
H
O
D
2
.
1
.
Resea
rc
h m
e
t
ho
do
lo
g
y
T
h
is
p
ap
er
f
o
llo
ws
a
th
eo
r
y
d
r
iv
en
co
n
s
tr
u
ctio
n
co
m
b
in
ed
with
f
o
r
m
al
a
n
aly
s
is
.
First,
we
s
u
r
v
e
y
r
esu
lts
o
n
b
lin
d
s
ig
n
at
u
r
es,
N
I
B
S,
p
ar
tial/fa
ir
b
lin
d
s
ig
n
atu
r
es,
an
d
lattice
-
b
ased
cr
y
p
to
g
r
ap
h
y
[
1
]
–
[
4
]
,
[
7
]
,
[
1
1
]
.
B
ased
o
n
th
is
,
we
s
elec
t
th
e
c
o
r
e
c
o
m
p
o
n
en
ts
:
tr
ap
d
o
o
r
s
f
o
r
p
u
b
lic
m
atr
ices,
h
ash
f
u
n
ctio
n
s
i
n
to
ℤ
,
id
en
tity
en
cr
y
p
tio
n
,
an
d
n
o
n
-
in
ter
ac
tiv
e
ze
r
o
-
k
n
o
wled
g
e
(
NI
Z
K)
p
r
o
o
f
s
f
o
r
lin
ea
r
r
elatio
n
s
.
T
h
ese
co
m
p
o
n
en
ts
ar
e
in
teg
r
ate
d
in
t
o
a
m
u
lti
-
m
o
d
e
ar
c
h
itectu
r
e
s
u
p
p
o
r
tin
g
f
u
ll
-
b
lin
d
,
p
ar
tial
-
b
l
in
d
,
an
d
n
o
n
-
b
lin
d
m
o
d
es th
r
o
u
g
h
i
n
p
u
t a
d
ap
tatio
n
.
2
.
2
.
L
a
t
t
ice
pa
ra
m
e
t
er
s
T
h
e
cr
y
p
to
s
y
s
tem
is
b
u
ilt
o
n
d
is
cr
ete
lattices
with
m
ain
p
ar
am
eter
s
in
clu
d
in
g
th
e
m
o
d
u
lu
s
,
th
e
d
im
en
s
io
n
o
f
th
e
s
p
ac
e
ℤ
,
an
d
th
e
len
g
th
(
with
>
to
en
s
u
r
e
th
e
ex
is
ten
ce
o
f
a
tr
ap
d
o
o
r
)
.
T
h
e
p
u
b
lic
m
atr
ix
∈
ℤ
×
is
p
ar
t o
f
th
e
p
u
b
lic
k
e
y
,
an
d
|
|
d
en
o
tes th
e
ℓ
2
n
o
r
m
o
f
v
ec
to
r
.
2
.
3
.
SI
S a
nd
o
ne
m
o
re
SI
S pro
blem
s
Secu
r
ity
r
elies
o
n
th
e
SIS
p
r
o
b
lem
[
1
2
]
:
g
iv
e
n
∈
ℤ
×
,
f
in
d
≠
s
u
ch
th
at
=
,
|
|
<
.
T
h
e
o
n
e
m
o
r
e
SIS
v
a
r
ian
t
[
1
1
]
:
th
e
a
d
v
er
s
ar
y
ca
n
q
u
er
y
a
n
o
r
ac
le
r
etu
r
n
i
n
g
s
u
ch
th
at
=
f
o
r
∈
ℤ
,
b
u
t m
u
s
t o
u
tp
u
t
ℓ
+
1
v
alid
p
air
s
(
,
)
,
ex
ce
ed
in
g
t
h
e
ℓ
q
u
er
ies.
2
.
4
.
T
ra
pd
o
o
rs f
o
r
m
a
t
rix
in
la
t
t
ice
-
ba
s
ed
cr
y
pto
g
ra
ph
y
A
tr
ap
d
o
o
r
f
o
r
m
atr
ix
is
s
ec
r
et
in
f
o
r
m
atio
n
th
at
en
ab
les
f
in
d
in
g
s
h
o
r
t
s
o
lu
tio
n
s
t
o
=
(
)
,
wh
er
e
∈
ℤ
×
an
d
∈
ℤ
.
T
h
is
p
r
o
b
lem
is
h
ar
d
with
o
u
t
a
tr
a
p
d
o
o
r
(
r
elate
d
to
SIS/L
W
E
[
1
3
]
–
[
1
5
]
)
,
b
u
t
ca
n
b
e
ef
f
icie
n
tly
s
o
lv
ed
v
ia
Gau
s
s
ian
s
am
p
lin
g
wh
e
n
th
e
tr
a
p
d
o
o
r
is
k
n
o
wn
[
1
6
]
.
A
ty
p
ical
tr
ap
d
o
o
r
is
a
s
h
o
r
t b
asis
o
f
th
e
k
er
n
el
lattice
⊥
(
)
=
{
∈
ℤ
:
=
(
)
}
.
T
h
e
tr
ap
d
o
o
r
is
g
e
n
er
ated
b
y
(
,
)
←
(
,
,
)
,
an
d
u
s
ed
t
o
s
am
p
le
s
h
o
r
t
s
o
lu
tio
n
s
←
(
,
,
)
.
T
h
is
tech
n
iq
u
e
u
n
d
er
lies
lat
tice
-
b
ased
s
y
s
tem
s
s
u
ch
as
GPV,
NT
R
U,
an
d
L
W
E
/SIS
v
ar
ian
ts
[
7
]
,
[
1
3
]
–
[
1
5
]
,
[
1
7
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
16
,
No
.
4
,
Au
g
u
s
t
20
26
:
1
9
7
6
-
1
984
1978
2
.
5
.
H
a
s
h f
un
ct
io
ns
a
nd
ra
n
do
m
nes
s
ex
t
ra
ct
io
n
Hash
f
u
n
ctio
n
s
1
,
2
ac
t
as
s
tr
o
n
g
r
an
d
o
m
n
ess
ex
t
r
ac
to
r
s
:
f
o
r
i
n
p
u
ts
with
s
u
f
f
icien
t
m
i
n
-
en
tr
o
p
y
an
d
u
n
iv
e
r
s
al
h
ash
f
am
ilies
,
t
h
e
o
u
tp
u
t
d
is
tr
ib
u
tio
n
is
s
tati
s
tically
clo
s
e
to
u
n
if
o
r
m
o
v
er
ℤ
ac
co
r
d
in
g
to
th
e
L
ef
to
v
er
Hash
L
em
m
a
(
L
H
L
)
[
1
8
]
–
[
2
0
]
,
t
h
u
s
r
e
v
e
a
l
i
n
g
n
o
i
n
f
o
r
m
a
t
i
o
n
a
b
o
u
t
t
h
e
i
n
p
u
t
.
T
h
e
p
u
b
l
i
c
k
e
y
t
y
p
i
c
a
l
l
y
h
as
t
h
e
f
o
r
m
=
+
1
(
)
,
w
h
e
r
e
∈
ℤ
×
,
i
s
Ga
u
s
s
i
a
n
n
o
is
e
,
a
n
d
1
(
)
i
s
n
e
a
r
l
y
u
n
i
f
o
r
m
.
T
h
e
r
e
f
o
r
e
,
l
e
a
k
s
al
m
o
s
t
n
o
i
n
f
o
r
m
a
t
i
o
n
a
b
o
u
t
w
i
t
h
o
u
t
t
h
e
t
r
ap
d
o
o
r
o
f
,
e
n
s
u
r
i
n
g
p
r
i
v
a
c
y
a
n
d
a
n
o
n
y
m
i
t
y
.
2
.
6
.
I
dentit
y
encr
y
ptio
n
m
o
du
le
T
h
e
id
en
tity
en
cr
y
p
tio
n
m
o
d
u
l
e
p
r
o
tects
b
y
en
cr
y
p
tin
g
it
as
=
(
)
,
wh
er
e
m
ay
b
e
E
lGam
al,
R
SA,
o
r
lattice
-
b
ase
d
s
ch
em
es
s
u
ch
as
R
eg
ev
o
r
NT
R
U
[
1
4
]
,
[
1
9
]
.
T
h
en
,
2
m
ap
s
to
a
v
ec
to
r
in
ℤ
:
=
2
(
)
∈
ℤ
.
2
ca
n
b
e
co
n
s
tr
u
cted
f
r
o
m
SHA
-
3
co
m
b
in
ed
with
a
PR
F
[
1
9
]
,
[
2
1
]
,
en
s
u
r
i
n
g
n
e
a
r
u
n
if
o
r
m
d
is
tr
ib
u
tio
n
an
d
lim
iti
n
g
in
f
o
r
m
atio
n
leak
ag
e.
2
.
7
.
No
n
-
inte
ra
c
t
iv
e
ze
ro
-
k
n
o
wledg
e
pro
o
f
s
No
n
-
in
ter
ac
tiv
e
ze
r
o
-
k
n
o
wled
g
e
(
NI
Z
K)
p
r
o
o
f
s
allo
w
co
r
r
ec
tn
ess
to
b
e
p
r
o
v
en
with
o
u
t
r
ev
ea
lin
g
in
f
o
r
m
atio
n
.
I
n
th
e
s
y
s
tem
,
it
is
n
ec
ess
ar
y
to
p
r
o
v
e:
=
+
2
(
)
,
an
d
th
at
is
a
v
alid
en
cr
y
p
tio
n
o
f
.
Su
itab
le
tech
n
iq
u
es
in
clu
d
e
NI
Z
K
f
o
r
lin
ea
r
r
elatio
n
s
[
2
2
]
,
Fiat
-
Sh
am
ir
tr
an
s
f
o
r
m
atio
n
s
o
n
lattices
[
2
3
]
,
o
r
Gr
o
th
-
Sah
ai
p
r
o
o
f
s
f
o
r
lin
e
ar
/b
ilin
ea
r
s
tatem
en
ts
[
2
4
]
.
2
.
8
.
Securit
y
def
ini
t
io
ns
2
.
8
.
1
.
Co
rr
ec
t
nes
s
Fo
r
an
h
o
n
est
u
s
er
an
d
s
ig
n
er
,
co
r
r
ec
tly
ex
ec
u
tin
g
I
s
s
u
e
an
d
Fin
alize
y
ield
s
a
s
ig
n
atu
r
e
=
(
,
,
in
fo
,
)
s
u
ch
t
h
at
=
1
(
in
fo
∥
)
+
2
(
)
,
|
|
<
th
r
esh
o
ld
.
C
o
r
r
ec
tn
ess
e
n
s
u
r
es
th
at
Ver
if
y
alwa
y
s
ac
ce
p
ts
;
th
is
h
o
ld
s
b
e
ca
u
s
e
is
s
am
p
led
f
r
o
m
an
a
p
p
r
o
p
r
iate
Gau
s
s
ian
d
is
tr
ib
u
tio
n
s
atis
f
y
in
g
th
e
r
eq
u
ir
ed
co
n
d
itio
n
s
with
h
ig
h
p
r
o
b
a
b
ilit
y
[
2
5
]
.
2
.
8
.
2
.
B
lin
dn
e
s
s
B
lin
d
n
ess
g
am
e
:
T
h
e
ad
v
er
s
ar
y
(
th
e
s
ig
n
er
)
ch
o
o
s
es
(
0
,
1
)
an
d
(
in
fo
0
,
in
fo
1
)
.
A
r
an
d
o
m
b
it
∈
{
0
,
1
}
is
ch
o
s
en
;
th
e
s
y
s
tem
s
ig
n
s
with
an
d
1
−
with
a
s
im
u
lated
s
i
g
n
er
.
T
h
e
a
d
v
er
s
ar
y
m
u
s
t
g
u
e
s
s
,
with
r
eq
u
ir
em
e
n
t:
|
[
g
u
ess
es c
o
r
r
ec
tly
]
−
1
2
|
≤
n
eg
l
(
)
.
I
n
th
e
s
ch
e
m
e,
h
id
es
d
u
e
to
1
co
m
b
in
e
d
with
n
o
is
e
,
p
r
e
v
en
tin
g
th
e
s
ig
n
er
f
r
o
m
d
is
tin
g
u
is
h
in
g
.
T
h
e
cip
h
e
r
tex
t
is
u
s
ed
c
o
n
s
is
ten
tly
b
etwe
en
is
s
u
an
ce
an
d
v
er
if
icatio
n
;
r
e
-
r
an
d
o
m
izatio
n
↦
′
[
2
6
]
is
co
n
s
id
er
ed
o
n
ly
in
ex
ten
d
ed
v
ar
ian
ts
.
B
lin
d
n
ess
is
ac
h
iev
ed
at
th
r
ee
lev
els:
i)
t
h
e
s
ig
n
er
ca
n
n
o
t
lin
k
to
a
s
ig
n
in
g
s
ess
io
n
;
ii)
with
o
u
t
,
ca
n
n
o
t
b
e
r
ec
o
v
er
e
d
f
r
o
m
;
iii)
ev
en
if
th
e
s
ig
n
er
co
llu
d
es
with
th
e
tr
u
s
tee
[
2
7
]
,
th
e
i
n
f
o
r
m
atio
n
r
e
v
ea
led
is
m
ain
ly
,
n
o
t
.
2
.
8
.
3
.
P
a
rt
i
a
l blin
dn
e
s
s
Par
tial
b
lin
d
n
ess
en
s
u
r
es
th
at
th
e
s
ig
n
er
ca
n
n
o
t
d
is
tin
g
u
is
h
b
etwe
en
two
h
id
d
en
m
ess
ag
es
g
iv
en
th
e
s
am
e
p
u
b
lic
in
f
o
r
m
atio
n
.
T
h
e
ad
v
er
s
ar
y
’
ad
v
an
t
ag
e
in
th
e
PB
lin
d
g
am
e
is
d
ef
in
ed
as:
,
(
)
=
|
[
1
←
P
B
lin
d
,
]
−
1
2
|
.
I
n
PB
lin
d
,
ch
o
o
s
es
(
0
,
1
)
an
d
a
co
m
m
o
n
;
th
e
s
y
s
tem
s
ig
n
s
ac
co
r
d
in
g
to
a
r
an
d
o
m
b
it
v
ia
o
r
ac
le
ac
ce
s
s
,
an
d
m
u
s
t
g
u
ess
[
2
8
]
,
[
2
9
]
.
T
h
e
s
ch
em
e
is
s
ec
u
r
e
if
th
e
a
d
v
an
ta
g
e
is
n
e
g
lig
ib
le.
I
n
th
e
d
esig
n
,
ap
p
e
ar
s
o
n
ly
th
r
o
u
g
h
1
(
∥
)
,
wh
er
e
is
r
an
d
o
m
an
d
h
id
d
e
n
,
s
o
ev
e
n
k
n
o
win
g
,
th
e
s
ig
n
er
ca
n
n
o
t lin
k
s
ig
n
atu
r
es to
s
p
ec
if
ic
m
ess
ag
es.
2
.
8
.
4
.
O
ne
mo
re
un
f
o
rg
ea
bil
it
y
U
n
f
o
r
g
e
a
b
i
l
i
t
y
i
n
m
u
lt
i
-
mode
N
I
B
S
r
e
q
u
i
r
e
s
s
e
c
u
r
it
y
e
v
e
n
w
h
e
n
t
h
e
a
d
v
e
r
s
a
r
y
s
e
l
ec
t
s
th
e
w
e
a
k
e
s
t
m
o
d
e
.
E
U
F
:
n
o
p
o
l
y
n
o
m
i
a
l
-
t
i
m
e
a
d
v
e
r
s
a
r
y
ca
n
p
r
o
d
u
c
e
a
v
a
l
i
d
s
i
g
n
a
t
u
r
e
o
n
a
n
o
n
-
q
u
e
r
i
e
d
m
e
s
s
a
g
e:
[
w
in
s
E
UF
]
≤
(
)
.
O
M
U
F
:
w
i
t
h
a
t
m
o
s
t
ℓ
s
i
g
n
i
n
g
q
u
e
r
i
e
s
,
t
h
e
a
d
v
e
r
s
a
r
y
c
a
n
n
o
t
p
r
o
d
u
c
e
ℓ
+
1
v
a
l
i
d
s
i
g
n
a
t
u
r
es
:
,
(
)
=
[
1
←
OMUF
,
]
,
a
n
d
[
p
r
o
d
u
ce
s
ℓ
+
1
s
ig
n
a
tu
r
es a
fter
ℓ
q
u
eries
]
≤
(
)
.
S
e
c
u
r
i
t
y
r
e
d
u
c
e
s
t
o
S
I
S
a
n
d
o
n
e
m
o
r
e
S
I
S:
e
a
c
h
s
i
g
n
i
n
g
s
ess
i
o
n
c
o
r
r
e
s
p
o
n
d
s
t
o
a
n
S
I
S
c
h
a
l
l
e
n
g
e
,
s
o
f
o
r
g
i
n
g
a
d
d
i
t
i
o
n
a
l
s
i
g
n
a
t
u
r
e
s
r
e
q
u
i
r
e
s
s
o
l
v
i
n
g
S
I
S
wi
t
h
o
u
t
t
h
e
t
r
a
p
d
o
o
r
;
m
e
a
n
w
h
i
l
e
,
r
e
m
a
i
n
s
h
i
d
d
e
n
t
h
r
o
u
g
h
o
u
t
I
s
s
u
e
,
Fin
alize
,
a
n
d
Ver
if
y
[
1
1
]
,
[
1
3
]
,
[
1
4
]
.
2
.
9
.
F
a
irness
a
nd
t
ra
ce
a
bil
it
y
a.
F
a
ir
n
ess
:
o
n
ly
th
e
tr
u
s
tee
with
ca
n
tr
ac
e
(
)
=
,
=
(
)
,
th
u
s
an
y
f
r
a
u
d
u
len
t
s
ig
n
atu
r
e
ca
n
b
e
tr
ac
ed
to
its
o
r
ig
in
.
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:
2088
-
8
7
0
8
A
n
o
n
-
in
tera
ctive
la
ttice
-
b
a
s
e
d
s
ch
eme
s
u
p
p
o
r
tin
g
m
u
ltip
le
b
lin
d
n
ess
mo
d
es
(
Din
h
Ha
i Le
)
1979
b.
R
ev
o
ca
b
ilit
y:
o
n
ly
th
e
tr
u
s
tee
ca
n
d
ec
r
y
p
t
,
en
s
u
r
in
g
a
n
o
n
y
m
ity
with
o
u
t p
r
o
p
er
au
th
o
r
ity
.
c.
N
o
n
-
fr
a
mea
b
ilit
y:
n
o
o
n
e
ca
n
p
r
o
d
u
ce
a
s
ig
n
atu
r
e
s
u
ch
t
h
at
(
)
=
′
f
o
r
′
≠
,
d
u
e
to
co
r
r
ec
t e
n
cr
y
p
tio
n
o
f
(
with
N
I
Z
K)
an
d
t
h
e
s
y
s
tem
’
s
u
n
f
o
r
g
e
ab
ilit
y
.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
3
.
1
.
G
ener
a
l sy
s
t
em
m
o
del
T
h
e
s
y
s
tem
co
n
s
is
ts
o
f
i
)
S
ig
n
er
is
s
u
in
g
s
ig
n
atu
r
es,
h
o
ld
in
g
(
,
)
;
ii
)
User
o
b
tain
in
g
an
d
u
n
b
lin
d
i
n
g
th
e
s
ig
n
at
u
r
e
u
s
in
g
s
ec
r
et/r
an
d
o
m
p
ar
am
ete
r
s
;
an
d
iii
)
Tr
u
s
tee
h
o
ld
in
g
(
,
)
,
r
es
p
o
n
s
ib
le
f
o
r
tr
ac
in
g
wh
en
n
ec
ess
ar
y
.
3
.
2
.
G
ener
a
l a
lg
o
rit
h
m
s
T
h
e
n
o
n
-
in
ter
ac
tiv
e
lattice
-
b
as
ed
b
lin
d
s
ig
n
at
u
r
e
s
y
s
tem
wo
r
k
s
as f
o
llo
ws
.
a.
S
etu
p
.
I
n
p
u
t:
s
ec
u
r
ity
p
ar
am
et
er
.
Ou
tp
u
t:
s
ig
n
e
r
k
e
y
s
(
,
)
,
tr
u
s
tee
k
ey
s
(
,
)
,
an
d
p
u
b
lic
p
ar
am
eter
s
(
lattice
d
escr
ip
tio
n
an
d
h
ash
f
u
n
ctio
n
s
).
b.
User
K
ey
Gen
(
o
p
tio
n
al)
.
I
n
p
u
t:
n
o
n
e
o
r
s
ess
io
n
s
p
ec
if
ic
r
a
n
d
o
m
n
ess
.
Ou
tp
u
t:
u
s
er
k
ey
s
(
,
)
o
r
r
an
d
o
m
s
ess
io
n
p
ar
am
eter
s
.
c.
I
s
s
u
e
.
I
n
p
u
t:
m
ess
ag
e
,
o
p
t
io
n
al
in
f
o
r
m
atio
n
in
f
o
,
p
u
b
lic
p
ar
am
eter
s
,
an
d
o
p
tio
n
al
(
,
)
.
Ou
tp
u
t:
b
lin
d
e
d
s
ig
n
atu
r
e
(
,
,
)
.
T
h
e
u
s
er
s
elec
ts
th
e
b
lin
d
n
e
s
s
m
o
d
e,
g
en
e
r
ates
,
an
d
co
m
p
u
tes
=
+
1
,
wh
er
e
1
=
1
(
in
fo
∥
)
∈
ℤ
,
th
en
s
en
d
s
(
,
in
fo
,
)
an
d
in
f
o
to
th
e
s
ig
n
er
.
T
h
e
s
ig
n
er
p
er
f
o
r
m
s
:
i)
g
e
n
er
ate
id
en
tity
en
cr
y
p
tio
n
=
E
n
c
(
;
)
,
ii)
co
m
p
u
te
2
=
2
(
)
,
iii)
s
o
lv
e
=
+
2
=
+
1
+
2
,
=
+
2
,
iv
)
u
s
e
th
e
tr
a
p
d
o
o
r
to
s
am
p
l
e
←
S
a
mp
leP
r
e
(
,
,
)
,
v
)
g
e
n
er
ate
a
ze
r
o
-
k
n
o
wled
g
e
p
r
o
o
f
to
p
r
o
v
e
th
e
v
alid
i
ty
o
f
an
d
,
an
d
v
i)
s
en
d
(
,
,
)
b
ac
k
to
t
h
e
u
s
er
.
d.
F
in
a
liz
e
.
I
n
p
u
t:
(
,
,
)
f
r
o
m
th
e
s
ig
n
er
,
s
ec
r
et
.
Ou
tp
u
t:
f
in
al
s
ig
n
atu
r
e
=
(
,
,
in
fo
,
′
)
.
T
h
e
u
s
er
v
er
if
ies
v
ia
=
?
+
2
(
)
,
an
d
if
v
alid
,
co
m
p
u
tes
=
−
,
ch
ec
k
s
th
at
=
(
−
)
=
(
+
2
)
−
=
1
+
2
,
with
1
=
1
(
in
fo
∥
)
an
d
2
=
2
(
)
,
o
p
tio
n
ally
r
e
-
en
cr
y
p
t
to
′
=
R
eR
a
n
d
(
;
′
)
to
p
r
ev
e
n
t d
ir
ec
t lin
k
ag
e.
e.
V
erif
y
.
I
n
p
u
t:
f
in
al
s
ig
n
atu
r
e
=
(
,
,
in
fo
,
′
)
an
d
p
u
b
lic
p
ar
am
ete
r
s
.
O
u
tp
u
t:
B
o
o
lean
in
d
icatin
g
v
alid
ity
.
A
th
ir
d
-
p
ar
ty
co
m
p
u
te
1
=
1
(
in
fo
∥
)
,
2
=
2
(
′
)
,
an
d
ch
e
ck
s
=
?
1
+
2
alo
n
g
with
|
|
<
,
wh
er
e
=
(
√
)
,
an
d
if
s
ati
s
f
ied
,
th
e
s
ig
n
atu
r
e
is
v
alid
.
f.
Tr
a
ce
.
I
n
p
u
t:
en
cr
y
p
ted
c
o
m
p
o
n
en
t
′
an
d
tr
u
s
tee
s
ec
r
et
k
ey
.
Ou
tp
u
t:
u
s
er
id
en
tity
an
d
o
p
tio
n
al
p
r
o
o
f
′
.
Dec
r
y
p
t
=
Dec
(
′
)
,
id
en
tify
th
e
u
s
er
f
r
o
m
,
p
r
o
v
i
d
e
p
r
o
o
f
′
if
n
ee
d
ed
,
an
d
if
f
r
au
d
is
d
etec
ted
(
two
s
ig
n
atu
r
es sh
ar
e
th
e
s
am
e
)
,
d
ec
r
y
p
t
b
o
th
′
to
c
h
ec
k
f
o
r
id
en
tical
.
T
h
e
s
y
s
te
m
e
n
s
u
r
es
n
o
n
-
i
n
t
e
r
ac
t
i
v
i
t
y
,
s
e
c
u
r
i
t
y
,
a
n
d
t
r
ac
e
a
b
i
li
ty
w
h
e
n
n
e
e
d
e
d
;
t
h
e
s
i
g
n
e
r
d
o
e
s
n
o
t
l
e
a
r
n
,
t
h
e
u
s
e
r
f
u
l
l
y
c
o
n
t
r
o
ls
u
n
b
l
i
n
d
i
n
g
a
n
d
v
e
r
i
f
i
c
a
t
i
o
n
,
a
n
d
t
h
e
t
r
u
s
t
e
e
h
o
l
d
s
t
r
a
ci
n
g
r
i
g
h
t
s
t
o
e
n
s
u
r
e
f
a
i
r
n
e
s
s
.
3
.
3
.
Alg
o
rit
hm
co
ns
t
ruct
io
n
T
h
e
m
u
lti
-
m
o
d
e
n
o
n
-
in
ter
ac
ti
v
e
b
lin
d
s
ig
n
atu
r
e
alg
o
r
ith
m
i
s
b
u
ilt
o
n
th
e
lattice
f
o
u
n
d
ati
o
n
,
clo
s
ely
f
o
llo
win
g
th
e
o
u
tlin
ed
m
o
d
el
an
d
co
n
ce
p
ts
.
Fo
r
clar
ity
,
th
e
p
ar
am
eter
s
an
d
f
u
n
ctio
n
s
u
s
ed
ar
e
s
u
m
m
ar
ized
as
f
o
llo
ws.
a.
P
a
r
a
mete
r
s
a
n
d
F
u
n
ctio
n
s
.
I
n
p
u
t:
n
o
n
e.
Ou
tp
u
t:
lattice
p
a
r
a
m
eter
s
,
h
ash
f
u
n
ctio
n
s
,
alg
o
r
ith
m
s
.
−
,
,
:
L
attice
p
ar
am
eter
s
,
f
o
r
ex
am
p
le
≈
256
o
r
512
f
o
r
1
2
8
-
b
it
s
ec
u
r
ity
,
≈
1024
,
an
d
is
a
lar
g
e
in
teg
er
.
−
1
:
{
0
,
1
}
∗
→
ℤ
: M
ess
ag
e
h
ash
f
u
n
ctio
n
.
−
2
:
{
0
,
1
}
∗
→
ℤ
: H
ash
f
u
n
ctio
n
f
o
r
t
r
ac
e
en
cr
y
p
tio
n
.
−
Tr
a
p
Gen
,
S
a
mp
leP
r
e
: A
lg
o
r
ith
m
s
f
o
r
tr
ap
d
o
o
r
g
e
n
er
atio
n
an
d
s
h
o
r
t
p
r
eim
ag
e
s
am
p
lin
g
f
o
r
m
atr
ix
.
−
E
n
c
,
Dec
:
Pu
b
lic
k
e
y
en
c
r
y
p
tio
n
s
y
s
tem
,
s
u
ch
as lattice
-
I
B
E
o
r
E
lG
am
al.
b.
S
etu
p
.
I
n
p
u
t:
s
ec
u
r
ity
p
a
r
am
e
ter
1
.
Ou
tp
u
t:
s
ig
n
er
k
ey
s
(
,
)
,
tr
u
s
tee
k
ey
s
(
,
)
,
p
u
b
lic
p
ar
am
eter
s
(
,
1
,
2
)
.
Gen
er
ate
tr
a
p
d
o
o
r
(
,
)
←
Tr
a
p
Gen
(
,
,
)
,
with
∈
ℤ
×
;
g
en
er
ate
tr
ac
i
n
g
k
ey
p
air
(
,
)
←
K
ey
Gen
E
n
c
(
1
)
;
p
u
b
lis
h
p
u
b
lic
k
ey
s
=
,
,
k
ee
p
s
ec
r
et
=
,
;
d
ef
in
e
r
a
n
d
o
m
h
ash
f
u
n
ctio
n
s
1
,
2
.
c.
I
s
s
u
e
-
R
eq
u
est
(
B
lin
d
)
.
I
n
p
u
t:
Mo
d
e
∈
{
fu
ll
-
b
lin
d
,
p
a
r
tia
l
-
b
lin
d
,
n
o
n
-
b
lin
d
}
,
ca
r
d
in
f
o
r
m
ati
o
n
in
f
o
,
m
ess
ag
e
(
if
a
n
y
)
.
Ou
tp
u
t:
b
lin
d
e
d
r
e
q
u
est
.
I
f
=
non
-
b
lin
d
th
en
s
et
=
.
Oth
er
wis
e,
ch
o
o
s
e
←
{
0
,
1
}
.
R
an
d
o
m
ly
s
elec
t
b
lin
d
in
g
v
ec
to
r
←
ℤ
,
(
B
lin
d
)
.
C
o
m
p
u
te
1
=
1
(
in
fo
∥
)
,
=
+
1
.
Sen
d
(
,
in
fo
,
)
to
th
e
s
ig
n
e
r
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
16
,
No
.
4
,
Au
g
u
s
t
20
26
:
1
9
7
6
-
1
984
1980
d.
I
s
s
u
e
-
R
esp
o
n
s
e.
I
n
p
u
t:
(
,
in
fo
,
)
,
tr
ap
d
o
o
r
,
,
u
s
er
d
ir
ec
to
r
y
.
Ou
tp
u
t:
(
,
,
)
.
Valid
ate
th
e
r
eq
u
est,
r
etr
iev
e
u
s
er
.
C
o
m
p
u
te
=
E
n
c
(
)
,
2
=
2
(
)
,
=
+
2
.
C
o
m
p
u
te
=
S
a
mp
leP
r
e
(
,
,
)
.
C
r
ea
te
p
r
o
o
f
=
N
I
ZK
p
r
o
o
f:
{
∃
,
s
u
ch
th
a
t:
=
E
n
c
(
)
,
=
+
2
(
)
s
h
o
win
g
th
at
−
2
=
an
d
=
E
n
c
(
)
.
Sen
d
(
,
,
)
to
th
e
u
s
er
.
e.
F
in
a
liz
e
(
Un
b
lin
d
)
.
I
n
p
u
t:
(
,
,
)
,
,
,
in
fo
.
Ou
tp
u
t:
f
in
al
s
ig
n
atu
r
e
=
(
,
,
in
fo
,
′
)
.
Ver
if
y
th
e
p
r
o
o
f
=
?
+
2
(
)
.
Per
f
o
r
m
Un
b
lin
d
to
o
b
tai
n
th
e
r
ea
l
s
ig
n
atu
r
e
=
−
.
Op
tio
n
ally
r
ef
r
esh
en
cr
y
p
tio
n
′
=
R
eR
a
n
d
(
)
.
Ou
tp
u
t f
in
al
s
ig
n
a
tu
r
e
=
(
,
,
in
fo
,
′
)
.
f.
V
erif
y.
I
n
p
u
t:
=
(
,
,
in
fo
,
′
)
,
.
Ou
tp
u
t:
ac
ce
p
t/re
ject.
C
o
m
p
u
te
1
=
1
(
in
fo
∥
)
,
2
=
2
(
′
)
.
Ver
if
y
=
?
1
+
2
,
|
|
≤
.
I
f
co
r
r
ec
t,
ac
ce
p
t; o
th
e
r
wis
e,
r
ejec
t.
N
o
te
th
e
mo
d
es.
N
o
n
-
b
lin
d
:
T
h
e
s
ig
n
atu
r
e
is
g
en
er
ated
d
ir
ec
tly
o
n
th
e
m
ess
ag
e
with
o
u
t
b
lin
d
in
g
,
s
o
th
e
s
ig
n
er
s
ee
s
th
e
c
o
n
ten
t.
T
h
is
m
o
d
e
is
s
im
p
le
b
u
t
o
f
f
er
s
n
o
m
ess
ag
e
p
r
iv
ac
y
.
P
a
r
tia
l
-
b
lin
d
/Fu
ll
-
b
lin
d
:
T
h
e
u
s
er
b
lin
d
s
th
e
m
ess
ag
e
b
ef
o
r
e
s
ig
n
in
g
.
I
n
p
ar
tial
b
lin
d
,
s
o
m
e
p
u
b
lic
in
f
o
r
m
atio
n
m
ay
b
e
v
is
ib
le;
in
f
u
ll
-
b
lin
d
,
th
e
en
tire
m
es
s
ag
e
is
h
id
d
en
.
Af
ter
th
e
s
ig
n
er
p
r
o
d
u
c
es
a
b
lin
d
ed
s
ig
n
atu
r
e,
th
e
u
s
er
u
n
b
lin
d
s
it
to
o
b
tain
a
v
al
id
s
ig
n
atu
r
e.
T
h
is
en
s
u
r
es
p
r
iv
ac
y
wh
ile
m
ai
n
tain
in
g
co
r
r
ec
tn
ess
an
d
v
er
if
iab
ilit
y
:
=
−
,
=
1
(
in
fo
∥
)
+
2
(
)
,
s
o
th
e
s
ig
n
er
ca
n
n
o
t
lin
k
s
ig
n
atu
r
es
to
m
ess
ag
es,
wh
ile
th
e
tr
u
s
tee
ca
n
tr
ac
e
u
s
er
s
if
n
ec
ess
ar
y
.
g.
Tr
a
ce
.
I
n
p
u
t:
=
(
,
,
in
fo
,
′
)
,
.
Ou
tp
u
t:
u
s
er
id
en
tity
an
d
p
r
o
o
f
if
n
ec
ess
ar
y
.
Dec
r
y
p
t
=
Dec
(
′
)
,
id
en
tify
th
e
u
s
er
f
r
o
m
,
p
r
o
v
id
e
p
r
o
o
f
′
if
n
ee
d
ed
,
an
d
if
f
r
au
d
is
d
etec
ted
,
d
ec
r
y
p
t
b
o
th
′
v
alu
es to
ch
ec
k
f
o
r
id
en
t
ical
.
T
h
e
s
y
s
tem
en
s
u
r
es
f
u
ll
n
o
n
-
in
ter
ac
tiv
ity
,
s
tr
o
n
g
s
ec
u
r
ity
g
u
ar
an
tees,
an
d
s
elec
tiv
e
tr
ac
ea
b
ilit
y
o
n
ly
wh
en
r
eq
u
ir
ed
.
T
h
e
s
ig
n
er
o
p
er
ates
with
o
u
t
k
n
o
wled
g
e
o
f
t
h
e
m
ess
ag
e
,
wh
ich
p
r
eser
v
es
u
s
er
p
r
iv
ac
y
an
d
p
r
ev
en
ts
an
y
leak
a
g
e
o
f
s
en
s
itiv
e
in
f
o
r
m
atio
n
d
u
r
in
g
th
e
s
i
g
n
atu
r
e
is
s
u
an
ce
p
r
o
ce
s
s
.
At
th
e
s
am
e
tim
e,
th
e
u
s
er
m
ain
tain
s
co
m
p
lete
co
n
tr
o
l
o
v
er
th
e
u
n
b
lin
d
in
g
a
n
d
v
e
r
if
icatio
n
p
r
o
ce
d
u
r
es,
allo
win
g
th
em
to
in
d
ep
en
d
en
tly
v
er
if
y
th
e
co
r
r
ec
tn
ess
o
f
s
ig
n
atu
r
es
an
d
p
r
e
v
en
t
u
n
au
th
o
r
ized
m
an
ip
u
latio
n
s
.
Mo
r
e
o
v
er
,
th
e
tr
u
s
tee
h
o
ld
s
th
e
ex
clu
s
iv
e
tr
a
cin
g
ca
p
ab
ilit
y
,
en
ab
lin
g
ac
co
u
n
tab
ilit
y
an
d
au
d
itab
ilit
y
in
ca
s
e
o
f
d
is
p
u
tes
o
r
f
r
au
d
u
le
n
t a
ctiv
ity
,
with
o
u
t c
o
m
p
r
o
m
is
in
g
th
e
c
o
n
f
id
e
n
tiality
o
f
h
o
n
est u
s
er
s
.
T
h
is
s
ep
ar
atio
n
o
f
r
o
les en
s
u
r
es
th
at
th
e
s
y
s
tem
s
im
u
ltan
eo
u
s
ly
ac
h
iev
es
p
r
iv
ac
y
,
c
o
r
r
ec
tn
ess
,
an
d
co
n
d
itio
n
al
ac
co
u
n
ta
b
ilit
y
,
p
r
o
v
i
d
in
g
a
r
o
b
u
s
t f
r
am
ewo
r
k
f
o
r
s
ec
u
r
e
a
n
d
f
air
m
u
lti
-
m
o
d
e
b
lin
d
s
ig
n
a
tu
r
es in
p
r
ac
tical
ap
p
licatio
n
s
.
3
.
4
.
P
er
f
o
r
m
a
nce
o
ptim
iz
a
t
i
o
n wit
h
ha
s
h t
re
es
in
no
n
-
i
nte
ra
ct
iv
e
bli
nd
s
ig
na
t
ures
A
k
ey
ch
allen
g
e
in
n
o
n
-
in
ter
ac
tiv
e
lattice
b
ased
b
lin
d
s
ig
n
atu
r
es
is
th
e
co
s
t
o
f
r
ep
ea
ted
r
ejec
tio
n
s
a
mp
lin
g
,
wh
ich
in
cr
ea
s
es
ab
o
r
t
p
r
o
b
a
b
ilit
y
an
d
r
ed
u
ce
s
ef
f
icien
cy
.
T
o
ad
d
r
ess
th
is
,
we
i
n
teg
r
ate
a
h
a
s
h
tr
ee
to
co
m
p
r
ess
m
u
ltip
le
co
m
m
itm
en
ts
in
to
a
s
in
g
le
r
o
o
t
an
d
r
ev
ea
l
o
n
ly
th
e
n
ec
ess
ar
y
p
a
r
ts
d
u
r
i
n
g
v
er
if
icatio
n
,
f
o
llo
win
g
id
ea
s
f
r
o
m
[
3
0
]
a
n
d
alig
n
in
g
with
c
o
m
m
itm
en
t
h
id
in
g
ap
p
r
o
ac
h
es
in
[
2
5
]
,
[
3
1
]
.
Sp
ec
if
ically
,
co
m
m
itm
en
ts
1
,
…
,
ar
e
o
r
g
an
ized
in
to
a
b
in
ar
y
h
ash
tr
ee
,
en
ab
lin
g
s
h
o
r
t
au
th
e
n
ticatio
n
p
ath
s
an
d
co
n
s
is
ten
cy
v
er
if
icatio
n
with
t
h
e
p
u
b
lis
h
ed
r
o
o
t.
T
o
m
an
a
g
e
in
d
ex
in
g
,
we
u
s
e
th
e
m
ap
p
i
n
g
2
I
n
t
,
,
(
,
,
)
=
+
(
−
1
)
+
(
−
1
)
,
wh
ich
p
r
o
v
id
es
a
u
n
if
ie
d
en
co
d
in
g
o
f
p
o
s
itio
n
s
in
th
e
tr
ee
.
T
h
is
r
ed
u
ce
s
ab
o
r
t
p
r
o
b
a
b
ilit
y
,
av
o
id
s
r
ev
ea
lin
g
r
ejec
ted
b
r
an
ch
es,
an
d
is
s
u
itab
le
f
o
r
o
n
e
-
r
o
u
n
d
d
esig
n
s
.
Fro
m
a
s
ec
u
r
ity
p
er
s
p
ec
tiv
e,
h
ash
t
r
ee
s
h
elp
p
r
ev
e
n
t
r
eu
s
e/lin
k
ab
ilit
y
o
f
co
m
m
itm
en
ts
;
lim
itatio
n
s
r
eg
ar
d
in
g
o
n
e
mo
r
e
u
n
fo
r
g
ea
b
ilit
y
h
a
v
e
b
ee
n
n
o
te
d
in
[
3
1
]
,
wh
ile
[
2
5
]
s
h
o
ws
th
at
co
r
r
ec
tn
ess
an
d
b
lin
d
n
ess
ar
e
p
r
eser
v
ed
u
n
d
er
m
u
lti
r
o
u
n
d
s
am
p
lin
g
.
Ou
r
e
x
ten
s
io
n
ap
p
lies
th
is
m
ec
h
a
n
is
m
to
m
u
lti
-
m
o
d
e
NI
B
S
to
im
p
r
o
v
e
ef
f
icien
c
y
wh
ile
m
ain
tain
in
g
p
o
s
t
-
q
u
an
t
u
m
s
ec
u
r
ity
.
Alg
o
r
ith
m
1
.
Ha
s
h
Tr
ee
(
0
,
…
,
−
1
)
1
.
ℎ
←
⌈
(
)
⌉
2
.
←
∅
3
.
f
o
r
∈
{
0
,
…
,
−
1
}
:
0
,
←
(
)
4
.
f
o
r
∈
{
,
…
,
2
ℎ
−
1
}
:
0
,
←
(
)
5
.
f
o
r
=
1
t
o
ℎ
:
f
o
r
=
0
t
o
2
ℎ
−
−
1
:
,
←
(
−
1
,
2
,
−
1
,
2
+
1
)
6
.
←
ℎ
,
0
;
ret
u
rn
(
,
)
Alg
o
r
ith
m
2
.
B
u
ild
A
u
th
(
,
,
ℎ
)
1
.
Ex
t
ra
c
t
(
0
,
0
,
…
,
ℎ
,
2
ℎ
−
−
1
)
f
r
o
m
t
h
e
t
ree
2
.
f
o
r
=
0
t
o
ℎ
−
1
:
←
⌊
/
2
⌋
;
←
2
if
=
1
:
←
,
−
1
;
e
l
s
e
←
,
+
1
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
A
n
o
n
-
in
tera
ctive
la
ttice
-
b
a
s
e
d
s
ch
eme
s
u
p
p
o
r
tin
g
m
u
ltip
le
b
lin
d
n
ess
mo
d
es
(
Din
h
Ha
i Le
)
1981
3
.
←
(
,
0
,
…
,
ℎ
−
1
)
4
.
r
e
t
u
rn
Alg
o
r
ith
m
3
.
R
o
o
tC
a
lc
(
,
)
Pa
rse
i
n
t
o
(
,
0
,
…
,
ℎ
−
1
)
;
set
0
←
(
)
;
f
o
r
=
1
t
o
ℎ
:
se
t
←
⌊
/
2
−
1
⌋
,
←
2
;
if
=
1
,
set
←
(
−
1
,
−
1
)
,
o
t
h
e
r
w
i
s
e
s
e
t
←
(
−
1
,
−
1
)
;
set
←
ℎ
a
n
d
r
e
t
u
rn
.
3
.
5
.
Securit
y
a
na
ly
s
is
W
e
s
eq
u
en
tially
ex
am
in
e
th
e
s
ec
u
r
ity
p
r
o
p
er
ties
an
d
s
k
etch
p
r
o
o
f
s
f
o
r
ea
ch
p
r
o
p
er
ty
,
b
ased
o
n
th
e
u
n
d
er
ly
i
n
g
ass
u
m
p
tio
n
s
s
tated
ea
r
lier
.
3
.
5
.
1
.
Co
rr
ec
t
nes
s
Gam
e
:
a.
T
h
e
s
ig
n
er
r
u
n
s
I
s
s
u
e
-
R
esp
o
n
s
e
an
d
o
u
t
p
u
ts
(
,
)
s
u
ch
th
at
=
+
2
(
)
.
b.
T
h
e
u
s
er
co
m
p
u
tes
=
−
an
d
ch
ec
k
s
=
?
1
(
in
fo
∥
)
+
2
(
)
,
∥
∥
≤
.
c.
Ou
tp
u
t
1
/
0
.
−
A
n
a
lysi
s
:
=
+
1
(
in
fo
∥
)
+
2
(
)
⇒
=
(
−
)
=
1
(
in
fo
∥
)
+
2
(
)
.
−
N
o
r
m
b
o
u
n
d
:
∥
∥
≤
(
√
)
,
∥
∥
≤
(
′
√
)
;
∥
∥
≤
∥
∥
+
∥
∥
≤
(
(
+
′
)
√
)
≈
(
√
)
−
C
o
n
clu
s
io
n
:
[
=
0
]
≤
(
)
.
−
Gam
e
:
m
ak
es
p
o
l
y
n
o
m
i
ally
m
an
y
s
ig
n
i
n
g
q
u
er
ies
an
d
o
u
tp
u
ts
a
n
ew
v
alid
∗
=
(
∗
,
∗
,
in
f
o
∗
,
∗
)
.
−
C
a
s
e
(
i)
:
∗
=
1
(
in
fo
∗
∥
∗
)
+
2
(
∗
)
im
p
lies
f
in
d
in
g
a
s
h
o
r
t
s
o
lu
tio
n
∗
to
a
r
an
d
o
m
s
y
n
d
r
o
m
e,
wh
ich
r
ed
u
ce
s
to
th
e
SIS
p
r
o
b
lem
.
−
C
a
s
e
(
ii):
2
(
∗
)
=
2
(
)
(
co
llis
io
n
)
or
(
′
−
)
=
0
im
p
lies
f
in
d
in
g
∈
with
s
m
all
∥
∥
,
wh
ich
r
ed
u
ce
s
to
SIS.
−
C
o
n
clu
s
io
n
:
[
=
1
]
≤
(
)
.
3
.
5
.
2
.
O
ne
mo
re
un
f
o
rg
ea
bil
it
y
pro
o
f
Gam
e
:
in
ter
ac
ts
in
at
m
o
s
t
ℓ
s
ess
io
n
s
b
u
t o
u
tp
u
ts
ℓ
+
1
v
alid
s
ig
n
atu
r
es.
a.
R
ed
u
ctio
n
to
o
n
e
mo
r
e
I
S
I
S
:
ℬ
r
ec
eiv
es
an
d
ac
ce
s
s
es
an
o
r
ac
le
th
at
i
)
s
am
p
les
r
an
d
o
m
an
d
ii
)
r
etu
r
n
s
s
u
ch
th
at
=
.
b.
S
ig
n
in
g
s
imu
la
tio
n
:
i
)
r
ec
eiv
e
;
ii
)
ch
o
o
s
e
,
co
m
p
u
te
=
E
n
c
(
)
,
2
=
2
(
)
;
iii
)
s
et
=
+
2
,
q
u
er
y
(
b
)
to
o
b
tain
with
=
;
(
4
)
r
etu
r
n
(
,
)
.
c.
Ou
tp
u
t o
f
:
=
(
,
,
in
fo
,
)
,
=
1
,
…
,
ℓ
+
1
;
=
1
(
in
fo
∥
)
+
2
(
)
.
d.
E
xtra
ctin
g
a
n
ew
s
o
lu
tio
n
:
th
er
e
ex
is
ts
∗
n
o
t
q
u
er
ied
,
∗
=
1
(
in
fo
∗
∥
∗
)
+
2
(
∗
)
,
∗
=
∗
.
T
h
u
s
(
∗
,
∗
)
s
o
lv
es o
n
e
m
o
r
e
I
SIS
with
o
u
t
q
u
er
y
i
n
g
(
b
)
o
n
∗
.
e.
C
o
n
clu
s
io
n
:
[
=
1
]
≤
(
)
.
3
.
5
.
3
.
B
lin
dn
e
s
s
a
nd
pa
rt
ia
l
bli
nd
nes
s
Gam
e
:
a.
ch
o
o
s
es
(
0
,
in
fo
0
)
,
(
1
,
in
fo
1
)
;
b.
S
am
p
le
←
{
0
,
1
}
;
0
r
u
n
s
with
(
,
in
fo
)
,
1
with
(
1
−
,
in
fo
1
−
)
;
c.
r
ec
eiv
es
,
=
+
1
(
in
fo
∥
)
,
∈
{
0
,
1
}
;
d.
C
o
m
p
u
te
=
E
n
c
(
)
,
=
,
+
2
(
)
,
=
S
a
mp
leP
r
e
(
,
,
)
;
e.
O
u
tp
u
t
′
.
−
A
n
a
lysi
s
:
|
[
′
=
]
−
1
2
⁄
|
>
;
,
=
+
1
(
in
fo
∥
)
,
−
2
(
)
=
,
.
Sin
ce
1
is
r
an
d
o
m
a
n
d
is
h
id
d
en
,
,
is
in
d
ep
en
d
en
t o
f
f
r
o
m
’
s
v
iew.
−
P
a
r
tia
l
-
b
lin
d
:
if
in
fo
0
=
in
fo
1
:
1
(
in
fo
∥
0
)
≈
1
(
in
fo
∥
1
)
im
p
lies
th
at
d
is
tin
g
u
is
h
in
g
r
eq
u
i
r
es
in
v
er
tin
g
1
.
−
C
o
n
clu
s
io
n
:
|
[
′
=
]
−
1
2
⁄
|
≤
(
)
.
3
.
5
.
4
.
F
a
irness
a
nd
t
ra
ce
a
bil
it
y
pro
o
f
Gam
e
:
a.
r
ec
eiv
es
=
,
;
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
16
,
No
.
4
,
Au
g
u
s
t
20
26
:
1
9
7
6
-
1
984
1982
b.
Q
u
er
ies th
e
s
ig
n
in
g
o
r
ac
le;
an
d
c.
O
u
tp
u
ts
∗
=
(
∗
,
∗
,
in
fo
∗
,
∗
)
s
u
ch
th
at
V
erif
y
(
∗
)
=
1
b
u
t
Dec
(
∗
)
=
′
≠
.
−
A
n
a
lysi
s
:
i)
E
n
cr
y
p
ti
o
n
i
n
co
n
s
is
ten
cy
:
∗
=
E
n
c
(
)
is
b
o
u
n
d
b
y
p
r
o
o
f
,
s
o
it
ca
n
n
o
t
b
e
f
o
r
g
e
d
with
o
u
t
k
n
o
win
g
.
ii)
Sig
n
atu
r
e
f
o
r
g
e
r
y
:
=
+
2
(
)
im
p
lies
th
at
with
o
u
t
,
o
n
e
m
u
s
t
s
o
lv
e
SIS
o
r
b
r
ea
k
E
n
c
.
−
Do
u
b
le
-
s
p
en
d
i
n
g
:
1
=
(
1
,
,
in
fo
,
1
)
,
2
=
(
2
,
,
in
fo
,
2
)
;
(
1
−
2
)
=
2
(
1
)
−
2
(
2
)
.
−
If
1
≠
2
,
th
en
=
1
−
2
is
an
SIS
s
o
lu
tio
n
.
−
C
o
n
clu
s
io
n
:
[
=
1
]
≤
(
)
.
3
.
6
.
P
a
ra
m
et
er
dis
cus
s
io
n a
nd
perf
o
rm
a
nce
3
.
6
.
1
.
Size
estim
a
t
io
n
All
f
ig
u
r
es
ar
e
esti
m
ates
u
n
d
er
ex
.
W
ith
=
1024
,
=
12289
:
|
|
r
aw
≈
⋅
⌈
l
og
2
⌉
=
1024
⋅
14
=
14336
b
its
≈
1
.
75
KB
.
−
Sig
n
atu
r
e
s
ize:
|
|
≈
|
|
+
|
|
+
|
|
+
|
|
+
|
|
;
|
|
∈
[
1
.
0
,
1
.
5
]
KB
,
|
|
∈
[
1
.
5
,
3
.
0
]
KB
;
|
|
∈
[
4
.
25
,
6
.
25
]
KB
.
−
Pu
b
lic
k
ey
s
ize:
|
|
≈
⋅
⋅
⌈
2
⌉
=
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[
1
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.
C
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[
2
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.
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3
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M
.
F
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[
4
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3
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3
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p
p
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7
2
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–
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2
.
[
5
]
L.
H
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P
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5
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–
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9
4
.
[
6
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.
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.
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[
7
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C
.
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2
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.
[
8
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B
.
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2
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.
[
9
]
S
.
A
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.
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