I
nte
rna
t
io
na
l J
o
urna
l o
f
E
lect
rica
l a
nd
Co
m
p
ute
r
E
ng
in
ee
ring
(
I
J
E
CE
)
Vo
l.
9
,
No
.
4
,
A
u
g
u
s
t
201
9
,
p
p
.
3
2
2
8
~
3
2
3
1
I
SS
N:
2088
-
8708
,
DOI
: 1
0
.
1
1
5
9
1
/
i
j
ec
e
.
v
9
i
4
.
pp
3
2
2
8
-
3231
3228
J
o
ur
na
l ho
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ep
a
g
e
:
h
ttp
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p
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ba
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l
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Dha
na
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hree
T
o
ra
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a
lle
1
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J
a
y
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bh
a
s
k
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uthu
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.
Sa
t
hy
a
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na
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1
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p
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KL
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In
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ia
3
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p
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IT
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h
n
a
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I
nfo
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T
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r
ticle
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J
ul
26
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2
0
1
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ev
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ed
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2
2
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2
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cc
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p
r
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Av
a
il
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a
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re
p
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it
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se
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s.
Dig
it
a
l
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ig
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tu
re
s
p
lay
a
p
iv
o
tal
ro
le
i
n
A
u
th
e
n
ti
c
a
ti
o
n
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h
e
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h
e
lp
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rify
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th
e
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teg
rit
y
o
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t
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h
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li
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stro
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g
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c
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in
Dig
it
a
l
S
ig
n
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s,
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d
m
u
c
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m
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h
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p
a
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s
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li
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Dig
it
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l
S
ig
n
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A
lg
o
rit
h
m
w
h
ich
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a
n
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m
p
ro
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d
a
n
d
se
c
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re
d
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e
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o
f
th
e
Dig
it
a
l
S
ig
n
a
t
u
re
Alg
o
rit
h
m
.
K
ey
w
o
r
d
s
:
Dig
ital
s
i
g
n
at
u
r
e
E
llip
tic
cu
r
v
e
E
llip
tic
cu
r
v
e
d
i
g
ital si
g
n
at
u
r
e
alg
o
r
ith
m
Fo
r
w
ar
d
s
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ec
y
Co
p
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rig
h
t
©
2
0
1
9
In
stit
u
te o
f
A
d
v
a
n
c
e
d
E
n
g
i
n
e
e
rin
g
a
n
d
S
c
ien
c
e
.
Al
l
rig
h
ts re
se
rv
e
d
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Dh
a
n
as
h
r
ee
K
T
o
r
a
d
m
alle
,
De
p
a
rtme
n
t
o
f
CS
E,
Ko
n
e
ru
L
a
k
sh
m
a
iah
Ed
u
c
a
ti
o
n
F
o
u
n
d
a
ti
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(
KL
EF
)
,
V
a
d
d
e
sw
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a
m
,
A
n
d
h
ra
P
ra
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sh
5
2
2
5
0
2
,
I
n
d
ia
.
E
m
ail:
d
h
a
n
as
h
r
ee
.
k
t@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
A
d
i
g
ital
s
ig
n
at
u
r
e
[
1
]
is
a
tech
n
iq
u
e
b
y
w
h
ic
h
th
e
Sen
d
er
ca
n
s
i
g
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a
n
elec
tr
o
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ep
o
r
t
f
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th
e
Ver
if
ier
to
k
ee
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as
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co
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m
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at
th
e
m
ess
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g
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to
b
e
s
u
r
e
s
en
t
in
itiall
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r
o
m
th
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Se
n
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er
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h
e
Natio
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al
I
n
s
tit
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te
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Sta
n
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ar
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an
d
T
ec
h
n
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lo
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y
(
NI
ST
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h
a
v
e
p
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p
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s
ed
Dig
ital
Si
g
n
atu
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e
s
as
s
ta
n
d
ar
d
s
w
h
ic
h
ar
e
w
o
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ld
l
y
ac
ce
p
ted
.
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h
e
p
r
i
m
ar
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c
h
o
ices a
v
ailab
le
f
o
r
p
u
b
lic
k
e
y
s
y
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te
m
s
ar
e:
-
R
S
A
-
Dif
f
ie
-
Hell
m
a
n
(
DH)
o
r
Dig
it
al
Sig
n
at
u
r
e
Alg
o
r
it
h
m
-
E
llip
tic
C
u
r
v
e
Di
g
ital Si
g
n
at
u
r
e
A
l
g
o
r
ith
m
R
S
A
is
a
f
r
a
m
e
w
o
r
k
t
h
at
w
a
s
d
is
tr
ib
u
ted
i
n
1
9
7
8
b
y
R
iv
e
s
t,
S
h
a
m
ir
,
a
n
d
A
d
le
m
an
,
b
a
s
ed
o
n
t
h
e
d
if
f
ic
u
lt
y
o
f
f
ac
to
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in
g
lar
g
e
in
teg
er
s
.
W
h
itfie
ld
Dif
f
ie
f
u
r
t
h
er
m
o
r
e,
Ma
r
tin
Hell
m
an
p
r
o
p
o
s
ed
th
e
g
en
er
al
p
o
p
u
latio
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k
e
y
f
r
a
m
e
w
o
r
k
p
r
esen
tl
y
ca
l
led
Di
f
f
ie
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ll
m
a
n
Ke
y
E
x
c
h
an
g
e
i
n
1
9
7
6
.
DH
an
d
DS
A
w
o
r
k
f
o
r
k
e
y
a
g
r
ee
m
e
n
t
a
n
d
Di
g
ital
s
i
g
n
at
u
r
e
r
esp
ec
ti
v
el
y
a
n
d
ca
n
b
e
co
n
s
o
lid
ate
d
to
d
o
v
er
if
ied
k
e
y
a
g
r
ee
m
e
n
t.
T
h
ey
ar
e
b
ased
o
n
t
h
e
d
i
f
f
ic
u
lt
y
o
f
s
o
l
v
in
g
th
e
d
is
cr
ete
l
o
g
ar
ith
m
p
r
o
b
le
m
i
n
th
e
m
u
l
tip
licativ
e
g
r
o
u
p
o
f
in
te
g
er
s
m
o
d
u
lo
a
p
r
i
m
e
p
.
I
n
1
9
8
5
ellip
tic
cu
r
v
e
g
r
o
u
p
s
w
er
e
p
r
esen
ted
b
y
Nea
l
an
d
Ko
b
litz
as
an
alter
n
ate
f
o
r
m
u
ltip
licati
v
e
g
r
o
u
p
s
m
o
d
u
lo
p
.
E
llip
tic
cu
r
v
e
b
ased
d
ig
ital
s
i
g
n
at
u
r
es
o
v
er
ca
m
e
all
t
h
e
d
r
aw
b
ac
k
s
o
f
its
p
r
ed
ec
ess
o
r
s
w
it
h
s
m
aller
k
e
y
s
ize
t
h
u
s
en
ter
i
n
g
th
e
f
o
r
ay
o
f
ap
p
licatio
n
s
w
i
th
r
eso
u
r
ce
co
n
s
tr
ain
t
s
.
[
2
].
T
h
e
m
aj
o
r
ar
ea
s
o
f
I
o
T
ap
p
l
icatio
n
s
[
3
]
f
ac
e
ch
alle
n
g
es
f
o
r
r
eso
u
r
ce
co
n
s
tr
ain
ed
ap
p
licatio
n
s
w
h
ic
h
w
ill
s
u
r
el
y
b
en
e
f
it
f
r
o
m
t
h
e
E
C
DS
A
b
ased
I
o
T
ap
p
licatio
n
s
in
te
r
m
s
o
f
s
ec
u
r
it
y
.
T
h
e
w
ir
eless
s
en
s
o
r
n
et
w
o
r
k
s
ar
e
an
o
th
er
d
o
m
ai
n
w
h
er
e
E
C
C
b
ased
ap
p
licatio
n
s
ar
e
in
v
o
g
u
e
[
4
]
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
-
8708
C
erti
f
ica
teless
a
n
d
p
r
o
va
b
ly
-
s
ec
u
r
e
d
ig
ita
l sig
n
a
tu
r
e
s
ch
em
e
…
(
Dh
a
n
a
s
h
r
ee
K
To
r
a
d
ma
lle
)
3229
E
llip
tical
C
u
r
v
e
C
r
y
p
to
g
r
ap
h
y
[
E
C
C
]
o
p
ti
m
izes
en
cr
y
p
tio
n
a
n
d
d
ec
r
y
p
tio
n
p
r
o
ce
s
s
es
o
f
s
e
v
er
a
l
m
et
h
o
d
s
.
T
h
e
p
r
o
ce
d
u
r
e
o
f
E
C
C
co
m
p
r
i
s
es o
f
f
o
llo
w
in
g
p
h
ases
[
5
]
:
-
Dete
r
m
i
n
i
n
g
t
h
e
p
r
i
m
e
p
o
in
t
s
o
n
th
e
ellip
ti
c
c
u
r
v
e
-
Fo
r
m
in
g
t
h
e
p
u
b
lic
an
d
p
r
iv
at
e
k
e
y
-
E
n
co
d
in
g
-
E
n
cr
y
p
tio
n
-
Dec
r
y
p
tio
n
-
Dec
o
d
in
g
Var
io
u
s
a
u
th
o
r
s
h
a
v
e
r
ep
r
esen
ted
th
e
e
l
lip
tical
c
u
r
v
e
d
ig
i
tal
s
i
g
n
at
u
r
e
al
g
o
r
ith
m
(
E
C
D
S
A
)
w
it
h
r
elatin
g
eq
u
atio
n
s
i
n
t
h
eir
lite
r
atu
r
e
[
6
-
8
]
.
T
h
ey
u
s
e
t
h
eir
o
w
n
co
n
v
en
tio
n
s
to
p
r
esen
t
t
h
e
E
C
DS
A
s
ch
e
m
e.
Ho
w
e
v
er
,
p
r
i
m
ar
il
y
E
C
DS
A
n
ee
d
s
th
e
ac
co
m
p
an
y
i
n
g
s
i
g
n
i
f
i
ca
n
t c
alcu
latio
n
s
:
-
Gen
er
atio
n
o
f
a
k
e
y
co
m
b
in
e
(
p
r
iv
ate
k
e
y
,
p
u
b
lic
k
e
y
)
,
-
T
h
e
ca
lcu
latio
n
o
f
a
s
i
g
n
at
u
r
e,
-
An
d
,
th
e
co
n
f
ir
m
atio
n
o
f
th
e
s
ig
n
a
tu
re
T
h
er
e
ar
e
m
an
y
ad
v
a
n
ta
g
es o
f
E
C
DS
A
o
v
er
it
s
p
r
ed
ec
ess
o
r
s
[
9
]
:
-
Mo
r
e
Secu
r
e
-
L
o
w
co
m
p
u
tatio
n
r
eso
u
r
ce
s
-
S
m
all
k
e
y
s
izes
I
n
r
ea
l
-
ti
m
e
t
h
r
ee
ca
s
es o
cc
u
r
m
o
s
t o
r
d
in
ar
il
y
in
s
id
e
th
e
m
et
h
o
d
o
f
co
m
m
u
n
icatio
n
:
-
Me
s
s
a
g
e
h
a
s
b
ee
n
ta
m
p
er
ed
.
-
T
h
e
s
en
d
er
d
en
ies
ca
u
s
in
g
t
h
e
m
es
s
ag
e.
-
T
h
e
r
ec
eiv
er
f
au
x
th
e
m
es
s
ag
e
E
C
DS
A
t
h
o
u
g
h
i
s
th
e
m
o
s
t
g
r
o
u
n
d
b
r
ea
k
in
g
o
f
a
ll
t
h
e
as
y
m
m
etr
ic
d
ig
ital
s
ig
n
at
u
r
e
s
tr
ateg
ie
s
,
s
p
ec
ialis
t
s
ar
e
p
u
tti
n
g
ev
er
y
o
n
e
o
f
t
h
eir
e
n
d
ea
v
o
u
r
s
to
m
a
k
e
i
t
m
o
r
e
g
r
o
u
n
d
ed
to
w
it
h
s
ta
n
d
d
if
f
er
e
n
t
d
if
f
ic
u
lt
ies.
Scie
n
ti
s
ts
h
av
e
al
s
o
p
r
o
p
o
s
ed
E
llip
tic
cu
r
v
e
Dig
ital
s
i
g
n
at
u
r
e
s
ch
e
m
e
b
ased
o
n
ce
r
tif
icate
s
[
1
0
]
.
T
h
e
f
o
llo
w
i
n
g
ar
e
t
h
e
p
ar
a
m
et
er
s
to
s
tr
en
g
t
h
e
n
th
e
E
C
DS
A
w
h
er
e
r
esear
ch
is
g
o
in
g
o
n
:
-
Fo
r
w
ar
d
Secr
ec
y
[
1
1
-
1
2
]
:
Dig
ital
Sig
n
at
u
r
es
e
m
p
o
w
er
t
h
e
Si
g
n
er
to
en
s
u
r
e
th
e
s
ec
u
r
i
t
y
o
f
m
ess
a
g
e
s
m
ar
k
ed
in
th
e
p
ast
r
eg
ar
d
less
o
f
w
h
et
h
er
h
is
m
y
s
t
er
y
k
e
y
is
u
n
co
v
er
ed
to
d
ay
.
-
A
ttac
k
s
o
n
Sec
u
r
it
y
:
Var
io
u
s
attac
k
s
li
k
e
f
o
r
g
er
y
attac
k
[
1
3
]
,
r
ep
lay
a
ttack
[
1
4
]
,
m
an
in
th
e
m
id
d
le
attac
k
p
o
s
e
a
d
an
g
er
to
s
ec
u
r
it
y
.
A
ttac
k
s
b
r
ea
k
t
h
e
s
ec
u
r
it
y
a
n
d
n
o
n
-
r
ep
u
d
iatio
n
a
ttrib
u
tes
o
f
t
h
e
E
C
DS
A
.
X
ian
m
i
n
W
ei
et
al
[
1
5
]
,
s
tates
i
m
p
r
o
v
e
m
e
n
ts
in
E
C
C
b
u
t
f
ail
s
to
ca
p
t
u
r
e
t
h
e
s
ec
u
r
it
y
asp
ec
ts
i
n
attac
k
s
b
y
j
u
s
t
f
o
c
u
s
i
n
g
o
n
th
e
m
o
d
u
lar
o
p
er
atio
n
s
.
Nee
tes
h
Sax
e
n
a
et
al
[
9
]
p
r
o
p
o
s
es
v
a
r
i
an
ts
to
E
C
DS
A
w
h
ic
h
f
o
cu
s
o
n
ef
f
icie
n
c
y
a
g
ai
n
,
u
n
d
er
esti
m
at
in
g
t
h
e
attac
k
s
o
n
s
ec
u
r
it
y
.
J
ie
L
iu
a
n
d
J
ian
h
u
a
L
i
[
1
6
]
ex
h
ib
its
a
cr
y
p
ta
n
al
y
s
i
s
o
f
C
h
an
g
et
al
'
s
.
Dig
ital
s
ig
n
at
u
r
e
s
ch
e
m
e,
w
h
i
ch
w
as
p
r
o
f
ess
ed
to
o
p
p
o
s
e
f
o
r
g
er
y
attac
k
s
w
ith
o
u
t
u
t
ilizi
n
g
an
y
o
n
e
w
a
y
h
as
h
ca
p
ac
it
y
o
r
p
ad
d
in
g
an
y
r
ed
u
n
d
an
c
y
.
F
u
r
th
er
t
h
e
y
also
p
r
o
p
o
s
e
i
m
p
r
o
v
ed
s
i
g
n
at
u
r
e
p
lan
s
,
in
w
h
ich
th
e
le
n
g
t
h
o
f
th
e
d
ig
ita
l
s
ig
n
at
u
r
e
is
a
lo
t
s
h
o
r
ter
.
L
ei
Niu
[
1
7
]
p
r
esen
ts
p
r
o
g
r
ess
i
v
el
y
f
o
r
g
er
y
attac
k
s
to
tell
u
n
m
i
s
ta
k
ab
l
y
t
h
e
b
es
t
w
a
y
to
o
b
tai
n
t
h
e
attac
k
s
.
J
ian
h
o
n
g
Z
h
an
g
a
n
d
S
h
e
n
g
n
a
n
Gao
[
18]
b
r
ea
k
d
o
w
n
t
h
e
b
lin
d
s
i
g
n
a
tu
r
es
a
n
d
d
e
m
o
n
s
t
r
ate
th
at
t
h
e
y
ar
e
d
ef
i
n
itel
y
n
o
t
s
ec
u
r
e;
f
i
n
all
y
g
iv
i
n
g
a
s
o
l
u
tio
n
f
o
r
t
h
e
s
a
m
e.
Xin
g
h
u
a
Z
h
an
g
[
1
9
]
d
is
cu
s
s
e
s
an
en
h
a
n
ce
d
tech
n
iq
u
e
to
o
v
er
co
m
e
f
o
r
g
er
y
attac
k
s
.
L
o
n
g
Z
h
ao
h
u
a
et
al
[
2
0
]
r
estrict
th
e
“
Ma
n
-
in
-
th
e
-
Mid
d
le
”
attac
k
s
b
u
t
r
eq
u
ir
es
th
r
ee
e
n
titi
e
s
p
ar
ticip
atin
g
i
n
id
en
tific
atio
n
au
th
e
n
tica
tio
n
p
r
o
ce
s
s
in
t
h
e
w
ir
ele
s
s
n
e
t
w
o
r
k
,
s
u
ch
as
Sta
t
io
n
(
ST
A
)
,
A
cc
es
s
P
o
in
t
(
A
P
)
,
an
d
Au
th
e
n
ticat
io
n
Ser
v
er
(
AS)
w
h
ic
h
is
a
n
o
v
er
h
ea
d
to
th
e
ap
p
licatio
n
.
2.
P
RO
P
O
SE
D
AL
G
O
R
I
T
H
M
T
h
e
Mid
d
le
Ma
n
o
r
in
tr
u
d
er
c
an
w
it
h
o
u
t
a
lo
t
o
f
s
tr
etch
m
o
d
if
y
or
s
u
p
er
v
en
e
u
p
o
n
t
h
e
m
ess
a
g
e
th
at
ca
n
'
t
b
e
p
er
ce
iv
ed
b
y
th
e
r
ec
eiv
er
,
b
y
m
er
el
y
ad
j
u
s
t
in
g
th
e
h
ash
v
al
u
e
R
esear
c
h
er
s
ar
e
ac
tin
g
o
n
th
e
o
n
to
p
of
p
r
o
b
lem
s
k
ee
p
in
g
in
m
in
d
t
h
e
n
ec
es
s
ities
o
f
E
C
DS
A
t
h
at
ar
e
s
m
a
ller
k
e
y
s
ize
an
d
h
i
g
h
s
ec
u
r
it
y
.
T
h
e
a
f
o
r
e
m
en
tio
n
ed
J
h
o
n
g
’
s
s
c
h
e
m
e
[
2
1
]
tr
ies
to
attain
p
o
ten
c
y
b
y
r
ed
u
cin
g
th
e
r
eser
v
e
s
ta
n
d
ar
d
in
v
er
s
e
o
p
er
atio
n
s
h
o
w
ev
er
it
f
ai
ls
to
attai
n
s
ec
u
r
it
y
;
b
ec
au
s
e
t
h
e
i
n
tr
u
d
er
w
ill
s
i
m
p
l
y
alter
t
h
e
m
es
s
ag
e
an
d
r
ep
lace
th
e
p
r
esen
t
m
es
s
ag
e
h
a
s
h
v
a
lu
e
w
it
h
c
h
a
n
g
ed
h
as
h
v
al
u
e
a
n
d
t
h
er
eb
y
it
f
ail
s
to
attai
n
s
ec
u
r
it
y
attr
ib
u
tes
o
f
a
d
ig
ita
l
s
ig
n
at
u
r
e
s
ch
e
m
e.
D
h
an
a
s
h
r
e
e
K
T
o
r
ad
m
alle
et
al
[
2
2
]
g
iv
es
a
p
o
in
t
b
y
p
o
in
t
c
r
y
p
ta
n
a
l
y
s
i
s
o
f
t
h
e
J
h
o
n
g
'
s
p
lan
an
d
s
h
o
w
s
h
o
w
J
h
o
n
g
's
t
ec
h
n
iq
u
e
is
i
n
cli
n
ed
to
m
a
n
in
th
e
ce
n
ter
as
s
a
u
lt
W
e
alo
n
g
t
h
ese
li
n
es
p
r
o
p
o
s
e
a
p
lan
w
h
ich
g
u
ar
an
tee
s
t
h
at
t
h
e
Fo
r
w
ar
d
Secr
ec
y
a
n
d
I
n
tr
u
d
er
ass
a
u
lts
ca
n
b
e
ta
k
e
n
c
ar
e
o
f
an
d
en
s
u
r
e
a
p
o
w
er
f
u
l
E
C
D
S
A
.
T
h
e
p
r
o
p
o
s
ed
A
l
g
o
r
ith
m
is
s
tated
as f
o
llo
w
s
:
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.
9
,
No
.
4
,
A
u
g
u
s
t
201
9
:
3
2
2
8
-
3
2
3
1
3230
2
.
1
.
K
ey
g
ener
a
t
io
n
Usi
n
g
g
en
er
ati
n
g
p
o
in
t G
an
d
r
an
d
o
m
in
te
g
er
n
u
m
b
er
r
th
e
p
u
b
lic
k
e
y
K
is
co
m
p
u
ted
as
f
o
llo
w
s
:
a.
C
h
o
o
s
e
a
r
an
d
o
m
i
n
te
g
er
n
u
m
b
er
r
in
in
ter
v
al
[
0
,
n
-
1
]
.
b.
C
o
m
p
u
te
K
=
r
*
G
c.
T
h
e
k
e
y
-
p
air
co
m
b
i
n
atio
n
is
(
r
,
K)
w
h
er
e
r
is
t
h
e
P
r
iv
ate
Ke
y
an
d
K
is
th
e
P
u
b
lic
k
e
y
.
2
.
2
.
Sig
na
t
ure
g
ener
a
t
io
n
T
o
s
ig
n
o
n
m
e
s
s
a
g
e
m
u
tili
zi
n
g
t
h
e
d
o
m
a
in
p
ar
a
m
eter
an
d
P
r
iv
ate
k
e
y
th
e
ac
co
m
p
a
n
y
in
g
ad
v
an
ce
s
ar
e
p
er
f
o
r
m
ed
b
y
th
e
Sig
n
er
:
a.
Selects a
r
an
d
o
m
i
n
te
g
er
p
(
s
ec
r
et
k
e
y
)
w
it
h
1
≤
p
≤
n
−1
.
b.
Dete
r
m
i
n
e
th
e
v
al
u
e
o
f
z
=
H(
m
)
c.
Dete
r
m
i
n
e
f
=
(
(
z
+
p
)
(p
+
r
))
d.
Dete
r
m
i
n
e
d
=
x
-
co
o
r
d
in
ato
r
(
f
*
G)
e.
Dete
r
m
i
n
e
s
=
(
z
*
r
)
+
f
m
o
d
n
.
I
f
s
=
0
th
e
n
r
etu
r
n
to
s
tep
1
.
f.
Sig
n
at
u
r
e
f
o
r
th
e
m
es
s
ag
e
m
i
s
(
d
,
s
)
.
2
.
3
.
Sig
na
t
ure
v
er
if
ica
t
io
n
A
t t
h
e
R
ec
e
iv
er
s
id
e
t
h
e
m
e
s
s
ag
e
m
o
u
g
h
t
to
b
e
v
alid
ated
w
ith
t
h
e
f
o
llo
w
i
n
g
s
tep
s
:
a.
Firstl
y
,
co
n
f
ir
m
t
h
at
s
i
s
an
i
n
t
eg
er
in
t
h
e
in
ter
i
m
[
1
,
n
−1
]
b.
C
o
m
p
u
te
th
e
h
as
h
v
al
u
e
z
o
f
t
h
e
m
e
s
s
a
g
e/d
o
cu
m
en
t
m
c.
W
=
(
x
1
,
y
1
)
=
s
*
G
–
z
*
K
d.
v
=
x
-
co
o
r
d
in
ate(
W
)
,
f
in
all
y
,
au
th
e
n
ticate
th
e
s
ig
n
at
u
r
e
b
y
ch
ec
k
i
n
g
w
h
et
h
er
th
e
eq
u
i
v
alen
ce
v
=
d
h
o
ld
s
.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
NS
I
n
th
e
e
v
en
t
i
f
t
h
e
s
i
g
n
a
tu
r
e
f
o
r
th
e
m
e
s
s
a
g
e
m
i
s
(
d
,
s
)
an
d
w
as
g
en
u
i
n
el
y
g
e
n
er
at
ed
b
y
th
e
au
th
o
r
ized
Se
n
d
er
th
e
n
s
=
(
z
*
r
)
+
f
m
o
d
n
.
T
h
e
co
r
r
e
ctn
es
s
o
f
th
e
al
g
o
r
it
h
m
ca
n
b
e
test
ed
u
s
in
g
t
h
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CO
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ted
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[1
]
S
u
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g
-
M
i
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Ye
n
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n
d
Ch
i
-
S
u
n
g
Laih
,
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I
m
p
ro
v
e
d
Dig
it
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l
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ig
n
a
tu
re
A
l
g
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rit
h
m
,"
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E
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ra
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ti
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Co
mp
u
ter
s
,
v
o
l
.
4
4
,
no
.
5
,
M
a
y
1995
.
[2
]
Kirstin
L
a
u
ter,
"
T
h
e
A
d
v
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n
tag
e
s
o
f
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2
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.
[3
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sra
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l
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.
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ld
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se
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ter
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EL
KOM
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mp
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ti
n
g
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l.
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p
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[4
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Yo
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s
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g
Ch
o
i,
"
Cry
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sis
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e
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so
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Ne
tw
o
rk
s,
"
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ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
mp
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ter
En
g
in
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g
(
IJ
ECE
)
,
v
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l.
8
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n
o
.
1
,
p
p
.
6
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8
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[6
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S
.
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By
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K.
Yi,
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[7
]
El
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B.
Ba
rk
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r
, "
Dig
it
a
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a
ji
d
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a
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b
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ian
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ro
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u
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if
ic
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Op
ti
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0
]
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a
e
Ho
o
n
L
im
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e
e
,
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re
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n
Dig
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l
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ig
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lg
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m
”
,
i
n
AS
IACR
Y
PT
'
9
8
Pr
o
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e
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in
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e
In
ter
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l
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n
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to
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g
y
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d
In
f
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rm
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ti
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n
S
e
c
u
rity: A
d
v
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n
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s in
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p
t
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o
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y
,
2
0
0
0
,
p
p
.
1
7
5
-
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8
6
.
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1
]
B.
B.
Am
b
e
r
k
e
r,
P
ra
sh
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n
t
Ko
u
lg
i,
N.R.
S
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n
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a
,
"
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o
r
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rd
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e
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g
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p
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ti
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s,
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n
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rk
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EE
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.
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2
]
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ong
Jin
g
x
in
,
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Ne
w
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rd
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e
c
u
re
Dig
it
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3
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in
g
h
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.
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4
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i
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5
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ian
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in
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2
,
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p
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5
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6
]
Jie
L
iu
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Jia
n
h
u
a
L
i
,
"
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y
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tan
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l
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Dig
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e
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E
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2
0
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8
.
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7
]
L
e
i
Niu
,
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n
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n
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g
Ni,
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ive
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.
[1
8
]
Jia
n
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n
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a
n
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n
a
n
G
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