TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.4, April 201
4, pp. 3200 ~ 3
2
0
7
DOI: http://dx.doi.org/10.11591/telkomni
ka.v12i4.4931
3200
Re
cei
v
ed Se
ptem
ber 21, 2013; Revi
se
d No
vem
ber
19, 2013; Accepted Decem
ber 10, 20
13
Attack the Anycast Sig
n
ature Scheme
Jinbin Zhen
g
Schoo
l of Math
ematics an
d C
o
mput
er Sci
e
n
c
e, Long
ya
n U
n
iversit
y
No. 1, Dong
Xi
ao North R
o
a
d
, Long
ya
n 3
6
4
0
12, Chi
na. +
8
6
-
059
7-27
93
77
8
email: j
b
zhe
n
g
518
@16
3
.com
A
b
st
r
a
ct
T
oday, the i
n
te
rnet is i
n
creas
i
ngly
bei
ng c
o
n
s
ider
ed
to
prov
ide s
e
rvices, a
nd n
o
t just i
n
order t
o
conn
ect. As this vi
ew
beca
m
e
more
un
iv
ersal, th
e
i
m
p
o
rtant factors
of provi
d
i
ng s
u
ch serv
ices
a
r
e
relia
bi
lity an
d avail
a
b
ility of the serv
ic
es to
me
et the ne
e
d
s of a larg
e
nu
mb
er of use
r
s. Anycast is a
communic
a
tio
n
mo
de
in w
h
ich
the sa
me
ad
dr
ess is ass
i
gn
e
d
to a gr
ou
p of
servers a
nd th
e router w
i
l
l
se
nd
the requ
est to the
”
b
est
”
ser
v
er. Al-Ibrahi
m and
Cer
n
y pr
opos
ed a
n
aut
hentic
atio
n sche
m
e of a
n
yc
ast
communic
a
tio
n
.
T
heir sche
m
e
is base
d
o
n
El
-Gama
l
ty
pe si
gnatur
e sche
m
e. W
e
prov
e th
at their pref
err
e
d
sche
m
e, w
h
ich
does not re
qui
re interacti
on a
m
o
ng the var
i
o
u
s sign
ers, is insecur
e
.
Ke
y
w
ords
: dig
i
tal sig
nature, a
n
ycast co
mmu
n
ic
ati
on, de
nia
l
attack, forgery attack
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Al-Ibrahi
m an
d Cerny describ
e an auth
enticatio
n scheme for an
ycast commu
nicatio
n
based
on El
-Gamal type
d
i
gital si
gnatu
r
e [1-[2],
[11].
They p
r
op
osed a
n
a
u
then
tication
sol
u
tion
were
simila
rly relat
ed to
th
e con
c
ept
of
proxy
signatu
r
es.
The
met
hod
appli
ed
a
strong
sch
e
m
e
from [3, 4] and obtaine
d by improving th
e scheme fro
m
[5, 15]. There a
r
e many
appro
a
che
s
for
improving the scalability of
a serv
ice, but the comm
on one is to
repli
c
ate the
servers. Serv
er
repli
c
ation i
s
the key approa
ch fo
r maintainin
g use
r
-perceive
d
quality of
servi
c
e withi
n
a
geog
rap
h
icall
y
wide-sp
re
ad network. This
is e
m
powered b
y
the unde
rlining n
e
twork
infrast
r
u
c
ture kno
w
n as anyca
st
com
m
un
ication.
Ea
ch
use
r
o
w
n
s
a
private key a
nd a p
ublic
key,
and all
arith
m
etic i
s
do
n
e
in a
co
m
m
on g
r
ou
p i
n
whi
c
h
the
discrete
log
a
r
ithm p
r
obl
e
m
is
intrac
table. In this
sc
heme,
the
autho
r p
r
ese
n
ts vari
eties d
enial a
ttac
k
s
.
Thus
, for this
sc
heme
is
inse
cu
re.
2. Rev
i
e
w
o
f
An
y
cast Signatur
e
Sche
me
In anyca
st co
mmuni
cation,
a commo
n IP addre
s
s( a
n
yca
s
t add
re
ss) is u
s
e
d
to define a
grou
p of
serv
ers
that provide
the
same
servi
c
e.
A
cli
ent send
er d
e
siri
ng
to
co
mmuni
cate
with
only one of the serve
r
s sen
d
s data
g
ram
s
with the IP
a
n
yca
s
t addre
ss [1]. Al-Ibra
h
im et al. firstly
prop
osed a
con
c
a
s
t sig
n
a
ture in 20
0
2
[11], Stinson pointe
d
o
u
t an attack for the con
c
a
s
t
scheme [1
2]; later, Liu ga
ve an improvement
[13] u
poun the
co
n
c
a
s
t schem
e. On the othe
r
hand, Al-Ib
r
a
h
im an
d Carny also
presented the
an
ycast authent
ication sig
nat
ure
i
n
20
03. The
operation con
c
eptio
n be de
scribe
d as foll
ow:
a. Initializatio
n. The com
m
unication o
f
eac
h serve
r
with the g
r
oup
coo
r
di
n
a
tor. A
sign
ature
del
egation
algo
ri
thm is
used i
n
this
co
mmu
nicatio
n
. Each serve
r
sta
r
t
s
playin
g the
role
of the coo
r
din
a
tor’s p
r
oxy.
b. The
actu
al
se
rving. T
h
e
anycast
se
rver u
s
e
s
th
e d
e
legate
d
sign
ature, tog
e
th
er
with
the proof of hi
s dele
gation.
The co
ncept is de
scribe
d a
s
follow [1].
Notation:
1)
q
p
,
: two large p
r
i
m
es
su
ch tha
t
)
1
(
|
p
q
.
2)
g
: a generato
r
with ord
e
r
*
p
Z
q
.
3)
i
U
and
V
: are de
note User’
s
ID.
4)
(.)
H
: denote a on
e way ha
sh functio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Attack the An
ycast Signatu
r
e Sch
e
m
e
(Jinbin Zhe
n
g
)
3201
2.1. The Scheme of Co
nc
ept
Defini
tion 1.
Di
screte
log
a
rithm
proble
m
is
)
,
,
(
y
g
p
DLP
a p
r
o
b
lem that
on
i
nput a
prime
p
and
int
egers
g
,
*
p
Z
y
, outputs
1
p
Z
y
satis
f
ying
)
(mod
q
y
g
x
if
su
ch
an
x
exists. Othe
rwise, it outputs
.
The above f
unctio
n
, which outputs
if
there is no
solution to the query, shoul
d be
expre
s
sed a
s
DLP [16] an
d the notatio
n DLP
sh
o
u
l
d
be u
s
ed
on
ly for a we
aker fun
c
tion
such
that nothing i
s
spe
c
ified fo
r the be
havio
r of the fu
n
c
ti
on in the
ca
se wh
en the
r
e
is no
sol
u
tio
n
to
the query [6].
G
e
n
a
ra
l W
o
rk
:
The Al-Ibrahi
m et al.’s schem
e consi
s
ts
of two
pha
se
s: Initializatio
n pha
se an
d
Verific
a
tion phase.
Initialization Phase:
Us
er
i
U
signs a
messag
e
M
in the followi
ng
way.
Step 1.
i
U
Computes
).
(
i
i
M
H
m
(1)
Step 2.
i
U
Selects a rando
m integer
i
k
, and compute
s
).
(mod
p
g
m
r
i
k
i
i
(2)
Step 3.
i
U
Computes
).
(mod
q
x
r
k
s
i
i
i
(3)
Step 4.
i
U
Sends the
)
,
,
(
i
i
i
r
s
M
with mes
s
ages
to the verifier.
Verification Phase:
After rec
e
iv
ing
)
,
,
(
i
i
i
r
s
M
the signatu
r
e, Verifier
V
c
an verifies
the following:
Step 1.
V
Computes
).
(
i
i
M
H
m
(4)
Step 2.
V
Computes
).
(mod
p
r
y
g
l
i
r
i
s
i
i
i
(5)
Step 3.
If it h
o
lds,
V
can b
e
certai
n that
)
,
,
(
i
i
i
r
s
M
is ind
eed the
sign
ature
gen
erate
d
by
i
U
when:
.
i
i
l
m
(5)
2.2. The An
y
cast Sch
e
me
The anyca
st operation will
play
the
role
of the
sig
n
e
r
by
gro
up
coordi
nato
r
G
, whic
h
deleg
ates hi
s signatu
r
e ri
g
h
ts to all the membe
r
of the anyca
st gro
up.
2.2.1. Initializatio
n
Re
ad
y
Stage
Us
er
i
U
signs a
messag
e
M
in the followi
ng
way.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 4, April 2014: 3200 – 3
207
3202
Step 1.
Coordinator
cho
o
ses the secret
key
p
Z
x
and com
putes the p
u
b
lic key
).
(mod
p
g
y
x
(7)
The key
y
is the identifier of the grou
p.
Step 2.
Coordinator
ran
d
o
m
ly choo
se
s a value
p
i
Z
z
and
comp
utes
).
(mod
p
g
U
i
z
i
(8)
Whe
r
e
n
i
1
, then it send
s
i
t
to
i
th s
e
rver.
Step 3.
Server
i
A
sele
cts a ra
ndomly value
p
i
Z
and comp
utes
).
(mod
p
u
g
t
i
i
i
(9)
belon
g to
*
p
Z
, th
en it send
s
i
t
to the coo
r
din
a
tor.
Step 4.
Coordinator
com
p
utes
).
(mod
p
z
x
t
v
i
i
i
(10)
Step 5.
Server
i
A
received
i
v
from Coo
r
di
nat
or and
com
p
u
t
es
).
(mod
p
v
x
i
i
i
(11)
Then che
c
ks:
).
(mod
p
t
y
g
i
t
x
i
i
(12)
if it is equality. If it is corre
ct, then acce
pts
i
x
as secret key legal.
2.2.2. Actu
al Serv
ing Stage
Se
v
e
r
i
A
node:
Step 1.
Comp
utes
).
(
i
i
M
H
m
(13)
Step 2.
Choo
se
s a ran
dom
numbe
r
i
k
and
compute
s
).
(mod
p
g
m
r
i
k
i
i
(14)
Step 3.
Comp
utes
).
(mod
q
x
r
k
s
i
i
i
i
(15)
Step 4.
Sends
)
,
,
,
(
i
i
i
i
t
r
s
M
to the c
lient.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Attack the An
ycast Signatu
r
e Sch
e
m
e
(Jinbin Zhe
n
g
)
3203
2.2.3. Client node:
Step 1.
Fetc
hes
the key
i
y
from the regi
stry.
Step 2.
Comp
utes
).
(
i
M
H
h
(16)
Step 3.
Comp
utes
).
(mod
)
(
p
r
t
y
g
l
i
r
i
t
i
s
i
i
i
i
(17)
Step 4.
Acce
pts the sig
nat
ure if:
.
l
h
(18)
With the rece
nt intere
st in
se
curi
ng g
r
o
up an
d broad
ca
st com
m
un
ication
and m
u
ltica
s
t
comm
uni
cati
on, there h
a
s
b
een
a g
r
e
a
t dema
nd f
o
r d
e
si
gnin
g
a ne
w
cla
s
s
of fast
signat
ure
scheme
s
tha
t
can handl
e
a vast number of sig
nat
ure from b
r
o
adcast com
m
unication a
n
d
multica
s
t co
mmuni
cation
or grou
p-b
a
se
d appli
c
a
t
ion efficientl
y
, rather than usi
ng typical
sign
ature
sch
e
mes. B
a
sed
on the th
re
sh
old p
r
oxy
one
-time
signatu
r
e sch
e
me, a
spe
c
ific ca
se
is
whe
n
1
t
, which depi
cts th
e anyca
st model. The
anyca
st auth
enticatio
n problem was
discu
s
sed i
n
[1] and
a
sol
u
tion was p
r
op
ose
d
b
a
sed
o
n
a
co
nventio
nal di
gital
sig
nature.
Briefl
y,
the
anycast model rep
r
e
s
ents
the situ
ation
wher
e
any of a gro
up of n serv
ers
(sign
e
rs)
ma
y
provide the
same (e
quival
ent) se
rv
ice to a client (ve
r
ifier) [14].
3. Weak
ness
es of An
y
c
a
s
t Scheme
Anycast i
s
a netwo
rk a
d
d
r
essing a
nd routing sch
e
m
e
whe
r
eby d
a
ta is ro
uted
to the
‘nearest’
or ‘
best’
de
stinat
ion a
s
vie
w
e
d
by th
e routi
ng top
o
logy [
10]. For a
n
ycast
schem
e, the
grou
p co
ordi
nator will pl
a
y
the role of the sig
ner, wh
ich del
egate
s
his sig
nature
rights to all th
e
membe
r
s of the anyca
st group. The term is in
tended
to echo the term
s unicast,
broad
ca
st a
nd
multicast.
a)
In unicast, there i
s
a on
e-t
o
-on
e
a
s
soci
ation betwee
n
network ad
dre
ss
and
net
work
endp
oint: ea
ch d
e
stin
atio
n add
re
ss
un
iquely identifi
e
s a
sin
g
le receive
r
en
dp
oint Figu
re 1.
In
comp
uter net
workin
g, uni
cast tran
smission i
s
the
se
nding
of me
ssage
s to
a
singl
e n
e
two
r
k
destin
a
tion id
entified by a uniqu
e add
re
ss [7].
Figure 1. Unic
as
t Servic
es [7].
b)
In bro
a
d
c
a
s
t, there
is a
o
ne-to
-many
a
s
soci
ation b
e
t
ween
net
work a
ddresse
s
and
netwo
rk
end
p
o
ints: ea
ch d
e
stinatio
n ad
dre
ss i
dentif
i
e
s a
set of re
ceiver
end
poi
nts, to whi
c
h
all
informatio
n is repli
c
ated
Fi
gure
2. Bro
a
d
c
a
s
ting
can
b
e
pe
rform
ed
as a
high
lev
e
l ope
ration
i
n
a
prog
ram, fo
r example b
r
oad
ca
sting
Messag
e Pa
ssi
ng Inte
rfa
c
e, o
r
it ma
y be a lo
w
leve
l
netwo
rki
ng o
peratio
n, for example b
r
oa
dca
s
ting o
n
Ethernet [8].
S
R
R
R
R
R
R
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 4, April 2014: 3200 – 3
207
3204
Figure 2. Bro
adcast Servi
c
es [8].
c)
In multicast, there is al
so
a one-to
-m
a
n
y
asso
ciation
betwee
n
network ad
dre
sses
and network endp
oints: ea
ch de
stinatio
n
ad
dre
s
s
i
d
e
n
tifies a
set o
f
re
ceiver en
d
points, to
whi
c
h
all informatio
n is repli
c
ate
d
Figure 3. Multica
s
t is most co
mmo
nly implemen
ted in IP multica
s
t,
whi
c
h is ofte
n employed i
n
Internet Protocol (I
P) a
pplication
s
of streami
ng m
edia and Inte
rnet
televis
i
on [9].
d)
In anycast, t
here
is al
so
a on
e-to
-m
an
y asso
ciation
between
net
work
add
re
sses
and network endp
oints: ea
ch de
stinatio
n
ad
dre
s
s
id
e
n
tifies a
set o
f
receiver end
points,
but o
n
ly
one of th
em i
s
cho
s
en
at a
n
y given time
to re
ce
ive inf
o
rmatio
n fro
m
any given
sen
der Figu
re 4.
On the Internet, anyca
st is usu
a
lly impleme
n
ted
by using
Borde
r
Gate
way Proto
c
ol
to
simultan
eou
sl
y anno
unce t
he
same
de
st
ination IP a
d
d
re
ss range
from m
any diff
erent
pla
c
e
s
on
the Internet [10].
Figure 3. Multic
as
t Servic
es
[9]
Figure 4. Anyca
s
t Service
s
[10]
As
k
n
own for a forgery a
ttac
k
in following [6].
Step 1.
Eve randomly cho
o
se
s a num
b
e
r
i
s
.
Step 2.
Eve calcul
ates:
).
(mod
)
1
(
)
(
2
q
p
g
M
H
r
i
s
i
i
(19)
Step 3.
Eve forge
d
sig
natu
r
e on the me
ssag
e
i
M
whe
n
she use
.
A sig
nature
forged
u
s
in
g
upo
n-de
scri
bed
metho
d
is valid, b
e
c
au
se
the
followin
g
equatio
ns h
o
l
d
:
Proof.
).
(mod
)
(
)
(mod
)
(
2
)
1
(
)
(
p
M
H
p
M
H
y
r
y
g
i
i
p
g
M
H
i
r
s
i
s
i
i
i
(20)
To actu
al se
rving of their schem
e, even for:
).
(mod
)
(
p
r
t
y
g
l
i
r
i
t
s
i
i
i
i
(21)
)
,
,
(
i
i
i
r
s
M
R
R
R
R
R
S
R
R
R
R
R
S
R
R
R
R
R
R
S
R
R
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Attack the An
ycast Signatu
r
e Sch
e
m
e
(Jinbin Zhe
n
g
)
3205
Eve compute:
).
(mod
)
(
)
(mod
)
(
)
(
)
(mod
)
(
2
)
1
(
)
(
p
M
H
p
M
H
t
y
p
r
t
y
g
l
i
i
p
g
M
H
i
t
i
i
r
i
t
i
s
i
i
s
i
i
i
i
i
(22)
3.1. Denial Atta
ck I
E
v
e let
s
se
cr
et
key
0
x
and
1
i
k
in firs
t.
Step 1.
Eve compute
s
:
).
(mod
1
0
p
g
g
y
x
i
(23)
Step 2.
Eve compute
s
:
).
(
i
i
M
H
m
(24)
Step 3.
Eve compute
s
:
).
(mod
)
(mod
1
p
g
m
p
g
m
r
i
k
i
i
i
(25)
Step 4.
Eve compute
s
:
).
(mod
1
)
(mod
0
1
)
(mod
q
q
q
x
r
k
s
i
i
i
(26)
After Eve finishe
d
the four steps
, she h
ad denie
d
the
valid signatu
r
e
)
,
,
(
i
i
i
r
s
M
of user
i
U
. Eve computes:
).
(mod
)
(mod
1
)
(mod
1
1
1
p
m
p
g
m
g
p
r
y
g
m
i
i
g
m
i
r
i
s
i
i
i
i
(27)
3.2. Denial Atta
ck II
Eve s
e
ts
secret k
e
y
1
p
x
and
.
2
p
k
i
Step 1.
Eve compute
s
:
).
(mod
1
)
(mod
)
(mod
1
p
p
g
p
g
y
p
x
i
(28)
Step 2.
Eve compute
s
:
).
(
i
i
M
H
m
(29)
Step 3.
Eve compute
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 4, April 2014: 3200 – 3
207
3206
).
(mod
)
(mod
)
(mod
)
(mod
1
1
1
)
2
(
p
g
m
p
g
g
m
p
g
m
p
g
m
r
i
p
i
p
i
k
i
i
i
(30)
Step 4.
Eve compute
s
:
).
(mod
1
)
(mod
0
1
)
(mod
q
q
q
x
r
k
s
i
i
i
(31)
After Eve finishe
d
the four steps
, she h
ad denie
d
the
valid signatu
r
e
)
,
,
(
i
i
i
r
s
M
of user
i
U
. Eve computes:
).
(mod
)
(mod
1
)
(mod
1
1
)
2
(
p
m
p
g
m
g
p
r
y
g
m
i
i
g
m
i
r
i
s
i
p
i
i
i
(32)
4. Conclusio
n
In the past, Al-Ibra
h
im et al. decribe
d an
authenti
c
atio
n schem
e for
con
c
a
s
t and
anyca
st
comm
uni
cati
on ba
sed
on
El-Gamal ty
pe digital
sig
nature. T
hey prop
osed a
n
authenti
c
at
ion
solutio
n
were
simila
rly rela
ted to the
con
c
ept
of
proxy sign
ature.
Fo
r any
ca
st sch
e
me, the
gro
up
coordinator
will pl
ay the rol
e
of the
signer,
whi
c
h
delegates
his signature rights
to all the
membe
r
s
of the
any
ca
st grou
p.We
al
ready kn
o
w
h
o
w to
de
ny and fo
rge
si
gnature
so t
hat
anyca
st is
effected. Fo
r fo
rged
attack, we
can m
a
ke
a set of forg
ery sig
natu
r
e
whi
c
h
su
cce
e
d
the anyca
st communi
catio
n
of authenticati
on. Thus, f
o
r this
schem
e is insecure.
Ackn
o
w
l
e
dg
ements
The auth
o
rswoul
d like to
thank
Che
n
g
lian Li
u fo
r
his comme
nts that help t
o
improve
themanu
scri
p
t. This p
ape
r pa
rtially
su
pporte
d from
coll
ege fu
n
d
ing
unde
r t
he info
rmatio
n
se
curity re
se
arch team project.
Referen
ces
[1]
M Al-Ibrahim,
A Cerny
.
Authentic
ati
on
of a
n
y
c
a
st comm
u
n
icati
on.
MMM
-ACNS
.
20
03; LNCS 27
76:
419-
423.
[2]
CP Schnorr. Efficient sig
natur
e gen
erati
on b
y
smart cards.
Journ
a
l of Cryp
tology
. 19
91; 4
(
3): 161-1
74.
[3]
K Z
han
g. T
h
resho
l
d
pro
x
y
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ature
sche
m
es.
Infor
m
ati
on s
e
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L
e
cture
Notes
i
n
C
o
mput
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e
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82-2
9
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[4]
H Gho
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Pie
p
rz
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iatio
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heati
ng
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iati
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ang
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gn
atu
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e
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m
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uter Scienc
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[5]
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o, K
Usud
a, E Oka
m
oto. Pro
x
y s
i
gnatur
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e
le
g
a
tion
of th
e p
o
w
e
r
to
sig
n
m
e
ssag
e
.
IEICE
T
r
ansactio
n
on
F
unda
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.
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[6]
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ian
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Yongn
in
g Gou. Securit
y
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al
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n
y
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gn
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Applie
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20
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2
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77-1
182.
[7]
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i
kiped
ia. Un
i
c
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Wikiped
ia w
e
b
s
ite, http://en.wikipe
d
i
a
.org/w
iki/Unicast.
2
012
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[8]
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i
kiped
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.
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kipedia.org/
w
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201
2.
[9]
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kiped
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ia w
e
b
s
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d
i
a
.org/w
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20
12.
[10] W
i
kiped
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en.wikipe
d
i
a
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iki/Anycas.
201
2.
[11]
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im, H Ghod
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y
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o
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e
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e.
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8.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Attack the An
ycast Signatu
r
e Sch
e
m
e
(Jinbin Zhe
n
g
)
3207
[12]
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Z
h
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yptan
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h
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