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wallet
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ch
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s
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ity
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:
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Dep
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ch
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I
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UCT
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itco
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d
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r
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cy
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s
h
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Nak
am
o
t
o
in
2
0
0
8
m
e
n
tio
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ed
th
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wo
r
d
[
1
]
.
T
h
e
b
itco
in
s
ar
e
s
to
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ed
in
wallet
ca
lled
d
ig
ital
wallet.
T
h
is
wallet
ca
n
also
p
lace
o
n
m
o
b
ile,
lap
to
p
,
h
ar
d
war
e
[
2
]
.
B
itco
in
tr
an
s
ac
tio
n
s
ar
e
h
ap
p
en
in
g
with
o
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t
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o
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e
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t
o
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th
ir
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ar
ty
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d
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d
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e
n
tr
alize
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ash
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s
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ar
e
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cr
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s
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g
d
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y
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y
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ay
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n
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y
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licatio
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s
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licatio
n
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s
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ch
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lin
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tio
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ad
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n
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i
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n
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g
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m
ar
t
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n
tr
ac
ts
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r
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estate.
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t
n
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w
u
s
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l
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ch
ain
tech
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s
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o
r
m
atio
n
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n
u
m
b
er
o
f
b
lo
c
k
ch
ain
wallet
u
s
er
s
h
as
ex
p
o
n
e
n
tially
g
r
o
w
n
s
in
ce
2
0
1
1
,
lead
in
g
to
s
ec
u
r
ity
is
s
u
es f
o
r
u
s
in
g
b
lo
ck
ch
ain
tech
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o
lo
g
y
[
3
]
.
T
h
er
e
ar
e
n
u
m
er
o
u
s
cr
y
p
to
c
u
r
r
en
cies
s
u
ch
Altco
in
,
B
itco
in
,
E
th
er
eu
m
,
L
iteco
i
n
,
an
d
R
ip
p
le.
b
ein
g
u
s
ed
[
4
]
.
B
u
t
m
o
s
tly
b
itco
in
i
s
p
r
ef
er
r
ed
cr
y
p
to
cu
r
r
en
cy
in
th
e
wo
r
ld
an
d
o
b
v
io
u
s
ly
th
e
B
itco
in
is
at
tack
er
’
s
ch
o
ice.
T
h
u
s
,
s
ec
u
r
ities
o
f
B
itco
in
tr
an
s
ac
tio
n
s
ar
e
im
p
o
r
tan
t
[
5
]
.
B
itco
in
u
s
er
u
s
e
s
p
r
iv
ate
k
ey
f
o
r
au
th
en
ticatio
n
as we
ll a
s
to
ac
ce
s
s
an
d
s
p
en
t th
e
cu
r
r
en
c
y
s
to
r
ed
at
wallet
d
u
r
in
g
th
e
tr
an
s
ac
tio
n
.
I
f
th
e
p
r
iv
ate
k
ey
is
lo
s
t
o
r
g
r
ab
b
e
d
b
y
atta
ck
er
o
r
in
tr
u
d
er
,
b
itco
in
u
s
er
will
n
o
t
ab
le
to
do
tr
an
s
ac
tio
n
s
an
d
th
u
s
lo
o
s
e
th
e
cu
r
r
en
c
y
.
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.
15
,
No
.
2
,
Ap
r
il
20
25
:
1
8
6
1
-
1
8
6
7
1862
T
h
e
f
o
llo
win
g
ty
p
es
o
f
attac
k
s
o
cc
u
r
r
ed
o
n
wallet
an
d
b
i
tco
in
tr
an
s
ac
tio
n
s
[
6
]
–
[
1
1
]
.
Attack
s
o
n
wallet
s
o
f
twar
e
–
t
h
is
is
done
by
tam
p
er
in
g
or
s
tealin
g
th
e
k
ey
.
T
h
e
attac
k
er
g
ets
th
e
co
n
tr
o
l
of
wallet
an
d
g
r
ab
s
th
e
m
o
n
ey
.
B
itco
in
ex
c
h
an
g
e
–
in
t
h
is
s
y
s
tem
,
u
s
er
’
s
p
r
iv
ate
k
e
y
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s
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y
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n
o
t
h
er
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ar
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ch
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a
f
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en
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.
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h
e
f
in
a
n
cial
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en
c
y
m
a
n
ag
es
t
h
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b
itco
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n
of
th
e
u
s
er
on
u
s
er
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s
b
eh
al
f
.
Sin
ce
it
in
v
o
lv
es
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n
o
t
h
e
r
p
ar
t
y
,
th
is
is
d
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g
er
o
u
s
,
an
d
tr
u
s
t
m
an
ag
em
en
t
b
etwe
en
th
e
u
s
er
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d
th
e
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an
k
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en
tial.
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ial
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of
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s
er
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er
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n
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le
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er
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u
ltip
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e
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l
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k
with
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k
.
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ait
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d
s
witch
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h
is
attac
k
is
o
cc
u
r
r
ed
wh
en
t
h
e
co
d
e
in
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er
ted
in
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o
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r
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c
o
d
e
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s
o
f
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to
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th
e
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s
.
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ich
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o
n
e
o
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th
e
lar
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est
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m
in
in
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e
attac
k
b
y
s
t
ea
lin
g
B
T
C
f
r
o
m
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itco
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let.
C
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ch
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n
el
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k
s
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n
also
ca
u
s
e
to
g
ain
th
e
k
ey
.
C
r
o
s
s
ch
an
n
el
attac
k
s
[
1
2
]
–
[
1
5
]
ca
n
b
e
class
if
ied
in
to
tim
e,
tr
ac
es
a
n
d
ac
ce
s
s
o
n
ch
an
n
el
.
I
n
tim
e
-
b
ased
attac
k
,
th
e
cr
y
p
t
o
g
r
ap
h
y
o
p
er
atio
n
tim
e
is
m
o
n
ito
r
ed
an
d
an
aly
ze
d
to
ex
tr
ac
t
th
e
k
ey
.
I
n
tr
ac
e
d
b
ased
attac
k
,
d
ev
ice
p
o
we
r
co
n
s
u
m
p
tio
n
o
r
elec
tr
o
m
ag
n
etic
r
ad
iatio
n
s
ar
e
co
n
tin
u
o
u
s
ly
m
o
n
ito
r
ed
to
ex
tr
ac
t
th
e
k
ey
.
I
n
ac
ce
s
s
-
b
ased
attac
k
,
attac
k
er
ch
ec
k
s
ca
ch
e
to
ex
tr
ac
t
c
o
n
f
i
d
en
tial
in
f
o
r
m
atio
n
an
d
k
e
y
,
e.
g
.
,
d
ata
an
d
in
s
tr
u
ct
io
n
ca
ch
e.
Du
e
to
th
ese
attac
k
s
,
it
is
p
o
s
s
ib
le
to
g
r
a
b
th
e
k
ey
by
th
e
i
n
tr
u
d
e
r
s
.
T
h
e
ch
allen
g
e
o
f
m
a
n
ag
in
g
s
ec
r
et
k
ey
s
in
B
itco
in
an
d
b
lo
ck
ch
ain
tech
n
o
lo
g
y
in
s
o
lv
in
g
p
r
o
b
lem
[
1
6
]
.
I
f
th
e
s
ec
r
et
k
ey
is
m
is
s
ed
,
o
wn
er
will u
n
ab
le
to
ac
ce
s
s
th
eir
elec
tr
o
n
ic
ass
e
ts
.
I
t p
o
s
es r
is
k
s
in
th
e
ev
en
t
o
f
b
itco
in
th
ef
t.
T
h
u
s
,
k
ey
m
an
ag
em
en
t
is
r
eq
u
ir
e
d
to
p
r
o
p
er
h
an
d
le
th
e
k
e
y
in
s
ec
u
r
e
way
.
T
h
is
p
ap
e
r
d
is
cu
s
s
es
ex
is
tin
g
k
ey
m
an
ag
em
en
t
m
eth
o
d
s
.
T
h
e
clo
u
d
b
ased
k
ey
s
p
lit
m
an
a
g
em
en
t
with
m
u
ltil
ev
el
k
e
y
s
p
litt
in
g
ap
p
r
o
ac
h
is
p
r
o
p
o
s
ed
to
p
r
o
tect
th
e
k
ey
f
r
o
m
th
e
at
tack
er
s
.
T
h
is
p
ap
er
also
d
escr
ib
es
an
d
co
m
p
a
r
es
th
e
ex
is
tin
g
ap
p
r
o
ac
h
es
f
o
r
k
ey
m
an
a
g
em
en
t.
Ou
r
c
o
n
tr
ib
u
tio
n
s
in
th
is
p
ap
er
ar
e
as
f
o
llo
ws
:
i)
Stu
d
y
o
f
ex
is
ten
t
k
ey
m
an
ag
em
en
t
te
ch
n
iq
u
es
f
o
r
h
a
n
d
lin
g
b
itco
in
k
ey
;
ii)
Desig
n
an
d
an
aly
s
is
o
f
k
ey
s
p
lit
m
an
ag
em
en
t te
c
h
n
iq
u
e
with
m
u
ltil
ev
el
ap
p
r
o
ac
h
;
a
n
d
iii)
Secu
r
ity
an
aly
s
is
o
f
k
ey
s
p
lit tec
h
n
iq
u
e.
2.
E
XI
ST
I
NG
K
E
Y
M
ANAG
E
M
E
N
T
T
E
CH
N
I
Q
UE
I
n
o
r
d
e
r
to
p
r
o
tect
th
e
d
ig
ita
l
wallet,
p
er
s
o
n
h
an
d
lin
g
th
e
b
itco
in
tr
an
s
ac
tio
n
s
,
k
ee
p
s
p
r
iv
ate
k
ey
s
ec
u
r
e.
C
u
r
r
en
t a
p
p
r
o
ac
h
es f
o
r
k
ey
m
a
n
ag
em
en
t
o
f
b
l
o
ck
ch
ai
n
ar
e
d
is
cu
s
s
ed
as b
elo
w.
a.
L
o
ca
l
k
ey
s
to
r
a
g
e
[
1
7
]
–
[
1
9
]
:
T
h
e
k
ey
is
s
to
r
ed
at
lo
ca
l
s
to
r
ag
e.
T
h
e
a
d
v
an
ta
g
e
is
th
at
k
e
y
ca
n
b
e
ea
s
ily
ac
ce
s
s
ed
.
B
u
t
i
t
i
s
n
o
t
s
af
e
d
u
e
to
attac
k
o
n
lo
ca
l
s
to
r
ag
e
b
y
v
ir
u
s
,
m
alicio
u
s
s
cr
ip
t,
lack
o
f
u
p
d
ates,
b
r
u
te
f
o
r
ce
attac
k
s
,
h
u
m
an
e
r
r
o
r
,
o
n
l
in
e
attac
k
s
,
an
d
f
o
r
g
o
tten
p
ass
wo
r
d
s
.
b.
W
allet
w
ith
p
ass
wo
r
d
p
r
o
tectio
n
[
2
0
]
–
[
2
2
]
:
T
h
e
wallet
ca
n
b
e
p
r
o
tecte
d
b
y
th
e
p
ass
wo
r
d
.
T
h
e
d
is
ad
v
an
tag
e
o
f
th
is
ap
p
r
o
ac
h
is
th
at
if
p
as
s
wo
r
d
is
lo
s
t
o
r
p
ass
wo
r
d
is
g
ain
ed
b
y
attac
k
er
s
,
th
e
b
itco
in
o
wn
er
will
n
o
t
b
e
ab
le
to
ac
ce
s
s
th
e
wa
llet.
F
in
ally
,
o
wn
er
lo
s
es
th
e
cu
r
r
en
cy
s
to
r
ed
in
th
e
wallet.
T
h
u
s
,
it
lead
s
lo
s
s
o
f
ac
ce
s
s
o
f
f
u
n
d
s
.
I
f
y
o
u
f
o
r
g
o
t
wallet
p
ass
wo
r
d
,
r
ec
o
v
er
y
o
p
tio
n
s
ar
e
n
o
t
also
av
ailab
le.
T
h
u
s
,
it
ch
allen
g
es
to
r
eg
ain
th
e
ac
ce
s
s
of
f
u
n
d
s
.
c.
Key
s
to
r
ag
e
at
o
f
f
l
i
n
e
p
l
a
c
e
[
2
3
]
,
[
2
4
]
:
K
e
y
s
a
r
e
m
ain
tain
ed
at
p
lace
in
o
r
d
er
to
av
o
i
d
o
n
li
n
e
ac
ce
s
s
of
th
e
s
am
e
lik
e
u
n
iv
er
s
al
s
er
ial
b
u
s
(
USB
)
or
p
ap
er
wallet.
B
u
t
it
m
ay
not
be
ea
s
ily
ac
ce
s
s
ed
wh
en
it
is
r
eq
u
ir
ed
due
to
p
h
y
s
ical
lo
s
s
or
d
am
ag
e,
h
u
m
an
er
r
o
r
,
lim
ited
a
cc
ess
ib
ilit
y
,
an
d
lack
of
u
p
d
ates.
d.
T
h
ir
d
p
ar
ty
a
p
p
r
o
ac
h
[
2
5
]
:
I
n
t
h
is
,
k
ey
s
ar
e
m
an
ag
ed
at
th
ir
d
p
ar
ty
by
th
e
o
wn
er
of
th
e
k
e
y
.
T
h
e
s
to
r
in
g
th
e
k
ey
at
th
ir
d
p
a
r
ty
is
r
is
k
y
d
u
e
to
s
ec
u
r
ity
co
n
ce
r
n
s
,
ce
n
tr
aliza
tio
n
r
is
k
s
,
r
eg
u
lato
r
y
r
is
k
s
,
lim
ited
co
n
tr
o
l
of
th
e
u
s
er
as
well
as
s
er
v
ice
d
o
wn
tim
e.
B
itc
o
i
n
u
s
es
b
l
o
c
k
c
h
a
in
f
o
r
t
r
a
n
s
ac
tio
n
s
.
Fig
u
r
e
1
s
h
o
ws
b
lo
ck
ch
ain
s
tr
u
ctu
r
e.
E
ac
h
b
lo
c
k
co
n
tain
s
th
e
c
u
r
r
en
t
h
ash
,
p
r
ev
io
u
s
b
lo
c
k
h
ash
in
f
o
r
m
atio
n
,
a
n
d
tr
an
s
ac
tio
n
i
n
f
o
r
m
atio
n
.
Fig
u
r
e
1
.
B
lo
ck
c
h
ain
s
tr
u
ctu
r
e
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
K
ey
ma
n
a
g
eme
n
t fo
r
b
itco
i
n
t
r
a
n
s
a
ctio
n
s
u
s
in
g
clo
u
d
b
a
s
ed
ke
y
s
p
litt
in
g
…
(
A
ma
r
B
u
ch
a
d
e
)
1863
3.
M
E
T
H
O
D
E
x
is
tin
g
k
ey
m
an
a
g
em
en
t
m
e
th
o
d
s
f
o
r
b
itco
i
n
tr
a
n
s
ac
tio
n
s
h
av
e
lim
itatio
n
s
as
p
e
r
d
is
cu
s
s
ed
in
th
e
s
ec
tio
n
2
.
Saf
eg
u
ar
d
i
n
g
th
e
k
ey
is
im
p
o
r
tan
t.
T
h
u
s
,
n
o
v
e
l
m
eth
o
d
o
lo
g
y
is
in
tr
o
d
u
ce
d
.
T
h
e
m
eth
o
d
o
lo
g
y
in
d
icate
s
h
o
w
to
s
af
eg
u
ar
d
s
th
e
k
ey
.
T
h
r
esh
o
ld
cr
y
p
to
g
r
a
p
h
y
with
clo
u
d
en
a
b
lin
g
is
p
r
e
s
en
ted
.
T
h
e
o
wn
er
s
p
lits
th
e
k
ey
in
to
m
u
ltip
le
s
p
l
its
.
T
h
ese
m
u
ltip
le
s
p
lit
s
m
ay
b
e
s
h
ar
ed
in
v
ir
tu
al
m
ac
h
i
n
es o
f
clo
u
d
co
m
p
u
tin
g
en
v
ir
o
n
m
en
t.
T
h
r
esh
o
ld
is
d
e
cid
ed
b
y
th
e
o
w
n
er
.
I
f
o
w
n
er
co
llects
k
ey
s
p
lits
at
least
th
r
esh
o
ld
n
u
m
b
er
o
f
k
ey
s
,
co
m
p
lete
k
ey
ca
n
b
e
co
n
s
tr
u
cted
o
th
er
wis
e
k
ey
will
n
o
t
b
e
r
ec
o
n
s
tr
u
cted
.
T
h
e
Fig
u
r
e
2
in
d
icate
s
th
at
d
ata/k
ey
o
wn
er
s
p
lits
th
e
k
ey
in
to
m
u
ltip
le
k
ey
s
p
lits
an
d
d
is
tr
ib
u
tes
th
e
k
ey
s
p
lits
to
v
ir
tu
al
m
ac
h
in
es
o
f
th
e
clo
u
d
en
v
ir
o
n
m
en
t.
T
h
r
esh
o
ld
cr
y
p
to
g
r
a
p
h
y
b
ase
d
Sh
am
ir
’
s
ap
p
r
o
ac
h
[
2
6
]
,
[
2
7
]
is
u
s
ed
to
d
iv
i
d
e
th
e
k
e
y
i
n
to
p
a
r
ts
as
p
er
s
ec
u
r
ity
r
e
q
u
ir
em
e
n
ts
.
T
h
e
alg
o
r
ith
m
co
n
s
id
er
s
t
h
e
th
r
e
s
h
o
ld
v
alu
e.
T
h
e
k
ey
ca
n
b
e
r
ec
o
n
s
tr
u
cted
f
r
o
m
at
least
th
r
esh
o
ld
n
u
m
b
e
r
.
T
h
e
th
r
esh
o
ld
v
alu
e
ca
n
b
e
d
ec
id
ed
b
y
th
e
o
wn
e
r
o
f
th
e
k
ey
.
T
h
e
alg
o
r
ith
m
p
r
o
v
id
e
s
f
lex
ib
ilit
y
f
o
r
s
p
lit
an
d
r
ec
o
n
s
t
r
u
cts
th
e
k
ey
.
T
h
e
th
r
esh
o
ld
v
a
lu
e
is
ad
ju
s
ted
b
ased
on
th
e
s
ec
u
r
ity
r
eq
u
ir
em
en
ts
.
T
h
e
th
r
esh
o
l
d
v
alu
e
ca
n
b
e
d
e
cid
ed
b
y
th
e
o
wn
er
o
f
th
e
k
ey
.
T
h
e
n
o
v
elty
o
f
th
e
ap
p
r
o
ac
h
is
th
at
th
e
th
r
esh
o
l
d
v
alu
e
ca
n
b
e
c
h
an
g
ea
b
le
as
p
er
o
wn
er
o
f
th
e
k
ey
r
eq
u
i
r
em
en
t.
T
h
e
in
cr
ea
s
e
in
th
e
th
r
es
h
o
ld
en
h
an
ce
s
th
e
s
ec
u
r
ity
.
T
h
is
ch
an
g
ea
b
le
th
r
e
s
h
o
ld
p
r
o
p
er
ty
allo
ws
th
e
k
e
y
o
wn
er
to
ad
a
p
t
to
s
ec
u
r
ity
n
ee
d
s
.
Fig
u
r
e
2.
Ke
y
s
p
lit
up
f
o
r
b
lo
c
k
ch
ain
k
e
y
m
an
ag
e
m
en
t
3
.
1
.
I
ncre
a
s
ing
deg
re
e
of
s
ec
urit
y
by
m
ultiple
s
pli
t
s
T
h
e
k
e
y
ca
n
b
e
s
af
e
g
u
ar
d
e
d
b
y
d
iv
id
in
g
it
in
to
m
u
ltip
le
le
v
el.
I
n
itially
,
k
ey
is
d
iv
id
ed
i
n
to
k
ey
p
ar
ts
.
At
th
e
s
u
b
s
eq
u
en
t le
v
el,
ea
ch
s
p
lit o
f
th
e
k
ey
ca
n
b
e
f
u
r
th
er
d
iv
i
d
ed
in
to
p
ar
tial k
e
y
p
ar
ts
an
d
s
o
o
n
.
I
t
u
s
es
th
r
esh
o
ld
cr
y
p
to
g
r
a
p
h
y
(
,
)
s
ch
em
e.
Fig
u
r
e
3
s
h
o
ws
th
e
m
u
ltil
ev
el
k
ey
s
p
lit
b
y
u
s
in
g
th
r
esh
o
ld
cr
y
p
to
g
r
ap
h
y
(
,
)
ap
p
r
o
ac
h
in
t
o
k
ey
s
h
ar
es.
T
h
e
n
u
m
b
er
o
f
k
e
y
p
ar
ts
at
ea
ch
lev
el
ca
n
b
e
g
i
v
en
b
y
f
o
r
m
u
la:
=
wh
er
e
is
n
u
m
b
er
o
f
k
e
y
p
ar
t
s
af
ter
k
ey
d
iv
id
es
at
ea
ch
lev
el
an
d
is
n
u
m
b
er
o
f
lev
els
u
p
to
wh
ich
k
ey
d
iv
id
e
h
as
to
b
e
p
er
f
o
r
m
ed
.
Fo
r
r
ec
o
n
s
tr
u
ctio
n
o
f
th
e
k
ey
,
b
ac
k
tr
ac
k
in
g
u
p
to
lev
el
0
is
r
eq
u
i
r
ed
.
Fo
r
ea
c
h
lev
el,
th
r
esh
o
ld
n
u
m
b
er
o
f
p
ar
tial k
ey
s
h
ar
es n
ee
d
s
to
b
e
co
ll
ec
ted
to
g
et
b
ac
k
th
e
k
ey
.
Fig
u
r
e
3.
Key
s
p
lit
up
tim
e
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.
15
,
No
.
2
,
Ap
r
il
20
25
:
1
8
6
1
-
1
8
6
7
1864
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
Saf
eg
u
ar
d
in
g
th
e
k
ey
is
im
p
o
r
tan
t
f
o
r
t
h
e
s
ec
u
r
ity
o
f
b
itco
in
s
s
to
r
ed
i
n
wallet.
T
h
e
k
e
y
d
iv
id
e
is
em
p
lo
y
ed
to
s
af
eg
u
a
r
d
th
e
k
e
y
f
r
o
m
v
ar
io
u
s
attac
k
s
.
T
h
is
s
ec
tio
n
ass
ess
e
s
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
tech
n
iq
u
e
by
m
ea
s
u
r
in
g
th
e
tim
e
tak
en
f
o
r
k
ey
d
iv
id
e.
T
h
e
s
ec
u
r
ity
a
n
aly
s
is
is
co
n
d
u
cted
in
s
ec
tio
n
5.
T
h
e
ex
p
er
im
en
t
was
c
o
n
d
u
cte
d
b
y
co
n
s
id
er
in
g
Sh
am
ir
’
s
s
ec
r
et
s
h
ar
in
g
alg
o
r
ith
m
.
Key
s
p
l
it
u
p
tim
e
f
o
r
d
if
f
er
e
n
t
k
ey
s
izes
is
ca
lc
u
lated
to
s
ee
how
m
u
ch
tim
e
is
n
ee
d
ed
to
d
iv
id
e
th
e
k
ey
.
Key
s
ize
was
tak
en
as
2
5
6
b
its
s
im
ilar
ly
as
a
d
v
an
ce
d
en
c
r
y
p
tio
n
s
tan
d
ar
d
(
AE
S)
alg
o
r
ith
m
.
I
n
itially
th
r
esh
o
ld
v
alu
e
was
tak
en
as
2
.
T
h
at
m
ea
n
s
if
an
y
two
k
ey
s
h
ar
es
ar
e
tak
en
f
r
o
m
th
e
p
o
o
l
o
f
k
ey
p
ar
ts
th
at
ar
e
s
p
r
ea
d
e
r
ac
r
o
s
s
th
e
v
ir
tu
a
l
m
ac
h
in
es,
co
m
p
lete
k
ey
ca
n
b
e
r
ec
o
n
s
tr
u
cte
d
.
T
h
e
to
tal
n
u
m
b
er
o
f
k
e
y
s
p
lits
v
ar
ied
f
r
o
m
1
0
.
5
0
.
T
h
e
k
ey
s
p
lit
tim
e
was
as
tak
en
as
p
er
f
o
r
m
a
n
ce
in
d
icato
r
.
I
t
is
f
o
u
n
d
th
at
as
k
ey
s
h
ar
es
ar
e
v
ar
ied
as
10,
20,
3
0
,
40
,
an
d
50,
th
e
k
ey
s
p
lit
up
tim
e
is
in
cr
e
asin
g
.
I
t
is
m
en
tio
n
e
d
in
Fig
u
r
e
4.
T
h
is
ex
p
er
im
en
tatio
n
is
p
er
f
o
r
m
ed
b
ec
a
u
s
e
th
er
e
s
h
o
u
ld
not
be
an
y
d
ela
y
to
ac
ce
s
s
th
e
b
itco
in
wallet
due
to
s
u
ch
f
ac
to
r
s
s
u
ch
k
ey
s
p
lit
an
d
k
e
y
f
o
r
m
atio
n
af
ter
g
ettin
g
th
r
esh
o
ld
n
u
m
b
e
r
of
k
ey
s
p
lit
s
(
ass
u
m
e
).
Ob
v
i
o
u
s
ly
th
r
o
u
g
h
our
e
x
p
er
im
e
n
t,
it
is
o
b
s
er
v
ed
th
at
k
ey
s
p
lit
up
tim
e
v
a
r
y
in
g
with
in
cr
ea
s
in
g
k
ey
s
ize
an
d
n
u
m
b
e
r
of
k
e
y
s
h
ar
es.
W
e
h
av
e
also
co
m
p
ar
e
d
o
u
r
ap
p
r
o
ac
h
t
o
o
t
h
er
k
ey
m
an
ag
em
en
t
m
et
h
o
d
s
s
u
ch
as
k
e
y
s
in
lo
ca
l
s
to
r
ag
e,
p
ass
wo
r
d
d
r
iv
e
n
k
ey
s
an
d
h
o
s
ted
wallet.
T
h
e
T
ab
le
1
g
iv
es
t
h
e
co
m
p
ar
is
o
n
s
.
T
h
e
p
ar
am
eter
s
s
u
ch
as
m
alwa
r
e
r
esis
tan
ce
,
o
f
f
lin
e
k
e
y
,
tr
u
s
ted
t
h
ir
d
p
ar
t
y
,
r
esis
tan
t
to
p
h
y
s
ical
th
ef
t,
r
esis
tan
t
to
p
ass
wo
r
d
lo
s
s
an
d
cr
o
s
s
d
ev
ice
p
o
r
tab
ilit
y
[
1
4
]
.
It
is
f
o
u
n
d
th
at
our
ap
p
r
o
ac
h
of
k
ey
m
an
ag
em
en
t
s
u
p
p
o
r
ts
all
t
h
ese
p
ar
am
eter
s
an
d
s
ec
u
r
e
f
r
o
m
o
th
er
m
eth
o
d
s
.
Fig
u
r
e
4
.
Key
s
p
lit u
p
tim
e
T
ab
le
1
.
C
o
m
p
a
r
is
o
n
o
f
ex
is
tin
g
k
ey
m
an
a
g
em
en
t m
eth
o
d
s
P
a
r
a
me
t
e
r
s
a
p
p
r
o
a
c
h
M
a
l
w
a
r
e
r
e
si
st
a
n
c
e
O
f
f
l
i
n
e
k
e
y
N
o
n
e
t
r
u
st
e
d
med
i
a
t
o
r
P
h
y
s
i
c
a
l
b
a
r
r
i
e
r
R
e
si
l
i
e
n
c
y
C
r
o
ss
d
e
v
i
c
e
p
o
r
t
a
b
i
l
i
t
y
O
u
r
s
Y
e
s
Y
e
s
Y
e
s
Y
e
s
Y
e
s
Y
e
s
K
e
y
s
i
n
l
o
c
a
l
st
o
r
a
g
e
Y
e
s
P
a
ssw
o
r
d
d
r
i
v
e
n
k
e
y
s
Y
e
s
Y
e
s
Y
e
s
H
o
st
e
d
w
a
l
l
e
t
Y
e
s
5.
SE
CUR
I
T
Y
ANA
L
YS
I
S
T
h
e
s
ec
u
r
ity
an
aly
s
is
d
ea
ls
w
ith
h
o
w
it
is
d
if
f
icu
lt
to
attac
k
b
y
ad
v
er
s
ar
ies
to
g
et
th
e
k
e
y
.
T
h
e
k
ey
p
ar
ts
ca
n
b
e
s
en
t to
v
ir
tu
al
m
ac
h
in
es in
clo
u
d
en
v
ir
o
n
m
e
n
t.
I
t is n
o
t p
o
s
s
ib
le
to
f
o
r
m
th
e
k
ey
s
in
ce
ad
v
er
s
ar
ies
h
av
e
to
co
m
p
r
o
m
is
e
at
least
t
h
r
esh
o
ld
n
u
m
b
er
o
f
k
e
y
s
p
lits
.
Fu
r
th
er
th
e
k
e
y
s
p
lits
ca
n
r
ef
r
esh
at
ea
ch
v
ir
tu
al
m
ac
h
in
e.
T
h
er
ef
o
r
e,
r
ec
o
n
s
tr
u
ctin
g
th
e
k
ey
f
r
o
m
its
p
ar
ts
is
n
o
t
f
ea
s
ib
le.
E
v
en
if
attac
k
e
r
s
o
b
tain
f
ewe
r
t
h
an
th
r
esh
o
ld
n
u
m
b
e
r
o
f
k
e
y
p
ar
t
s
,
th
ey
ca
n
n
o
t
ass
em
b
le
t
h
e
k
ey
th
r
o
u
g
h
th
e
k
ey
p
ar
ts
.
T
h
e
u
s
e
o
f
th
r
esh
o
l
d
-
b
ased
Sh
am
ir
’
s
s
ec
r
et
s
h
ar
in
g
p
r
ev
en
ts
th
e
attac
k
er
s
to
ca
p
tu
r
e
th
e
s
id
e
ch
an
n
el
in
f
o
r
m
atio
n
b
y
r
ef
r
esh
in
g
th
e
k
ey
s
h
ar
es
at
v
ir
tu
al
m
ac
h
in
es
.
T
h
u
s
,
it
d
o
es
n
o
t
ca
u
s
e
s
id
e
ch
an
n
el
attac
k
.
E
v
en
if
th
e
less
th
an
t
n
u
m
b
er
o
f
v
ir
tu
al
m
ac
h
in
es
cr
ash
ed
/b
ec
o
m
es
f
au
lty
,
th
e
k
ey
ca
n
n
o
t
b
e
f
o
r
m
ed
.
T
h
u
s
,
it
is
r
esil
ien
ce
to
lo
s
s
/f
au
lt.
Mu
ltil
ev
el
k
ey
s
p
lit
u
p
a
p
p
r
o
a
ch
is
en
h
a
n
cin
g
k
ey
s
ec
u
r
ity
a
t
m
u
ltip
le
lev
els.
User
h
as
to
d
ef
in
e
th
e
lev
els
u
p
to
wh
ich
k
e
y
ca
n
b
e
s
p
lit u
p
.
T
h
u
s
,
en
h
a
n
cin
g
t
h
e
k
ey
s
ec
u
r
ity
in
b
lo
ck
c
h
ain
n
etwo
r
k
.
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
K
ey
ma
n
a
g
eme
n
t fo
r
b
itco
i
n
t
r
a
n
s
a
ctio
n
s
u
s
in
g
clo
u
d
b
a
s
ed
ke
y
s
p
litt
in
g
…
(
A
ma
r
B
u
ch
a
d
e
)
1865
6.
CO
NCLU
SI
O
N
Key
m
an
ag
em
en
t
is
cr
u
cial
in
ca
s
e
of
B
i
tco
in
m
an
ag
em
en
t.
T
h
e
clo
u
d
-
b
a
s
e
d
k
ey
s
p
lit
up
t
ec
h
n
iq
u
e
is
u
s
ed
to
p
r
o
tect
th
e
k
ey
ag
ain
s
t
in
tr
u
d
er
s
.
Mu
ltil
ev
el
k
ey
s
p
litt
in
g
ap
p
r
o
ac
h
f
u
r
t
h
er
en
h
an
ce
s
th
e
s
ec
u
r
ity
of
k
ey
m
an
ag
em
en
t.
W
e
co
m
p
ar
ed
o
u
r
a
p
p
r
o
ac
h
to
o
th
er
ap
p
r
o
ac
h
es
to
in
th
e
co
n
te
x
t
o
f
s
ec
u
r
ity
th
e
k
e
y
f
o
r
b
lo
ck
ch
ain
.
tr
an
s
ac
tio
n
s
.
I
t
is
f
o
u
n
d
th
at
o
u
r
ap
p
r
o
ac
h
is
p
r
o
v
in
g
th
e
b
est
co
m
p
a
r
ed
to
o
th
er
s
.
T
h
e
s
ec
u
r
ity
ass
es
s
m
en
t
r
ev
ea
ls
th
at
r
ec
o
n
s
tr
u
ctin
g
th
e
co
m
p
lete
k
ey
is
ch
allen
g
in
g
f
o
r
a
n
attac
k
er
,
th
er
eb
y
p
r
ev
en
tin
g
ac
ce
s
s
to
th
e
B
itco
in
wallet.
RE
F
E
R
E
NC
E
S
[
1
]
S
.
N
a
k
a
m
o
t
o
,
“
B
i
t
c
o
i
n
:
a
p
e
e
r
-
to
-
p
e
e
r
e
l
e
c
t
r
o
n
i
c
c
a
sh
sy
s
t
e
m,”
U
n
p
u
b
l
i
s
h
e
d
,
p
p
.
1
–
9
,
2
0
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1
6
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1866
B
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RAP
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AUTH
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Am
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fr
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c
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tac
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m
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h
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Evaluation Warning : The document was created with Spire.PDF for Python.