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Science
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l.
3
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l
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K
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w
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s
:
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lo
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Fo
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wan
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ad
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s
u
ch
as
q
u
an
tity
,
o
r
ig
in
ality
,
an
d
q
u
ality
o
f
th
e
p
r
o
d
u
cts
to
th
e
b
l
o
ck
ch
ai
n
ap
p
licatio
n
.
T
h
e
o
wn
er
s
h
ip
o
f
t
h
e
p
r
o
d
u
cts
is
tr
an
s
f
er
r
e
d
to
th
e
n
ex
t
e
n
tity
,
th
e
f
o
o
d
p
r
o
ce
s
s
o
r
,
th
r
o
u
g
h
a
s
m
ar
t c
o
n
tr
ac
t,
an
d
a
n
ew
b
lo
c
k
is
ad
d
ed
to
th
e
tr
an
s
ac
tio
n
.
b)
Fo
o
d
p
r
o
ce
s
s
o
r
:
th
e
f
o
o
d
p
r
o
c
ess
o
r
is
th
e
s
ec
o
n
d
en
tity
p
ar
ticip
atin
g
in
th
e
b
lo
ck
ch
ain
.
T
h
ey
p
r
o
c
ess
th
e
f
o
o
d
item
s
an
d
m
a
k
e
th
em
r
e
ad
y
f
o
r
d
eliv
er
y
.
On
ce
th
e
o
wn
er
s
h
ip
o
f
th
e
p
r
o
d
u
cts
is
t
r
an
s
f
er
r
ed
to
th
e
d
is
tr
ib
u
to
r
,
a
n
ew
b
lo
ck
is
ad
d
ed
to
th
e
tr
a
n
s
ac
tio
n
.
c)
Dis
tr
ib
u
to
r
:
t
h
e
d
is
tr
ib
u
to
r
is
r
esp
o
n
s
ib
le
f
o
r
d
is
tr
ib
u
tin
g
th
e
f
o
o
d
item
s
to
r
etailer
s
.
T
h
e
p
r
o
ce
s
s
o
f
tr
an
s
f
er
r
in
g
o
wn
e
r
s
h
ip
f
r
o
m
t
h
e
d
is
tr
ib
u
t
o
r
t
o
th
e
r
etailer
i
s
r
ep
ea
ted
,
an
d
a
n
ew
b
lo
ck
is
ad
d
ed
to
th
e
tr
an
s
ac
tio
n
.
d)
R
etailer
:
t
h
e
r
etailer
p
u
r
ch
ases
th
e
item
s
f
r
o
m
th
e
d
is
tr
ib
u
to
r
an
d
tr
an
s
f
er
s
th
em
to
th
e
c
u
s
to
m
er
s
.
e)
C
o
n
s
u
m
er
:
t
h
e
co
n
s
u
m
e
r
i
s
th
e
f
in
al
en
tity
in
th
is
p
r
o
ce
s
s
.
T
h
ey
ca
n
tr
ac
e
th
e
o
r
i
g
in
ality
o
f
th
e
f
o
o
d
item
s
th
r
o
u
g
h
th
e
tr
a
n
s
ac
tio
n
d
etails r
ec
o
r
d
e
d
in
th
e
b
lo
ck
c
h
ain
.
Fig
u
r
e
2
.
B
lo
ck
c
h
ain
b
ased
a
g
r
i
-
FSC
m
an
ag
em
en
t sy
s
tem
C
u
r
r
en
tly
,
b
l
o
ck
ch
ain
ap
p
lica
tio
n
s
in
th
e
FSC
,
as
well
as
o
th
er
d
o
m
ain
s
,
o
f
f
er
tr
ac
ea
b
i
lity
an
d
a
ce
r
tain
lev
el
o
f
p
r
i
v
ac
y
th
r
o
u
g
h
th
e
u
s
e
o
f
p
er
m
is
s
io
n
ed
b
l
o
ck
ch
ain
p
latf
o
r
m
s
lik
e
h
y
p
er
led
g
er
f
ab
r
ic
.
So
m
e
r
esear
ch
er
s
h
av
e
em
p
lo
y
ed
cr
y
p
to
g
r
a
p
h
ic
al
g
o
r
ith
m
s
to
e
n
h
an
ce
d
ata
p
r
iv
ac
y
d
u
r
in
g
tr
a
n
s
ac
tio
n
s
.
R
ec
en
tly
,
th
e
u
s
e
o
f
ze
r
o
-
k
n
o
wled
g
e
p
r
o
o
f
(
Z
KP)
alg
o
r
ith
m
s
[
3
]
,
[
4
]
,
p
ar
ticu
lar
ly
Z
K
-
SNAR
K,
h
as
b
ee
n
ex
p
lo
r
e
d
t
o
im
p
lem
en
t
p
r
iv
ac
y
in
b
lo
c
k
ch
ain
ap
p
licatio
n
s
.
T
h
ese
cr
y
p
to
g
r
a
p
h
ic
alg
o
r
ith
m
s
,
in
cl
u
d
in
g
Z
K
-
SNAR
K,
p
r
o
v
id
e
d
ata
s
ec
u
r
ity
.
Ho
wev
er
,
a
lim
itatio
n
is
th
at
th
ey
ar
e
s
u
s
ce
p
tib
le
to
q
u
a
n
tu
m
attac
k
s
.
I
n
th
e
co
m
in
g
y
ea
r
s
,
q
u
an
t
u
m
co
m
p
u
ter
s
with
th
eir
im
m
en
s
e
co
m
p
u
tin
g
p
o
wer
co
u
l
d
p
o
ten
tially
c
o
m
p
r
o
m
is
e
b
lo
ck
c
h
ain
ap
p
licatio
n
s
with
ea
s
e,
p
o
s
in
g
a
s
ig
n
if
ica
n
t
th
r
ea
t.
T
h
e
r
e
f
o
r
e,
t
h
e
m
o
tiv
atio
n
b
eh
in
d
th
is
r
esear
ch
is
to
d
ev
elo
p
d
ef
en
ce
s
ag
ai
n
s
t
q
u
an
tu
m
attac
k
s
[
5
]
wh
ile
en
s
u
r
in
g
ef
f
icien
t
d
ata
p
r
iv
ac
y
in
b
lo
c
k
ch
ain
ap
p
licatio
n
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
52
In
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
3
7
,
No
.
2
,
Feb
r
u
a
r
y
20
2
5
:
1
10
2
-
1
11
1
1104
T
h
e
p
r
im
a
r
y
co
n
tr
ib
u
tio
n
o
f
th
is
r
esear
ch
p
ap
er
is
th
e
ap
p
licatio
n
o
f
a
m
o
d
i
f
ied
ZK
-
STARK
p
r
iv
a
cy
-
p
r
eser
v
in
g
alg
o
r
ith
m
t
o
th
e
b
lo
c
k
ch
ain
-
b
ased
FSC
.
T
h
e
k
ey
s
tep
s
ar
e
as f
o
llo
ws:
i)
C
o
n
v
er
tin
g
in
f
o
r
m
atio
n
th
at
n
ee
d
s
p
r
iv
ac
y
p
r
eser
v
atio
n
in
to
m
ath
em
atica
l e
x
p
r
ess
io
n
s
.
ii)
Mo
d
if
y
in
g
Z
K
-
STARK
with
th
r
ee
d
if
f
er
en
t p
o
ly
n
o
m
ial
in
te
r
p
o
latio
n
s
(
lag
r
an
g
e
p
o
l
y
n
o
m
i
al
in
ter
p
o
latio
n
,
b
ar
y
ce
n
tr
ic
la
g
r
an
g
e
in
ter
p
o
latio
n
,
an
d
f
ast f
o
u
r
ier
tr
an
s
f
o
r
m
(
FF
T
)
)
f
o
r
alg
e
b
r
aic
tr
a
n
s
f
o
r
m
atio
n
.
iii)
T
esti
n
g
an
d
co
m
p
ar
in
g
th
e
p
e
r
f
o
r
m
a
n
ce
o
f
th
ese
th
r
ee
p
o
ly
n
o
m
ial
in
ter
p
o
latio
n
s
with
in
t
h
e
Z
K
-
STARK
alg
o
r
ith
m
.
iv
)
I
m
p
lem
en
tin
g
th
e
b
lo
ck
ch
ain
FSC
u
s
in
g
h
y
p
er
led
g
er
co
m
p
o
s
er
.
T
h
is
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
ws:
s
ec
tio
n
2
p
r
esen
ts
th
e
r
el
ated
wo
r
k
,
s
er
v
in
g
as
a
liter
atu
r
e
r
ev
iew
o
f
p
r
ev
io
u
s
s
tu
d
ies.
I
n
s
ec
tio
n
3
i
n
tr
o
d
u
ce
s
th
e
p
r
o
p
o
s
ed
n
o
v
el
Z
K
-
STARK
alg
o
r
ith
m
.
I
n
s
ec
tio
n
4
d
is
cu
s
s
es
th
e
ex
p
er
im
e
n
ts
an
d
r
esu
lts
.
T
h
e
f
in
al
s
ec
tio
n
o
f
f
er
s
th
e
c
o
n
clu
s
io
n
.
2.
RE
L
AT
E
D
WO
RK
T
o
d
ate,
m
o
s
t
o
f
th
e
wo
r
k
in
th
is
ar
ea
h
as
u
s
ed
v
ar
io
u
s
c
r
y
p
to
g
r
ap
h
ic
tech
n
iq
u
es,
s
u
ch
as
p
r
o
x
y
re
-
en
cr
y
p
tio
n
,
r
in
g
s
ig
n
atu
r
es,
h
o
m
o
m
o
r
p
h
ic
en
c
r
y
p
tio
n
,
s
ec
u
r
e
m
u
ltip
ar
ty
co
m
p
u
tatio
n
,
an
d
ze
r
o
-
k
n
o
wled
g
e
p
r
o
o
f
s
(
s
p
ec
if
ically
ZK
-
SNAR
K)
.
T
h
e
Fig
u
r
e
3
en
lis
t
th
ese
tech
n
iq
u
es
in
b
r
ief
.
Her
e
is
a
b
r
ief
ex
p
lan
atio
n
o
f
ea
ch
tech
n
iq
u
e:
−
Z
er
o
-
k
n
o
wled
g
e
p
r
o
o
f
s
[
4
]
all
o
w
a
u
s
er
to
p
r
o
v
e
th
at
th
ey
k
n
o
w
r
eq
u
ir
ed
in
f
o
r
m
atio
n
with
o
u
t
ac
ce
s
s
in
g
th
e
ac
tu
al
in
f
o
r
m
atio
n
.
T
h
is
p
r
o
tects
th
e
p
r
i
v
ac
y
o
f
u
s
er
s
wh
o
p
ar
ticip
ate
in
b
lo
ck
c
h
ain
tr
an
s
ac
tio
n
s
b
y
allo
win
g
th
em
to
p
r
o
v
e
th
eir
id
en
tity
o
r
o
wn
e
r
s
h
ip
o
f
ce
r
ta
in
ass
ets
with
o
u
t
r
ev
ea
lin
g
an
y
d
etails
ab
o
u
t
th
e
in
f
o
r
m
atio
n
.
T
h
er
e
ar
e
t
h
r
ee
cr
iter
ia
th
at
a
Z
KP
m
u
s
t
s
atis
f
y
:
i)
c
o
m
p
leten
ess
:
i
f
th
e
s
tatem
en
t
is
tr
u
e,
an
h
o
n
est
v
e
r
if
ier
will
b
e
co
n
v
in
ce
d
o
f
its
tr
u
th
b
y
th
e
p
r
o
v
er
;
ii)
s
o
u
n
d
n
ess
:
i
f
th
e
s
tatem
en
t
is
f
alse,
th
e
p
r
o
v
er
ca
n
n
o
t
p
r
o
v
e
o
r
c
o
n
v
i
n
ce
th
e
v
er
if
ier
o
f
its
tr
u
th
;
an
d
iii)
z
er
o
k
n
o
wled
g
e:
i
f
th
e
s
tatem
en
t
is
tr
u
e,
th
e
v
er
if
ie
r
will
n
o
t
g
ai
n
an
y
in
f
o
r
m
a
tio
n
o
th
er
th
an
th
e
f
ac
t
it
s
elf
.
I
n
a
p
r
ac
tical
ex
a
m
p
le
with
in
t
h
e
co
n
tex
t
o
f
b
lo
ck
c
h
ain
s
u
p
p
ly
ch
ain
s
,
let
’
s
c
o
n
s
id
er
a
tr
a
n
s
ac
tio
n
wh
er
e
a
p
ar
ticip
an
t
f
ar
m
er
co
n
d
u
cts
a
tr
an
s
ac
tio
n
with
a
f
o
o
d
p
r
o
ce
s
s
o
r
.
I
n
th
is
s
ce
n
ar
io
,
th
e
f
ar
m
er
ca
n
p
r
o
v
e
to
th
e
f
o
o
d
p
r
o
ce
s
s
o
r
th
at
th
e
tr
an
s
ac
tio
n
d
ata
co
n
tain
s
co
r
r
ec
t
in
f
o
r
m
atio
n
r
e
g
ar
d
in
g
th
e
q
u
ality
an
d
o
r
ig
in
ality
o
f
th
e
f
o
o
d
item
,
with
o
u
t
r
ev
ea
lin
g
an
y
o
th
er
in
f
o
r
m
atio
n
,
s
u
ch
as
th
e
f
ar
m
er
’
s
p
er
s
o
n
al
id
en
tity
.
G
o
n
g
a
t
a
l.
[
4
]
p
r
esen
ted
a
p
ap
er
o
n
co
m
p
ar
ativ
e
an
a
l
y
s
is
o
f
Z
KP
a
lg
o
r
ith
m
s
as
Z
K
-
SNAR
K,
Z
K
-
STAR
K,
MP
C
b
ased
a
lg
o
r
ith
m
an
d
B
u
lletPro
o
f
in
d
if
f
er
e
n
t a
s
p
ec
ts
as g
iv
en
in
th
e
T
a
b
le
1
.
−
Pro
x
y
r
e
-
en
c
r
y
p
tio
n
[
6
]
allo
ws
a
u
s
er
to
en
cr
y
p
t
d
ata
s
o
th
at
o
n
ly
an
o
th
er
u
s
er
ca
n
d
ec
r
y
p
t
it.
T
h
is
tech
n
iq
u
e
p
r
o
tects
th
e
p
r
i
v
ac
y
o
f
d
ata
tr
an
s
ac
tio
n
s
b
y
allo
win
g
u
s
er
s
to
s
h
ar
e
t
h
eir
en
c
r
y
p
ted
d
ata
with
o
th
er
s
with
o
u
t r
e
v
ea
lin
g
th
e
p
l
ain
tex
t c
o
n
ten
t.
−
R
in
g
s
ig
n
atu
r
es
[
7
]
allo
w
a
u
s
er
to
s
ig
n
a
m
es
s
ag
e
with
o
u
t
r
ev
ea
lin
g
th
eir
id
en
tity
.
T
h
is
ca
n
b
e
u
s
ed
to
p
r
o
tect
th
e
p
r
iv
ac
y
o
f
u
s
er
s
w
h
o
p
ar
ticip
ate
in
b
lo
c
k
ch
ain
tr
an
s
ac
tio
n
s
.
−
Ho
m
o
m
o
r
p
h
ic
en
cr
y
p
tio
n
[
8
]
p
er
f
o
r
m
s
co
m
p
u
tatio
n
s
o
n
en
cr
y
p
ted
d
ata
with
o
u
t
its
d
ec
r
y
p
tio
n
.
T
h
is
p
r
o
tects th
e
p
r
iv
ac
y
o
f
d
a
ta
tr
an
s
ac
tio
n
s
with
o
u
t r
ev
ea
li
n
g
th
e
p
lain
tex
t c
o
n
te
n
t.
−
Secu
r
e
m
u
ltip
ar
ty
co
m
p
u
t
atio
n
[
9
]
in
clu
d
es
d
if
f
e
r
en
t
p
ar
tie
s
with
th
eir
o
wn
in
p
u
t
an
d
p
er
f
o
r
m
s
f
u
n
ctio
n
o
n
en
cr
y
p
ted
d
ata
with
h
id
in
g
in
p
u
ts
.
Fig
u
r
e
3
.
E
x
is
tin
g
en
cr
y
p
tio
n
t
ec
h
n
iq
u
es in
b
lo
ck
ch
ai
n
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52
P
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1105
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B
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No
P
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f
s
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e
sma
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p
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si
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w
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c
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Lo
w
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o
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p
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p
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V
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q
u
a
n
t
u
m a
t
t
a
c
k
s
B
o
o
et
a
l.
[
1
0
]
p
r
o
p
o
s
ed
a
m
o
d
el
th
at
d
e
v
elo
p
e
d
a
lig
h
tweig
h
t
v
er
s
io
n
o
f
th
e
Z
KP
p
r
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t
o
co
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s
u
itab
le
f
o
r
b
lo
ck
c
h
ain
tr
an
s
ac
tio
n
s
.
T
h
e
au
th
o
r
s
aim
ed
to
ad
d
r
ess
th
e
s
y
s
tem
o
v
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ea
d
ca
u
s
ed
b
y
s
to
r
in
g
d
ata
o
n
in
ter
n
et
o
f
th
in
g
s
(
I
o
T
)
d
ev
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T
h
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in
tr
o
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a
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f
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s
p
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ically
Z
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-
SNAR
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wh
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m
in
im
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Me
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R
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Pi
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wh
ile
th
e
Gan
ac
h
e
-
cli
E
th
er
eu
m
p
latf
o
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m
was
u
s
ed
to
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a
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lo
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ch
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y
s
t
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.
T
h
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u
lts
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f
th
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s
tu
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y
in
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icate
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th
at
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tili
zin
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th
e
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tweig
h
t
Z
KP
a
p
p
r
o
ac
h
im
p
r
o
v
ed
ef
f
icien
c
y
an
d
s
h
o
wed
p
r
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m
is
in
g
p
o
ten
tial
f
o
r
r
ea
l
-
wo
r
ld
im
p
lem
e
n
tatio
n
.
I
n
a
r
esear
ch
p
ap
er
,
Mo
u
r
is
a
n
d
T
s
o
u
ts
o
s
[
1
1
]
d
ev
el
o
p
ed
a
n
d
ex
ec
u
te
d
th
e
Z
lich
f
r
am
ew
o
r
k
,
a
Z
KP
s
y
s
tem
,
u
s
in
g
th
e
Z
er
o
jav
a
lan
g
u
ag
e
with
a
cr
o
s
s
-
co
m
p
iler
.
Un
lik
e
o
th
er
m
o
d
els,
th
is
f
r
am
ewo
r
k
d
o
es
n
o
t
r
ely
o
n
a
tr
u
s
ted
s
etu
p
f
o
r
Z
KP
.
I
n
s
tead
,
it
u
tili
ze
s
tr
ad
itio
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al
in
s
tr
u
ctio
n
s
eq
u
e
n
ce
s
r
at
h
er
th
a
n
ar
ith
m
etic
cir
cu
its
.
T
h
e
Z
lich
f
r
am
ewo
r
k
is
c
h
ar
ac
ter
ized
b
y
its
tr
an
s
p
ar
en
cy
,
u
n
iv
e
r
s
ality
,
an
d
r
esil
ien
ce
ag
ain
s
t
p
o
s
t
-
q
u
an
tu
m
th
r
ea
ts
,
ac
h
ie
v
ed
b
y
in
co
r
p
o
r
atin
g
th
e
Z
K
-
STARK
p
r
o
to
c
o
l.
L
i
et
a
l
.
[
1
2
]
d
es
ig
n
ed
s
h
ellp
r
o
o
f
an
ef
f
icien
t
Z
KP
b
y
m
o
d
if
y
i
n
g
t
h
e
B
u
lletp
r
o
o
f
in
n
e
r
p
r
o
d
u
ct
ar
g
u
m
en
t
b
y
u
s
in
g
co
m
p
r
ess
io
n
tech
n
iq
u
e.
T
h
is
r
esear
ch
Sh
ellp
r
o
o
f
r
e
d
u
ce
d
p
r
o
o
f
s
ize
an
d
c
o
m
p
u
tatio
n
co
s
t
b
y
h
alf
o
f
b
u
lletp
r
o
o
f
p
r
o
o
f
s
ize
as
well
co
m
p
u
tatio
n
co
s
t.
Gab
a
et
a
l.
[
1
3
]
s
p
ec
if
ically
f
o
cu
s
o
n
th
e
h
ea
lth
ca
r
e
s
ec
to
r
an
d
p
r
o
p
o
s
e
a
m
eth
o
d
f
o
r
m
ain
tain
in
g
d
at
a
p
r
iv
ac
y
t
h
r
o
u
g
h
au
th
en
t
icatio
n
k
ey
m
an
a
g
em
en
t
b
as
ed
o
n
Z
KP
.
T
h
eir
wo
r
k
d
e
m
o
n
s
tr
ates
th
at
th
e
p
r
o
p
o
s
ed
m
eth
o
d
is
b
o
th
s
ec
u
r
e
an
d
r
o
b
u
s
t
ag
ain
s
t
v
ar
io
u
s
attac
k
s
,
s
u
ch
as
m
an
-
in
-
th
e
-
m
id
d
le
(
MI
T
M)
attac
k
s
an
d
r
ep
lay
attac
k
s
.
Fu
r
th
er
m
o
r
e
,
it
o
f
f
er
s
d
ata
in
teg
r
ity
,
co
n
f
id
en
tiality
,
an
d
p
r
o
tec
tio
n
ag
ain
s
t
cy
b
er
-
attac
k
s
.
Ko
n
k
in
a
n
d
Z
ap
ec
h
n
ik
o
v
[
1
4
]
s
h
ed
s
lig
h
t
o
n
th
e
t
o
p
ic
o
f
p
r
iv
ac
y
i
n
tr
a
n
s
ac
tio
n
s
,
s
p
ec
if
ically
ad
d
r
ess
in
g
id
en
tity
p
r
iv
ac
y
an
d
tr
an
s
ac
tio
n
p
r
iv
ac
y
.
I
n
th
eir
r
esear
ch
,
th
ey
u
tili
z
ed
a
n
o
n
-
in
te
r
ac
ti
v
e
ze
r
o
k
n
o
wled
g
e
p
r
o
o
f
(
NI
Z
K)
p
r
o
to
co
l
with
in
a
co
r
p
o
r
ate
b
lo
c
k
ch
ain
f
r
am
ew
o
r
k
ca
lled
Ma
s
ter
ch
ain
,
wh
ich
is
b
u
ilt o
n
th
e
E
th
er
eu
m
p
latf
o
r
m
.
Ho
wev
er
,
t
h
is
ar
ticle
d
o
es
n
o
t p
r
o
v
id
e
a
n
y
s
p
ec
if
ic
r
esu
lt
s
.
Gu
an
et
a
l.
[
1
5
]
d
esig
n
ed
B
lo
ck
Ma
ze
f
o
r
ac
c
o
u
n
t
m
o
d
el
b
l
o
ck
ch
ain
(
E
th
e
r
eu
m
)
u
s
in
g
Z
K
-
SNAR
K
f
o
r
s
ec
u
r
e
tr
a
n
s
ac
tio
n
s
.
T
h
is
r
esear
ch
u
s
ed
L
ib
s
n
ar
k
an
d
g
o
-
E
th
er
eu
m
f
o
r
im
p
lem
en
tatio
n
.
Yan
g
an
d
L
i
[
1
6
]
p
r
o
p
o
s
ed
a
p
r
o
to
co
l
B
Z
DI
MS
f
o
r
k
ee
p
in
g
id
en
tity
p
r
iv
ate
u
s
in
g
Z
KP
s
y
s
tem
in
b
lo
ck
ch
ai
n
b
y
im
p
lem
en
tin
g
ch
allen
g
e
r
esp
o
n
s
e
m
o
d
el.
Z
h
en
g
et
a
l.
[
1
7
]
u
s
ed
n
o
n
-
in
ter
ac
tiv
e
Z
K
-
SNAR
K
an
d
h
o
m
o
m
o
r
p
h
ic
en
c
r
y
p
tio
n
to
p
r
eser
v
e
p
r
i
v
ac
y
o
f
th
e
p
a
tien
t
in
f
o
r
m
atio
n
a
n
d
in
s
u
r
a
n
ce
co
m
p
an
y
w
h
ile
tr
an
s
ac
tin
g
with
b
lo
ck
ch
ain
.
Ma
et
a
l.
[
1
8
]
d
esig
n
e
d
a
p
r
iv
ac
y
p
r
eser
v
in
g
ac
c
o
u
n
t
m
o
d
el
in
s
u
p
p
ly
ch
ain
u
s
in
g
h
o
m
o
m
o
r
p
h
ic
en
cr
y
p
tio
n
an
d
n
o
v
el
NI
Z
K
f
o
r
en
cr
y
p
tio
n
o
f
b
alan
ce
a
n
d
t
r
an
s
ac
tio
n
a
m
o
u
n
t.
T
h
is
n
o
v
el
NI
Z
K
alg
o
r
ith
m
p
r
o
v
es
b
etter
in
ter
m
s
o
f
s
m
all
p
r
o
o
f
s
ize,
m
in
im
u
m
co
m
p
u
tatio
n
co
s
t
th
an
Z
K
-
SNAR
K,
Z
K
-
STARK
an
d
b
u
lletp
r
o
o
f
.
J
u
n
ejo
et
a
l.
[
1
9
]
u
s
ed
Z
K
-
SNAR
K
to
p
r
eser
v
e
p
r
iv
ac
y
in
th
eir
s
y
s
tem
.
Sh
ar
m
a
et
a
l.
[
2
0
]
d
ev
elo
p
e
d
n
o
v
el
au
t
h
en
ticatio
n
s
y
s
tem
f
o
r
h
ea
lth
ca
r
e
in
s
u
r
an
ce
s
ch
em
e
u
s
in
g
ZK
-
SNAR
K
an
d
p
r
o
x
y
e
n
cr
y
p
tio
n
(
h
y
b
r
id
s
y
m
m
etr
ic
-
asy
m
m
etr
ic
en
cr
y
p
tio
n
)
f
o
r
ac
ce
s
s
co
n
t
r
o
l.
E
-
ca
r
d
s
h
ar
ed
with
c
u
s
to
m
er
u
s
ed
to
g
en
er
ate
Z
KP
.
Data
s
to
r
ed
u
s
in
g
I
PF
S.
R
esu
lts
s
h
o
wn
it
p
er
f
o
r
m
s
b
etter
th
an
AW
S
S3
.
B
h
ad
r
a
et
a
l.
[
2
1
]
d
ev
elo
p
ed
a
n
o
v
el
b
lo
ck
c
h
ain
FSC
o
v
er
c
o
m
in
g
th
e
lim
itatio
n
s
o
f
p
ay
m
en
t
s
y
s
tem
,
g
o
v
er
n
a
n
ce
.
I
n
b
lo
ck
ch
ain
s
u
p
p
ly
c
h
ain
,
th
eir
o
wn
p
ay
m
en
t
s
y
s
tem
im
p
lem
en
te
d
.
T
h
e
g
o
v
er
n
m
en
t
p
o
licies
ar
e
i
n
clu
d
ed
f
o
r
f
ar
m
er
,
th
o
s
e
in
co
m
e
less
th
an
s
o
m
e
cr
iter
ia.
T
h
e
im
p
lem
en
te
d
p
l
atf
o
r
m
is
E
th
er
eu
m
an
d
test
ed
b
y
h
y
p
e
r
led
g
er
ca
lip
er
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
52
In
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
3
7
,
No
.
2
,
Feb
r
u
a
r
y
20
2
5
:
1
10
2
-
1
11
1
1106
3.
P
RO
P
O
SE
D
M
E
T
H
O
D
3
.
1
.
ZK
-
ST
ARK
a
lg
o
rit
hm
ZK
-
STARK
is
a
ze
r
o
-
k
n
o
wle
d
g
e
s
ca
lab
le
tr
an
s
p
ar
e
n
t
ar
g
u
m
en
t
o
f
k
n
o
wled
g
e.
I
t
is
o
n
e
t
y
p
e
o
f
Z
KP
in
tr
o
d
u
ce
d
in
San
tis
et
a
l.
[
2
2
]
,
B
er
en
ts
en
et
a
l.
[
2
3
]
,
B
en
-
Sas
s
o
n
et
a
l.
[
2
4
]
.
Step
s
ar
e
wr
itten
as
f
o
llo
win
g
f
o
r
Z
K
-
STARK.
1)
Def
in
in
g
s
tatem
en
t to
b
e
p
r
o
v
ed
b
y
p
r
o
v
er
.
2)
C
o
n
v
er
t th
e
s
tatem
en
t in
to
al
g
eb
r
aic
p
r
o
b
lem
I
w
o
r
k
in
g
with
p
o
ly
n
o
m
ials
an
d
tr
a
n
s
f
o
r
m
ati
o
n
.
3)
Ver
if
y
in
g
p
o
ly
n
o
m
ials
is
o
f
l
o
w
d
eg
r
ee
o
r
n
o
t
b
y
u
s
in
g
FR
I
(
f
ast
r
ee
d
-
s
o
lo
m
o
n
in
ter
ac
ti
v
e
o
r
ac
le
p
r
o
o
f
s
o
f
p
r
o
x
im
ity
)
p
r
o
t
o
co
l.
4)
If
it is
a
lo
w
d
eg
r
ee
,
th
en
t
h
e
i
n
itial st
atem
en
t is tr
u
e.
ZK
-
STARK
is
ef
f
icien
t,
s
ca
la
b
le
an
d
tr
a
n
s
p
ar
en
t a
s
it is
n
o
t
u
s
in
g
an
y
tr
u
s
ted
s
etu
p
an
d
is
s
ec
u
r
e.
As with
o
u
t
r
ev
ea
lin
g
o
t
h
er
in
f
o
r
m
atio
n
,
th
e
p
r
o
v
e
r
ca
n
p
r
o
v
e
th
e
d
ata
i
n
teg
r
ity
.
3
.
2
.
ZK
-
ST
ARK
al
g
o
rit
hm
in blo
ck
cha
in f
o
o
d su
pp
ly
ch
a
in
T
h
e
o
b
jectiv
e
o
f
o
u
r
p
r
o
p
o
s
ed
wo
r
k
is
to
u
tili
ze
ZK
-
STA
R
K
f
o
r
b
lo
ck
ch
ain
in
FSC
to
en
s
u
r
e
th
e
p
r
iv
ac
y
o
f
s
en
s
itiv
e
in
f
o
r
m
atio
n
,
in
clu
d
i
n
g
p
er
s
o
n
al
id
en
tity
an
d
th
e
q
u
ality
o
f
f
o
o
d
p
r
o
d
u
cts,
wh
ile
k
ee
p
in
g
th
e
f
o
o
d
p
r
o
ce
s
s
in
g
tec
h
n
iq
u
e
s
co
n
f
id
en
tial.
As
s
h
o
wn
i
n
t
h
e
Fig
u
r
e
4
,
all
p
a
r
ticip
atin
g
en
titi
es
ar
e
p
r
o
v
in
g
th
eir
tr
an
s
ac
tio
n
d
etails
to
t
h
e
n
ex
t
en
tity
.
So
,
in
ev
e
r
y
tr
an
s
ac
tio
n
wh
il
e
tr
an
s
f
er
r
i
n
g
o
w
n
er
s
h
ip
,
th
e
ZK
-
STARK
p
r
o
to
co
l
will
b
e
in
clu
d
ed
,
it
ex
ec
u
tes
an
d
p
r
o
v
e
th
e
p
r
o
o
f
.
Ou
r
ca
s
e
s
tu
d
y
f
o
c
u
s
es
o
n
th
e
p
r
o
d
u
ctio
n
o
f
jag
g
e
r
y
f
r
o
m
s
u
g
ar
ca
n
e
c
r
o
p
s
.
Du
r
in
g
th
e
c
o
n
v
er
s
io
n
p
r
o
ce
s
s
o
f
s
u
g
ar
ca
n
e
to
jag
g
e
r
y
,
wh
ic
h
in
v
o
lv
es
v
ar
i
o
u
s
f
o
o
d
p
r
o
ce
s
s
in
g
tech
n
iq
u
es,
it
is
cr
u
cial
t
o
m
ain
tain
th
e
co
n
f
i
d
en
tiality
o
f
th
ese
m
eth
o
d
s
.
T
h
e
cu
s
to
m
er
s
h
o
u
l
d
o
n
ly
h
a
v
e
ac
ce
s
s
to
in
f
o
r
m
atio
n
r
e
g
a
r
d
in
g
th
e
o
r
ig
in
ality
an
d
q
u
al
ity
o
f
th
e
jag
g
er
y
,
with
o
u
t b
ein
g
ex
p
o
s
ed
to
th
e
s
p
ec
if
ic
f
o
o
d
p
r
o
ce
s
s
in
g
s
ec
r
ets.
Fig
u
r
e
4
.
Z
K
-
STARK
f
o
r
b
lo
c
k
ch
ain
ag
r
icu
ltu
r
e
FSC
T
h
e
s
tep
s
in
v
o
lv
ed
f
o
r
tr
a
n
s
f
e
r
r
in
g
in
f
o
r
m
atio
n
u
s
in
g
ZK
-
S
T
AR
K
f
r
o
m
o
n
e
en
tity
t
o
an
o
th
er
ar
e
as
f
o
llo
w.
W
e
ass
u
m
e
th
at
jag
g
e
r
y
h
as
b
ee
n
p
r
o
d
u
ce
d
b
y
a
f
o
o
d
p
r
o
ce
s
s
o
r
a
n
d
it
is
n
o
w
t
r
an
s
f
er
r
in
g
to
t
h
e
n
ex
t
en
tity
d
is
tr
ib
u
to
r
.
W
e
h
a
v
e
to
k
ee
p
s
ec
r
et
d
ata
as
f
o
o
d
p
r
o
ce
s
s
in
g
tech
n
iq
u
e.
Alg
o
r
ith
m
1
s
h
o
ws
th
e
wo
r
k
in
g
o
f
th
e
alg
o
r
ith
m
.
Alg
o
r
ith
m
1
.
U
s
in
g
Z
K
-
STARK f
o
r
p
r
eser
v
in
g
p
r
iv
ac
y
Entities involved
–
Food processor (FD), distributor (D)
Input
-
Jaggery
item
s
erial
number,
food
pro
cessing
technique,
food
safety
re
su
lt
,
location, quantity, price
Steps
-
1.
Tw
o
in
pu
ts
,
Ja
gg
er
y
se
ri
al
nu
mb
er
an
d
fo
od
sa
fe
t
y
re
su
lt
,
wi
ll
be
pr
ov
i
d
ed
to
th
e
ZK
-
STARK protocol.
2.
These inputs will generate a polynomial representation of the data.
3.
Th
e
pr
ov
er
wi
ll
ou
tp
u
t
a
po
ly
no
mi
al
th
at
de
mo
ns
t
ra
te
s
a
sp
ec
if
ic
pr
op
e
rt
y
of
th
e
food item, it is safe and of desired quality.
4.
Th
e
ve
ri
fi
er
wi
ll
us
e
th
e
FR
I
pr
ot
oc
ol
to
ch
ec
k
if
th
e
po
ly
no
mi
al
cr
ea
te
d
by
th
e
prover possesses the desired property, provided it is of low degree.
5.
If
th
e
po
ly
no
mi
al
is
of
lo
w
de
gr
ee
,
it
in
di
ca
te
s
th
at
th
e
pr
ov
er
’s
st
at
em
en
t
is
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2
5
0
2
-
4
7
52
P
r
iva
cy
p
r
eser
vin
g
ZK
-
S
TAR
K
b
a
s
ed
b
lo
ck
ch
a
in
fo
r
…
(
M
a
d
h
u
r
i S
a
d
a
s
h
iv
A
r
a
d
e
)
1107
true, confirming that the jaggery item is of the desired quality and origin.
6.
By
pr
ov
in
g
th
e
cl
ai
me
d
q
ua
li
ty
of
th
e
fo
od
it
em
wi
th
ou
t
re
ve
al
in
g
ot
he
r
da
ta
,
th
e
privacy of the transaction between the food
processor and distributor is preserved.
Output
–
Verified proof
T
h
e
Z
K
-
STARK
alg
o
r
ith
m
u
s
es
lag
r
an
g
e
p
o
ly
n
o
m
ial
in
te
r
p
o
latio
n
[
2
5
]
b
y
d
e
f
au
lt.
Fo
r
th
is
r
esear
ch
,
we
ex
p
er
im
en
ted
with
d
if
f
e
r
en
t
i
n
ter
p
o
latio
n
s
s
u
ch
as
b
ar
y
ce
n
tr
ic
lag
r
an
g
e
in
ter
p
o
latio
n
[
2
6
]
an
d
FF
T
[
2
7
]
,
an
d
co
m
p
ar
ed
th
eir
p
e
r
f
o
r
m
an
ce
a
g
ain
s
t th
e
lag
r
an
g
e
p
o
l
y
n
o
m
ia
l in
ter
p
o
latio
n
.
First,
we
will
f
o
r
m
u
late
o
u
r
o
r
g
an
ic
jag
g
e
r
y
u
s
ec
ase
in
to
th
e
m
ath
em
atica
l
ex
p
r
ess
io
n
(
J
)
.
W
e
u
s
e
I
=4
,
wh
er
e
I
m
ea
n
s
in
g
r
ed
ien
t
s
(
I
1
, I
2
ar
e
o
r
g
an
ic
i
n
g
r
e
d
ien
ts
an
d
I
3
,
I
4
ar
e
in
o
r
g
a
n
ic
in
g
r
e
d
ien
ts
)
.
=
[
1
,
2
,
3
,
4
]
=
[
1
,
1
,
0
,
0
]
(
1
)
I
n
(
1
)
s
atis
f
ies
th
e
s
tatem
en
t
(I
1
,
I
2
ar
e
o
r
g
a
n
ic
in
g
r
e
d
ien
ts
v
alu
e
s
et
to
1
,
I
3
,
I
4
ar
e
n
o
n
-
o
r
g
an
ic
in
g
r
ed
ien
ts
r
ep
r
esen
ted
b
y
0
)
.
=
[
1
,
1
,
2
,
2
]
(
2
)
In
(
2
)
d
o
es
n
o
t
s
atis
f
y
th
e
s
tatem
en
t
(
as
I
3
,
I
4
ar
e
s
et
to
o
th
er
th
a
n
0
,
in
d
icatin
g
p
r
ese
n
ce
o
f
n
o
n
-
o
r
g
an
ic
in
g
r
ed
ien
ts
)
.
T
h
e
p
r
o
v
er
a
n
d
v
e
r
if
ier
m
u
s
t a
g
r
ee
o
n
th
e
co
n
d
itio
n
s
f
o
r
f
o
ll
o
win
g
s
tatem
en
t is tr
u
e.
2
−
=
0
, w
h
er
e
=
0
,
1
,
…
−
1
(
3
)
W
e
u
s
ed
th
r
ee
d
if
f
er
e
n
t
p
o
ly
n
o
m
ial
in
ter
p
o
latio
n
s
lan
g
r
an
g
e
p
o
l
y
n
o
m
ial
in
ter
p
o
latio
n
,
b
ar
y
ce
n
tr
ic
lag
r
an
g
e
in
ter
p
o
latio
n
,
FFT
to
co
n
v
e
r
t
(
3
)
in
to
p
o
ly
n
o
m
ial
ex
p
r
ess
io
n
g
iv
en
in
T
ab
le
2
.
T
h
is
p
o
ly
n
o
m
ial
in
ter
p
o
latio
n
in
clu
d
es
th
r
ee
s
tep
s
:
i)
c
r
ea
tin
g
p
o
ly
n
o
m
ial
in
ter
p
o
latio
n
e
q
u
atio
n
s
,
ii)
f
in
d
in
g
co
n
s
t
r
ain
t
p
o
ly
n
o
m
ial
,
an
d
iii)
f
o
r
m
in
g
co
m
p
o
s
itio
n
p
o
l
y
n
o
m
ial
.
T
h
e
co
m
p
o
s
itio
n
p
o
ly
n
o
m
ial
will c
r
ea
te
M
er
k
le
tr
ee
p
r
o
o
f
wh
ich
will b
e
u
s
ed
f
o
r
lo
w
d
eg
r
ee
test
in
g
.
As
g
iv
en
in
T
ab
le
3
,
we
ca
n
u
s
e
th
e
co
n
s
tr
ain
t
t
o
tr
ac
e
th
e
p
o
ly
n
o
m
ial
co
n
tain
s
1
o
r
0
if
t
h
e
s
ta
tem
en
t
is
tr
u
e.
2
−
wh
er
e,
=
0
;
1
;
…
;
−
1
an
d
d
ef
i
n
e
th
is
ex
p
r
ess
io
n
as th
e
co
n
s
tr
ain
t p
o
ly
n
o
m
ial
(
)
with
(
4
)
.
(
)
=
(
)
2
−
(
)
=
0
(
4
)
T
ab
le
2
.
Po
ly
n
o
m
ial
in
ter
p
o
la
t
io
n
s
with
f
o
r
m
u
las an
d
(
)
v
alu
es
S
r
.
n
o
P
o
l
y
n
o
m
i
a
l
i
n
t
e
r
p
o
l
a
t
i
o
n
e
q
u
a
t
i
o
n
P
o
l
y
n
o
m
i
a
l
e
q
u
a
t
i
o
n
f
o
r
m
u
l
a
(
)
1
La
g
r
a
n
g
e
i
n
t
e
r
p
o
l
a
t
i
o
n
(
)
=
∑
.
(
)
3
i
=
0
W
h
e
r
e
(
)
:
-
La
g
r
a
n
g
e
i
n
t
e
r
p
o
l
a
t
i
o
n
p
o
l
y
n
o
mi
a
l
,
:
-
y
-
c
o
o
r
d
i
n
a
t
e
s
(
)
:
-
La
g
r
a
n
g
e
b
a
s
i
s
p
o
l
y
n
o
m
i
a
l
s.
(
)
=
−
60
^
3
−
68
−
128
2
B
a
r
y
c
e
n
t
r
i
c
l
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g
r
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n
g
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i
n
t
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r
p
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l
a
t
i
o
n
(
)
=
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=
0
∑
−
=
0
W
h
e
r
e
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):
-
B
a
r
y
c
e
n
t
r
i
c
i
n
t
e
r
p
o
l
a
t
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o
l
y
n
o
m
i
a
l
,
:
-
W
e
i
g
h
t
a
t
e
a
c
h
p
o
i
n
t
,
:
-
D
a
t
a
F
a
c
t
o
r
(
)
=
2
^
3
−
771
^
2
+
12561
+
13758208
3
FFT
=
∑
−
2
/
−
1
=
0
F
o
r
=
0
,
1
,
…
−
1
,
H
e
r
e
,
Y
k
a
r
e
t
h
e
v
a
l
u
e
s
o
f
t
h
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p
o
l
y
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mi
a
l
a
t
t
h
e
n
-
t
h
r
o
o
t
s
o
f
u
n
i
t
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(
)
=
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2
+
18
+
19983
T
ab
le
3
.
C
o
n
s
tr
ain
t p
o
ly
n
o
m
ia
ls
(
)
=
(
)
2
−
(
)
S
r
.
N
o
C
o
n
st
r
a
i
n
t
p
o
l
y
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o
m
i
a
l
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(
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2
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(
)
1
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g
r
a
n
g
e
i
n
t
e
r
p
o
l
a
t
i
o
n
(
)
=
2
^
6
−
64
^
4
−
2
^
2
+
64
2
B
a
r
y
c
e
n
t
r
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c
l
a
g
r
a
n
g
e
i
n
t
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r
p
o
l
a
t
i
o
n
(
)
=
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^
6
−
128
^
4
−
122
^
3
−
4
^
2
−
104
−
98
3
FFT
(
)
=
^
4
−
36
^
3
−
63
^
2
+
27
−
80
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
2
5
0
2
-
4
7
52
In
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
3
7
,
No
.
2
,
Feb
r
u
a
r
y
20
2
5
:
1
10
2
-
1
11
1
1108
T
h
e
p
r
o
v
er
tr
an
s
f
o
r
m
s
(
)
u
s
in
g
th
e
p
r
o
p
er
ties
o
f
r
o
o
ts
o
f
p
o
ly
n
o
m
ials
to
g
et
an
o
t
h
er
c
o
m
p
o
s
itio
n
p
o
ly
n
o
m
i
al
(
)
g
iv
en
in
T
ab
le
4
.
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h
e
u
p
p
er
b
o
u
n
d
o
f
th
e
d
e
g
r
e
e
o
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er
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,
i.e
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=
2
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2
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)
−
1
∀
∈
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d
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{
,
1
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,
−
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Af
ter
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lcu
latin
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an
d
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lcu
l
ate
d
m
er
k
le
tr
ee
r
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f
M
T
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f
f
o
r
(
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an
d
MT
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p
f
o
r
(
)
,
=
[
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
]
f
o
r
s
en
d
in
g
t
o
v
er
if
ie
r
.
I
t
u
se
s
SHA
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2
5
6
h
ash
f
u
n
ctio
n
.
Pr
o
v
er
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e
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d
s
Me
r
k
le
r
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o
t
o
f
M
T
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an
d
MT
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p
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v
e
r
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ab
le
4
.
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o
m
p
o
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ly
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o
m
ials
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r
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p
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t
i
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l
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a
l
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g
r
a
n
g
e
i
n
t
e
r
p
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l
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t
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n
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^
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64
2
B
a
r
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c
e
n
t
r
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c
l
a
g
r
a
n
g
e
i
n
t
e
r
p
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l
a
t
i
o
n
(
)
=
4
^
2
−
128
3
FFT
(
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=
1
T
h
e
th
ir
d
s
tep
is
to
test
f
o
r
l
o
w
d
eg
r
ee
u
s
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g
FR
I
p
r
o
to
c
o
l
(
f
ast
r
ee
d
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s
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lo
m
o
n
in
ter
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tiv
e
o
r
ac
le
p
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o
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r
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im
ity
)
.
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h
e
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e
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ier
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n
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f
y
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ter
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th
e
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o
ly
n
o
m
ial
i
s
o
f
lo
w
d
eg
r
ee
d
(
f
o
r
o
u
r
ex
am
p
le
d
=2
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.
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f
th
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u
m
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er
o
f
s
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s
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ex
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en
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e
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ig
h
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r
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b
ab
ilit
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th
at,
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o
ly
n
o
m
ial
is
o
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d
e
g
r
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.
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f
p
o
l
y
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o
m
ial
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lo
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d
eg
r
ee
th
e
n
d
ata
r
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e
iv
ed
to
th
e
v
er
if
ier
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r
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ec
t
.
I
n
th
is
ex
p
er
im
en
t,
s
in
ce
th
e
d
ata
was
p
r
o
v
id
ed
ac
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r
d
in
g
to
e
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u
atio
n
1
,
th
e
lo
w
-
d
eg
r
ee
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o
f
th
e
p
o
ly
n
o
m
ial
was su
cc
ess
f
u
l,
co
n
f
ir
m
in
g
th
at
t
h
e
r
ec
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e
d
d
ata
is
ac
cu
r
ate.
4.
E
XP
E
R
I
M
E
N
T
S
AN
D
RE
S
UL
T
4
.
1
.
E
x
perim
ent
a
l
s
et
up
Fo
r
th
is
r
esear
ch
,
we
im
p
lem
e
n
ted
th
e
m
o
d
if
ied
Z
K
-
STARK
alg
o
r
ith
m
u
s
in
g
Py
th
o
n
p
r
o
g
r
am
m
in
g
.
W
e
in
s
talled
th
e
Ub
u
n
tu
2
2
.
0
4
ap
p
o
n
W
in
d
o
ws
1
1
v
ia
th
e
W
in
d
o
ws
Su
b
s
y
s
tem
f
o
r
L
in
u
x
(
W
SL)
f
ea
tu
r
e
o
n
a
lap
to
p
with
8
GB
R
AM
an
d
a
C
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r
e
i5
p
r
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ce
s
s
o
r
.
T
h
e
lap
t
o
p
s
er
v
e
d
as
a
s
er
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er
,
wh
ile
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ar
ticip
an
ts
ac
ce
s
s
ed
th
e
s
y
s
tem
th
r
o
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g
h
th
e
W
eb
A
PI
to
o
l v
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r
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s
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W
e
in
s
talled
Hy
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er
C
o
m
p
o
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er
[
2
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]
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d
Hy
p
e
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er
Fab
r
ic,
o
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tin
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f
o
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e
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Fab
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o
r
m
d
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m
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ased
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atu
r
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.
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p
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W
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API
f
r
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s
ed
f
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ased
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ic
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ef
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e
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b
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UR
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ttp
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o
ca
lh
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.
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.
2
.
Resul
t
s
W
e
im
p
lem
en
ted
th
r
ee
d
i
f
f
e
r
en
t
p
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ly
n
o
m
ial
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ter
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o
latio
n
s
f
o
r
th
e
Z
K
-
STARK
alg
o
r
i
th
m
u
s
in
g
p
y
th
o
n
:
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r
a
n
g
e
p
o
ly
n
o
m
ial
i
n
ter
p
o
latio
n
,
b
a
r
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ce
n
tr
ic
lag
r
a
n
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e
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ter
p
o
latio
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,
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d
FF
T
.
T
h
e
p
er
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o
r
m
a
n
ce
o
f
th
ese
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ter
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o
latio
n
s
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m
ea
s
u
r
ed
u
s
in
g
d
if
f
e
r
en
t
p
ar
am
et
er
s
as
g
iv
en
i
n
T
ab
le
5
,
p
r
o
o
f
g
e
n
er
atio
n
tim
e
(
s
ec
o
n
d
s
)
,
p
r
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o
f
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er
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n
t
im
e
(
s
ec
o
n
d
s
)
,
p
r
o
o
f
s
ize
(
K
B
)
,
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d
th
r
o
u
g
h
p
u
t
(
o
p
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n
s
p
er
s
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o
n
d
)
.
T
h
e
g
r
ap
h
f
o
r
Fig
u
r
e
5
is
b
ased
o
n
th
e
v
al
u
es
p
r
esen
ted
in
T
a
b
le
5
.
B
ased
o
n
th
e
p
er
f
o
r
m
a
n
ce
r
esu
lts
in
T
ab
le
5
,
th
e
FF
T
p
r
o
v
id
es
b
etter
t
h
r
o
u
g
h
p
u
t
c
o
m
p
a
r
ed
to
t
h
e
o
th
er
two
in
ter
p
o
latio
n
m
eth
o
d
s
in
Z
K
-
STARK.
Ad
d
itio
n
ally
,
th
e
p
r
o
o
f
v
er
i
f
icatio
n
tim
e
f
o
r
FF
T
is
s
ig
n
if
ican
tly
s
h
o
r
ter
th
a
n
th
at
f
o
r
lag
r
a
n
g
e
an
d
b
ar
y
ce
n
tr
i
c
lag
r
an
g
e
in
te
r
p
o
latio
n
m
eth
o
d
s
.
W
e
im
p
lem
en
ted
th
e
FS
C
u
s
in
g
h
y
p
er
led
g
er
c
o
m
p
o
s
er
,
in
v
o
lv
in
g
p
ar
ticip
a
n
ts
lik
e
f
ar
m
er
s
,
f
o
o
d
p
r
o
ce
s
s
o
r
s
,
d
is
tr
ib
u
to
r
s
,
r
etail
er
s
,
an
d
cu
s
to
m
er
s
.
T
h
e
ass
et
s
tar
ts
with
th
e
f
a
r
m
er
an
d
tr
an
s
f
er
s
th
r
o
u
g
h
th
e
ch
ain
v
ia
tr
an
s
ac
tio
n
lo
g
ic,
en
d
in
g
with
th
e
cu
s
to
m
er
.
All
tr
an
s
ac
tio
n
s
ar
e
r
ec
o
r
d
ed
an
d
v
is
ib
le
to
p
ar
ticip
an
ts
,
ea
ch
with
a
u
n
iq
u
e
I
D
f
o
r
lo
g
g
in
g
in
an
d
p
er
f
o
r
m
in
g
tr
an
s
ac
tio
n
s
.
T
h
e
Z
K
-
STARK
alg
o
r
ith
m
,
im
p
lem
en
ted
s
ep
ar
ately
u
s
in
g
Py
th
o
n
o
n
Go
o
g
le
C
o
lab
,
v
er
if
ies
th
e
q
u
ality
claim
ed
b
y
th
e
p
r
o
v
er
u
s
in
g
in
p
u
ts
lik
e
p
r
o
d
u
ct
n
u
m
b
er
an
d
q
u
ality
.
T
h
e
Fig
u
r
e
6
d
ep
ict
s
s
o
m
e
ex
ec
u
tio
n
s
o
f
th
is
s
u
p
p
ly
ch
ain
p
r
o
ce
s
s
in
Hy
p
er
led
g
e
r
C
o
m
p
o
s
er
,
wh
e
r
e
Fig
u
r
e
6
(
a)
d
is
p
lay
s
(
a)
b
u
s
in
ess
n
etwo
r
k
f
ar
m
er
with
p
r
o
d
u
ct
an
d
(
b
)
b
u
s
in
ess
n
etwo
r
k
s
h
o
ws co
m
m
o
d
ity
ass
et
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2
5
0
2
-
4
7
52
P
r
iva
cy
p
r
eser
vin
g
ZK
-
S
TAR
K
b
a
s
ed
b
lo
ck
ch
a
in
fo
r
…
(
M
a
d
h
u
r
i S
a
d
a
s
h
iv
A
r
a
d
e
)
1109
Fig
u
r
e
5
.
Gr
a
p
h
o
f
p
er
f
o
r
m
a
n
ce
co
m
p
ar
is
o
n
s
Z
K
-
STARK w
ith
v
ar
io
u
s
p
o
l
y
n
o
m
ial
i
n
ter
p
o
latio
n
T
ab
le
5
.
Per
f
o
r
m
an
ce
co
m
p
a
r
is
o
n
f
o
r
v
ar
io
u
s
p
o
ly
n
o
m
ial
in
t
er
p
o
latio
n
s
in
Z
K
-
STARK
S
r
.
N
o
.
P
o
l
y
n
o
m
i
a
l
i
n
t
e
r
p
o
l
a
t
i
o
n
P
r
o
o
f
g
e
n
e
r
a
t
i
o
n
t
i
m
e
(
se
c
o
n
d
)
P
r
o
o
f
v
e
r
i
f
i
c
a
t
i
o
n
t
i
m
e
(
se
c
o
n
d
)
P
r
o
o
f
s
i
z
e
(
KB
)
Th
r
o
u
g
h
p
u
t
(
o
p
/
sec
o
n
d
)
1
La
g
r
a
n
g
e
i
n
t
e
r
p
o
l
a
t
i
o
n
0
.
0
2
4
4
0
.
0
5
3
5
0
.
5
1
2
1
2
.
8
3
6
9
2
B
a
r
y
c
e
n
t
r
i
c
l
a
g
r
a
n
g
e
i
n
t
e
r
p
o
l
a
t
i
o
n
0
.
0
7
2
3
0
.
0
4
4
8
0
.
5
1
2
8
.
5
3
9
7
3
FFT
0
.
0
3
8
3
0
.
0
2
9
3
0
.
5
1
2
1
4
.
7
9
2
8
(
a)
(
b
)
Fig
u
r
e
6
.
Sn
a
p
s
h
o
t o
f
th
e
h
y
p
e
r
led
g
er
c
o
m
p
o
s
er
b
lo
ck
c
h
ain
(
a)
b
u
s
in
ess
n
etwo
r
k
f
a
r
m
er
wi
th
p
r
o
d
u
ct
an
d
(
b
)
b
u
s
in
ess
n
etwo
r
k
s
h
o
ws co
m
m
o
d
ity
ass
et
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
52
In
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
3
7
,
No
.
2
,
Feb
r
u
a
r
y
20
2
5
:
1
10
2
-
1
11
1
1110
B
ased
o
n
th
ese
r
esu
lts
,
th
e
f
u
tu
r
e
task
is
to
in
teg
r
ate
th
e
FFT
p
o
ly
n
o
m
ial
in
ter
p
o
latio
n
in
to
th
e
ZK
-
STARK
a
lg
o
r
ith
m
an
d
th
e
b
lo
ck
c
h
ain
FS
C
co
d
e
,
th
e
n
co
m
p
a
r
e
its
p
e
r
f
o
r
m
an
ce
t
o
th
e
cu
r
r
en
t
s
y
s
tem
.
B
y
in
co
r
p
o
r
atin
g
th
e
Z
K
-
S
T
AR
K
alg
o
r
ith
m
in
to
th
e
b
lo
ck
ch
ain
n
etwo
r
k
m
a
y
in
tr
o
d
u
ce
ad
d
itio
n
al
co
m
p
u
tatio
n
al
o
v
e
r
h
ea
d
,
p
o
te
n
tially
im
p
ac
tin
g
s
y
s
tem
p
e
r
f
o
r
m
an
ce
.
T
o
m
it
ig
ate
th
ese
ef
f
ec
ts
,
in
f
u
tu
r
e
o
u
r
r
esear
ch
will
ex
p
lo
r
e
s
tr
ateg
i
es
f
o
r
o
p
tim
izin
g
t
h
e
d
i
v
is
io
n
o
f
o
p
e
r
atio
n
s
b
etwe
en
o
n
-
c
h
ain
an
d
o
f
f
-
ch
ai
n
p
r
o
ce
s
s
es.
Ad
d
itio
n
ally
,
we
w
ill
in
v
esti
g
ate
m
eth
o
d
s
to
r
ed
u
ce
th
e
s
ize
o
f
th
e
c
r
y
p
to
g
r
ap
h
ic
p
r
o
o
f
s
,
th
er
eb
y
en
h
an
c
in
g
th
e
o
v
er
all
ef
f
icien
cy
o
f
th
e
s
y
s
tem
.
5.
CO
NCLU
SI
O
N
T
h
e
ex
is
tin
g
b
lo
ck
ch
ai
n
FSC
s
y
s
tem
p
r
o
v
id
es
tr
ac
ea
b
ilit
y
b
u
t
f
ac
es
lim
itatio
n
s
in
m
ain
t
ain
in
g
th
e
p
r
iv
ac
y
o
f
p
er
s
o
n
al
in
f
o
r
m
ati
o
n
.
T
h
is
r
esear
ch
p
r
o
p
o
s
es
u
s
i
n
g
th
e
Z
K
-
STARK
alg
o
r
ith
m
to
en
h
a
n
ce
p
r
iv
ac
y
in
b
lo
ck
ch
ain
-
b
ased
ag
r
i
-
FSC
.
I
t
em
p
h
asizes
th
e
im
p
o
r
tan
c
e
o
f
p
r
iv
ac
y
p
r
eser
v
atio
n
in
b
lo
ck
ch
ain
s
y
s
tem
s
an
d
id
en
tifie
s
th
e
lim
itatio
n
s
o
f
cu
r
r
en
t
m
eth
o
d
s
.
T
o
co
u
n
t
er
th
e
th
r
ea
t
o
f
q
u
an
tu
m
attac
k
s
,
we
em
p
lo
y
th
e
ef
f
icien
t
Z
K
-
STARK
alg
o
r
it
h
m
.
W
e
m
o
d
if
ied
t
h
is
al
g
o
r
ith
m
u
s
in
g
d
i
f
f
er
en
t
p
o
ly
n
o
m
ial
in
ter
p
o
latio
n
m
eth
o
d
s
an
d
f
o
u
n
d
th
at
th
e
F
FT
p
er
f
o
r
m
ed
th
e
b
est.
Fu
tu
r
e
wo
r
k
in
v
o
lv
es
in
teg
r
atin
g
th
is
FF
T
-
b
ased
Z
K
-
STARK
alg
o
r
ith
m
in
to
th
e
b
lo
ck
ch
ain
FS
C
an
d
ev
alu
atin
g
its
im
p
ac
t.
Sin
ce
ad
d
i
n
g
th
is
alg
o
r
ith
m
t
o
t
h
e
b
lo
ck
ch
ain
n
etwo
r
k
m
ay
in
cr
ea
s
e
s
y
s
tem
o
v
er
h
ea
d
,
f
u
tu
r
e
r
esear
ch
will
ex
p
lo
r
e
wh
ich
o
p
er
atio
n
s
s
h
o
u
ld
b
e
p
er
f
o
r
m
ed
o
f
f
-
c
h
ain
o
r
o
n
-
ch
a
in
an
d
h
o
w
to
m
i
n
im
ize
p
r
o
o
f
s
ize.
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
s
h
s
y
st
e
m,
”
D
e
c
e
n
t
ra
l
i
z
e
d
Bu
s
i
n
e
ss
Re
v
i
e
w
,
p
p
.
1
–
9
,
2
0
0
8
,
[
O
n
l
i
n
e
]
.
A
v
a
i
l
a
b
l
e
:
h
t
t
p
s:
/
/
g
i
t
.
d
h
i
mm
e
l
.
c
o
m/
b
i
t
c
o
i
n
-
w
h
i
t
e
p
a
p
e
r
/
.
[
2
]
H
y
p
e
r
l
e
d
g
e
r
,
“
C
a
se
s
t
u
d
y
:
h
o
w
w
a
l
mart
b
r
o
u
g
h
t
u
n
p
r
e
c
e
d
e
n
t
e
d
t
r
a
n
sp
a
r
e
n
c
y
t
o
t
h
e
f
o
o
d
s
u
p
p
l
y
c
h
a
i
n
w
i
t
h
h
y
p
e
r
l
e
d
g
e
r
f
a
b
r
i
c
c
h
a
l
l
e
n
g
e
,
”
H
y
p
e
r
l
e
d
g
e
r
,
p
.
7
,
2
0
1
9
,
[
O
n
l
i
n
e
]
.
A
v
a
i
l
a
b
l
e
:
h
t
t
p
s
:
/
/
w
w
w
.
h
y
p
e
r
l
e
d
g
e
r
.
o
r
g
/
w
p
-
c
o
n
t
e
n
t
/
u
p
l
o
a
d
s/
2
0
1
9
/
0
2
/
H
y
p
e
r
l
e
d
g
e
r
_
C
a
seSt
u
d
y
_
W
a
l
m
a
r
t
_
P
r
i
n
t
a
b
l
e
_
V
4
.
p
d
f
.
[
3]
Y
.
Zh
o
n
g
,
J
.
H
o
v
a
n
e
s
,
a
n
d
U
.
G
u
i
n
,
“
O
n
-
d
e
m
a
n
d
d
e
v
i
c
e
a
u
t
h
e
n
t
i
c
a
t
i
o
n
u
si
n
g
z
e
r
o
-
k
n
o
w
l
e
d
g
e
p
r
o
o
f
s
f
o
r
smar
t
sy
s
t
e
ms,”
i
n
Pro
c
e
e
d
i
n
g
s
o
f
t
h
e
AC
M
G
re
a
t
L
a
k
e
s
S
y
m
p
o
s
i
u
m
o
n
VLS
I
,
G
L
S
VL
S
I
,
J
u
n
.
2
0
2
3
,
p
p
.
5
6
9
–
5
7
4
,
d
o
i
:
1
0
.
1
1
4
5
/
3
5
8
3
7
8
1
.
3
5
9
0
2
7
5
.
[
4
]
Y
.
G
o
n
g
,
Y
.
J
i
n
,
Y
.
Li
,
Z
.
Li
u
,
a
n
d
Z
.
Z
h
u
,
“
A
n
a
l
y
si
s
a
n
d
c
o
m
p
a
r
i
s
o
n
o
f
t
h
e
m
a
i
n
z
e
r
o
-
k
n
o
w
l
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