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o
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Co
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Science
Vo
l.
3
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.
2
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Ma
y
20
2
5
,
p
p
.
732
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SS
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.v
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.
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:
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ttp
:
//ij
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cs
.
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esco
r
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co
m
An
ef
ficien
t
ha
rd
wa
re impleme
nta
tion o
f
num
ber
th
eo
retic
trans
form for
CR
YSTAL
S
-
K
y
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po
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qua
ntum
cry
ptog
ra
phy
T
ra
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o
a
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T
u Dinh Anh
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h Q
ua
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a
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Art
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ticle
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y:
R
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Mar
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4
R
ev
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25
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202
4
Acc
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ted
No
v
11
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2
0
2
4
CRYST
ALS
-
Ky
b
e
r
wa
s
c
h
o
se
n
to
be
th
e
sta
n
d
a
rd
ize
d
k
e
y
e
n
c
a
p
su
latio
n
m
e
c
h
a
n
ism
s
(KEM
s)
o
u
t
o
f
t
h
e
fin
a
li
sts
in
th
e
t
h
ir
d
ro
u
n
d
o
f
t
h
e
Na
ti
o
n
a
l
In
stit
u
te
o
f
S
ta
n
d
a
rd
s
a
n
d
Tec
h
n
o
lo
g
y
(NIS
T)
p
o
st
-
q
u
a
n
t
u
m
c
ry
p
to
g
ra
p
h
y
(P
QC)
sta
n
d
a
rd
iza
ti
o
n
p
r
o
g
ra
m
.
S
i
n
c
e
th
e
n
u
m
b
e
r
t
h
e
o
re
ti
c
tran
sfo
rm
(NTT
)
wa
s
u
se
d
t
o
re
d
u
c
e
t
h
e
c
o
m
p
u
tatio
n
a
l
c
o
m
p
lex
it
y
o
f
p
o
ly
n
o
m
ial
m
u
lt
ip
li
c
a
ti
o
n
,
i
t
h
a
s
a
lwa
y
s
b
e
e
n
a
c
ru
c
ial
a
rit
h
m
e
ti
c
c
o
m
p
o
n
e
n
t
in
CRYST
ALS
-
Ky
b
e
r
d
e
sig
n
.
I
n
t
h
i
s
p
a
p
e
r,
a
sim
p
le
a
n
d
e
fficie
n
t
a
r
c
h
it
e
c
tu
re
fo
r
NTT
is
p
re
se
n
ted
wh
e
re
we
e
a
sily
a
rc
h
iv
e
d
t
h
e
f
u
n
c
ti
o
n
a
li
t
y
o
f
p
o
l
y
n
o
m
ial
m
u
lt
i
p
li
c
a
ti
o
n
wit
h
e
fficie
n
t
c
o
m
p
u
tatio
n
ti
m
e
.
O
n
ly
8
5
7
Lo
o
k
-
Up
Tab
les
a
n
d
7
4
4
fl
ip
-
fl
o
p
s
we
re
u
ti
li
z
e
d
in
o
u
r
NTT
d
e
si
g
n
,
w
h
ich
c
o
n
siste
d
o
f
two
p
ro
c
e
ss
in
g
e
lem
e
n
ts
(P
Es)
a
n
d
tw
o
b
u
tt
e
rfl
y
c
o
re
s
with
in
e
a
c
h
P
E.
K
ey
w
o
r
d
s
:
C
R
Y
STAL
S
-
Ky
b
er
Har
d
war
e
im
p
lem
en
tatio
n
Nu
m
b
er
th
e
o
r
etic
tr
an
s
f
o
r
m
Po
ly
n
o
m
ial
m
u
ltip
licatio
n
Po
s
t
-
q
u
an
tu
m
cr
y
p
to
g
r
ap
h
y
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
T
r
an
g
Ho
a
n
g
Facu
lty
o
f
E
lectr
ical
-
E
lectr
o
n
ics,
Ho
C
h
i M
in
h
C
ity
Un
iv
er
s
ity
o
f
T
ec
h
n
o
lo
g
y
Vietn
am
Natio
n
al
Un
iv
er
s
ity
Ho
C
h
i M
in
h
C
ity
2
6
8
L
y
T
h
u
o
n
g
Kiet,
Dis
tr
ict
1
0
,
Ho
C
h
i M
in
h
C
ity
,
Vietn
am
E
m
ail
:
h
o
an
g
tr
a
n
g
@
h
cm
u
t.e
d
u
.
v
n
1.
I
NT
RO
D
UCT
I
O
N
Sin
ce
th
e
ap
p
licatio
n
o
f
Sh
o
r
’
s
alg
o
r
ith
m
,
class
ical
p
u
b
lic
-
k
ey
cr
y
p
t
o
g
r
ap
h
y
p
r
o
to
c
o
ls
h
av
e
b
ec
o
m
e
in
cr
ea
s
in
g
ly
v
u
ln
er
a
b
le
to
q
u
an
tu
m
co
m
p
u
ter
attac
k
s
[
1
]
.
C
R
Y
STAL
S
-
Ky
b
er
is
o
n
e
o
f
th
e
f
in
alis
ts
in
th
e
th
ir
d
r
o
u
n
d
o
f
p
o
s
t
-
q
u
an
t
u
m
c
r
y
p
to
g
r
ap
h
y
(
PQC
)
alg
o
r
it
h
m
ev
alu
atio
n
b
y
t
h
e
Natio
n
al
I
n
s
titu
te
o
f
Stan
d
a
r
d
s
an
d
T
ec
h
n
o
lo
g
y
(
N
I
ST)
,
a
c
o
m
p
etitio
n
to
d
eter
m
in
e
v
ar
io
u
s
alg
o
r
ith
m
s
to
with
s
tan
d
atta
ck
s
f
r
o
m
q
u
a
n
tu
m
co
m
p
u
ter
s
.
Sp
ec
if
ically
,
th
e
a
lg
o
r
ith
m
is
a
lattice
-
b
ased
c
r
y
p
to
s
y
s
tem
b
ased
o
n
th
e
m
o
d
u
le
lear
n
i
n
g
-
with
-
er
r
o
r
s
p
r
o
b
lem
(
ML
E
)
.
I
n
J
u
ly
2
0
2
2
,
C
R
YSTA
L
S
-
Ky
b
er
was
s
elec
ted
as
th
e
s
t
an
d
ar
d
Pu
b
lic
-
Key
E
n
cr
y
p
tio
n
/Key
E
n
ca
p
s
u
latio
n
Me
ch
an
is
m
[
2
]
.
C
R
Y
STAL
S
-
Ky
b
er
an
d
o
th
er
lattice
-
b
ased
cr
y
p
to
s
y
s
tem
s
ex
ten
s
iv
ely
r
ely
o
n
p
o
ly
n
o
m
ial
m
u
ltip
licatio
n
.
I
t
s
er
v
es
as
th
e
p
r
im
ar
y
o
p
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atio
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,
b
u
t
its
im
p
lem
en
tatio
n
m
ig
h
t
b
e
co
m
p
u
tatio
n
ally
in
ten
s
iv
e,
ca
u
s
in
g
a
b
o
ttlen
ec
k
[
3
]
.
T
o
o
v
er
co
m
e
th
is
is
s
u
e,
an
alg
o
r
ith
m
b
ased
o
n
n
u
m
b
er
th
eo
r
eti
c
tr
an
s
f
o
r
m
(
NT
T
)
f
o
r
p
o
ly
n
o
m
ial
m
u
ltip
licatio
n
h
as
b
ee
n
u
s
ed
.
T
h
is
alg
o
r
ith
m
is
a
ty
p
ica
l
m
eth
o
d
f
o
r
ca
l
cu
latin
g
p
o
ly
n
o
m
ial
m
u
ltip
licatio
n
with
less
co
m
p
lex
o
p
er
atio
n
s
,
th
e
r
eb
y
d
ec
r
ea
s
in
g
th
e
co
m
p
u
tatio
n
al
b
u
r
d
en
o
f
lattice
-
b
ased
cr
y
p
to
s
y
s
tem
s
.
B
y
ap
p
ly
in
g
t
h
e
NT
T
-
b
ased
p
o
l
y
n
o
m
ial
m
u
ltip
licatio
n
m
eth
o
d
,
t
h
e
p
er
f
o
r
m
an
ce
o
f
lattice
-
b
ased
cr
y
p
to
s
y
s
tem
s
ca
n
b
e
s
ig
n
if
ican
tly
en
h
a
n
ce
d
,
m
ak
in
g
th
em
m
o
r
e
a
p
p
licab
le
an
d
ef
f
ec
tiv
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in
a
r
a
n
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e
o
f
co
n
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ts
.
Op
tim
izin
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th
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co
m
p
lex
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o
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ar
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e
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ce
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at
o
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th
e
m
o
s
t
cr
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ac
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r
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d
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a
p
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f
o
r
s
ch
em
es.
Fo
r
th
e
p
u
r
p
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s
e
o
f
v
alid
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p
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a
v
ar
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im
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p
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s
.
Desp
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Evaluation Warning : The document was created with Spire.PDF for Python.
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d
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C
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m
p
Sci
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4
7
52
A
n
efficien
t h
a
r
d
w
a
r
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imp
leme
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tio
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733
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p
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in
f
er
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o
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to
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at
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f
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p
latf
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m
s
[
4
]
.
A
h
y
b
r
i
d
d
esig
n
o
f
s
o
f
twar
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an
d
h
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o
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o
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est
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o
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ar
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g
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if
icatio
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s
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n
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tr
ain
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im
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.
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o
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.
Ap
p
licatio
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C
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d
f
ield
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am
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a
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le
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ate
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ay
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t
wo
p
r
im
ar
y
ar
c
h
itectu
r
es
u
s
ed
f
o
r
h
a
r
d
war
e
im
p
lem
en
ta
tio
n
,
an
d
th
e
y
ar
e
f
r
eq
u
e
n
tly
em
p
lo
y
e
d
in
r
esear
ch
an
al
y
s
is
an
d
d
ev
elo
p
m
en
t.
T
h
e
NI
ST
r
ec
o
m
m
e
n
d
s
t
h
e
u
s
e
o
f
Xilin
x
Ar
tix
-
7
FP
GA
f
o
r
h
ar
d
war
e
im
p
lem
e
n
tatio
n
in
o
r
d
er
to
co
m
p
ar
e
th
e
d
esig
n
with
g
r
ea
ter
p
r
ec
is
io
n
[
5
]
.
ASI
C
r
esu
lts
,
o
n
th
e
o
t
h
er
h
a
n
d
,
ar
e
h
ig
h
l
y
d
ep
en
d
e
n
t
o
n
t
h
e
tech
n
o
lo
g
y
l
ib
r
ar
y
an
d
s
y
s
tem
co
n
f
i
g
u
r
ati
o
n
s
u
s
ed
d
u
r
in
g
th
e
im
p
lem
en
tatio
n
p
r
o
ce
s
s
.
T
h
is
m
ak
es it d
if
f
icu
lt to
co
m
p
ar
e
d
esig
n
s
to
o
th
er
s
,
as th
e
im
p
le
m
en
tatio
n
d
etails o
f
d
if
f
er
en
t
p
r
o
jects
ca
n
v
ar
y
s
ig
n
if
ican
tly
.
Desp
ite
th
ese
o
b
s
tacle
s
,
ASI
C
s
co
n
tin
u
e
t
o
b
e
an
im
p
o
r
ta
n
t
an
d
wid
ely
em
p
lo
y
ed
to
o
l
in
th
e
f
ield
o
f
h
ar
d
wa
r
e
d
esig
n
,
esp
ec
ially
f
o
r
lar
g
e
-
s
ca
le
an
d
co
m
p
lex
s
y
s
tem
s
th
at
r
eq
u
ir
e
a
h
ig
h
d
eg
r
ee
o
f
p
r
ec
i
s
io
n
an
d
d
ep
e
n
d
ab
ilit
y
[
6
]
.
Fo
r
ex
am
p
le,
B
an
er
jee
et
a
l.
[
6
]
p
r
esen
ted
a
l
attice
cr
y
p
to
g
r
ap
h
y
p
r
o
ce
s
s
o
r
with
co
n
f
ig
u
r
ab
le
p
ar
am
eter
s
th
at
h
ad
an
NT
T
b
lo
ck
ac
ce
ler
ate
d
b
y
a
s
in
g
le
-
p
o
r
t
R
AM
-
b
ased
m
em
o
r
y
ar
ch
ite
ctu
r
e
o
n
an
ASI
C
th
at
aim
ed
to
o
p
tim
ize
r
eso
u
r
ce
s
,
b
u
t
th
eir
d
esig
n
was
in
ef
f
icien
t,
esp
ec
ially
in
ter
m
s
o
f
f
r
eq
u
e
n
cy
an
d
laten
cy
.
Mo
r
eo
v
er
,
a
lo
w
-
p
o
wer
an
d
r
eso
u
r
ce
-
ef
f
icien
t
NT
T
ASI
C
d
esig
n
was
p
r
esen
ted
in
[
7
]
.
Alth
o
u
g
h
th
e
ar
ea
an
d
p
o
wer
r
esu
lts
wer
e
g
o
o
d
,
th
e
d
esig
n
d
id
n
o
t
o
f
f
er
a
g
o
o
d
tr
a
d
e
-
o
f
f
b
etwe
en
tim
in
g
an
d
r
eso
u
r
ce
ef
f
icien
c
y
.
So
n
g
et
a
l.
[
8
]
also
p
r
o
p
o
s
ed
o
n
e
o
f
th
e
q
u
ic
k
est
an
d
m
o
s
t
en
er
g
y
-
e
f
f
icien
t
NT
T
s
o
n
ASI
C
,
b
u
t
with
o
p
aq
u
e
r
eso
u
r
ce
s
,
wh
ich
co
u
l
d
b
e
in
ter
p
r
eted
as
a
tr
ad
e
-
o
f
f
b
etwe
en
r
eso
u
r
ce
s
,
tim
in
g
,
an
d
p
o
wer
.
T
h
e
co
m
p
ar
is
o
n
s
o
n
th
e
FP
GA
s
id
e
d
id
n
o
t
lo
o
k
g
o
o
d
eith
er
,
wh
er
ea
s
d
esig
n
er
s
u
s
e
d
d
if
f
e
r
en
t
FP
GA
f
am
ilie
s
an
d
th
er
e
wer
e
u
s
u
ally
co
n
f
licts
b
etwe
en
th
r
ee
asp
ec
ts
:
r
eso
u
r
ce
s
,
tim
in
g
,
an
d
p
o
wer
.
Fritzm
an
n
et
a
l.
[
9
]
,
R
I
SQ
-
V,
a
tig
h
tly
c
o
u
p
le
d
R
I
SC
-
V
ac
ce
ler
ato
r
f
o
r
b
o
th
ASI
C
an
d
Xilin
x
Z
y
n
q
-
7
0
0
0
FP
GA
was
p
r
o
p
o
s
ed
.
Kar
ab
u
lu
t
an
d
Ay
s
u
[
1
0
]
also
cr
ea
te
d
a
r
eso
u
r
ce
-
o
p
tim
ized
R
I
SC
-
V
NT
T
c
o
r
e
o
n
a
Xilin
x
Vir
tex
-
7
FP
GA,
alb
eit
with
h
ig
h
tim
in
g
laten
cy
.
I
n
[
4
]
an
d
[
11
]
,
Xilin
x
Ar
tix
-
7
was
u
s
ed
as
th
e
im
p
lem
en
tatio
n
p
latf
o
r
m
f
o
r
th
e
NT
T
d
esig
n
;
h
o
wev
er
,
th
e
NT
T
d
esig
n
in
tr
o
d
u
ce
d
in
[
4
]
was
m
o
r
e
tim
in
g
-
ef
f
icien
t
th
an
th
at
i
n
[
1
1
]
d
u
e
to
th
e
d
o
u
b
le
n
u
m
b
er
o
f
b
u
t
ter
f
ly
co
r
es,
r
esu
ltin
g
in
a
h
i
g
h
er
f
r
eq
u
en
cy
an
d
lo
wer
laten
cy
.
T
h
e
f
r
e
q
u
en
c
y
r
esu
lts
f
o
r
[
9
]
an
d
[
1
0
]
wer
e
n
u
ll.
On
th
e
o
th
er
h
a
n
d
,
th
e
d
e
s
ig
n
er
s
o
m
itted
th
e
r
eso
u
r
ce
r
esu
lts
in
[
4
]
an
d
[
11
]
,
m
ak
in
g
it d
i
f
f
icu
lt t
o
co
m
p
a
r
e
th
e
d
esig
n
a
p
p
r
o
ac
h
.
Me
n
tio
n
in
g
FP
GA
r
eso
u
r
ce
s
,
th
e
n
u
m
b
er
o
f
lo
o
k
-
u
p
tab
les (
L
UT
s
)
an
d
f
lip
f
lo
p
s
(
FF
s
)
u
s
e
d
in
[
6
]
is
en
o
r
m
o
u
s
d
u
e
to
th
e
lar
g
e
n
u
m
b
er
o
f
m
u
ltip
lier
s
,
wh
er
ea
s
d
esig
n
er
co
u
ld
u
s
e
th
e
d
ig
ital
s
ig
n
al
p
r
o
ce
s
s
in
g
(
DSP)
m
o
d
u
l
e
in
th
e
FP
GA
f
o
r
in
teg
er
m
u
ltip
lier
to
r
e
d
u
c
e
th
e
n
u
m
b
er
o
f
L
UT
s
an
d
D
FF
s
th
at
m
ig
h
t
b
e
u
s
ed
.
T
h
is
m
ay
also
b
alan
ce
th
e
FP
GA
r
eso
u
r
ce
s
to
co
n
s
e
r
v
e
th
em
f
o
r
o
th
er
lo
g
ic
c
o
m
p
o
n
en
ts
with
in
th
e
C
R
Y
STAL
S
-
Ky
b
er
h
ar
d
war
e.
T
h
e
NT
T
h
ar
d
war
e
d
escr
ib
ed
in
[
4
]
u
tili
z
ed
o
n
ly
o
n
e
b
lo
ck
R
AM
(
B
R
AM
)
f
o
r
s
to
r
in
g
p
o
ly
n
o
m
ials
,
r
esu
ltin
g
in
a
d
esig
n
with
a
h
ig
h
laten
c
y
.
I
n
s
u
m
m
ar
y
,
at
th
e
m
o
m
en
t
,
m
o
s
t
s
tu
d
ies
o
n
NT
T
h
a
r
d
war
e
im
p
lem
e
n
tatio
n
h
a
v
e
th
eir
o
wn
wea
k
n
ess
es
th
at
co
u
ld
b
e
ad
d
r
ess
ed
f
o
r
b
etter
p
er
f
o
r
m
an
ce
.
All
th
e
af
o
r
em
en
tio
n
ed
f
ac
to
r
s
led
u
s
to
d
esig
n
a
Xilin
x
Ar
tix
-
7
FP
GA
an
d
ASI
C
NT
T
with
b
alan
ce
d
f
r
e
q
u
en
cy
,
laten
c
y
,
an
d
p
o
wer
e
f
f
i
cien
cy
.
Ou
r
d
esig
n
also
u
tili
ze
d
th
e
FP
GA
r
eso
u
r
ce
b
y
in
co
r
p
o
r
atin
g
th
e
DSP
an
d
B
R
AM
u
n
it,
wh
ich
p
r
ev
en
ted
th
e
ex
ce
s
s
iv
e
u
s
e
o
f
L
UT
a
n
d
FF
an
d
th
e
r
i
s
k
o
f
FP
GA
r
eso
u
r
ce
o
v
er
-
u
tili
za
tio
n
wh
en
i
n
teg
r
atin
g
th
e
NT
T
d
esig
n
in
to
th
e
co
m
p
lete
C
R
YSTA
L
S
-
Ky
b
er
h
ar
d
war
e
d
esig
n
.
Sp
ec
if
ically
,
th
e
u
s
e
o
f
DSP
in
o
u
r
FP
GA
r
esu
lted
in
a
3
3
%
r
ed
u
ctio
n
in
th
e
n
u
m
b
er
o
f
L
UT
s
an
d
DFF
u
s
ed
.
Mo
r
e
o
v
er
,
we
u
s
ed
th
r
e
e
B
R
AM
s
p
er
b
u
tter
f
ly
co
r
e
to
s
to
r
e
p
o
ly
n
o
m
ials
an
d
twid
d
le
f
ac
t
o
r
s
,
allo
win
g
o
u
r
b
u
tter
f
ly
c
o
r
es
to
o
p
er
ate
in
p
ar
allel
an
d
r
ed
u
cin
g
laten
c
y
b
y
6
4
.
5
% r
elativ
e
to
[
4
]
.
C
o
n
tr
ib
u
tio
n
o
f
th
is
wo
r
k
:
Po
ly
n
o
m
ial
m
u
ltip
licatio
n
ar
it
h
m
etic
is
o
n
e
o
f
th
e
m
o
s
t
im
p
o
r
tan
t
co
m
p
o
n
e
n
ts
o
f
th
e
C
R
YSTA
L
S
Ky
b
er
h
ar
d
war
e
im
p
lem
en
tati
o
n
s
in
ce
it
h
as
a
s
ig
n
i
f
ican
t
i
m
p
ac
t
o
n
th
e
laten
cy
an
d
ef
f
i
cien
cy
o
f
th
e
d
esig
n
[
1
2
]
–
[
1
7
]
.
B
y
u
tili
zin
g
th
e
N
T
T
co
r
e
to
ap
p
l
y
NT
T
-
b
ased
p
o
ly
n
o
m
ial
m
u
ltip
licatio
n
,
we
m
ay
lo
wer
t
h
e
o
p
er
atio
n
co
m
p
le
x
ity
an
d
b
o
o
s
t th
r
o
u
g
h
p
u
t w
h
ile
co
n
s
u
m
in
g
f
ewe
r
r
eso
u
r
ce
s
.
T
h
is
p
ap
er
p
r
esen
ts
a
r
eso
u
r
ce
-
ef
f
icien
t
NT
T
h
ar
d
war
e
d
esig
n
with
a
b
alan
ce
o
f
f
r
eq
u
en
c
y
,
laten
cy
,
an
d
p
o
wer
.
I
n
c
o
m
p
ar
is
o
n
with
o
th
er
wo
r
k
s
th
at
h
an
d
le
NT
T
in
h
ar
d
war
e
im
p
lem
en
tatio
n
,
we
wo
u
ld
lik
e
to
p
r
o
v
e
o
u
r
ef
f
icien
c
y
u
p
o
n
o
u
ts
tan
d
in
g
wo
r
k
in
g
f
r
eq
u
e
n
cy
,
im
p
r
o
v
e
d
tim
in
g
o
p
er
atio
n
,
an
d
less
r
eso
u
r
ce
co
s
t
(
L
UT
an
d
FF
)
lead
in
g
to
p
o
wer
o
p
tim
izatio
n
.
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
8
,
No
.
2
,
May
20
2
5
:
7
3
2
-
7
4
3
734
−
Pu
r
e
h
ar
d
wa
r
e
im
p
lem
e
n
tatio
n
with
b
alan
ce
d
b
e
n
ef
its
:
W
e
p
r
o
p
o
s
ed
a
p
u
r
e
h
ar
d
war
e
ca
p
ab
le
o
f
h
an
d
lin
g
NT
T
an
d
I
NT
T
(
I
n
v
e
r
s
e
NT
T
)
o
p
e
r
atio
n
s
f
o
r
th
e
C
R
YST
AL
S
-
Ky
b
er
PQC
alg
o
r
ith
m
with
a
b
alan
ce
o
f
r
eso
u
r
ce
s
an
d
p
er
f
o
r
m
a
n
ce
.
B
y
o
p
tim
izin
g
th
e
r
eso
u
r
ce
s
o
n
th
e
FP
GA
f
o
r
th
e
p
r
o
ce
s
s
in
g
u
n
its
an
d
m
an
ag
in
g
th
e
m
e
m
o
r
y
ac
ce
s
s
ef
f
icien
tly
,
we
h
av
e
b
ee
n
ab
le
to
r
ed
u
ce
th
e
o
v
er
all
s
ize
an
d
m
em
o
r
y
u
s
ag
e
with
o
u
t slo
win
g
d
o
w
n
th
e
p
e
r
f
o
r
m
an
ce
.
−
Stan
d
ar
d
b
en
ch
m
a
r
k
f
o
r
f
u
t
u
r
e
v
er
if
icatio
n
:
B
y
im
p
lem
e
n
tin
g
o
n
b
o
th
FP
GA
(
Xilin
x
Ar
t
ix
-
7
)
a
n
d
ASI
C
(
T
SMC
6
5
n
m
tech
n
o
lo
g
y
)
,
w
e
o
f
f
e
r
o
u
r
d
esig
n
as
a
s
tan
d
a
r
d
b
e
n
ch
m
ar
k
f
o
r
o
th
er
r
esear
ch
er
s
to
clea
r
ly
ev
alu
ate
th
e
NT
T
an
d
I
NT
T
p
ar
ts
in
th
eir
C
R
YSTA
LS
-
Ky
b
er
h
ar
d
war
e
d
esig
n
s
.
T
h
is
aim
s
to
an
aly
ze
th
e
ad
v
an
tag
es
an
d
d
is
ad
v
an
tag
e
s
o
f
ea
ch
d
esig
n
r
atio
n
ale
f
o
r
C
R
YST
AL
S
-
Ky
b
er
h
ar
d
wa
r
e,
wh
ich
h
elp
s
d
esig
n
er
s
s
o
o
n
d
ete
r
m
in
e
an
d
d
ev
elo
p
t
h
e
m
o
s
t su
itab
le
h
ar
d
war
e
d
esig
n
ap
p
r
o
ac
h
o
f
t
h
eir
o
wn
.
−
Ou
ts
tan
d
in
g
p
er
f
o
r
m
a
n
ce
in
c
o
m
p
ar
is
o
n
to
p
r
ev
i
o
u
s
s
tu
d
ies:
Ou
r
r
esu
lts
o
n
Xilin
x
Ar
tix
-
7
m
ad
e
u
s
e
o
f
th
e
DSPs
an
d
B
R
A
Ms
o
f
th
e
FP
GA
s
o
th
at
th
e
n
u
m
b
er
o
f
L
UT
s
an
d
FF
s
lo
g
ic
was
s
m
al
l
in
co
m
p
ar
is
o
n
to
[
9
]
,
[
6
]
,
an
d
th
e
co
m
p
u
tati
o
n
tim
e
was
r
ed
u
ce
d
co
m
p
ar
ed
to
[
4
]
,
[
1
1
]
.
B
y
u
tili
zin
g
e
f
f
icien
t
m
em
o
r
y
ac
ce
s
s
,
o
u
r
ASI
C
r
esu
lts
o
u
tp
er
f
o
r
m
e
d
o
th
e
r
NT
T
h
ar
d
war
e
d
esig
n
s
in
[
6
]
,
[
7
]
.
T
h
e
r
em
ain
d
er
o
f
th
is
p
ap
er
is
o
r
g
an
ized
as f
o
llo
ws:
−
Sectio
n
2
ex
p
lain
s
th
e
m
ath
e
m
atica
l
f
o
u
n
d
atio
n
s
o
f
th
e
NT
T
an
d
I
NT
T
alg
o
r
ith
m
s
in
C
R
YSTA
L
S
-
Ky
b
e
r
,
wh
ich
co
n
tain
s
a
n
u
m
b
e
r
o
f
al
g
o
r
ith
m
s
in
p
s
eu
d
o
co
d
e
f
o
r
m
s
an
d
th
eir
d
escr
ip
tio
n
s
in
d
etail.
−
I
n
Sectio
n
3
,
we
d
escr
ib
e
o
u
r
s
tr
ateg
y
f
o
r
h
ar
d
war
e
d
esig
n
an
d
th
e
o
v
e
r
all
m
o
d
u
le
ar
c
h
itectu
r
e,
wh
er
e
m
ajo
r
co
m
p
o
n
e
n
ts
ar
e
d
e
p
ic
ted
,
in
clu
d
i
n
g
th
e
p
o
ly
n
o
m
i
al
m
u
ltip
licatio
n
s
,
b
u
tter
f
l
y
u
n
its
,
m
em
o
r
y
ad
d
r
ess
co
n
tr
o
ls
an
d
th
e
o
v
er
a
ll d
esig
n
co
n
tain
in
g
th
em
.
−
T
h
e
f
in
d
in
g
s
an
d
co
m
p
ar
is
o
n
s
with
o
th
er
d
esig
n
s
ar
e
an
al
y
ze
d
in
Sectio
n
4
.
Mo
s
t
o
f
th
e
r
esu
lts
wer
e
o
b
tain
ed
f
r
o
m
th
e
s
y
n
th
esis
an
d
im
p
lem
en
tatio
n
p
r
o
ce
s
s
es
s
in
ce
th
e
d
esig
n
was
b
ase
d
o
n
h
a
r
d
war
e.
Par
allel
im
p
lem
en
tatio
n
o
n
FP
GA
an
d
ASI
C
w
as
ex
ec
u
ted
f
o
r
m
u
tu
al
d
is
cu
s
s
io
n
s
as
we
ll
as
co
m
p
ar
is
o
n
to
o
th
er
wo
r
k
f
o
r
ef
f
icien
cy
.
−
T
h
e
co
n
clu
s
io
n
o
f
th
is
wo
r
k
is
p
r
esen
ted
in
th
e
f
in
al
s
ec
tio
n
,
wh
er
e
th
e
s
tu
d
y
is
s
u
m
m
ar
ized
,
an
d
s
o
m
e
im
p
licatio
n
s
ca
n
b
e
s
tated
.
2.
B
ACK
G
RO
UND
2
.
1
.
NT
T
-
ba
s
ed
po
ly
no
m
ia
l m
ultiplica
t
io
n
E
f
f
icien
t
p
o
l
y
n
o
m
ial
m
u
ltip
licatio
n
,
esp
ec
ially
f
o
r
lar
g
e
d
e
g
r
ee
s
,
is
f
u
n
d
a
m
en
tal
in
e
n
cr
y
p
tio
n
a
n
d
lattice
-
b
ased
cr
y
p
to
g
r
a
p
h
y
b
u
t
ca
n
b
e
tim
e
-
co
n
s
u
m
in
g
th
o
u
g
h
.
I
n
Ky
b
er
,
p
o
ly
n
o
m
ials
ar
e
d
ef
in
ed
in
th
e
r
in
g
ℤ
[
]
/
(
+
1
)
.
T
h
e
o
p
er
atio
n
tak
es
p
o
ly
n
o
m
ials
(
)
=
∑
(
)
−
1
=
0
an
d
(
)
=
∑
(
)
−
1
=
0
as
in
p
u
ts
an
d
r
etu
r
n
th
e
o
u
tp
u
t
p
o
ly
n
o
m
ia
l
(
)
=
∑
(
)
−
1
=
0
as
m
u
ltip
licatio
n
o
u
tp
u
t.
As
u
s
u
al,
th
e
tech
n
iq
u
e
f
o
r
m
u
ltip
ly
in
g
two
p
o
ly
n
o
m
ials
h
as a
(
2
)
co
m
p
lex
ity
,
wh
ic
h
lead
s
to
s
lo
w
p
r
o
ce
s
s
in
g
tim
e
wh
en
d
ea
lin
g
with
lar
g
e
-
d
eg
r
ee
p
o
ly
n
o
m
ials
.
NT
T
is
u
s
ed
to
s
p
ee
d
u
p
th
is
o
p
er
atio
n
s
in
ce
NT
T
p
er
f
o
r
m
s
it
with
(
.
)
co
m
p
lex
ity
.
T
h
e
r
esu
ltan
t
p
o
ly
n
o
m
ial
(
)
ca
n
b
e
f
u
r
th
er
r
ed
u
ce
d
with
n
eg
at
iv
e
wr
ap
p
e
d
co
n
v
o
lu
tio
n
tech
n
iq
u
e
s
h
o
wn
with
in
Alg
o
r
ith
m
1
,
w
h
er
ea
s
,
th
e
r
ed
u
ctio
n
p
o
ly
n
o
m
ial,
(
)
=
(
+
1
)
an
d
≡
1
(
2
)
.
T
h
is
tech
n
iq
u
e
h
en
ce
d
ir
ec
tly
r
ed
u
ce
s
th
e
d
eg
r
ee
o
f
th
e
r
esu
ltin
g
p
o
ly
n
o
m
ial
(
)
to
d
eg
r
ee
−
1
,
wh
ich
is
ac
co
m
p
lis
h
ed
b
y
m
u
ltip
ly
in
g
t
h
e
co
ef
f
icien
ts
o
f
th
e
in
p
u
t a
n
d
o
u
tp
u
t p
o
ly
n
o
m
ials
b
y
th
e
p
o
wer
o
f
an
d
−
1
,
r
esp
ec
tiv
ely
,
wh
er
e
is
a
p
r
im
itiv
e
2
-
th
r
o
o
t
o
f
u
n
ity
in
s
atis
f
y
in
g
2
≡
1
(
)
an
d
∀
<
2
,
≠
1
(
)
,
wh
en
≡
1
(
2
)
[
1
8
]
.
Alg
o
r
ith
m
1
.
NT
T
-
b
ased
Po
ly
n
o
m
ial
Mu
ltip
licatio
n
with
n
e
g
ativ
e
wr
ap
p
e
d
co
n
v
o
lu
tio
n
(
NW
T
)
[
1
6
]
Input:
(
)
,
(
)
∈
[
]
/
(
+
1
)
Input:
Primitive
2
-
th root of unity
∈
Output:
(
)
=
(
)
×
(
)
,
(
)
∈
[
]
/
(
+
1
)
1
̂
=
(
0
,
1
,
.
.
.
,
−
1
)
⊙
(
1
,
1
,
2
,
.
.
.
,
−
1
)
2
̂
=
(
0
,
1
,
.
.
.
,
−
1
)
⊙
(
1
,
1
,
2
,
.
.
.
,
−
1
)
3
̅
=
(
̂
)
4
̅
=
(
̂
)
5
̅
=
̅
⊙
̅
6
̂
=
(
̅
)
7
(
)
=
(
̂
0
,
̂
1
,
.
.
.
,
̂
−
1
)
⊙
(
1
,
−
1
,
−
2
,
.
.
.
,
−
(
−
1
)
)
8
return
(
)
2
.
2
.
Num
ber
t
heo
re
t
ic
t
ra
ns
f
o
rm
a
t
io
n
A
n
(
−
1
)
d
eg
r
ee
p
o
ly
n
o
m
ial
(
)
=
∑
−
1
=
0
is
tr
an
s
f
o
r
m
ed
in
to
NT
T
d
o
m
a
in
as
̅
(
)
=
∑
−
1
=
0
b
y
u
s
in
g
a
n
-
p
t
f
o
r
war
d
N
T
T
o
p
e
r
atio
n
.
T
h
e
co
ef
f
icien
t
o
f
̅
(
)
in
NT
T
d
o
m
ai
n
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
A
n
efficien
t h
a
r
d
w
a
r
e
imp
leme
n
ta
tio
n
o
f
n
u
mb
er th
eo
r
etic
t
r
a
n
s
fo
r
m
fo
r
… (
Tr
a
n
g
Ho
a
n
g
)
735
∑
−
1
=
0
o
v
er
ℤ
f
o
r
=
0
,
1
,
.
.
.
,
−
1
.
Af
ter
p
o
in
twis
e
m
u
ltip
ly
in
g
̅
(
)
an
d
̅
(
)
in
NT
T
d
o
m
ai
n
,
a
n
n
-
p
o
in
t
I
NNT
is
u
s
ed
to
tr
an
s
f
o
r
m
th
e
r
esu
lt
b
ac
k
to
th
e
p
o
ly
n
o
m
ial
d
o
m
ain
with
=
−
1
∑
−
−
1
=
0
in
ℤ
.
Mo
r
eo
v
er
,
NT
T
an
d
I
NT
T
r
e
g
u
lar
ly
u
s
e
th
e
twid
d
le
f
ac
t
o
r
,
∈
ℤ
an
d
its
m
o
d
u
lar
in
v
e
r
s
e,
−
1
∈
ℤ
as
in
p
u
t.
I
t
is
a
p
r
im
itiv
e
-
th
r
o
o
t
o
f
u
n
ity
in
ℤ
an
d
th
e
co
n
d
itio
n
s
≡
1
(
mod
)
an
d
∀
<
,
≠
1
(
mod
)
,
wh
er
e
≡
1
(
)
.
I
n
th
is
s
tu
d
y
,
th
e
iter
ativ
e
NT
T
(
Alg
o
r
ith
m
2
)
an
d
I
N
NT
(
Alg
o
r
ith
m
3
)
,
wh
ich
u
tili
ze
th
e
Gen
tlem
an
-
San
d
e
b
u
tter
f
ly
p
h
en
o
m
e
n
o
n
,
wer
e
ap
p
lied
.
T
h
e
NT
T
an
d
I
NT
T
alg
o
r
it
h
m
s
tr
an
s
f
o
r
m
th
e
p
o
ly
n
o
m
ial
f
r
o
m
n
o
r
m
al
o
r
d
e
r
to
b
it
-
r
e
v
er
s
ed
o
r
d
er
a
n
d
v
i
c
e
v
er
s
a.
T
h
e
b
it
-
r
ev
er
s
al
o
p
er
atio
n
o
n
(
−
1
)
-
b
it
in
teg
er
k
,
wh
e
r
e
=
is
ex
ec
u
ted
b
y
th
e
(
,
−
1
)
o
p
er
atio
n
in
Alg
o
r
ith
m
3
[
1
8
]
.
I
n
a
d
d
itio
n
,
th
e
co
ef
f
icien
ts
o
f
th
e
o
u
tp
u
t
p
o
ly
n
o
m
ial
m
u
s
t a
lway
s
b
e
m
u
ltip
lied
b
y
(
1
/
)
in
th
e
I
NT
T
o
p
e
r
atio
n
s
in
ce
th
e
b
it
r
e
v
er
s
io
n
,
as
s
h
o
wn
i
n
s
tep
s
1
9
-
2
1
o
f
Alg
o
r
ith
m
3
.
Alg
o
r
ith
m
2
ca
n
also
b
e
f
u
r
th
er
m
o
d
if
ie
d
to
im
p
lem
en
t
th
e
I
NT
T
o
p
e
r
atio
n
b
y
s
u
b
s
titu
tin
g
with
−
1
an
d
h
av
in
g
t
h
e
o
u
tp
u
t
p
o
ly
n
o
m
ial
co
ef
f
icien
ts
d
iv
id
ed
b
y
in
.
Alg
o
r
ith
m
2
.
I
ter
ativ
e
NT
T
Al
g
o
r
ith
m
[
1
4
]
Input:
(
)
∈
[
]
/
(
+
1
)
in normal order
Input:
∈
,
=
2
Output:
̅
(
)
=
(
)
∈
[
]
/
(
+
1
)
in bit
-
reversed order
1
f
or
from 1 by 1 to
do
2
|
=
2
−
3
|
for
from 0 by 1 to
2
−
1
−
1
do
4
| |
for
from 0 by 1 to
−
1
do
5
| | |
←
2
∙
∙
+
6
| | |
←
2
∙
∙
+
+
7
| | |
←
2
−
1
∙
8
| | |
←
[
]
9
| | |
←
[
]
10
| | |
←
11
| | |
←
(
+
)
12
| | |
←
(
−
)
∙
13
| | |
[
]
←
14
| | |
[
]
←
15
| |
end
for
16
|
end
for
17
end
for
18
return
Alg
o
r
ith
m
3
.
I
ter
ativ
e
I
NT
T
Alg
o
r
ith
m
[
1
4
]
Input:
̅
(
)
∈
[
]
/
(
+
1
)
in bit
-
reversed order
Input:
−
1
∈
,
=
2
Output:
(
)
=
(
)
∈
[
]
/
(
+
1
)
in normal order
1
=
1
2
=
3
while
>
1
do
4
|
for
from 0 by 1 to
−
1
do
5
| |
=
0
6
| |
for
from
by
2
∙
to
(
−
2
)
do
7
| | |
←
[
]
8
| | |
←
[
+
]
9
| | |
←
(
+
)
10
| | |
←
(
−
)
∙
−
(
,
−
1
)
11
| | |
[
]
←
12
| | |
[
+
]
←
13
| | |
=
+
1
14
| |
end
for
15
|
end
for
16
|
=
2
∙
17
|
=
/
2
18
end
while
19
for
from 0 by 1 to
−
1
do
20
|
[
]
←
[
]
∙
(
1
/
)
(
)
21
end
for
22
return
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
8
,
No
.
2
,
May
20
2
5
:
7
3
2
-
7
4
3
736
3.
DE
S
I
G
N
RAT
I
O
NA
L
E
I
n
th
is
s
ec
tio
n
,
o
u
r
h
ar
d
war
e
d
esig
n
ap
p
r
o
ac
h
a
n
d
th
e
o
v
er
all
ar
ch
itectu
r
e
o
f
th
e
m
ain
m
o
d
u
les
ar
e
g
iv
en
.
As
d
escr
ib
ed
i
n
Sectio
n
3
.
1
,
th
e
m
u
ltip
lier
u
s
in
g
M
o
n
tg
o
m
e
r
y
'
s
m
o
d
u
lar
alg
o
r
ith
m
at
th
e
wo
r
d
lev
el
p
er
f
o
r
m
s
th
e
m
o
d
u
lar
m
u
ltip
l
icatio
n
in
o
u
r
h
ar
d
war
e
.
T
h
e
p
r
im
ar
y
ar
ith
m
e
tic
o
p
e
r
atio
n
in
NT
T
an
d
I
NT
T
alg
o
r
ith
m
s
is
th
e
b
u
tter
f
ly
o
p
e
r
atio
n
;
W
e
d
escr
ib
e
o
u
r
p
r
o
ce
s
s
in
g
elem
en
ts
h
ar
d
war
e
with
th
e
b
u
tter
f
l
y
u
n
it
in
Sectio
n
3
.
2
.
I
n
Sectio
n
3
.
3
,
o
u
r
ef
f
icien
t
m
e
m
o
r
y
an
d
its
a
d
d
r
ess
g
en
er
ato
r
ar
e
g
i
v
en
,
w
h
ich
en
h
a
n
ce
s
th
e
p
er
f
o
r
m
an
ce
o
f
o
u
r
d
esig
n
.
Sectio
n
3
.
4
d
escr
ib
es
th
e
o
v
er
all
s
tr
u
ctu
r
e.
T
h
e
p
r
o
p
o
s
ed
ar
ch
itectu
r
e
ca
n
b
e
im
p
lem
en
ted
u
s
in
g
eith
er
FP
GA
o
r
ASI
C
tech
n
o
lo
g
y
.
3
.
1
.
NT
T
-
ba
s
ed
po
ly
no
m
ia
l m
ultiplica
t
io
n
Mo
d
u
lar
m
u
ltip
lier
is
o
n
e
o
f
th
e
m
o
s
t
ess
en
tial
co
m
p
o
n
en
t
s
in
NT
T
s
y
s
tem
.
T
h
e
af
o
r
e
m
en
tio
n
ed
co
m
p
o
n
en
t
in
v
o
l
v
es
two
d
if
f
er
en
t
b
lo
ck
s
:
a
DSP
-
b
ased
in
teg
er
m
u
ltip
licatio
n
u
n
it
an
d
a
wo
r
d
-
lev
el
Mo
n
tg
o
m
er
y
m
o
d
u
lar
r
ed
u
ctio
n
u
n
it.
B
o
th
b
lo
c
k
s
ar
e
in
d
e
p
en
d
en
t
o
f
th
e
o
th
er
.
T
h
e
Mo
n
tg
o
m
er
y
[
1
8
]
an
d
B
ar
r
ett
alg
o
r
ith
m
s
[
6
]
a
r
e
th
e
m
o
s
t c
o
m
m
o
n
o
n
es u
s
ed
in
m
o
d
u
lar
r
e
d
u
ctio
n
,
an
d
th
ey
ar
e
d
esig
n
ed
to
ac
h
iev
e
ef
f
icien
cy
.
Fo
r
th
is
d
esig
n
,
we
d
ec
id
ed
to
b
u
ild
a
Mo
n
tg
o
m
e
r
y
r
ed
u
ctio
n
u
n
it,
s
in
ce
th
e
alg
o
r
ith
m
u
s
es
f
ewe
r
co
m
p
o
n
en
ts
,
an
d
p
r
o
ce
s
s
es
th
r
o
u
g
h
f
ewe
r
s
tag
es
in
co
m
p
ar
is
o
n
to
B
ar
r
ett’
s
;
th
er
ef
o
r
e,
it
ca
n
b
e
h
ar
d
war
e
im
p
lem
en
ted
in
to
s
m
aller
d
esig
n
s
in
ter
m
s
o
f
ar
ea
,
as
well
a
s
ca
n
wo
r
k
in
lar
g
er
f
r
eq
u
en
ci
es.
T
h
e
u
n
it
h
en
ce
ca
n
b
e
u
s
ed
f
o
r
th
e
w
o
r
d
-
lev
el
Mo
n
tg
o
m
e
r
y
m
o
d
u
lar
r
ed
u
ctio
n
o
p
er
atio
n
f
o
r
m
o
d
u
lu
s
-
s
atis
f
y
in
g
≡
1
(
2
)
.
As
s
h
o
wn
in
Fig
u
r
e
1
,
th
e
DSP
u
n
it
o
f
th
e
FP
GA
is
u
tili
z
ed
f
o
r
t
h
e
in
teg
er
m
u
ltip
lier
u
n
it
to
cu
t
d
o
wn
o
n
th
e
n
u
m
b
er
o
f
L
UT
s
an
d
FF
s
.
Mo
r
eo
v
er
,
th
e
in
teg
e
r
m
u
ltip
licatio
n
u
n
it
th
at
h
as
b
ee
n
p
r
o
p
o
s
ed
u
s
ed
p
ip
elin
in
g
tech
n
iq
u
e
to
en
s
u
r
e
th
at
th
e
p
r
o
d
u
ct
o
f
th
e
m
u
ltip
licatio
n
is
s
y
n
ch
r
o
n
ized
wi
th
th
e
s
y
s
tem
.
T
h
e
o
u
tp
u
t
o
f
th
e
m
u
ltip
lier
,
h
o
w
ev
er
,
n
ee
d
s
to
h
a
v
e
its
b
it
len
g
th
b
r
o
u
g
h
t
d
o
wn
to
m
atch
t
h
at
o
f
t
h
e
m
o
d
u
lu
s
,
wh
ich
we
ca
ll
th
e
r
ed
u
ctio
n
o
p
er
atio
n
.
T
h
e
Mo
n
t
g
o
m
er
y
m
o
d
u
lar
wo
r
d
-
lev
el
alg
o
r
ith
m
o
f
th
at
o
p
er
atio
n
is
p
r
o
v
id
e
d
in
Alg
o
r
ith
m
4
.
An
y
NT
T
p
r
im
e
,
p
o
s
s
ess
in
g
th
e
≡
1
(
2
)
p
r
o
p
er
t
y
wh
en
th
e
n
e
g
ativ
e
wr
ap
p
ed
c
o
n
v
o
lu
tio
n
m
eth
o
d
is
ap
p
lied
,
ca
n
b
e
wr
itten
as
=
∙
2
+
1
;
an
d
b
y
h
ar
n
ess
in
g
th
is
p
r
o
p
er
t
y
,
a
Mo
n
tg
o
m
er
y
r
ed
u
ctio
n
o
p
e
r
atio
n
ca
n
b
e
p
er
f
o
r
m
ed
at
th
e
wo
r
d
lev
el
with
th
e
wo
r
d
s
ize
=
(
2
)
.
T
h
is
p
r
o
p
er
t
y
allo
ws
th
e
r
ed
u
ctio
n
o
p
er
atio
n
to
b
e
h
an
d
le
d
in
m
u
ltip
le
s
tag
es,
r
ath
er
th
an
r
u
n
n
i
n
g
it
all
at
o
n
ce
.
T
o
p
er
f
o
r
m
th
e
m
o
d
u
lar
r
e
d
u
cti
o
n
o
p
er
atio
n
o
n
a
-
b
it
m
o
d
u
lu
s
,
=
/
iter
atio
n
s
ar
e
also
r
eq
u
i
r
ed
.
T
h
e
Mo
n
tg
o
m
er
y
m
o
d
u
lar
r
ed
u
ct
io
n
co
n
s
tan
t,
wh
ic
h
was
p
r
e
v
io
u
s
ly
wr
itten
as
=
−
−
1
2
)
,
is
n
o
w
wr
itten
as
−
1
2
.
T
h
is
ch
a
n
g
e
m
ak
e
s
it
p
o
s
s
ib
le
to
u
s
e
a
s
im
p
le
two
’
s
co
m
p
lem
en
t
o
p
er
atio
n
in
s
tead
o
f
a
m
u
ltip
licatio
n
o
p
er
atio
n
∙
∙
(
2
)
in
th
e
Mo
n
tg
o
m
er
y
s
ch
em
e,
a
s
d
em
o
n
s
tr
ated
i
n
Step
6
o
f
Alg
o
r
ith
m
4
.
I
n
ea
ch
NT
T
c
o
m
p
o
n
e
n
t
o
f
C
R
YSTA
L
S
-
Ky
b
er
,
a
f
ix
e
d
m
o
d
u
lu
s
=
3329
is
u
s
ed
[
1
9
]
,
wh
ile
th
e
p
ar
am
eter
s
=
128
an
d
=
12
,
ca
n
b
e
wr
itten
as
∙
2
8
+
1
,
with
wo
r
d
s
ize
=
8
.
So
,
we
n
ee
d
=
12
/
8
=
2
iter
atio
n
s
f
o
r
th
e
alg
o
r
ith
m
t
o
wo
r
k
.
−
1
ca
n
b
e
ca
lcu
lated
a
s
−
1
=
2
=
13
2
=
169
in
C
R
Y
STAL
S
-
Ky
b
er
.
Fig
u
r
e
1
.
12
-
b
it
m
o
n
tg
o
m
er
y
m
o
d
u
lar
m
u
ltip
lier
Alg
o
r
ith
m
4
.
W
o
r
d
-
L
e
v
el
Mo
n
tg
o
m
er
y
R
ed
u
ctio
n
Alg
o
r
ith
m
f
o
r
NT
T
-
f
r
ien
d
ly
m
o
d
u
lu
s
[
2
0
]
[
2
1
]
I
np
ut:
=
∙
(
a
2
-
b
it p
o
s
itiv
e
in
teg
er
)
I
np
ut:
(
a
-
b
it m
o
d
u
l
u
s
)
,
=
∙
2
+
1
I
np
ut:
=
(
2
)
(
wo
r
d
s
ize)
O
utput
:
=
∙
−
1
(
)
wh
er
e
=
2
∙
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
A
n
efficien
t h
a
r
d
w
a
r
e
imp
leme
n
ta
tio
n
o
f
n
u
mb
er th
eo
r
etic
t
r
a
n
s
fo
r
m
fo
r
… (
Tr
a
n
g
Ho
a
n
g
)
737
1
←
/
2
←
3
f
o
r
f
r
o
m
0
to
do
4
|
1
←
>
>
5
|
1
←
(
2
)
6
|
2
←
′
1
7
|
←
2
[
−
1
]
∨
1
[
−
1
]
8
|
←
1
+
(
∙
2
[
−
1
:
0
]
)
+
9
end
f
o
r
10
4
←
−
11
if
(
4
<
0
)
t
hen
=
else
=
4
12
r
etu
r
n
As
ca
n
b
e
s
ee
n
in
S
tep
8
o
f
Alg
o
r
ith
m
4
,
th
e
wo
r
d
-
lev
el
M
o
n
tg
o
m
e
r
y
m
o
d
u
lar
r
ed
u
ctio
n
alg
o
r
ith
m
m
ak
es
u
s
e
o
f
a
n
u
m
b
e
r
o
f
m
u
ltip
ly
an
d
ac
cu
m
u
late
(
M
AC
)
o
p
er
atio
n
u
n
it
s
,
wh
ich
is
r
esp
o
n
s
ib
le
f
o
r
p
er
f
o
r
m
in
g
th
e
X
·
Y
+Z
+Cin
o
p
er
atio
n
.
Fig
u
r
e
2
d
ep
icts
th
e
h
ar
d
war
e
ar
ch
itectu
r
e
th
at
wa
s
d
ev
elo
p
ed
f
o
r
th
e
wo
r
d
-
lev
el
Mo
n
tg
o
m
er
y
m
o
d
u
lar
r
ed
u
ctio
n
alg
o
r
ith
m
.
T
h
is
ar
ch
itectu
r
e
in
clu
d
es two
Mo
d
u
lo
R
ed
u
ctio
n
s
u
b
-
b
lo
ck
s
.
T
h
e
f
ir
s
t
Mo
d
u
lo
R
e
d
u
ctio
n
s
u
b
-
b
lo
ck
p
e
r
f
o
r
m
s
a
r
ed
u
ctio
n
th
at
tak
es
th
e
2
4
-
b
it
in
p
u
t
d
ata
P
an
d
tr
an
s
f
o
r
m
s
it
i
n
to
th
e
1
6
-
b
it
i
n
ter
m
ed
iate
d
ata
P
_
r
ed
[
1
]
.
Af
te
r
th
at,
th
e
d
ata
is
r
e
d
u
ce
d
b
y
t
h
e
s
ec
o
n
d
Mo
d
u
lo
R
ed
u
ctio
n
s
u
b
-
b
lo
ck
f
o
r
a
s
ec
o
n
d
tim
e
in
o
r
d
er
to
o
b
tain
th
e
1
4
-
b
it
d
ata
P
_
r
ed
[
2
]
.
B
y
u
tili
zin
g
a
s
u
b
tr
ac
to
r
an
d
a
m
u
ltip
lex
e
r
,
th
e
m
o
d
u
l
ar
v
alu
e
o
f
P
_
r
ed
[
2
]
is
o
b
tain
ed
,
wh
ich
is
also
th
e
o
u
tp
u
t
o
f
th
e
Mo
n
tg
o
m
er
y
m
o
d
u
lar
r
ed
u
ctio
n
alg
o
r
ith
m
a
t th
e
wo
r
d
lev
el.
T
o
b
e
m
o
r
e
s
p
ec
if
ic,
t
h
e
Mo
d
u
lo
R
ed
u
ct
io
n
Su
b
’
s
p
r
o
p
o
s
ed
h
ar
d
war
e
is
s
h
o
wn
in
Fig
u
r
e
2
,
wh
ich
is
th
e
h
ar
d
wa
r
e
im
p
lem
e
n
tatio
n
f
o
r
Step
4
to
Step
8
o
f
Alg
o
r
it
h
m
4
.
T
h
e
m
-
b
it
in
p
u
t d
ata
T
1
is
d
iv
id
ed
i
n
to
two
p
ar
ts
:
T
2
L
=
T
1
[
7
:0
]
(
8
last
b
its
)
an
d
T
2
H_
t
=
T
1
[
m
:8
]
(
th
e
r
est)
d
u
e
to
th
e
wo
r
d
s
ize
w
=8
o
f
th
e
Mo
n
tg
o
m
er
y
r
e
d
u
ctio
n
alg
o
r
ith
m
.
On
e
a
d
d
er
is
also
u
s
ed
to
ca
lcu
late
th
e
m
u
lt
t,
ca
r
r
y
t,
a
n
d
T
2
H
t,
th
er
e
f
o
r
e
th
e
r
ed
u
ctio
n
r
esu
lt C
t c
an
b
e
o
b
tain
ed
.
Fig
u
r
e
2
.
Mo
d
u
lar
r
ed
u
ctio
n
s
u
b
-
u
n
it h
ar
d
war
e
3
.
2
.
B
utt
er
f
ly
un
it
Af
ter
we
h
ad
co
m
p
le
ted
a
n
ef
f
ec
tiv
e
im
p
lem
en
tatio
n
f
o
r
th
e
m
o
d
u
lar
ar
ith
m
etic,
th
e
co
n
s
t
r
u
ctio
n
o
f
th
e
h
ar
d
war
e
f
o
r
th
e
b
u
tter
f
ly
u
n
its
was
co
n
ce
n
tr
ated
.
T
h
ese
b
u
tter
f
ly
u
n
its
m
ak
e
u
s
e
o
f
m
o
d
u
lar
o
p
er
atio
n
s
an
d
ar
e
lo
ca
ted
with
in
th
e
PE
s
(
p
r
o
ce
s
s
in
g
elem
e
n
ts
)
.
T
h
e
b
u
tter
f
ly
o
p
er
atio
n
is
c
o
n
d
u
cted
b
y
th
e
PEs,
ea
ch
o
f
wh
ich
r
ec
eiv
e
s
o
n
e
twid
d
le
f
ac
to
r
an
d
two
co
ef
f
icien
ts
as
in
p
u
ts
.
E
ac
h
PE
th
en
g
en
er
ate
s
two
r
esu
ltin
g
co
ef
f
icien
ts
,
wh
ich
ar
e
r
ef
e
r
r
ed
to
as
th
e
o
d
d
(
O)
a
n
d
ev
e
n
(
E
)
co
e
f
f
icien
ts
,
as
o
u
tp
u
ts
.
As
ca
n
b
e
s
ee
n
in
Fig
u
r
e
3
,
th
e
p
r
o
p
o
s
ed
PE
m
o
d
u
le
to
im
p
lem
en
t
th
e
b
u
tter
f
ly
o
p
e
r
atio
n
co
n
s
is
ts
o
f
o
n
e
m
o
d
u
lar
a
d
d
er
,
o
n
e
m
o
d
u
lar
s
u
b
tr
ac
to
r
,
a
n
d
o
n
e
m
o
d
u
lar
m
u
ltip
lier
.
I
n
ea
ch
P
E
,
th
r
ee
d
u
al
-
p
o
r
t
B
R
AM
s
ar
e
u
s
ed
f
o
r
n
ec
ess
ar
y
d
ata
s
to
r
a
g
e
.
On
e
o
f
th
em
is
ca
lled
th
e
twid
d
le
f
ac
to
r
B
R
A
M
(
T
W
B
R
AM
)
,
wh
ile
th
e
o
th
er
two
ar
e
ca
lled
th
e
in
p
u
t a
n
d
in
ter
m
ed
iate
c
o
ef
f
ic
ien
t BR
AM
(
b
o
th
ar
e
ca
lled
D
AT
A
B
R
A
M)
.
T
h
e
ev
en
co
ef
f
icien
t
o
u
tp
u
t
o
f
th
e
PE
is
th
e
o
u
tp
u
t
o
f
th
e
m
o
d
u
lar
a
d
d
er
,
wh
ile
th
e
o
d
d
co
ef
f
icien
t
o
u
tp
u
t
o
f
t
h
e
PE
is
th
e
o
u
t
p
u
t
o
f
th
e
m
o
d
u
lar
s
u
b
tr
ac
to
r
an
d
m
u
ltip
lier
,
as
s
h
o
wn
in
s
tep
s
11
-
1
2
o
f
Alg
o
r
ith
m
2
.
T
o
m
ain
tain
s
y
n
c
h
r
o
n
izati
o
n
b
etwe
en
th
e
o
u
tp
u
t
o
f
th
e
o
d
d
an
d
e
v
en
co
ef
f
icien
ts
,
ad
d
itio
n
al
f
lip
-
f
l
o
p
s
wer
e
in
s
er
ted
at
th
e
m
o
d
u
lar
a
d
d
er
h
ar
d
war
e
o
u
tp
u
t.
Fo
r
a
n
-
p
o
in
t
NT
T
o
p
er
atio
n
,
th
e
m
a
x
im
u
m
n
u
m
b
e
r
o
f
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
8
,
No
.
2
,
May
20
2
5
:
7
3
2
-
7
4
3
738
p
r
o
ce
s
s
in
g
u
n
its
th
at
ca
n
b
e
i
n
clu
d
ed
in
th
e
d
esig
n
is
eq
u
al
to
/
2
,
an
d
t
h
e
n
u
m
b
er
o
f
p
r
o
ce
s
s
in
g
u
n
its
m
u
s
t
b
e
a
p
o
wer
o
f
2
.
I
n
th
e
d
esig
n
th
at
we
h
av
e
p
r
o
p
o
s
ed
,
we
m
ak
e
u
s
e
o
f
2
PEs,
wh
ich
in
d
icate
s
th
at
th
e
NT
T
o
p
er
atio
n
is
ca
r
r
ied
o
u
t
th
r
o
u
g
h
two
b
u
tter
f
ly
u
n
its
.
T
h
e
wh
o
le
h
ar
d
wa
r
e
d
esig
n
f
o
r
a
ty
p
ical
PE,
wh
ich
co
n
tain
s
a
b
u
tter
f
l
y
u
n
it,
is
d
e
m
o
n
s
tr
ated
in
Fig
u
r
e
3
.
B
y
ass
ig
n
in
g
th
e
v
alu
e
0
to
th
e
in
p
u
t
s
ig
n
al
in
0
,
t
h
e
f
ir
s
t
m
u
ltip
lican
d
to
th
e
in
p
u
t
s
ig
n
al
i
n
1
,
an
d
th
e
s
ec
o
n
d
m
u
ltip
lican
d
to
th
e
in
p
u
t
s
ig
n
al
in
m
u
lt,
it
is
p
o
s
s
i
b
le
to
u
tili
ze
th
e
b
u
tter
f
ly
h
ar
d
war
e
to
h
an
d
le
a
m
o
d
u
lar
m
u
ltip
l
icatio
n
o
p
e
r
atio
n
,
as
illu
s
tr
ated
in
Fig
u
r
e
3
.
Her
e,
we
r
ef
er
r
ed
to
th
e
2
-
in
p
u
t
b
u
tter
f
ly
u
n
it
as
an
NT
T
2
u
n
it.
T
o
c
o
m
p
u
te
th
e
m
o
d
u
lar
a
d
d
itio
n
an
d
s
u
b
tr
ac
tio
n
o
f
th
e
two
d
ata
s
ets,
th
e
NT
T
2
u
n
it
p
r
o
ce
s
s
es
two
s
ets
o
f
1
2
-
b
it
in
p
u
t
d
ata
ca
lled
in
0
an
d
in
1
.
T
h
e
m
o
d
u
la
r
s
u
m
is
s
y
n
ch
r
o
n
iz
ed
af
ter
it
is
p
ass
ed
th
r
o
u
g
h
a
s
h
if
t
r
eg
is
ter
,
an
d
t
h
en
th
e
v
alu
e
is
u
s
ed
as
th
e
ev
en
in
d
e
x
o
u
tp
u
t
o
f
th
e
NT
T
2
d
ev
ice.
F
o
r
th
e
m
o
d
u
lar
m
u
ltip
lier
u
n
it
to
p
r
o
d
u
ce
th
e
1
2
-
b
it
o
u
tp
u
t
d
ata
MO
Do
u
t,
its
in
p
u
ts
co
n
s
is
t
o
f
th
e
r
esu
lt
o
f
th
e
m
o
d
u
lar
s
u
b
tr
ac
tio
n
,
th
e
m
o
d
u
lo
,
an
d
th
e
in
p
u
t
d
ata
MU
L
in
,
an
d
o
n
e
DFF is
u
s
ed
to
s
y
n
ch
r
o
n
ize
th
is
s
ig
n
al
to
o
b
tain
th
e
o
d
d
in
d
e
x
o
u
t
p
u
t
o
f
th
e
NT
T
2
.
Fig
u
r
e
3
.
Pro
ce
s
s
in
g
E
lem
e
n
t
an
d
B
u
tter
f
ly
Un
it h
a
r
d
war
e
3
.
3
.
M
emo
ry
a
cc
ess
a
nd
a
dd
re
s
s
g
ener
a
t
o
r
I
n
C
R
YSTA
L
S
-
Ky
b
er
’
s
NT
T
&
I
NT
T
h
ar
d
wa
r
e,
ac
ce
s
s
in
g
th
e
m
em
o
r
y
n
ee
d
s
to
b
e
im
p
lem
en
ted
well
an
d
o
r
d
er
l
y
to
av
o
i
d
b
o
ttl
en
ec
k
p
r
o
b
lem
s
[
2
2
]
–
[
2
5
]
.
T
h
e
I
ter
ativ
e
NT
T
,
wh
ich
is
illu
s
tr
ated
in
Alg
o
r
ith
m
2
,
co
n
s
is
ts
o
f
s
tag
es,
an
d
th
er
e
ar
e
/
2
b
u
tter
f
ly
o
p
er
atio
n
s
u
s
ed
in
ea
ch
s
tag
e.
Ad
d
itio
n
ally
,
th
e
r
ea
d
ad
d
r
ess
p
atter
n
f
o
r
th
e
in
p
u
t
co
ef
f
icien
ts
v
ar
ies
f
r
o
m
s
tag
e
to
s
tag
e.
T
h
e
ca
lcu
latio
n
o
f
th
e
in
d
ex
o
cc
u
r
s
b
etwe
en
Step
s
5
an
d
6
o
f
Alg
o
r
ith
m
2
in
th
e
NT
T
p
r
o
c
ess
in
g
f
lo
w.
T
o
h
av
e
co
n
tr
o
l
o
v
er
th
e
B
R
AM
s
p
r
esen
tin
g
i
n
ea
ch
PE,
a
n
a
d
d
r
ess
g
en
er
ato
r
is
r
eq
u
i
r
ed
.
T
h
is
u
n
it
g
r
an
ts
th
e
NT
T
b
lo
ck
th
e
ab
ilit
y
to
r
ea
d
th
e
in
p
u
t
c
o
ef
f
icien
ts
f
o
r
th
e
p
r
o
ce
s
s
o
f
th
e
cu
r
r
en
t
NT
T
s
tag
e,
an
d
it
also
g
r
a
n
ts
th
e
NT
T
b
lo
ck
th
e
ab
ilit
y
t
o
s
to
r
e
th
e
o
u
tp
u
t
c
o
ef
f
icien
ts
i
n
th
e
a
p
p
r
o
p
r
iate
in
d
ex
o
r
d
e
r
f
o
r
th
e
s
u
b
s
eq
u
e
n
t
NT
T
s
tag
e
s
.
T
h
e
s
tate
d
iag
r
am
f
o
r
th
e
ad
d
r
ess
g
en
er
ato
r
ca
n
b
e
s
ee
n
in
Fig
u
r
e
4
,
w
h
ich
is
a
f
in
ite
-
s
tate
m
ac
h
in
e,
s
u
it
ab
le
f
o
r
h
ar
d
war
e
im
p
lem
en
tatio
n
.
T
h
er
e
ar
e
th
r
ee
s
tates
in
th
e
ad
d
r
ess
g
en
er
at
or
:
I
DL
E
,
NT
T
,
an
d
W
AI
T
s
tate.
I
n
NT
T
s
tate,
r
ea
d
ad
d
r
ess
es
f
o
r
th
e
in
p
u
t
c
o
ef
f
i
cien
ts
an
d
th
e
c
o
r
r
esp
o
n
d
in
g
twid
d
le
f
ac
to
r
,
,
ar
e
g
en
er
ate
d
f
o
r
th
e
PEs
to
p
er
f
o
r
m
NT
T
p
r
o
ce
s
s
in
g
.
T
h
e
wr
ite
ad
d
r
ess
es
ar
e
also
g
en
er
ated
to
s
to
r
e
th
e
NT
T
o
u
tp
u
t
co
ef
f
icie
n
ts
in
th
e
B
R
AM
s
,
th
ese
co
ef
f
icien
ts
ar
e
th
en
u
s
ed
as
in
p
u
ts
f
o
r
th
e
n
ex
t
NT
T
s
tag
e.
T
h
er
e
ar
e
7
s
tag
es
in
a
1
2
8
-
p
t
NT
T
,
s
o
th
e
NT
T
s
tate
(
STA
T
E
1
)
is
iter
ated
7
tim
es
to
g
et
th
e
f
in
al
NT
T
r
esu
lt,
as
s
h
o
wn
in
Step
1
o
f
Alg
o
r
ith
m
2
.
T
h
e
s
tates
b
etwe
en
th
ese
NT
T
s
tates
ar
e
ca
lled
W
AI
T
s
tates.
T
h
ese
s
tates
s
ta
r
t
af
ter
c
o
m
p
letin
g
th
e
g
en
er
atio
n
o
f
th
e
r
ea
d
ad
d
r
ess
es
an
d
en
d
wh
en
all
th
e
o
u
tp
u
t
co
ef
f
icien
ts
ar
e
s
to
r
ed
in
th
e
B
R
AM
s
with
th
e
g
en
er
ated
wr
ite
ad
d
r
ess
es.
T
h
e
n
ex
t
NT
T
s
tag
e
p
r
o
ce
s
s
ca
n
s
tar
t
o
n
ly
if
t
h
e
cu
r
r
en
t
W
AI
T
s
tate
f
in
is
h
es.
Af
ter
7
W
AI
T
s
tates,
wh
ich
co
r
r
esp
o
n
d
to
7
r
esp
ec
tiv
e
NT
T
s
tates,
th
e
s
y
s
tem
ca
n
tr
a
n
s
it
f
r
o
m
th
e
f
in
a
l
W
AI
T
s
tate
b
ac
k
to
I
DL
E
s
tate
f
o
r
th
e
n
ex
t N
T
T
p
r
o
ce
s
s
.
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
A
n
efficien
t h
a
r
d
w
a
r
e
imp
leme
n
ta
tio
n
o
f
n
u
mb
er th
eo
r
etic
t
r
a
n
s
fo
r
m
fo
r
… (
Tr
a
n
g
Ho
a
n
g
)
739
Fig
u
r
e
4
.
Ad
d
r
ess
Gen
er
ato
r
s
tate
d
iag
r
am
3
.
4
.
O
v
er
a
ll desi
g
n
Du
e
to
th
e
p
r
o
p
er
t
y
th
at
an
-
p
t
NT
T
o
p
er
atio
n
ca
n
b
e
im
p
lem
en
ted
b
y
two
(
/
2
)
-
p
t
NT
T
o
p
er
atio
n
,
we
ca
n
im
p
lem
e
n
t
C
R
YSTA
L
S
-
Ky
b
er
’
s
2
5
6
-
p
t
NT
T
o
p
er
atio
n
b
y
u
s
in
g
tw
o
s
ep
ar
ated
class
ic
128
-
p
t
NT
T
,
o
f
wh
ich
alg
o
r
it
h
m
is
s
h
o
wn
in
Alg
o
r
ith
m
2
(
Fig
u
r
e
5
)
.
T
h
ese
two
NT
T
s
w
ill
g
ath
er
th
eir
d
ata
allo
ca
ted
in
th
e
B
R
A
MS,
wh
er
e
d
ata
in
an
d
o
u
t
o
f
th
e
NT
T
b
lo
ck
ar
e
s
to
r
ed
.
An
ad
d
r
e
s
s
g
en
er
ato
r
is
also
r
eq
u
ir
ed
to
in
s
tr
u
ct
th
e
B
R
AM
S to
o
u
tp
u
t t
h
e
co
r
r
ec
t in
f
o
r
m
atio
n
f
o
r
ea
ch
NT
T
r
esp
ec
tiv
el
y
.
B
ef
o
r
e
s
tar
tin
g
th
e
NT
T
/I
NT
T
o
p
er
atio
n
,
th
e
h
ar
d
war
e
s
to
r
es
twid
d
le
f
ac
to
r
s
(
f
o
r
NT
T
o
p
er
atio
n
)
,
m
o
d
u
lar
in
v
er
s
e
twid
d
le
f
ac
to
r
s
(
f
o
r
I
NNT
o
p
e
r
atio
n
)
,
an
d
t
h
e
in
p
u
t
co
ef
f
icien
ts
in
to
th
e
B
R
AM
s
o
f
ea
ch
PE.
T
h
e
twid
d
le
f
ac
to
r
an
d
its
m
o
d
u
lar
in
v
e
r
s
e
v
alu
es
ar
e
s
to
r
ed
i
n
2
B
R
AM
,
wh
ile
th
e
in
p
u
t
co
ef
f
icien
ts
ar
e
s
to
r
ed
in
4
B
R
AM
S:
2
B
R
A
Ms
f
o
r
th
e
f
ir
s
t
PE
an
d
2
B
R
AM
s
f
o
r
th
e
s
ec
o
n
d
PE.
Af
ter
th
e
NT
T
2
o
p
er
atio
n
,
th
e
o
u
t
p
u
t
c
o
ef
f
icien
ts
at
th
e
cu
r
r
en
t
s
tag
e
ar
e
th
en
s
to
r
ed
b
ac
k
to
th
e
s
am
e
4
B
R
AM
s
t
o
b
e
u
s
ed
as
in
p
u
t
co
ef
f
i
cien
ts
o
f
t
h
e
n
e
x
t
s
tag
e.
T
h
is
d
ata
s
to
r
in
g
p
r
o
ce
s
s
is
h
an
d
led
at
th
e
to
p
lev
el
u
s
in
g
th
e
g
en
e
r
ated
r
ea
d
an
d
wr
ite
ad
d
r
ess
es
f
r
o
m
th
e
a
d
d
r
ess
g
en
er
ato
r
as
m
en
tio
n
ed
ab
o
v
e.
Af
ter
f
i
n
is
h
in
g
7
NT
T
s
tag
es,
th
e
DOUT
B
L
OC
K
u
n
it
wo
u
ld
s
et
th
e
d
o
n
e
s
ig
n
al
to
h
ig
h
t
o
in
d
icate
t
h
e
co
m
p
letio
n
o
f
NT
T
/
I
NT
T
o
p
er
atio
n
,
w
h
ile
also
p
ass
in
g
th
e
o
u
tp
u
t
c
o
ef
f
icien
ts
d
ata
th
r
o
u
g
h
th
e
d
o
u
t
s
ig
n
al.
Fig
u
r
e
5
s
h
o
ws
o
u
r
p
r
o
p
o
s
ed
NT
T
o
v
er
all
d
esig
n
s
tr
u
ctu
r
e.
Fig
u
r
e
5
.
NT
T
t
o
p
o
v
er
all
ar
c
h
itectu
r
e
4.
E
XP
E
R
I
M
E
N
T
A
L
RE
SUL
T
S
AND
CO
M
P
AR
I
SO
N
4
.
1
.
E
x
perim
ent
a
l scena
rio
Ou
r
h
ar
d
war
e
d
esig
n
was w
r
itten
in
Ver
ilo
g
Har
d
war
e
Desc
r
ip
tio
n
L
an
g
u
ag
e,
th
e
m
o
s
t c
o
m
m
o
n
o
n
e
f
o
r
h
ar
d
war
e
im
p
lem
en
t
at
i
o
n
in
th
e
m
ea
n
tim
e.
On
th
e
o
th
er
h
an
d
,
o
u
r
d
esig
n
was
s
y
n
th
esized
an
d
im
p
lem
en
ted
u
s
in
g
Xilin
x
Viv
ad
o
to
o
ls
,
o
n
th
e
Xilin
x
A
r
tix
-
7
FP
GA
o
f
n
am
e
x
c
7
a1
2
tcp
g
2
3
8
-
3
,
s
p
ec
if
ically
.
I
n
p
ar
allel,
th
e
d
esig
n
was
als
o
s
y
n
th
esized
an
d
p
o
s
t
-
s
y
n
th
e
s
is
v
er
if
ied
u
s
in
g
Sy
n
o
p
s
y
s
D
esig
n
C
o
m
p
iler
an
d
Sy
n
o
p
s
y
s
Fo
r
m
ality
to
o
ls
with
th
e
T
SMC
6
5
n
m
lib
r
ar
y
,
as
a
m
eth
o
d
f
o
r
co
m
p
ar
is
o
n
.
T
h
e
NT
T
s
o
f
twar
e
f
o
r
th
e
r
ef
er
e
n
ce
m
o
d
el
was
wr
itten
in
Py
th
o
n
an
d
b
ased
o
n
th
e
NI
ST
s
u
b
m
is
s
io
n
s
’
r
e
f
er
en
c
e
C
s
o
u
r
ce
co
d
e
o
f
th
e
C
R
YSTA
L
S Ky
b
er
d
ev
el
o
p
in
g
team
.
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
8
,
No
.
2
,
May
20
2
5
:
7
3
2
-
7
4
3
740
4.
2
.
E
x
perim
ent
a
l scena
rio
Ou
r
p
r
o
p
o
s
ed
d
esig
n
was
s
y
n
th
esized
with
t
h
e
C
R
YST
AL
S
-
Ky
b
er
p
a
r
am
eter
s
o
f
q
=3
3
2
9
an
d
n
=2
5
6
.
T
h
er
e
wer
e
2
P
E
s
u
s
ed
in
o
u
r
d
esig
n
an
d
each
of
th
o
s
e
h
ad
2
b
u
tter
f
ly
u
n
its
.
T
h
e
s
y
n
th
esis
r
esu
lt
u
s
in
g
Sy
n
o
p
s
y
s
Desig
n
C
o
m
p
iler
to
o
ls
with
T
SMC
6
5
n
m
te
ch
n
o
lo
g
y
lib
r
a
r
y
is
s
h
o
wn
in
T
ab
le
1
.
On
e
o
f
th
e
m
o
s
t
cr
u
cial
an
d
p
r
ec
io
u
s
f
ac
to
r
s
o
f
th
e
s
y
n
th
esi
ze
d
d
esig
n
was
its
m
ax
im
u
m
f
r
eq
u
e
n
cy
to
wo
r
k
p
r
o
p
e
r
ly
.
T
h
e
v
alu
e
o
f
o
u
r
d
esig
n
was
ap
p
r
o
x
i
m
ately
4
9
7
MH
z,
wh
ic
h
o
u
t
weig
h
s
m
o
s
t
o
f
th
e
cr
y
p
to
s
y
s
tem
s
at
th
e
cu
r
r
en
t
tim
e.
T
h
e
v
alu
e
was
m
ea
s
u
r
ed
b
y
ch
a
n
g
in
g
th
e
f
r
eq
u
en
c
y
v
alu
e
in
th
e
s
d
c
(
Sy
n
o
p
s
y
s
Desig
n
C
o
n
s
tr
ain
ts
)
f
ile
an
d
r
e
-
r
u
n
th
e
s
y
n
th
esis
p
r
o
ce
s
s
u
n
til
we
g
o
t
th
e
lar
g
e
s
t
v
alu
e
p
o
s
s
ib
le
to
f
u
lf
ill
th
e
s
etu
p
an
d
h
o
ld
co
n
s
tr
ain
ts
.
Me
an
wh
ile,
o
n
th
e
a
r
ea
s
id
e,
th
e
g
ate
co
u
n
t
v
alu
e
o
f
o
u
r
d
esig
n
o
n
th
e
T
SMC
6
5
n
m
lib
r
ar
y
was
ar
o
u
n
d
4
7
2
K
with
m
o
s
t
o
f
th
e
u
s
ed
a
r
ea
f
o
r
n
o
n
-
co
m
b
in
ati
o
n
al
lo
g
ic
(
6
4
.
8
%),
wh
ile
th
e
co
m
b
in
atio
n
al
lo
g
ic
ac
co
u
n
ted
f
o
r
3
5
.
2
% o
f
th
e
t
o
tal
ar
ea
.
Fro
m
an
o
th
e
r
p
er
s
p
ec
tiv
e,
T
a
b
le
2
r
ep
o
r
ts
th
e
s
y
n
th
esis
an
d
im
p
lem
e
n
tatio
n
r
esu
lts
u
s
in
g
Xilin
x
Viv
ad
o
to
o
ls
.
wh
ich
r
esu
lted
in
an
ar
ea
-
f
r
ien
d
l
y
NT
T
d
esig
n
with
a
r
elativ
ely
h
ig
h
f
r
eq
u
en
cy
o
f
1
0
2
MH
z.
T
h
e
v
alu
e
was
m
o
d
er
ately
l
o
wer
th
an
th
e
v
alu
e
o
f
4
9
7
MH
z
m
en
tio
n
e
d
a
b
o
v
e
,
wh
ich
ca
n
b
e
e
x
p
lain
ed
b
y
th
e
f
ac
t
th
at
th
e
h
ar
d
war
e
o
p
tio
n
s
f
o
r
FP
GA
ar
e
m
u
ch
m
o
r
e
h
in
d
er
ed
in
co
m
p
ar
is
o
n
t
o
th
at
f
o
r
ASI
C
.
I
n
c
o
n
tr
ast,
th
e
n
u
m
b
er
o
f
L
UT
s
u
s
ed
in
th
e
im
p
lem
en
tatio
n
d
esig
n
was
m
u
ch
less
in
co
m
p
ar
is
o
n
to
th
e
s
y
n
th
esis
d
esig
n
,
s
in
ce
th
e
b
etter
p
h
y
s
ical
o
p
ti
m
izatio
n
an
d
f
u
ll
im
p
lem
e
n
ta
tio
n
wo
r
k
o
f
th
e
FP
GA.
Ad
d
itio
n
ally
,
th
e
d
esig
n
o
n
ly
u
s
ed
4
.
6
5
%
o
f
th
e
to
tal
am
o
u
n
t
o
f
u
s
ab
le
r
eg
is
ter
an
d
th
er
e
was
n
o
latch
g
en
er
ated
in
o
u
r
d
esig
n
.
T
h
is
ca
n
b
e
s
ee
n
as a
n
o
p
tim
is
t r
esu
lt in
th
e
ar
ea
a
n
d
ti
m
in
g
ef
f
ic
ien
cy
T
ab
le
1
.
Sy
n
t
h
esis
R
esu
lt o
n
ASI
C
Li
b
r
a
r
y
TSM
C
6
5
n
m
F
r
e
q
u
e
n
c
y
(
M
H
z
)
4
9
7
A
r
e
a
(
µ
m
2
)
To
t
a
l
9
0
6
1
1
3
.
7
4
7
2
C
o
m
b
i
n
a
t
i
o
n
a
l
3
1
9
1
0
0
.
1
5
9
8
B
u
f
/
I
n
v
6
3
8
9
.
7
5
9
9
7
N
o
n
c
o
m
b
i
n
a
t
i
o
n
a
l
5
8
7
0
1
3
.
5
8
7
4
T
ab
le
2
.
Sy
n
t
h
esis
an
d
I
m
p
le
m
en
tatio
n
r
esu
lts
o
n
FP
GA
D
e
si
g
n
S
y
n
t
h
e
si
s
I
mp
l
e
me
n
t
a
t
i
o
n
F
r
e
q
u
e
n
c
y
(
M
H
z
)
1
0
2
1
0
2
R
e
s
o
u
r
c
e
s
LU
T
8
7
2
8
5
7
R
EG
7
4
4
7
4
4
D
S
P
6
6
B
R
A
M
3
3
4
.
3
.
Co
m
pa
riso
n t
o
prio
r
wo
rk
T
ab
le
3
an
d
Fig
u
r
e
6
co
m
p
ar
e
th
e
r
esu
lts
in
o
u
r
wo
r
k
an
d
p
r
ev
io
u
s
wo
r
k
s
.
T
h
e
r
elatio
n
s
h
i
p
b
etwe
en
th
e
n
u
m
b
er
o
f
b
u
tter
f
l
y
u
n
its
u
s
ed
in
th
e
d
esig
n
an
d
im
p
le
m
en
tatio
n
tim
in
g
r
esu
lts
ar
e
s
h
o
wn
in
T
ab
le
3
an
d
Fig
u
r
e
6
(
a)
.
T
h
e
m
o
r
e
b
u
tter
f
ly
u
n
its
th
er
e
wer
e,
th
e
m
o
r
e
wo
r
k
was
s
h
ar
ed
f
o
r
ea
ch
b
u
tter
f
ly
u
n
it,
w
h
ich
h
en
ce
d
e
cr
ea
s
ed
th
e
NT
T
/I
N
T
T
p
r
o
ce
s
s
in
g
tim
e
an
d
in
c
r
ea
s
ed
th
e
m
a
x
im
u
m
wo
r
k
in
g
f
r
eq
u
en
cy
o
f
th
e
im
p
lem
en
tatio
n
d
esig
n
.
Usi
n
g
two
o
f
th
ese
u
n
its
,
it
ca
n
b
e
s
ee
n
th
at
o
u
r
wo
r
k
s
f
ar
s
u
r
p
ass
ed
[
1
1
]
,
wh
ich
o
n
ly
h
ad
o
n
e,
in
ter
m
s
o
f
o
p
er
atin
g
f
r
eq
u
en
c
y
as we
ll a
s
laten
cy
.
Ou
r
h
ar
d
war
e
d
esig
n
’
s
r
eso
u
r
ce
ef
f
icien
cy
ca
n
b
e
af
f
ir
m
ed
b
y
th
e
co
m
p
a
r
ativ
e
an
aly
s
is
o
f
r
eso
u
r
ce
u
tili
za
tio
n
am
o
n
g
th
e
d
esig
n
s
f
ea
tu
r
ed
in
T
ab
le
3
a
n
d
Fig
u
r
e
6
(
b
)
.
T
h
is
ac
h
iev
em
e
n
t
was
a
r
esu
lt
o
f
th
e
s
tr
ateg
ic
o
p
tim
izatio
n
o
f
FP
GA
D
SP
f
o
r
ca
lc
u
latin
g
o
p
er
atio
n
s
an
d
th
e
r
e
d
u
ct
io
n
o
f
n
ec
ess
ar
y
B
R
AM
b
lo
ck
s
f
o
r
m
em
o
r
y
o
n
es.
R
eg
ar
d
i
n
g
th
e
tim
in
g
an
d
p
er
f
o
r
m
an
ce
,
th
e
m
ax
im
u
m
f
r
eq
u
en
cy
o
f
o
u
r
wo
r
k
was
1
0
2
MH
z,
wh
ich
is
r
elativ
ely
m
e
d
iu
m
co
m
p
a
r
ed
to
o
th
er
wo
r
k
(
5
9
,
1
5
5
,
an
d
1
6
1
MH
z)
.
Ho
wev
er
,
b
y
g
en
e
r
atin
g
th
e
r
ea
d
a
n
d
wr
ite
ad
d
r
ess
e
f
f
icien
tly
ac
ce
s
s
in
g
th
e
m
em
o
r
y
,
th
e
laten
cy
o
f
o
u
r
d
esig
n
was
m
u
ch
s
m
aller
th
an
o
th
e
r
s
tu
d
ies
in
[
1
1
]
,
[
4
]
,
an
d
[
6
]
,
with
th
e
r
esp
ec
tiv
e
f
ig
u
r
es b
ei
n
g
6
.
8
6
,
1
1
6
.
6
1
,
1
1
.
8
3
,
an
d
3
.
1
8
m
icr
o
s
ec
o
n
d
s
.
Ou
r
ASI
C
d
esig
n
,
as
s
h
o
wn
in
T
ab
le
4
,
b
y
u
tili
zin
g
c
o
h
er
en
t
d
esig
n
s
ch
em
es
an
d
p
ip
elin
in
g
,
ac
h
iev
ed
a
f
r
eq
u
e
n
cy
o
f
4
9
7
MH
z,
an
d
f
ar
s
u
r
p
ass
ed
th
e
NT
T
h
ar
d
war
e
d
esig
n
s
in
[
6
]
an
d
[
7
]
.
Ho
wev
er
,
th
is
o
p
tim
izatio
n
ca
m
e
at
th
e
co
s
t
o
f
a
h
ig
h
g
ate
co
u
n
t
o
f
4
7
2
K
s
in
ce
th
e
tr
ad
e
-
o
f
f
b
etwe
en
ar
ea
an
d
tim
in
g
p
r
o
p
er
ties
.
Ou
r
d
esig
n
’
s
ar
c
h
itectu
r
e
th
o
u
g
h
r
esu
lted
in
a
r
elativ
ely
s
m
all
laten
cy
o
f
ju
s
t
6
8
6
an
d
an
in
s
ig
n
if
ican
t
p
r
o
ce
s
s
in
g
tim
e
o
f
1
.
3
8
m
icr
o
s
ec
o
n
d
s
f
o
r
t
h
e
NT
T
o
p
er
atio
n
.
T
h
is
laten
cy
an
d
o
p
er
atio
n
tim
e
ar
e
n
o
tab
l
y
lo
wer
th
an
o
th
er
wo
r
k
s
s
u
ch
as
[
6
]
a
n
d
[
7
]
,
p
r
i
m
ar
ily
d
u
e
to
o
u
r
well
-
p
lan
n
e
d
m
em
o
r
y
r
ea
d
a
n
d
wr
ite
s
ch
em
e
th
at
em
p
lo
y
ed
th
e
ad
d
r
ess
g
en
er
at
o
r
b
lo
ck
.
D
esp
ite
o
u
r
d
esig
n
’
s
r
elativ
ely
s
m
all
laten
cy
f
o
r
th
e
NT
T
o
p
er
atio
n
,
th
at
s
am
e
v
a
lu
e
was
lar
g
er
th
an
th
at
o
f
[
8
]
(
0
.
5
m
icr
o
s
ec
o
n
d
s
)
,
wh
ich
was
ac
h
iev
ed
b
y
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a
r
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imp
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741
u
tili
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ig
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r
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(
ar
ea
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t
h
e
s
y
n
th
esized
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esig
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u
r
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n
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o
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i
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er
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o
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m
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ce
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n
ASI
C
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with
o
u
t
u
s
in
g
u
p
a
lar
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e
n
u
m
b
e
r
o
f
r
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r
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s
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en
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e
r
in
g
it
a
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r
ig
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ter
s
o
lu
tio
n
f
o
r
d
esig
n
s
th
at
o
r
ien
t p
e
r
f
o
r
m
an
c
e
o
n
ASI
C
p
latf
o
r
m
.
T
ab
le
3
.
C
o
m
p
a
r
is
o
n
o
f
im
p
le
m
en
tatio
n
r
esu
lts
f
o
r
NT
T
d
es
ig
n
(
q
=
3
3
2
9
)
o
n
FP
GA
W
o
r
k
[
9
]
[
1
0
]
[
1
1
]
[
4
]
[
6
]
O
u
r
s
P
l
a
t
f
o
r
m
Zy
n
q
7
0
0
0
V
i
r
t
e
x
7
A
r
t
i
x
7
A
r
t
i
x
7
A
r
t
i
x
7
A
r
t
i
x
7
B
u
t
t
e
r
f
l
y
2
1
1
2
2
2
N
TT/
I
N
TT
l
a
t
e
n
c
y
[
C
C
s]
1
9
3
5
/
1
9
3
0
4
3
7
5
6
/
-
6
8
6
8
/
6
3
6
7
1
8
3
4
/
-
5
1
2
/
5
7
6
6
8
6
/
8
4
2
F
r
e
q
[
M
H
z
]
-
-
59
1
5
5
1
6
1
1
0
2
Ti
me
[
u
s]
-
-
1
1
6
.
6
1
1
1
.
8
3
3
.
1
8
6
.
8
6
LU
Ts
2
9
0
8
4
1
7
-
-
1
7
3
7
5
8
7
FFs
1
7
0
4
6
2
-
-
1
1
6
7
7
4
4
D
S
P
s
9
0
-
-
2
6
B
R
A
M
s
0
0
-
-
3
3
(
a)
(
b
)
Fig
u
r
e
6
.
C
o
m
p
a
r
is
o
n
o
f
NT
T
im
p
lem
en
tatio
n
o
n
FP
GA
r
eg
ar
d
in
g
(
a)
tim
in
g
s
an
d
(
b
)
r
eso
u
r
ce
s
T
ab
le
4
.
C
o
m
p
a
r
is
o
n
o
f
s
y
n
th
esis
r
esu
lts
f
o
r
NT
T
d
esig
n
(
q
=3
3
2
9
)
ASI
C
f
lo
w
W
o
r
k
P
l
a
t
f
o
r
m
n
q
N
TT
l
a
t
e
n
c
y
(
C
C
s)
F
r
e
q
(
M
H
z
)
Ti
me
(
u
s)
G
a
t
e
c
o
u
n
t
[
6
]
4
0
n
m
C
M
O
S
2
5
6
13
1
2
8
9
72
17
1
0
6
K
[
8
]
4
0
n
m
C
M
O
S
2
5
6
13
1
6
0
3
0
0
0
.
5
-
[
7
]
U
M
C
6
5
nm
2
5
6
13
2
0
5
6
25
82
1
4
K
O
u
r
s
TSM
C
6
5
nm
2
5
6
12
6
8
6
4
9
7
1
.
3
8
4
7
2
K
Evaluation Warning : The document was created with Spire.PDF for Python.