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r
a
nt
e
e
d.
C
om
put
a
t
i
ona
l
i
ns
ol
va
bi
l
i
t
y
of
di
s
c
r
e
t
e
l
oga
r
i
t
hm
pr
obl
e
m
i
n
e
llip
tic
c
u
r
v
e
s
f
or
m
s
t
he
m
a
t
he
m
a
t
i
c
a
l
f
ounda
t
i
on f
or
i
t
s
unbr
e
a
ka
bl
e
c
r
ypt
og
r
a
phi
c
s
t
r
uc
t
ur
e
.
E
C
C
ha
ve
be
c
om
e
t
he
f
a
vor
i
t
e
c
hoi
c
e
f
o
r
a
b
r
oa
d s
pe
c
t
r
um
of
a
ppl
i
c
a
t
i
ons
r
a
ngi
ng
f
r
om
t
he
s
e
ns
or
s
t
o b
l
oc
kc
ha
i
n due
t
o
its
s
tr
o
n
g
s
e
c
u
r
ity
w
ith
s
ma
l
l
ke
y s
i
z
e
a
nd l
ow
pow
e
r
di
s
s
i
pa
t
i
on [
10]
.
E
C
D
S
A
a
r
c
hi
t
e
c
t
ur
e
c
a
n be
pr
ot
ot
ype
d
e
i
t
he
r
i
n
s
of
t
w
a
r
e
or
ha
r
dw
a
r
e
dom
a
i
n.
T
h
i
s
pa
pe
r
s
ol
e
l
y
t
a
r
ge
t
s
on t
he
ha
r
dw
a
r
e
i
m
pl
e
m
e
nt
a
t
i
on o
f
di
gi
t
a
l
s
i
gna
t
ur
e
s
t
r
uc
t
ur
e
i
n
E
C
C
s
i
nc
e
ha
r
dw
a
r
e
de
s
i
g
n e
na
bl
e
s
s
p
eed
y
ex
ec
ut
i
on w
he
n c
om
pa
r
e
d
t
o
i
t
s
s
of
t
w
a
r
e
c
ount
e
r
pa
r
t
.
N
e
ve
r
t
he
l
e
s
s
,
ha
r
dw
a
r
e
m
ode
l
of
E
C
D
S
A
w
i
t
h
l
ow
r
e
s
our
c
e
ut
i
l
i
z
a
t
i
on a
nd
l
ow
l
a
t
e
nc
y
i
s
qui
t
e
a
de
m
a
ndi
ng t
a
s
k c
ons
i
de
r
i
ng t
he
f
a
c
t
t
ha
t
bot
h pa
r
a
m
e
t
e
r
s
ar
e co
n
t
r
ad
i
ct
o
r
y
.
T
h
u
s
ar
ea
-
l
at
en
cy
t
r
ad
e
-
o
f
f
i
s e
sse
n
t
i
al
t
o
ach
i
ev
e g
r
eat
er
ef
f
i
ci
en
cy
.
T
h
e m
ai
n
f
o
c
u
s
o
f
t
h
i
s
r
e
s
e
a
r
c
h w
or
k i
s
t
o de
s
i
gn f
a
s
t
e
r
a
nd a
r
e
a
e
f
f
i
c
i
e
nt
c
r
ypt
ogr
a
phi
c
m
odul
e
s
f
o
r
E
C
D
S
A
f
r
a
m
e
w
o
r
k.
T
hi
s
ha
r
dw
a
r
e
pa
r
a
di
gm
c
a
n be
i
nt
e
gr
a
t
e
d w
i
t
h ha
r
dw
a
r
e
bl
oc
kc
ha
i
n t
o ove
r
c
om
e
t
he
s
e
c
ur
i
t
y i
s
s
ue
s
br
o
ug
ht
i
n by
a s
o
f
t
w
ar
e b
as
ed
d
i
g
i
t
al
s
i
g
n
at
u
r
e.
2.
LI
T
ER
A
TU
R
E R
EV
I
EW
T
he
w
or
k done
i
n [
11]
de
l
i
be
r
a
t
e
s
a
bout
t
he
r
ol
e
of
e
llip
tic
c
u
r
v
e
d
ig
ita
l s
ig
n
a
tu
r
e
a
lg
o
r
ith
m
i
n
bl
oc
kc
ha
i
n
t
r
a
ns
a
c
t
i
ons
.
D
a
t
a
p
r
ove
na
nc
e
i
s
e
ns
ur
e
d t
hr
ough
t
hi
s
s
i
gna
t
ur
e
s
c
he
m
e
a
nd
t
he
pa
r
t
i
e
s
i
nvol
ve
d
s
ta
n
d
in
n
e
e
d
to
d
e
a
l
w
ith
ma
tte
r
o
f
t
r
u
s
t.
D
r
u
g
c
ount
e
r
f
e
i
t
i
ng
,
i
t
s
e
f
f
e
c
t
s
on
va
r
i
ous
dom
a
i
ns
a
nd how
bl
oc
kc
ha
i
n t
e
c
hni
que
s
a
l
ong w
i
t
h E
C
D
S
A
c
oul
d b
e
a
ppl
i
e
d
t
o c
ur
b dr
ug
f
a
br
i
c
a
t
i
on
i
s
de
t
a
i
l
e
d i
n [
1
2]
.
F
l
a
w
s
in
s
uppl
y
ch
ai
n
is
t
he
f
unda
m
e
nt
a
l
cau
s
e
f
or
dr
ug
c
ount
e
r
f
e
i
t
i
ng.
T
hi
s
wo
r
k
e
xpl
a
i
ns
t
he
b
en
ef
i
t
s
of
bl
oc
kc
ha
i
n
to
t
r
ack
,
d
et
ect
an
d
s
af
eg
u
ar
d
s
uppl
y
ch
ai
n
of
dr
ugs
.
T
he
publ
i
c
l
ed
g
er
t
e
c
hnol
ogy
r
eco
r
d
s
t
he
dr
ug
c
ons
t
i
t
ue
nt
s
a
l
ong
w
ith
its
uni
que
s
er
i
al
num
be
r
s
fro
m
pr
oduc
e
r
s
to
c
ons
um
e
r
s
.
S
i
n
ce
e
n
tir
e
t
r
an
s
act
i
o
n
s
ar
e
d
ig
ita
lly
s
i
gn
e
d
an
d
am
en
d
ed
in
t
he
d
is
tr
ib
u
te
d
l
ed
g
er
ev
en
a
s
l
i
ght
mo
d
if
ic
a
tio
n
in
an
y
pha
s
e
an
d
f
r
a
udul
e
nt
in
d
iv
id
u
a
ls
c
oul
d
be
r
eco
g
n
i
zed
.
N
y
am
e
e
t a
l.
[
13]
p
r
opos
e
d
a
dopt
s
E
CD
S
A
to
e
s
ta
b
lis
h
a
vi
a
bl
e
an
d
ef
f
ect
i
v
e
cl
i
en
t
v
e
r
if
ic
a
tio
n
an
d
a
ppr
ova
l
pr
ot
oc
ol
f
o
r
m
a
na
gi
ng know
l
e
dge
t
r
a
ns
m
i
s
s
i
ons
i
n
r
ol
e
-
b
as
ed
acc
e
s
s
co
n
t
r
o
l
(
R
B
A
C
)
.
D
ig
ita
l
s
i
gna
t
ur
e
a
l
gor
i
t
hm
c
on
tr
ib
u
te
s
to
b
u
ild
a
tr
u
s
tw
o
r
-
t
hy m
e
c
ha
ni
s
m
t
o
ve
r
i
f
y us
e
r
s
pr
i
o
r
t
o s
ha
r
e
,
e
xc
ha
nge
a
nd
s
t
or
i
ng i
nf
o
r
m
a
t
i
on
i
n
t
he
know
l
e
dge
r
e
pos
i
t
or
y
.
S
ys
t
e
m
m
ode
l
p
r
opos
e
d m
a
ke
us
e
of
bl
oc
kc
ha
i
n
t
o e
ns
ur
e
tr
a
n
s
p
a
r
e
n
c
y
a
n
d
immu
ta
b
ility
in
a
ll
ex
ch
an
g
e
s
p
er
f
o
r
m
ed
a
m
ong
en
t
i
t
i
es
.
T
h
er
ef
o
r
e,
t
h
e act
i
o
n
o
n
ce co
m
m
i
t
t
ed
c
a
n ne
ve
r
be
di
vi
de
d
a
s
t
he
y
a
r
e
i
nt
e
r
l
i
nke
d.
K
no
w
l
e
dge
m
an
ag
em
en
t
sy
st
e
m
s
(
K
MS
)
is
a
f
unc
t
i
on
-
o
r
i
e
nt
e
d
d
at
a
sy
st
e
m
in
w
h
i
ch
u
se
r
g
en
er
at
es
,
sh
a
r
e
a
nd
r
e
s
e
r
ve
know
l
e
dge
t
o
e
nha
nc
e
pe
r
f
or
m
a
nc
e
of
a
n
or
ga
ni
z
a
t
i
on [
14
]
,
[
15]
.
A
u
th
e
n
tic
ity
o
f
th
e
in
f
o
r
ma
tio
n
t
r
a
n
s
mitte
d
in
car
t
o
i
n
f
r
as
t
r
u
ct
u
r
e s
y
s
t
em
(
C
I
T
S
)
i
s
of
s
upr
e
m
e
im
-
por
t
a
nc
e
t
o c
ur
b t
he
i
nf
l
ue
nc
e
of
pr
i
or
i
t
y
ve
hi
c
l
e
s
on t
r
a
f
f
i
c
f
l
ow
a
nd t
r
a
f
f
i
c
l
i
ght
s
.
I
n t
he
w
or
k de
m
o
ns
t
r
a
t
e
d
i
n [
16]
de
ve
l
ops
E
C
DS
A
s
i
gna
t
ur
e
s
c
he
m
e
w
i
t
h l
ow
l
a
t
e
nc
y a
nd hi
gh t
hr
oughput
w
i
t
h a
n a
bi
l
i
t
y
t
o a
ut
he
nt
i
c
a
t
e
a
bout
2700 ve
r
i
f
i
c
a
t
i
on
pe
r
s
e
c
ond.
P
ip
e
lin
e
ar
ch
i
t
ect
u
r
e
t
h
at
m
ak
es
u
se
of
car
r
y
l
ook
ah
ead
ad
d
er
an
d
l
ong
wo
r
d
s
u
mma
tio
n
s
is
a
dopt
e
d i
n
[
17]
to
ha
ndl
e
gr
oup
o
pe
r
a
t
i
ons
in
E
C
DS
A.
FPG
A
b
as
ed
ar
ch
i
t
ect
u
r
e
to
p
e
rfo
rm
ma
th
e
ma
tic
a
l o
p
e
r
a
tio
n
s
r
eq
u
i
r
ed
by
E
CC
p
r
imitiv
e
s
i
s
pr
e
s
e
nt
e
d i
n
[
18]
w
hi
l
e
t
he
w
or
k
done
i
n
[
19
]
el
ab
o
r
at
es
on
E
CC
e
nc
r
ypt
i
on
an
d
s
ugge
s
t
a
t
e
c
hni
que
t
o
s
e
g
m
e
nt
or
i
gi
na
l
m
e
s
s
a
ge
i
nt
o di
gi
t
a
l
bl
oc
k
c
ode
s
a
nd t
o m
a
p
i
t
s
e
q
u
e
n
tia
lly
in
to
s
p
e
c
if
ic
p
o
in
ts
in
e
llip
tic
c
u
r
v
e
.
Ho
w
ev
er
,
de
t
a
i
l
s
on t
he
i
m
pl
e
m
e
nt
a
t
i
on of
t
he
p
r
opos
e
d
s
ys
t
e
m
i
s
not
pr
ovi
de
d but
t
he
w
or
k
i
ng pr
i
nc
i
pl
e
r
e
ga
r
di
ng t
he
e
xe
c
ut
i
on of
E
C
C
a
l
go
r
i
t
hm
i
s
i
l
l
us
t
r
a
t
e
d.
A
nove
l
m
a
ppi
ng
m
e
t
hod
is
a
dopt
e
d
in
[
20]
to
co
n
v
er
t
une
nc
r
ypt
e
d
t
ex
t
in
to
c
or
r
e
s
pondi
ng
A
m
er
i
can
S
t
an
da
r
d C
ode
f
or
I
n
f
or
m
a
t
i
on
I
nt
e
r
c
ha
nge
(
A
S
C
I
I
)
v
al
u
es
an
d
t
h
en
tr
a
n
s
la
te
in
to
its
h
ex
ad
eci
m
al
eq
u
i
v
al
en
t
.
T
hi
s
t
wo
-
p
h
a
se
c
onve
r
s
i
on
c
ont
r
i
but
e
s
to
s
ecu
r
e
m
e
s
s
a
ge
e
nc
r
ypt
i
on us
i
ng E
C
C
s
i
nc
e
c
i
phe
r
i
nput
c
ons
i
de
r
s
h
ex
ad
eci
m
al
v
al
u
e i
n
r
ev
er
s
e o
r
d
er
.
T
he
or
e
t
i
c
a
l
a
s
pe
c
t
s
of
E
C
C
a
r
e
di
s
c
us
s
e
d i
n [
21]
.
T
hi
s
pa
pe
r
c
onve
r
s
e
a
b
o
u
t th
e
k
e
y
p
r
in
c
ip
le
s
a
n
d
d
e
s
ig
n
s
tr
a
te
g
ie
s
to
i
mp
le
me
n
t a
r
ith
me
tic
ope
r
a
t
i
ons
in
E
CC.
A
r
ea
r
ed
u
ct
i
o
n
in
E
CC
ar
ch
i
t
ect
u
r
e
is
ach
i
ev
ed
in
[
22]
by
m
ean
s
of
M
ont
gom
e
r
y
l
a
dde
r
a
l
gor
i
t
hm
.
R
e
duc
e
d c
om
pl
e
xi
t
y
a
nd s
hi
f
t
ope
r
a
t
i
on i
n
pl
a
c
e
of
di
vi
s
i
on
e
nha
nc
e
s
c
om
put
a
t
i
ona
l
s
pe
e
d a
nd a
dd
a
r
e
a
c
om
pa
c
t
ne
s
s
t
o
t
he
s
ugge
s
t
e
d
pr
ot
ot
ype
.
N
ove
l
a
r
c
hi
t
e
c
t
ur
e
s
of
e
llip
tic
c
ur
ve
op
e
r
a
t
i
ons
on t
w
i
s
t
e
d E
dw
a
r
ds
cu
r
v
e
f
o
r
256
-
bi
t
ke
y
[
23]
a
nd
hybr
i
d pi
pe
l
i
ne
t
e
c
hni
que
a
l
ong w
i
t
h M
ont
gom
e
r
y
l
a
dde
r
a
l
gor
i
t
hm
i
s
a
dopt
e
d i
n [
24
]
t
o a
c
hi
e
ve
hi
g
h s
pe
e
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
:
1693
-
6930
T
E
L
KOM
NI
KA
T
el
eco
m
m
u
n
C
om
put
E
l
C
ont
r
o
l
,
Vo
l
.
19
, N
o
.
5
,
O
c
t
obe
r
2021:
1636
-
1647
1638
b
in
a
r
y
f
ie
ld
p
o
in
t
mu
ltip
lic
a
tio
n
.
P
a
r
a
lle
lis
m
i
n
E
C
C
gr
oup ope
r
a
t
i
ons
i
s
e
xpl
oi
t
e
d i
n
[
25]
t
o
br
i
ng
out
hi
gh
s
pe
e
d a
nd l
e
s
s
c
om
pl
e
x poi
nt
m
ul
t
i
pl
i
c
a
t
i
on
h
a
r
d
w
ar
e.
2.
1.
C
on
t
r
i
b
u
t
i
on
s
In
th
is
w
or
k,
h
ar
d
w
ar
e
imp
le
me
n
ta
tio
n
of
ar
ea
an
d
s
p
eed
ef
f
i
ci
en
t
r
e
c
onf
i
gur
a
bl
e
E
CD
S
A
ar
ch
i
t
ect
u
r
e
f
or
ve
r
i
f
i
c
a
t
i
on of
b
l
oc
kc
ha
i
n
t
r
a
ns
a
c
t
i
ons
i
s
pr
opos
e
d.
M
a
i
n obj
e
c
t
i
ve
of
t
he
r
e
s
e
a
r
c
h i
s
t
o
opt
i
m
i
z
e
c
om
pu
ta
tio
n
a
lly
in
tr
ic
a
te
o
p
e
r
a
t
io
n
s
s
u
c
h
a
s
mu
lt
ip
lic
a
tiv
e
in
v
e
r
s
e
,
mo
d
u
la
r
mu
ltip
lic
a
tio
n
a
n
d
f
in
ite
f
ie
ld
ope
r
a
t
i
ons
t
o e
ns
ur
e
hi
gh
pe
r
f
o
r
m
i
ng
E
C
D
S
A
f
r
a
m
e
w
or
k f
or
a
ppl
i
c
a
t
i
ons
t
ha
t
ut
i
l
i
z
e
s
bl
oc
kc
ha
i
n t
e
c
hnol
ogy.
T
h
i
s
p
ap
er
pr
opos
e
s
a
nove
l
m
e
t
hodol
ogy
to
u
nr
a
ve
l
t
he
c
o
mp
le
x
ity
of
f
in
ite
f
ie
ld
ope
r
a
t
i
ons
by
imp
l
e
me
n
tin
g
s
imp
le
a
nd
h
ig
h
ly
e
f
f
ic
ie
n
t a
r
ith
me
tic
u
n
its
th
a
t f
o
r
ms
th
e
b
u
ild
in
g
b
lo
c
k
s
o
f
E
C
DS
A.
S
i
gni
f
i
c
a
nt
c
ont
r
i
bu
t
i
ons
put
f
or
w
a
r
d
by t
hi
s
pa
pe
r
c
a
n be
out
l
i
ne
d
a
s
gi
ve
n:
−
A
n e
f
f
i
c
i
e
nt
pr
ot
ot
ype
f
or
e
l
l
i
pt
i
c
c
ur
ve
c
r
ypt
ogr
a
p
hy ba
s
e
d s
i
gna
t
ur
e
ge
ne
r
a
t
i
on
a
nd
v
er
i
f
i
cat
i
o
n
h
as
b
een
pr
opos
e
d t
o a
t
t
a
i
n be
t
t
e
r
pe
r
f
o
r
m
a
nc
e
i
n
t
e
r
m
s
of
s
pe
e
d a
nd a
r
e
a
ove
r
he
a
d.
−
N
ove
l
a
r
c
hi
t
e
c
t
ur
e
f
o
r
m
odul
a
r
m
ul
t
i
pl
i
c
a
t
i
on us
i
ng c
ount
e
r
m
e
c
ha
ni
s
m
i
s
a
dopt
e
d
t
o opt
i
m
i
z
e
r
es
o
u
r
ce
ut
i
l
i
z
a
t
i
on a
nd ope
r
a
t
i
ona
l
f
r
e
que
nc
y i
n
E
C
C
f
i
ni
t
e
f
i
e
l
d
ope
r
a
t
i
ons
.
−
N
e
w
ha
r
dw
a
r
e
de
s
i
gn
i
s
i
n
t
r
oduc
e
d
f
or
m
odul
a
r
i
nve
r
s
i
on t
o
a
l
l
e
vi
a
t
e
t
he
c
om
put
a
t
i
ona
l
c
om
pl
e
xi
t
y of
mu
ltip
lic
a
tiv
e
in
v
e
r
s
e
a
l
gor
i
t
hm
.
−
E
ve
r
y a
r
i
t
hm
e
t
i
c
m
odul
e
i
nc
l
udi
ng
m
odul
a
r
m
ul
t
i
pl
i
c
a
t
i
on,
m
odul
a
r
i
nve
r
s
i
o
n,
m
odul
a
r
s
qua
r
i
ng a
nd
g
r
oup
ope
r
a
t
i
ons
t
ha
t
f
or
m
s
t
he
di
gi
t
a
l
s
i
gna
t
ur
e
c
i
r
c
ui
t
i
s
de
s
i
gne
d t
o
be
r
e
c
onf
i
gur
a
bl
e
a
nd
f
l
e
xi
bl
e
e
nou
gh t
o
ha
ndl
e
a
ny bi
t
-
si
z
e
v
al
u
es
.
−
A
ddi
t
i
ona
l
l
y,
ha
r
dw
a
r
e
r
e
s
our
c
e
c
ons
um
pt
i
on a
nd
ope
r
a
t
i
ng f
r
e
que
nc
y o
f
t
he
pr
opos
e
d
E
C
C
a
r
ch
i
t
ect
u
r
es
a
r
e
be
t
t
e
r
i
n
c
om
pa
r
i
s
on t
o
r
e
l
a
t
e
d w
or
ks
w
hi
c
h
a
s
s
ur
e
s
i
m
pr
ove
d pe
r
f
or
m
a
nc
e
of
a
l
l
t
he
de
s
i
gns
pr
opos
e
d.
T
h
e
r
e
s
t o
f
th
e
p
a
p
e
r
is
f
o
r
mu
la
te
d
a
s
f
o
llo
w
s
:
f
u
nda
m
e
nt
a
l
s
of
e
l
l
i
pt
i
c
c
u
r
ve
c
r
yp
t
ogr
a
phy
a
nd t
he
s
t
e
ps
i
nvol
ve
d i
n E
C
D
S
A
a
l
gor
i
t
hm
i
s
s
u
mma
r
iz
e
d
in
s
e
c
tio
n
2.
S
ect
i
o
n
3
di
s
c
us
s
e
s
a
bout
t
he
pr
opos
e
d
h
ar
d
w
ar
e
ar
ch
i
t
ect
u
r
es
f
or
m
odul
a
r
mu
ltip
lic
a
ti
o
n
,
m
odul
a
r
i
nve
r
s
i
on
an
d
gr
oup
ope
r
a
t
i
ons
in
E
CC.
I
mp
le
me
n
ta
tio
n
r
e
s
u
lts
of
t
he
de
s
i
gne
d
EC
C
pr
ot
ot
ype
s
ar
e
co
n
f
er
r
ed
in
s
ect
i
o
n
4
.
S
ect
i
o
n
5
hi
ghl
i
ght
s
t
he
c
om
pa
r
i
s
on r
e
s
ul
t
s
of
t
he
p
r
opos
e
d
de
s
i
gns
w
ith
e
xi
s
t
i
ng
w
or
ks
.
S
ect
i
o
n
6
c
onc
l
ude
s
t
he
p
ap
er
a
l
ong
w
it
h
fu
t
u
re
s
c
ope
of
t
h
e r
es
ear
ch
w
or
k.
3.
F
UNDA
M
E
NT
AL
S
O
F
ELLI
P
T
I
C
CUR
VE
CR
YP
T
O
G
RAP
H
Y
3.
1.
B
a
si
c
co
n
cep
t
s
o
f
el
l
i
p
t
i
c cu
rv
e
c
r
yp
t
ogr
ap
h
y
T
he
ne
e
d f
or
s
t
r
ong s
e
c
ur
i
t
y a
nd i
m
p
r
ove
d ba
ndw
i
dt
h i
n t
he
a
r
e
a
of
c
om
m
uni
c
a
t
i
on ur
ge
d
t
w
o
sc
i
e
n
tis
ts
n
a
me
d
V
ic
to
r
M
ille
r
a
n
d
K
o
b
litz
to
in
tr
o
d
u
c
e
e
llip
tic
c
u
r
v
e
s
i
nt
o
t
he
w
or
l
d
of
c
r
ypt
og
r
a
phy
i
n
1985.
T
h
e o
b
j
ect
i
v
e o
f
E
C
C
i
s
t
o
i
n
cr
eas
e t
h
e
ma
th
e
ma
t
ic
a
l c
o
mp
le
x
ity
o
f
D
is
c
r
e
te
L
o
g
a
r
ith
m p
r
o
b
le
m th
r
o
u
g
h
its
tr
a
n
s
la
tio
n
to
e
ll
ip
tic
cu
r
v
es
.
B
es
i
d
es
e
nc
r
ypt
i
on
an
d
de
c
r
ypt
i
on
E
CC
a
l
so
r
eal
i
zes
k
ey
e
xc
ha
nge
s
ch
em
es
a
nd
d
ig
ita
l s
ig
n
a
tu
r
e
s
.
I
n
E
C
C
imp
le
me
n
ta
tio
n
s
imp
le
e
n
c
r
y
p
tio
n
a
lg
o
r
i
th
m
is
ma
p
p
e
d
t
o
r
e
lia
b
le
e
llip
t
ic
cu
r
v
e.
T
h
er
ef
o
r
e,
t
he
el
em
en
t
ar
y
ope
r
a
t
i
ons
su
c
h
as
m
odul
a
r
a
ddi
t
i
on
an
d
m
odul
a
r
mu
ltip
lic
a
tio
n
as
in
RS
A
t
ur
ns
in
to
poi
nt
a
ddi
t
i
on a
nd
poi
nt
m
u
l
t
i
pl
i
c
a
t
i
on
r
e
s
pe
c
t
i
ve
l
y i
n t
hi
s
ne
w
f
or
m
of
publ
i
c
ke
y
c
r
ypt
og
r
a
phy.
Wei
er
s
t
r
as
s
el
l
i
p
t
i
c cu
r
v
e eq
u
at
i
o
n
f
o
r
a p
r
i
m
e f
i
el
d
F
p
(p
>
3)
i
s
gi
ve
n by
t
he
f
o
r
m
:
E:
y
2
=
x
3
+
ax
+
b
(
1)
f
or
c
ons
t
a
nt
pa
r
a
m
e
t
e
r
s
a
a
nd b w
he
n
t
he
s
pe
c
i
f
i
c
c
ondi
t
i
on 4
a
2
+2
7
b
3
=
0
is
s
a
tis
f
ie
d
[
2
6
]
,
[
27]
.
I
f
t
w
o
poi
nt
s
on
t
he
c
ur
ve
a
r
e
r
e
pr
e
s
e
nt
e
d a
s
A
(
x
1
, y
1
)
a
n
d
B
(
x
2
, y
2
)
,
t
he
n E
C
C
ope
r
a
t
i
on
know
n a
s
poi
nt
a
ddi
t
i
on
r
e
s
ul
t
s
i
n a
not
he
r
po
i
nt
C
(
x
3
, y
3
)
o
n
t
h
e cu
r
v
e w
h
er
e C
=A
+B
w
h
i
ch
can
b
e cal
cu
l
at
ed
a
s
:
x
3
=
m
2
−
x
1
−
x
2
(
2)
y
3
=
m
(
x
1
−
x
3
)
−
y
1
(
3)
w
h
er
e m
=
2
−
1
2
−
1
gi
ve
s
t
he
s
l
ope
of
t
he
l
i
ne
be
t
w
e
e
n A
a
nd B
.
A
ddi
t
i
on o
f
s
a
m
e
poi
nt
s
A
(
x
1
, y
1
)
to
i
ts
e
lf
r
e
s
u
lts
in
C
(
x
3
, y
3
)
on
t
he
c
ur
ve
t
hr
ough
a
not
he
r
gr
oup
ope
r
a
t
i
on
c
a
l
l
e
d poi
nt
doubl
i
ng w
he
r
e
C
=
A
+
A
=
2
A
i
s
c
om
put
e
d a
s
f
ol
l
ow
s
:
x
3
=
m
2
−
2
x
1
(4
)
y
3
=
m
(
x
1
−
x
3
)
−
y
1
(5
)
w
h
er
e m
=
3
2
+
2
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
el
eco
m
m
u
n
C
om
put
E
l
C
ont
r
o
l
E
f
f
i
c
i
e
nt
har
dw
ar
e
pr
ot
ot
y
pe
of
E
C
D
SA
m
odul
e
s
f
or
bl
oc
k
c
hai
n appl
i
c
at
i
ons
(
D
evi
ka
K
.
N
.)
1639
T
he
a
bove
e
qua
t
i
ons
de
m
a
nd a
r
i
t
h
m
e
t
i
c
ope
r
a
t
i
ons
s
uc
h a
s
a
ddi
t
i
on,
s
ubt
r
a
c
t
i
on a
nd
m
odul
o
m
ul
t
i
pl
i
c
a
t
i
on.
C
om
put
i
ng t
he
s
l
ope
of
t
he
c
ur
ve
’
m
’
ne
c
e
s
s
i
t
a
t
e
s
ha
r
dw
a
r
e
pr
ot
ot
ype
f
or
m
odul
a
r
mu
ltip
lic
a
tiv
e
in
v
e
r
s
e
.
S
i
nc
e
m
odul
o
-
p m
ul
t
i
pl
i
c
a
t
i
on a
nd i
nve
r
s
i
on a
r
e
ex
ecu
t
ed
i
n
th
e
p
r
ime
f
ie
ld
F
p
,
la
tte
r
b
eco
m
es
t
oo c
os
t
l
y t
o a
f
f
o
r
d w
i
t
h
r
e
s
pe
c
t
t
o pe
r
f
or
m
a
nc
e
a
nd r
e
s
our
c
e
s
i
n c
om
pa
r
i
s
on w
i
t
h
t
he
f
o
r
m
e
r
.
3.
2.
S
t
e
p
s
f
o
r
E
CDS
A
s
i
gn
at
u
r
e
ge
n
e
r
at
i
on
an
d
v
eri
f
i
ca
t
i
o
n
S
e
nde
r
A
us
e
s
hi
s
pr
i
va
t
e
ke
y
d
A
t
o
s
i
g
n
t
h
e
m
es
s
ag
e M
t
o
b
e s
en
t
t
o
t
h
e
r
ecei
v
er
B
.
H
er
e t
h
e m
es
s
ag
e
pr
ovi
de
d c
a
n be
o
f
a
ny bi
t
s
i
z
e
.
T
h
e
k
ey
v
al
u
es
ar
e
p
r
ed
ef
i
n
ed
by t
he
s
e
nde
r
pr
i
or
t
o
t
r
a
ns
m
i
s
s
i
on.
3.
2.
1.
S
t
e
ps
unde
r
s
i
gn
at
u
r
e
g
en
era
t
i
o
n
−
H
a
sh
of
t
he
m
e
ssa
g
e
M
is
cal
cu
l
at
ed
to
g
et
Z.
T
y
p
i
cal
l
y
t
he
h
a
sh
f
unc
t
i
on
ap
p
l
i
ed
is
S
HA
-
1.
Z
=
h
a
sh
(
M)
−
S
e
l
e
c
t
a
r
a
ndom
va
l
ue
K
w
i
t
hi
n
t
he
r
a
nge
[
1,
n
-
1]
.
−
C
om
put
e
c
o
-
or
di
na
t
e
(
x
1
,
y
1
)
=
kG
w
he
r
e
G
i
s
t
he
ba
s
e
poi
nt
.
−
D
et
er
m
i
n
e r
=
x
1
m
od
n
.
−
C
om
put
e
S
=
K
-
1
(
z +
d
A
r)
m
od
n
.
−
I
f
r
=
0
a
nd s
=
0,
go f
o
r
a
ne
w
r
a
ndom
va
l
ue
’k
’.
−
S
i
gna
t
ur
e
pa
i
r
g
en
er
at
ed
i
s
(r,
s
)
.
A
f
t
e
r
E
C
D
S
A
s
i
gna
t
ur
e
ge
ne
r
a
t
i
on,
A
t
r
a
ns
m
i
t
s
s
i
gne
d m
e
s
s
a
g
e
t
o B
.
B
pos
s
e
s
s
A
’
s
publ
i
c
ke
y Q
A
.
B
v
al
i
d
at
es
t
he
a
ut
hor
s
hi
p of
t
r
a
ns
a
c
t
i
on t
hr
ough
ve
r
i
f
i
c
a
t
i
on.
3.
2.
2.
S
t
ep
s
f
o
r
s
i
gn
at
u
r
e
v
eri
f
i
ca
t
i
o
n
−
C
e
r
tif
ie
s
r
a
n
d
s
lie
s
in
th
e
r
an
g
e [
1
,
n
-
1
].
−
C
om
put
e
W
= s
−1
m
od
n
.
−
C
al
cu
l
at
e
u
1
=
Zw
m
od
n
w
h
er
e
Z
i
s
t
h
e
h
as
h
o
f
m
es
s
ag
e M
.
−
C
al
cu
l
at
e
u
2
= r
w
m
od
n
.
−
C
om
put
e
c
o
-
or
di
na
t
e
s
(x
2
, y
2
)
= u
1
G +
u
2
Q
A
.
−
I
f
x
2
= r
s
i
g
n
at
u
r
e i
s
v
er
i
f
i
ed
an
d
v
al
i
d
at
ed
el
s
e i
t
i
s
r
ej
ect
ed
o
r
co
n
s
i
d
er
ed
in
v
a
lid
.
4.
P
RO
P
O
S
E
D H
ARDW
ARE
I
M
P
L
E
M
E
NT
AT
I
O
N O
F
E
CDS
A M
O
DUL
E
S
4.
1.
M
od
u
l
ar
m
u
l
t
i
p
l
i
c
at
i
o
n
M
o
d
u
la
r
mu
ltip
lic
a
tio
n
c
o
n
s
titu
te
s
o
n
e
a
mo
n
g
th
e
mo
s
t time
in
te
n
s
iv
e
ma
th
e
ma
tic
a
l o
p
e
r
a
tio
n
s
in
el
l
i
pt
i
c
c
u
r
ve
c
r
ypt
og
r
a
phy
ove
r
a
f
i
ni
t
e
f
i
e
l
d
.
A
do
pt
i
on of
e
f
f
i
c
i
e
nt
a
l
gor
i
t
hm
s
s
uc
h a
s
Mo
n
t
gom
e
r
y
,
r
e
s
i
due
num
be
r
s
ys
t
e
m
(
R
N
S
)
or
i
nt
e
r
l
e
a
ve
d m
odul
a
r
m
ul
t
i
pl
i
c
a
t
i
on
c
a
n i
m
p
r
ove
t
he
l
a
t
e
nc
y a
nd
s
p
eed
of
c
om
put
a
t
i
ona
l
pr
oc
e
s
s
[
28
]
-
[
34]
.
H
ow
e
ve
r
,
M
ont
gom
e
r
y t
e
c
hni
que
ne
e
ds
e
xt
r
a
pr
oc
e
s
s
i
ng ope
r
a
t
i
ons
t
o
co
n
s
t
r
ai
n
v
a
lu
e
s
w
ith
in
th
e
s
p
e
c
if
ie
d
f
in
ite
f
ie
ld
.
R
N
S
mu
ltip
lic
a
tio
n
s
c
h
e
me
r
e
s
u
lts
in
s
ig
n
if
ic
a
n
t a
r
e
a
o
v
e
r
h
e
a
d
a
nd
pow
e
r
c
ons
um
pt
i
on
t
o
i
m
pl
e
m
e
nt
i
t
s
ha
r
dw
a
r
e
c
ount
e
r
pa
r
t
[
35]
,
[
36]
.
H
e
nc
e
t
o
r
e
duc
e
t
he
a
r
e
a
o
ve
r
he
a
d
as
w
el
l
as
t
o i
m
pr
ove
t
he
pe
r
f
or
m
a
nc
e
i
n
t
e
r
m
s
of
s
pe
e
d,
m
odul
a
r
m
ul
t
i
pl
i
e
r
us
i
ng c
ount
e
r
m
e
c
ha
ni
s
m
i
s
de
s
i
gne
d a
nd a
dopt
e
d.
M
o
d
u
la
r
mu
ltip
lic
a
tio
n
o
f
tw
o
N
-
bi
t
va
l
ue
s
A
a
nd
B
ove
r
pr
i
m
e
f
i
e
l
d
G
F
(
q)
i
s
gi
ve
n by
t
he
f
or
m
ul
a
:
M =
AB
m
od
q
(
6)
=
{b
n−
1
(2
n−
1
A
)
+
b
n−
2
(2
n−
2
A
)
+
..
..
..
.
+
b
1
(2
1
A
)
+
b
0
A}
(
7)
=
{
∑
(
2
−
1
=
0
)
m
od
q}
(
8)
F
i
gur
e
1
illu
s
tr
a
te
s
t
he
f
l
o
w
ch
ar
t
of
pr
opos
e
d
m
odu
l
a
r
mu
ltip
lic
a
tio
n
ci
r
cu
i
t
us
i
ng
c
ount
e
r
m
ech
an
i
s
m
.
In
th
is
t
e
c
hni
que
,
l
ef
t
s
h
i
ft
r
eg
i
s
t
er
s
h
if
ts
t
he
va
l
ue
st
o
r
e
d
in
r
eg
P
by
one
bi
t
f
or
ev
er
y
i
t
h
bi
t
of
m
u
ltip
lie
r
B
.
Wh
en
ev
er
B
i
i
s
one
a
c
c
um
ul
a
t
or
a
dds
t
he
out
put
va
l
ue
of
s
hi
f
t
r
e
gi
s
t
e
r
a
l
ong w
i
t
h
m
ul
t
i
pl
i
c
a
nd A
a
nd s
t
or
e
s
t
he
r
e
s
ul
t
i
n
r
e
g
F.
V
al
u
e
s
t
o
r
ed
i
n
r
eg
F
a
f
t
e
r
“
N
”
i
t
e
r
a
t
i
ons
f
or
m
s
t
he
f
i
na
l
p
r
oduc
t
of
A
a
nd
B
af
t
er
mu
ltip
lic
a
tio
n
.
T
o pe
r
f
or
m
m
odul
o ope
r
a
t
i
on t
he
c
ont
e
nt
of
r
e
g G
i
s
r
e
pe
a
t
e
dl
y s
ubt
r
a
c
t
e
d by pr
i
m
e
va
l
ue
‘
q’
unt
i
l
t
he
di
f
f
e
r
e
nc
e
be
c
om
e
l
e
s
s
t
ha
n i
nput
’
q’
.
T
he
m
odul
e
m
a
ke
us
e
of
t
hr
e
e
m
ul
t
i
p
l
ex
er
s
w
h
er
e
th
e
f
ir
s
t
m
u
x
c
he
c
ks
e
a
c
h bi
t
of
B
f
or
1
a
nd i
f
t
he
c
ondi
t
i
on
i
s
s
a
t
i
s
f
i
e
d i
t
e
na
bl
e
s
r
e
gi
s
t
e
r
F
t
o
s
t
or
e
t
he
s
um
of
A
an
d
accu
m
u
l
at
o
r
c
ont
e
nt
or
e
l
se
r
et
ai
n
s
t
he
accu
m
u
l
at
o
r
va
l
ue
.
T
he
ot
h
e
r
t
wo
m
uxe
s
ai
d
s
t
o
pe
r
f
o
r
m
m
odul
o
ope
r
a
t
i
on.
I
n
t
h
e
pr
opos
e
d f
r
a
m
e
w
or
k
N
-
b
it in
p
u
t r
e
q
u
ir
e
s
’
N
’
c
lo
c
k
c
y
c
le
s
to
c
o
mp
le
te
mo
d
u
la
r
mu
lt
ip
lic
a
tio
n
.
S
am
e
s
t
r
uc
t
ur
e
wo
r
k
as
s
qua
r
i
ng
ci
r
cu
i
t
w
h
en
i
d
en
t
i
cal
i
nput
s
ar
e
co
n
s
i
d
er
ed
as
bot
h
mu
lti
p
lie
r
a
n
d
mu
ltip
lic
a
n
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
:
1693
-
6930
T
E
L
KOM
NI
KA
T
el
eco
m
m
u
n
C
om
put
E
l
C
ont
r
o
l
,
Vo
l
.
19
, N
o
.
5
,
O
c
t
obe
r
2021:
1636
-
1647
1640
F
i
gur
e
1.
P
r
opos
e
d
m
odu
l
a
r
m
ul
t
i
pl
i
c
a
t
i
on us
i
ng c
ount
e
r
m
e
c
ha
ni
s
m
4.
2.
M
od
u
l
ar
m
u
l
t
i
p
l
i
c
at
i
ve
i
n
ve
r
s
e
I
n num
be
r
t
he
or
y
m
ul
t
i
pl
i
c
a
t
i
ve
i
nve
r
s
e
of
a
n
i
nt
e
g
e
r
A
i
s
s
a
i
d t
o
be
B
i
f
a
nd
onl
y i
f
t
he
pr
oduc
t
of
A
a
nd B
i
s
c
ongr
ue
nt
t
o 1
i
n
r
e
s
pe
c
t
o
f
m
odul
us
N
[
37]
.
A
s
pe
r
t
he
c
onve
nt
i
o
na
l
a
nnot
a
t
i
on
,
t
he
c
ongr
ue
nc
y of
i
nve
r
s
e
f
unc
t
i
on i
s
gi
ve
n
by t
he
f
or
m
ul
a
:
AB
≡
1
m
od
N
(
9)
M
u
ltip
lic
a
tiv
e
i
nve
r
s
e
ope
r
a
t
i
on
c
o
n
s
titu
te
s
t
he
m
o
st
r
es
o
u
r
ce
i
nt
e
ns
i
ve
an
d
time
-
c
ons
um
i
ng
ar
i
t
h
m
et
i
c p
r
o
ces
s
in
E
CC.
It
is
a
m
a
nda
t
or
y
act
i
o
n
unde
r
t
a
ke
n
in
poi
n
t
a
ddi
t
i
on
an
d
po
i
nt
doubl
i
ng
to
cal
cu
l
at
e
t
he
s
l
ope
of
t
he
c
ur
ve
.
S
e
v
e
r
a
l a
lg
o
r
ith
ms
c
u
r
r
e
n
tly
e
x
is
t to
a
id
th
e
m
a
th
e
ma
tic
a
l c
o
mp
u
ta
tio
n
o
f
mo
d
u
la
r
i
nve
r
s
i
on
[3
8
]
-
[
41]
.
N
one
t
he
l
e
s
s
,
t
he
E
xt
e
nde
d E
uc
l
i
de
a
n m
e
t
hod
e
s
t
a
bl
i
s
h t
he
s
i
m
pl
e
a
nd
ef
f
ect
u
al
ap
p
r
o
ach
t
o
d
o
so
.
T
he
s
t
e
ps
i
nvol
ve
d i
n E
xt
e
nde
d E
uc
l
i
de
a
n a
l
go
r
i
t
hm
f
or
i
npu
t
s
A
,
p a
nd ou
t
put
Z
=
a
−
1
m
od
p
i
s
s
u
m
m
ar
i
zed
b
el
o
w
:
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
el
eco
m
m
u
n
C
om
put
E
l
C
ont
r
o
l
E
f
f
i
c
i
e
nt
har
dw
ar
e
pr
ot
ot
y
pe
of
E
C
D
SA
m
odul
e
s
f
or
bl
oc
k
c
hai
n appl
i
c
at
i
ons
(
D
evi
ka
K
.
N
.)
1641
F
i
gur
e
2 de
t
a
i
l
s
t
he
s
e
que
nc
e
of
a
r
i
t
hm
e
t
i
c
ope
r
a
t
i
ons
i
nvol
ve
d i
n t
he
i
nve
r
s
i
on ope
r
a
t
i
on.
T
he
pr
o
-
po
s
e
d de
s
i
gn e
m
pl
oys
m
ul
t
i
pl
i
e
r
us
i
ng c
ount
e
r
m
e
t
hod a
nd ba
s
i
c
a
r
i
t
hm
e
t
i
c
c
i
r
c
ui
t
s
t
o opt
i
m
i
z
e
h
ar
d
w
ar
e
r
es
o
u
r
ce
u
tiliz
a
tio
n
.
N
-
bi
t
i
nput
s
ar
e
in
itia
lly
s
t
o
r
ed
in
r
eg
A
an
d
r
eg
B
r
es
p
ect
i
v
el
y
.
O
ut
put
of
r
eg
B
is
de
not
e
d
a
s
va
l
B
w
h
ile
r
e
g
is
te
r
R
d
e
liv
e
r
s
va
l
r
.
D
i
vi
de
r
c
i
r
c
ui
t
t
a
ke
s
i
n A
a
nd B
a
nd pr
ovi
de
quot
i
e
nt
’
q’
a
s
t
h
e
out
put
w
h
i
ch
is
ev
en
t
u
al
l
y
st
o
r
e
d
in
r
eg
q.
S
imila
r
ly
,
r
em
ai
n
d
er
c
om
put
a
t
i
on
dur
i
ng
di
vi
s
i
on
is
ex
ecu
t
ed
us
i
ng
m
odul
o
ci
r
cu
i
t
to
g
et
va
l
r
.
T
wo
v
al
u
es
w
ith
in
r
eg
‘
B’
an
d
re
g
‘
r’
ar
e
co
m
p
ar
ed
.
If
va
l
B
is
g
r
eat
er
t
h
an
va
l
r
,
co
n
t
en
t
of
r
eg
A
is
r
ep
l
aced
w
ith
t
h
at
of
r
eg
B
an
d
la
tte
r
is
o
ccu
p
i
ed
w
ith
va
l
r
.
C
om
put
a
t
i
on
of
quot
i
e
nt
an
d
r
e
m
ai
n
d
er
us
i
ng a
bove
c
ondi
t
i
on c
ont
i
nue
s
unt
i
l
va
l
r
is
0
.
T
h
is
d
e
te
r
min
e
s
th
e
n
u
mb
e
r
o
f
ite
r
a
tio
n
s
to
c
a
lc
u
la
te
th
e
in
v
e
r
s
e
of
A
w
ith
r
es
p
ect
to
B.
Re
g
P
is
in
itia
liz
e
d
w
ith
1.
P
r
e
vi
ous
c
ont
e
nt
w
i
th
in
r
eg
P
P
[
c
t
r]
is
mu
ltip
lie
d
w
ith
quot
i
e
nt
v
al
u
e ‘
q
’
f
o
r
each
i
t
e
r
at
i
o
n
an
d
s
u
b
t
r
act
ed
f
r
o
m
t
h
e p
r
ev
i
o
u
s
v
al
u
e
s
t
o
r
ed
i
n
P
[
ct
r
+1
]
w
h
er
e
‘
ct
r
’
i
n
d
i
cat
es
t
h
e
i
t
e
r
a
t
i
on va
l
ue
.
T
he
f
i
na
l
r
e
s
ul
t
i
s
s
t
or
e
d i
n
r
e
g
Z
c
or
r
e
s
pondi
ng t
o R
[
c
t
r
]
be
i
ng
1.
F
i
gur
e
2.
P
r
opos
e
d
a
r
ch
i
t
ec
tu
r
e
f
o
r
mu
lt
ip
lic
a
tiv
e
i
n
v
er
s
e ci
r
cu
i
t
4
.
3
.
E
l
l
i
p
t
i
c cu
rv
e f
i
el
d
o
p
era
t
i
o
n
s
E
l
l
i
pt
i
c
c
ur
ve
f
i
e
l
d
ope
r
a
t
i
ons
m
a
i
nl
y
c
om
p
r
i
s
e
of
poi
nt
a
ddi
t
i
on
a
nd
poi
nt
doubl
i
ng
t
ha
t
a
r
e
p
er
-
f
o
r
me
d
f
o
r
d
e
f
in
ite
c
o
n
s
e
c
u
tiv
e
s
ta
g
e
s
to
e
x
e
c
u
te
e
llip
tic
c
u
r
v
e
mu
ltip
l
ic
a
tio
n
th
a
t
f
o
r
ms
th
e
c
r
itic
a
l
ope
r
a
t
i
on i
n
E
CC.
If
P
an
d
Q
ar
e
t
wo
poi
nt
s
on
a
gi
v
e
n
e
llip
tic
c
ur
ve
so
t
h
at
k
P
=Q
,
t
h
en
c
om
put
a
t
i
on
of
‘
k’
is
in
f
e
a
s
ib
le
e
ve
n i
f
pr
ov
i
de
d w
i
t
h
P
a
nd Q
w
he
n k i
s
s
i
gni
f
i
c
a
nt
l
y l
a
r
ge
.
H
e
r
e
‘
k
’
i
s
t
he
s
c
a
l
a
r
va
l
ue
t
ha
t
t
ur
ns
out
t
o be
t
he
di
s
c
r
e
t
e
l
oga
r
i
t
hm
of
Q
f
or
ba
s
e
P
.
F
i
g
ur
e
s
3 a
nd 4 por
t
r
a
ys
t
he
s
e
r
i
e
s
of
a
r
i
t
hm
e
t
i
c
ope
r
a
t
i
ons
i
nvol
ve
d
i
n pr
opos
e
d a
r
c
hi
t
e
c
t
ur
e
s
of
poi
nt
a
ddi
t
i
on a
nd po
i
nt
doubl
i
ng
r
es
p
ect
i
v
el
y
.
P
r
opos
e
d a
r
c
hi
t
e
c
t
ur
e
f
or
poi
nt
a
ddi
t
i
on
r
e
qui
r
e
s
2M
+
2S
+
1i
nve
r
s
i
on ope
r
a
t
i
ons
w
hi
l
e
poi
nt
doubl
i
ng
ne
e
ds
3M
+
1S
+
1i
nve
r
s
i
on.
T
o
a
c
hi
e
ve
opt
i
m
i
z
e
d
p
er
f
o
r
m
an
ce i
n
t
er
m
s
o
f
ar
ea,
s
p
eed
an
d
l
at
en
cy
t
h
e s
u
b
-
m
o
d
u
l
e s
t
r
u
ct
u
r
es
ar
e ef
f
i
ci
en
t
l
y
d
es
i
g
n
ed
an
d
ef
f
ect
i
v
el
y
act
i
v
at
ed
at
r
eq
u
i
r
ed
s
t
ag
es
.
M
u
l
t
i
p
l
i
cat
i
o
n
an
d
s
qua
r
i
ng ope
r
a
t
i
ons
ha
ve
a
l
a
t
e
nc
y of
N
+
1 c
l
oc
k c
yc
l
e
s
.
P
o
in
t mu
ltip
lic
a
tio
n
c
o
n
s
titu
te
s
a
s
e
r
ie
s
o
f
f
ie
ld
o
p
e
r
a
tio
n
s
a
s
p
e
r
th
e
b
in
a
r
y
p
a
tte
r
n
o
f
s
c
a
la
r
‘
k’
a
n
d
t
he
pr
opos
e
d s
t
r
uc
t
ur
e
f
or
E
C
C
m
ul
t
i
pl
i
c
a
t
i
on
i
s
de
pi
c
t
e
d i
n F
i
gur
e
5.
D
oubl
e
a
nd a
dd (
le
f
t to
r
ig
h
t
)
a
lg
o
r
ith
m is
t
he
s
i
m
pl
e
s
t
m
e
t
hod t
o e
xe
c
ut
e
poi
n
t mu
l
tip
lic
a
tio
n
w
h
e
r
e
in
poi
nt
doubl
i
ng i
s
pe
r
f
or
m
e
d
f
or
e
a
c
h bi
t
va
l
ue
of
‘
k’
w
hi
l
e
poi
nt
a
ddi
t
i
on
f
unc
t
i
ons
onl
y
w
he
n
i
t
h
bi
t
of
‘
k’
i
s
1 ove
r
a
p
r
i
m
e
f
i
e
l
d
P.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
:
1693
-
6930
T
E
L
KOM
NI
KA
T
el
eco
m
m
u
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put
E
l
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Vo
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r
2021:
1636
-
1647
1642
F
i
gur
e
3.
F
l
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c
ha
r
t
of
va
r
i
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ope
r
a
t
i
ons
pe
r
f
or
m
e
d i
n
t
he
p
r
opos
e
d de
s
i
gn of
poi
n
t
a
ddi
tio
n
F
i
gur
e
4.
F
l
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ha
r
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of
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ope
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a
t
i
ons
pe
r
f
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e
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n
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r
opos
e
d de
s
i
gn of
poi
n
t
doubl
i
n
g
F
i
gur
e
5.
P
r
opos
e
d a
r
c
hi
t
e
c
t
ur
e
of
poi
nt
m
ul
t
i
pl
i
c
a
t
i
on
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
el
eco
m
m
u
n
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om
put
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l
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ont
r
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l
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f
f
i
c
i
e
nt
har
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e
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ot
ot
y
pe
of
E
C
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m
odul
e
s
f
or
bl
oc
k
c
hai
n appl
i
c
at
i
ons
(
D
evi
ka
K
.
N
.)
1643
5.
I
M
P
LEM
E
N
TA
T
I
O
N
R
ES
U
LTS
E
f
f
i
ci
en
t
H
ar
d
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ar
e
ar
ch
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t
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r
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ugge
s
t
e
d
f
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er
y
m
at
h
em
at
i
cal
p
r
o
ces
s
in
E
CD
S
A
ha
ve
b
e
en
m
od
e
l
l
e
d us
i
ng ha
r
dw
a
r
e
pr
ogr
a
m
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l
a
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ge
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ve
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M
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m
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t
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t
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e
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t
r
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t
ur
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.
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v
e
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odul
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r
e
s
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s
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z
e
d a
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m
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e
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nt
e
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n
Xi
l
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ir
te
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7 F
P
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c
e
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l
i
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14.
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de
s
i
gn s
ui
t
e
.
T
he
r
e
s
ul
t
s
obt
a
i
ne
d
af
t
er
imp
le
me
n
ta
tio
n
of
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l
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ng
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oc
ks
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odul
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r
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ltip
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tio
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odul
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r
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ltip
lic
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tiv
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nve
r
s
e
pr
ot
o
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t
ype
s
f
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ous
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t
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s
u
l
at
ed
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T
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l
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es
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el
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d
ot
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de
s
i
gns
r
e
s
u
lts
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e
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ep
r
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r
ap
h
i
cal
l
y
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s
i
ng t
he
m
e
nt
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d V
i
r
t
e
x
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7 F
P
G
A
,
t
he
r
e
s
ul
t
s
l
i
s
t
e
d s
how
s
t
ha
t
a
l
l
s
t
r
uc
t
ur
e
s
s
ugge
s
t
e
d w
or
ks
at
an
a
ve
r
a
ge
f
r
e
que
nc
y of
137
M
H
z f
o
r
a b
i
t
-
l
e
ngt
h
of
256 bi
t
s
.
I
f
t
he
s
i
z
e
of
N
i
s
t
a
ke
n t
o be
256
,
m
odul
a
r
m
ul
t
i
pl
i
c
a
t
i
on c
ons
um
e
d onl
y 141
s
l
i
c
e
s
on t
he
ot
he
r
h
a
n
d
ma
th
e
ma
tic
a
lly
in
tr
ic
a
te
mu
l
tip
lic
a
tiv
e
in
v
e
r
s
e
ex
-
pe
nde
d
a
bout
900
sl
i
c
e
s.
E
CC
G
r
oup
ope
r
a
t
i
on
s
su
c
h
as
poi
nt
a
ddi
t
i
on
m
ad
e
u
se
of
1321
at
t
he
sa
m
e
time
1385 s
l
i
c
e
s
w
er
e
t
ak
en
ove
r
f
or
po
i
nt
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i
ng.
A
r
ea
c
ons
um
pt
i
on
f
or
poi
nt
mu
ltip
lic
a
tio
n
,
s
i
gna
t
ur
e
ge
ne
r
a
t
i
on
a
nd ve
r
i
f
i
c
a
t
i
on w
e
r
e
f
ound
t
o be
6030
,
6924
a
nd
21055 s
l
i
c
e
s
r
es
p
ect
i
v
el
y
.
T
a
bl
e
1.
S
ynt
he
s
i
s
r
e
s
ul
t
s
of
m
odu
l
a
r
mu
lt
ip
lic
a
tio
n
u
s
in
g
X
ilin
x
I
S
E
d
e
s
ig
n
s
u
ite
B
it
-
s
iz
e
#
R
e
g
is
te
r
s
#
LU
T
s
#
LU
T
-
FF
p
a
i
rs
#
IO
B
s
A
re
a
(
S
lic
e
s
)
S
p
eed
(M
h
z
)
24
101
140
79
98
13
384.20
32
134
183
104
130
17
366.77
64
263
357
200
258
33
295.29
86
351
478
266
346
44
260.47
103
419
570
318
414
53
238.24
142
576
770
450
570
72
200.20
160
648
867
491
642
81
186.35
163
660
880
492
654
83
184
192
776
1035
541
770
97
165.94
224
904
1198
549
898
113
149.577
256
1123
1305
592
1014
141
136.59
T
a
bl
e
2.
S
ynt
he
s
i
s
r
e
s
ul
t
s
of
m
odu
l
a
r
mu
lt
ip
lic
a
tiv
e
in
v
e
r
s
e
in
X
ilin
x
I
S
E
d
e
s
ig
n
s
u
ite
B
it
-
s
iz
e
#
R
e
g
is
te
r
s
#
LU
T
s
#
LU
T
-
FF
p
a
i
rs
#
IO
B
s
A
re
a
(
S
lic
e
s
)
S
p
eed
(M
h
z
)
24
689
1743
589
74
87
264.53
32
911
2318
779
98
114
250.33
64
1809
4500
1593
194
226
231.30
86
2426
6024
2077
260
304
214.97
103
2897
7335
2523
311
362
205.62
142
3995
10060
3422
428
500
185.62
160
4500
11220
3908
482
563
177.44
163
4584
11417
3925
491
573
176.18
192
5395
13327
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145.87
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137.22
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I
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T
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6.
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37]
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38
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39]
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41]
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39
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40
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41]
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35]
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ar
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et
er
s
f
o
r
E
C
D
S
A
s
i
g
n
at
u
r
e v
er
i
f
i
cat
i
o
n
i
n
d
i
cat
es
t
h
at
t
h
e s
u
g
g
es
t
ed
d
es
i
g
n
f
o
r
E
C
D
S
A
ex
h
i
b
i
t
ed
b
et
t
er
p
er
f
o
r
m
an
ce i
n
al
l
p
ar
am
et
er
s
ex
am
i
n
ed
.
K
n
ezev
i
c
e
t a
l.
[
16
]
c
on
s
i
de
r
e
d
NAND g
a
t
e
c
om
pl
e
m
e
nt
a
r
y m
e
t
a
l
oxi
de
s
e
m
i
c
onduc
t
or
s
(
C
M
O
S
)
t
e
c
hnol
ogy
f
or
45nm
f
or
i
t
s
A
S
I
C
i
m
pl
e
m
e
nt
a
t
i
on but
de
m
a
nde
d huge
l
og
i
c
c
ons
um
pt
i
on.
A
l
l
ot
he
r
w
or
ks
[
17
]
,
[
18
]
,
[
36]
ha
d l
ow
e
r
e
xe
c
ut
i
on
s
pe
e
d w
he
n c
om
pa
r
e
d t
o
t
he
de
s
i
gn
pr
opos
e
d i
n
t
h
i
s
w
or
k.
F
i
gu
r
e
6
i
l
l
us
t
r
a
t
e
s
t
he
a
r
e
a
ut
i
l
i
z
a
t
i
on a
n
d s
pe
e
d
of
ope
r
a
t
i
on
a
t
t
a
i
ne
d
by
va
r
i
ous
E
C
D
S
A
c
om
po
ne
nt
s
imp
le
me
n
te
d
in
F
P
G
A
f
or
di
f
f
e
r
e
nt
bi
t
-
si
z
e
s.
T
h
e
g
r
ap
h
i
cal
r
es
u
l
t
r
ev
eal
s
th
a
t a
ll
th
e
e
le
me
n
ts
o
f
E
C
D
S
A
w
e
r
e
a
b
le
to
a
tta
in
c
o
n
s
is
te
n
c
y
in
te
r
ms
o
f
o
p
e
r
a
tio
n
a
l
s
pe
e
d a
m
ong t
he
m
s
e
l
ve
s
.
H
ow
e
ve
r
,
i
t
di
s
pl
a
ye
d a
l
i
ne
a
r
i
nc
r
e
a
s
e
i
n a
r
e
a
c
ons
um
pt
i
on w
i
t
h
t
he
bi
t
-
s
i
ze
v
al
u
e.
(a)
(b
)
F
i
gur
e
6.
C
om
pa
r
i
s
on of
pe
r
f
o
r
m
a
nc
e
pa
r
a
m
e
t
e
r
s
a
m
ong va
r
i
ous
E
C
D
S
A
c
om
pone
nt
s
f
or
va
r
yi
ng bi
t
-
s
i
ze,
(a
)
ope
r
a
t
i
ona
l
f
r
e
que
nc
y,
(
b)
a
r
e
a
u
tiliz
a
tio
n
7.
CO
NCL
US
I
O
N AND F
UT
URE
S
CO
P
E
I
n t
hi
s
w
or
k,
hi
ghl
y e
f
f
i
c
i
e
nt
r
e
-
c
onf
i
gur
a
bl
e
ha
r
d
w
a
r
e
pr
ot
ot
ype
s
a
r
e
i
nt
r
oduc
e
d t
o a
s
s
e
m
bl
e
e
llip
tic
c
ur
ve
di
gi
t
a
l
s
i
gna
t
ur
e
ar
ch
i
t
ect
u
r
e f
o
r
an
y
N
-
bi
t
va
l
ue
.
N
ove
l
a
r
c
hi
t
e
c
t
ur
e
s
a
r
e
s
ugge
s
t
e
d f
or
m
odul
a
r
mu
ltip
lic
a
tio
n
an
d
mu
ltip
lic
a
tiv
e
i
nve
r
s
e
ci
r
cu
i
t
ry
to
o
p
timiz
e
r
es
o
u
r
ce
u
tiliz
a
tio
n
an
d
i
m
pr
ove
t
he
o
p
er
at
i
o
n
al
s
pe
e
d of
t
he
e
nt
i
r
e
E
C
D
S
A
f
r
a
m
e
w
or
k.
X
i
l
i
nx
V
ir
te
x
7
is
th
e
F
P
G
A
d
e
v
ic
e
u
t
iliz
e
d
to
imp
le
me
n
t a
ll
d
e
s
ig
n
s
pr
opos
e
d up t
o b
i
t
s
i
z
e
of
256 b
i
t
s
.
T
he
r
e
s
ul
t
s
s
how
s
t
ha
t
256
-
bi
t
E
C
C
s
i
gna
t
ur
e
ge
ne
r
at
i
o
n
m
ak
e u
s
e o
f
4956 s
l
i
c
e
s
r
unni
ng w
i
t
h a
f
r
e
que
nc
y of
a
bout
136
.
81
M
H
z.
Wh
i
l
e t
h
e s
am
e s
i
ze E
C
C
v
er
i
f
i
cat
i
o
n
r
u
n
s
w
ith
e
qui
va
l
e
nt
s
p
eed
but
c
ons
um
i
ng
a
bout
21055
s
l
i
ces
ow
i
ng
to
its
hi
ghe
r
c
o
mp
le
x
ity
.
P
er
f
o
r
m
an
ce
an
al
y
s
i
s
w
ith
s
i
m
i
l
a
r
w
or
ks
pr
ove
t
ha
t
a
l
l
de
s
i
gns
s
ugge
s
t
e
d w
e
r
e
f
ound t
o m
a
ni
f
e
s
t
be
t
t
e
r
pe
r
f
o
r
m
a
nc
e
w
i
t
h r
e
s
pe
c
t
t
o a
r
e
a
a
nd s
pe
e
d.
C
om
pa
r
i
s
on r
e
s
ul
t
s
w
i
t
h e
xi
s
t
i
ng w
or
ks
c
l
e
a
r
l
y hi
ghl
i
ght
s
t
he
t
r
a
de
-
of
f
be
t
w
e
e
n f
r
e
que
nc
y
a
nd
ar
ea
c
ons
um
pt
i
on f
or
t
he
m
odu
l
e
s
de
s
i
gne
d
w
i
t
h ot
he
r
e
qui
va
l
e
nt
s
t
r
uc
t
ur
e
s
.
F
u
t
ur
e
s
c
ope
o
f
t
hi
s
w
or
k
i
s
t
o ve
r
i
f
y
bl
oc
kc
ha
i
n
t
r
an
s
act
i
o
n
s
us
i
ng
t
he
a
bove
r
eal
i
zed
re
-
c
onf
i
gur
a
bl
e
s
t
r
u
ct
u
r
es
to
en
ab
l
e
a
p
p
lic
a
tio
n
of
bl
oc
kc
ha
i
n
t
e
c
hnol
ogy i
n ha
r
dw
a
r
e
s
ecu
r
i
t
y
.
R
EF
ER
EN
C
ES
[1
]
J.
Al
-
Ja
r
oo
di a
n
d N.
M
oh
a
m
e
d,
“
B
loc
kc
ha
in i
n I
nd
us
tr
ie
s
: A S
ur
ve
y,
”
in
I
E
EE Ac
c
e
ss
,
v
ol.
7,
pp.
36
50
0
-
3
65
15,
201
9,
do
i: 10.
1
10
9/
AC
C
ES
S
.
20
19.
2
90
35
54.
[2
]
T.
Ali S
ye
d,
A.
Alz
a
hr
a
ni,
S
.
Ja
n,
M
.
S
.
S
iddi
qu
i,
A.
Na
de
e
m
a
nd T.
Al
gha
m
di,
“
A C
om
pa
r
a
t
ive
A
na
l
ys
is
of
B
loc
kc
ha
in Ar
c
hi
te
c
t
ur
e
a
n
d i
ts
Ap
pl
ic
a
t
io
ns
: P
r
ob
l
e
m
s a
nd R
e
c
om
m
e
nda
ti
on
s,
”
in
I
E
EE Ac
c
e
ss
,
v
ol.
7,
pp.
17
68
38
-
1
76
86
9,
20
19,
d
oi
: 10.
11
09
/AC
C
ES
S
.
20
19.
295
76
60.
[3
]
B
.
S
ha
hz
a
d a
nd J.
C
r
o
wc
r
of
t,
“
Tr
u
st
wor
th
y Ele
c
tr
o
nic
Vot
in
g U
si
ng A
dj
us
te
d B
l
oc
kc
ha
i
n Te
c
h
no
lo
gy,
”
i
n
I
EE
E
A
c
c
e
s
s
, v
o
l
. 7
,
pp.
2
44
77
-
24
48
8,
20
19,
d
oi
: 10.
11
09
/AC
C
ES
S
.
20
19.
2
89
56
70.
[4
]
S
.
M
onda
l,
K.
P
.
W
ije
wa
r
d
e
na
,
S
.
Ka
r
up
pu
swa
m
i,
N.
Kr
i
ti,
D.
K
um
a
r
a
n
d P
.
C
ha
ha
l,
“
B
loc
kc
ha
in I
ns
pir
e
d
RF
ID
-
B
a
se
d I
nf
or
m
a
t
io
n Ar
c
h
ite
c
tur
e
f
or
F
oo
d S
up
pl
y
C
ha
in,
”
in
I
EE
E I
nte
r
ne
t o
f T
hin
gs
J
ou
rn
al
,
vol.
6,
no
.
3,
pp.
58
03
-
5
81
3,
Ju
ne
20
19,
d
oi
: 1
0.
11
09
/JI
OT.
20
19.
2
90
765
8.
[5
]
J.
L
iu a
n
d Z
.
L
iu,
“
A S
ur
ve
y o
n S
e
c
ur
it
y Ve
r
if
ic
a
ti
on
of
B
loc
kc
ha
in S
m
a
r
t C
o
ntr
a
c
ts,
”
in
I
EE
E Ac
c
e
ss
,
vo
l.
7
,
pp.
77
89
4
-
77
90
4,
20
19,
d
oi
: 10.
11
09
/AC
C
ES
S
.
20
19.
2
9
216
24.
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