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Dep
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Un
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u
1.
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Giv
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eq
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p
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[
1
]
.
T
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ch
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cr
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2
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ased
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task
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4
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g
o
r
ith
m
s
ar
e
cu
r
r
en
tly
th
e
m
ain
c
r
y
p
to
g
r
ap
h
ic
m
ea
n
s
o
f
r
eli
ab
le
p
r
o
tectio
n
o
f
co
n
f
id
en
tiality
wh
e
n
p
r
o
ce
s
s
in
g
co
n
f
id
en
tial
in
f
o
r
m
atio
n
in
in
f
o
r
m
atio
n
an
d
telec
o
m
m
u
n
i
ca
tio
n
s
y
s
tem
s
[
5
]
.
Mo
d
er
n
s
y
m
m
etr
ic
b
l
o
ck
cip
h
er
s
ar
e
p
r
im
a
r
ily
b
u
ilt
o
n
th
e
b
asis
o
f
two
ap
p
r
o
ac
h
es:
th
e
Feis
tel
n
etwo
r
k
an
d
th
e
s
u
b
s
titu
tio
n
-
p
er
m
u
tatio
n
n
etwo
r
k
(
SP
n
etwo
r
k
)
.
As
y
o
u
k
n
o
w,
cip
h
er
s
ar
e
b
ased
o
n
r
e
v
er
s
ib
le
tr
an
s
f
o
r
m
atio
n
s
o
f
p
lain
tex
t.
W
h
en
d
ev
elo
p
in
g
th
em
,
it
is
n
ec
ess
ar
y
to
en
s
u
r
e
th
at
ea
ch
o
f
th
e
o
p
er
atio
n
s
p
er
f
o
r
m
ed
is
b
o
th
cr
y
p
to
g
r
a
p
h
ically
s
ec
u
r
e
a
n
d
r
ev
er
s
ib
le
i
f
th
e
k
ey
is
k
n
o
w
n
[
6
]
.
Mo
d
er
n
cip
h
e
r
s
ar
e
b
ased
o
n
Ker
k
h
o
f
f
’
s
p
r
i
n
cip
le,
ac
co
r
d
in
g
to
wh
ich
th
e
s
ec
r
ec
y
o
f
th
e
cip
h
er
is
en
s
u
r
ed
b
y
th
e
s
ec
r
ec
y
o
f
th
e
k
ey
,
an
d
n
o
t
b
y
th
e
s
ec
r
ec
y
o
f
th
e
en
cr
y
p
tio
n
alg
o
r
ith
m
.
B
lo
ck
cip
h
er
alg
o
r
ith
m
s
ar
e
an
in
te
g
r
al
p
ar
t
o
f
m
o
d
e
r
n
in
f
o
r
m
atio
n
tech
n
o
lo
g
y
an
d
co
n
tin
u
e
to
b
e
r
ele
v
an
t
a
n
d
in
d
em
an
d
in
th
e
e
v
er
-
ev
o
lv
in
g
f
ield
o
f
cy
b
er
s
ec
u
r
ity
.
T
h
an
k
s
to
th
e
e
f
f
o
r
ts
o
f
s
cien
tis
ts
,
b
lo
ck
cip
h
er
alg
o
r
ith
m
s
co
n
tin
u
e
to
im
p
r
o
v
e,
en
h
a
n
cin
g
th
e
lev
el
o
f
d
ata
s
ec
u
r
ity
,
wh
o
s
e
r
o
le
is
co
n
s
tan
tly
in
cr
ea
s
in
g
in
th
e
r
ap
id
ly
c
h
an
g
i
n
g
wo
r
ld
o
f
d
ig
ital te
ch
n
o
lo
g
y
.
Me
th
o
d
s
o
f
cr
y
p
t
o
g
r
a
p
h
ic
in
f
o
r
m
atio
n
p
r
o
tectio
n
ar
e
d
iv
e
r
s
e
d
ep
en
d
i
n
g
o
n
f
u
n
ctio
n
al
task
s
.
Fo
r
ex
am
p
le,
en
c
r
y
p
tio
n
o
f
la
r
g
e
a
m
o
u
n
ts
o
f
i
n
f
o
r
m
atio
n
at
h
i
g
h
s
p
ee
d
s
.
Nu
m
er
o
u
s
s
tu
d
ies
h
a
v
e
b
ee
n
u
n
d
e
r
tak
en
to
ad
d
r
ess
th
ese
ch
allen
g
es,
r
esu
ltin
g
in
th
e
d
ev
elo
p
m
e
n
t
o
f
a
n
ew
b
lo
ck
en
c
r
y
p
tio
n
alg
o
r
ith
m
[
7
]
.
I
n
th
e
d
ev
elo
p
e
d
alg
o
r
ith
m
,
to
s
o
lv
e
s
u
ch
p
r
o
b
lem
s
,
two
d
if
f
er
en
t
m
ath
em
atica
l
m
eth
o
d
s
ar
e
u
s
ed
.
T
h
ey
ar
e:
i)
p
o
l
y
n
o
m
ial
s
y
s
tem
o
f
r
e
s
id
u
e
class
es
o
r
n
o
n
-
p
o
s
itio
n
al
p
o
l
y
n
o
m
ial
n
o
tatio
n
s
y
s
tem
s
(
NPNs
)
;
an
d
ii)
ca
lcu
latio
n
o
f
th
e
d
eg
r
ee
u
s
in
g
an
in
d
ex
tab
le
in
th
e
m
o
d
u
lar
ex
p
o
n
e
n
tiatio
n
in
ex
ten
d
ed
Galo
is
f
ield
(
)
.
No
n
-
p
o
s
itio
n
al
p
o
ly
n
o
m
ial
n
o
tatio
n
s
(
NPNs
)
.
T
h
er
e
ar
e
n
u
m
er
o
u
s
wo
r
k
s
b
y
s
cien
tis
ts
o
n
n
u
m
b
e
r
s
y
s
tem
s
,
in
clu
d
in
g
th
e
r
esid
u
e
n
u
m
b
er
s
y
s
tem
(
R
NS)
.
I
n
1
9
5
5
,
th
e
C
ze
ch
en
g
in
ee
r
M.
Vala
c
h
f
ir
s
t in
tr
o
d
u
ce
d
th
e
id
ea
o
f
u
s
in
g
r
esid
u
al
class
es
in
th
e
f
ield
o
f
c
o
m
p
u
ter
t
ec
h
n
o
lo
g
y
,
an
d
h
e
was
ac
tiv
e
ly
s
u
p
p
o
r
ted
b
y
th
e
C
ze
ch
m
ath
em
atician
A.
Sv
o
b
o
d
a.
I
n
p
r
ac
tice
,
t
h
is
id
ea
h
a
s
p
r
o
v
en
to
b
e
th
e
m
o
s
t
ef
f
ec
tiv
e
ap
p
r
o
a
ch
,
b
ased
o
n
th
e
C
h
in
ese
r
em
ain
d
e
r
th
e
o
r
em
[
8
]
.
Prio
r
to
th
is
,
th
e
c
o
n
ce
p
t
was
co
n
s
id
er
ed
a
f
u
n
d
a
m
en
tal
th
eo
r
em
in
ab
s
tr
ac
t
alg
eb
r
a,
ca
p
tu
r
in
g
th
e
in
ter
est
o
f
m
an
y
g
r
o
u
p
s
o
f
s
c
ien
tis
ts
,
u
ltima
tely
lead
in
g
to
t
h
e
em
er
g
e
n
ce
o
f
a
n
ew
s
cien
tific
d
is
cip
lin
e
k
n
o
wn
as
m
o
d
u
lar
ar
ith
m
etic.
C
u
r
r
en
tly
,
th
e
r
esid
u
al
class
es
ar
e
u
s
ed
in
r
ad
i
o
en
g
in
ee
r
in
g
,
s
p
ac
e
tech
n
o
lo
g
y
,
v
ar
io
u
s
s
ch
em
e
tec
h
n
iq
u
es,
c
r
y
p
to
g
r
ap
h
y
an
d
m
an
y
o
th
er
f
i
eld
s
[
9
]
.
On
e
o
f
th
e
tr
en
d
s
o
f
m
o
d
u
le
ar
ith
m
etic
d
ev
elo
p
m
en
t,
as
ex
p
lo
r
ed
in
th
e
wo
r
k
s
o
f
Kaz
ak
h
s
tan
's
s
cien
tis
t
B
iy
ash
ev
an
d
Ny
s
s
an
b
ay
ev
a
[
3
]
,
in
v
o
lv
es
in
v
esti
g
atin
g
th
e
c
r
ea
tio
n
,
a
n
aly
s
is
,
an
d
ap
p
licatio
n
o
f
non
-
p
o
s
itio
n
al
p
o
ly
n
o
m
ial
n
o
tatio
n
s
.
He
em
p
h
asized
th
at
p
o
ly
n
o
m
ial
alg
eb
r
a
co
u
l
d
en
co
m
p
ass
an
y
ir
r
ed
u
cib
le
p
o
ly
n
o
m
ial
m
o
d
u
le,
p
r
o
v
id
ed
p
r
o
o
f
o
f
th
e
C
h
in
ese
r
em
ain
d
e
r
th
e
o
r
em
f
o
r
p
o
ly
n
o
m
ials
,
a
n
d
estab
lis
h
ed
r
u
les
f
o
r
ar
ith
m
etic
o
p
er
atio
n
s
with
in
th
e
p
o
ly
n
o
m
ial
s
y
s
tem
,
as
well
as
d
e
f
in
in
g
p
o
ly
n
o
m
ial
r
ec
o
v
er
y
b
y
r
esid
u
e.
L
et
u
s
d
escr
ib
e
th
e
co
n
s
tr
u
ctio
n
o
f
n
o
n
-
p
o
s
itio
n
al
p
o
ly
n
o
m
ial
n
o
tatio
n
s
.
I
f
th
e
n
u
m
b
er
o
f
p
o
ly
n
o
m
ials
1
(
)
,
2
(
)
,
…
,
(
)
wh
ich
ca
lled
w
o
r
k
in
g
b
ases
ar
e
g
iv
e
n
,
th
e
n
i
n
NPNs
an
y
p
o
ly
n
o
m
ial
(
)
,
ca
n
b
e
r
ep
r
esen
ted
as
a
s
eq
u
en
ce
o
f
r
esid
u
es
o
f
d
iv
id
in
g
it
b
y
th
e
c
h
o
s
en
wo
r
k
in
g
b
ase
n
u
m
b
er
s
[
1
0
]
r
esp
ec
tiv
ely
:
(
)
=
(
1
(
)
2
(
)
,
3
(
)
,
…
,
(
)
)
.
(1
)
wh
er
e
(
)
,
=
1
,
is
d
ef
in
ed
b
y
(
2
)
:
(
)
≡
(
)
(
(
)
)
.
(
2
)
T
h
en
th
e
wo
r
k
in
g
r
an
g
e
in
NP
Ns is
d
ef
in
ed
as
(
3
)
:
(
)
=
∏
(
)
.
=
1
(
3
)
I
f
th
e
wo
r
k
in
g
b
ase
n
u
m
b
er
s
d
eg
r
ee
eq
u
al
to
1
,
2
,
…
,
,
th
en
th
e
NP
Ns’
wo
r
k
in
g
r
an
g
e
d
e
g
r
ee
m
will
b
e
eq
u
al
to
th
eir
s
u
m
:
=
∑
=
1
.
(
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
2
,
Ap
r
il
20
25
:
1
9
0
0
-
1
9
1
1
1902
T
h
e
o
p
er
atio
n
o
f
m
o
d
u
lar
e
x
p
o
n
e
n
tiatio
n
in
th
e
ex
ten
d
e
d
Galo
is
f
ield
(
)
[
1
1
]
.
I
n
m
a
n
y
s
cien
tific
p
ap
er
s
s
h
o
w
n
th
at
t
h
e
f
ield
h
as
m
an
y
p
o
s
s
ib
ilit
ies
in
th
e
d
ev
el
o
p
m
en
t
o
f
v
a
r
io
u
s
cr
y
p
t
o
g
r
a
p
h
ic
f
u
n
ctio
n
s
,
p
lain
tex
t
en
cr
y
p
tio
n
,
an
d
e
n
s
u
r
in
g
th
e
co
n
f
id
en
t
iality
an
d
in
teg
r
ity
o
f
in
f
o
r
m
atio
n
[
1
2
]
.
On
e
o
f
th
em
is
cu
r
r
en
tly
o
p
er
atio
n
o
f
m
o
d
u
lar
ex
p
o
n
en
tiatio
n
u
s
ed
in
th
e
R
iv
est
–
Sh
am
ir
–
Ad
lem
an
(
R
SA
)
an
d
El
-
Gam
al,
Dif
f
ie
-
Hellm
an
alg
o
r
ith
m
s
.
T
h
e
d
ata
en
c
r
y
p
ti
o
n
f
o
r
m
u
la
b
y
u
s
in
g
th
e
o
p
er
atio
n
o
f
m
o
d
u
lar
ex
p
o
n
e
n
tiatio
n
in
th
e
ex
ten
d
e
d
f
ield
(
)
.
is
d
ef
in
ed
as
(
5
)
[
1
3
]
:
(
)
=
(
)
(
)
.
(
5
)
wh
er
e
(
)
is
p
lain
tex
t;
is
k
ey
;
an
d
(
)
is
cip
h
er
tex
t.
Me
s
s
ag
e
d
ec
r
y
p
tio
n
f
o
r
m
u
la:
(
)
≡
√
(
)
(
)
.
(
6
)
Her
e
we
ca
lcu
late
th
e
p
lain
tex
t b
y
f
in
d
in
g
th
e
in
v
er
s
e
elem
e
n
t o
f
K
th
at
s
atis
f
ies th
e
eq
u
ati
o
n
:
⋅
(
)
−
1
≡
1
(
2
(
)
−
1
)
.
(
7
)
wh
er
e
-
th
e
d
eg
r
ee
to
(
)
.
T
h
en
,
th
e
d
ec
r
y
p
tio
n
f
o
r
m
u
la
b
ased
o
n
(
7
)
ca
n
b
e
e
x
p
r
ess
ed
as (
8
)
:
(
)
≡
(
)
−
1
(
)
.
(
8
)
2.
SYM
M
E
T
R
I
C
E
N
CRYP
T
I
O
N
AL
G
O
RIT
H
M
(
SE
A1
2
8
)
I
n
th
e
d
esig
n
o
f
t
h
e
p
r
o
p
o
s
ed
en
cr
y
p
tio
n
alg
o
r
ith
m
,
t
h
e
ex
p
o
n
e
n
tiatio
n
m
o
d
u
lo
(
E
M)
tr
an
s
f
o
r
m
m
eth
o
d
is
u
s
ed
.
T
h
is
m
eth
o
d
f
u
n
ctio
n
s
in
a
n
o
n
-
p
o
s
itio
n
a
l
p
o
ly
n
o
m
ial
n
o
tatio
n
s
y
s
tem
,
u
tili
zin
g
m
o
d
u
lar
ex
p
o
n
e
n
tiatio
n
i
n
th
e
ex
te
n
d
ed
Galo
is
f
ield
(
)
,
an
d
i
n
c
o
r
p
o
r
ates
an
S
-
b
lo
ck
s
u
b
s
titu
tio
n
ta
b
le.
All
m
eth
o
d
s
u
s
ed
ar
e
d
escr
i
b
ed
b
elo
w.
Fig
u
r
es
1
an
d
2
illu
s
tr
ate
th
e
p
r
o
p
o
s
ed
b
l
o
c
k
en
cr
y
p
tio
n
an
d
d
ec
r
y
p
tio
n
alg
o
r
ith
m
.
T
h
e
m
a
in
p
ar
am
eter
o
f
th
e
alg
o
r
ith
m
:
i)
b
lo
ck
s
ize
1
2
8
b
its
,
ii)
k
ey
s
ize
1
2
8
b
its
,
an
d
iii)
n
u
m
b
er
o
f
r
o
u
n
d
s
8
.
Fig
u
r
e
1
.
T
h
e
s
ch
em
e
o
f
b
lo
c
k
en
cr
y
p
tio
n
alg
o
r
ith
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Dev
elo
p
men
t a
n
d
a
n
a
lysi
s
o
f
s
ymm
etr
ic
en
cryp
tio
n
a
lg
o
r
ith
m
(
A
r
d
a
b
ek
K
h
o
mp
ysh
)
1903
Fig
u
r
e
2
.
T
h
e
s
ch
em
e
o
f
b
lo
c
k
d
ec
r
y
p
tio
n
alg
o
r
ith
m
T
h
e
en
cr
y
p
tio
n
p
r
o
ce
s
s
ca
n
b
e
d
iv
id
ed
i
n
to
4
s
tag
es:
Stag
e
1
:
I
n
co
m
i
n
g
d
ata
is
d
i
v
id
ed
in
to
1
2
8
-
b
it
s
eg
m
en
ts
.
I
f
th
e
f
i
n
al
s
eg
m
en
t
is
s
h
o
r
ter
th
an
1
2
8
b
its
,
it
is
p
ad
d
ed
with
ze
r
o
s
(
wh
ich
ar
e
later
r
em
o
v
ed
d
u
r
in
g
d
ec
r
y
p
tio
n
)
.
E
ac
h
1
2
8
-
b
it
s
eg
m
e
n
t
is
th
en
co
m
b
in
ed
with
a
1
2
8
-
b
it k
ey
u
s
in
g
an
XOR
(
⨁
)
o
p
er
atio
n
.
T
h
e
1
2
8
-
b
it
r
esu
lt
is
s
p
lit
in
to
f
o
u
r
3
2
-
b
it
s
u
b
-
b
lo
ck
s
,
wh
ic
h
ar
e
th
e
n
p
r
o
ce
s
s
ed
in
th
e
n
ex
t stag
es.
Stag
e
2
:
T
h
e
f
ir
s
t a
n
d
s
ec
o
n
d
3
2
-
b
it su
b
-
b
lo
ck
s
u
n
d
e
r
g
o
a
n
E
M
co
n
v
er
s
io
n
m
eth
o
d
as p
er
a
s
p
ec
if
ied
s
ch
em
e.
Af
ter
th
is
co
n
v
er
s
io
n
,
a
b
it sh
i
f
t o
p
er
atio
n
is
p
er
f
o
r
m
ed
o
n
th
ese
s
u
b
-
b
lo
ck
s
.
Stag
e
3
:
T
h
e
th
ir
d
an
d
f
o
u
r
th
3
2
-
b
it
s
u
b
-
b
lo
c
k
s
ar
e
p
r
o
ce
s
s
ed
u
s
in
g
a
n
S
-
b
o
x
s
u
b
s
titu
tio
n
tab
le,
ac
co
r
d
i
n
g
to
a
p
r
ed
e
f
in
ed
s
ch
em
e
.
T
h
e
r
esu
lts
f
r
o
m
th
e
f
ir
s
t
an
d
s
ec
o
n
d
s
u
b
-
b
lo
ck
s
in
Stag
e
2
ar
e
th
e
n
co
m
b
in
e
d
with
th
e
p
r
o
ce
s
s
ed
th
ir
d
an
d
f
o
u
r
th
s
u
b
-
b
lo
c
k
s
u
s
in
g
a
m
o
d
u
lar
o
p
e
r
atio
n
.
Stag
e
4
:
E
ac
h
i
n
ter
n
al
b
lo
ck
u
n
d
er
g
o
es
s
p
ec
if
ic
m
o
v
em
en
t
s
b
ased
o
n
a
d
e
f
in
ed
s
ch
em
e
in
ea
ch
en
cr
y
p
tio
n
r
o
u
n
d
.
Af
ter
th
e
f
in
al
r
o
u
n
d
,
an
ad
d
itio
n
al
k
ey
is
ad
d
ed
to
th
e
r
esu
ltin
g
b
lo
ck
u
s
in
g
a
m
o
d
u
lar
o
p
er
atio
n
,
co
m
p
letin
g
th
e
e
n
cr
y
p
tio
n
p
r
o
ce
s
s
.
B
y
f
o
llo
win
g
th
ese
s
tep
s
,
th
e
d
ata
is
s
ec
u
r
ely
en
cr
y
p
ted
an
d
ca
n
later
b
e
d
ec
r
y
p
ted
b
y
r
ev
e
r
s
in
g
th
e
p
r
o
ce
s
s
.
T
h
e
d
ec
r
y
p
tio
n
s
ch
em
e
o
f
th
e
alg
o
r
ith
m
is
s
h
o
wn
in
Fig
u
r
e
2
.
All
th
e
m
eth
o
d
s
u
s
ed
ar
e
d
escr
ib
ed
b
elo
w.
No
w
let
u
s
talk
s
ep
ar
ately
ab
o
u
t
th
e
co
n
v
er
s
io
n
m
eth
o
d
s
co
n
tain
e
d
in
th
is
p
r
o
p
o
s
ed
SEA
1
2
8
alg
o
r
ith
m
.
T
h
ese
m
eth
o
d
s
ar
e
cr
u
cial
f
o
r
e
n
s
u
r
in
g
th
e
p
r
o
p
er
tr
an
s
f
o
r
m
atio
n
o
f
d
ata
d
u
r
i
n
g
th
e
d
ec
r
y
p
tio
n
p
r
o
ce
s
s
.
E
ac
h
m
eth
o
d
s
er
v
es
a
s
p
ec
if
ic
p
u
r
p
o
s
e,
s
u
ch
as
b
it
m
an
ip
u
latio
n
,
d
ata
s
u
b
s
titu
tio
n
,
an
d
p
e
r
m
u
tatio
n
,
to
en
s
u
r
e
th
at
th
e
o
r
ig
in
al
e
n
cr
y
p
ted
d
ata
is
ac
cu
r
ately
r
esto
r
ed
.
T
h
e
co
m
b
in
atio
n
o
f
th
ese
m
eth
o
d
s
is
d
esig
n
ed
to
p
r
o
v
i
d
e
a
h
i
g
h
lev
el
o
f
s
ec
u
r
ity
wh
ile
m
ain
tai
n
in
g
ef
f
icien
cy
in
d
ec
r
y
p
tio
n
.
2
.
1
.
E
x
po
nentia
t
io
n
m
o
du
lo
t
ra
ns
f
o
rm
m
et
ho
d
NPNs
b
ased
o
n
th
e
o
p
er
atio
n
o
f
m
o
d
u
lar
ex
p
o
n
en
tiatio
n
in
th
e
ex
ten
d
ed
Galo
is
f
ield
(
)
,
co
n
s
is
ts
o
f
th
r
ee
s
tag
es
:
i)
cr
ea
tio
n
o
f
wo
r
k
in
g
b
ases
s
y
s
tem
an
d
s
elec
tio
n
o
f
ar
r
a
n
g
em
en
t
o
r
d
er
,
ii)
r
o
u
n
d
k
ey
s
f
o
r
m
atio
n
,
an
d
iii)
in
p
u
t
d
ata
co
n
v
er
s
io
n
an
d
in
v
e
r
s
e
c
o
n
v
er
s
io
n
.
T
h
e
f
ir
s
t
s
tag
e
in
v
o
lv
es
estab
lis
h
in
g
a
wo
r
k
in
g
b
ase
s
y
s
tem
an
d
d
e
ter
m
in
in
g
th
e
o
r
d
e
r
o
f
ar
r
an
g
em
en
t,
wh
ich
is
cr
itical
f
o
r
th
e
ef
f
icien
cy
o
f
s
u
b
s
eq
u
en
t
o
p
er
atio
n
s
.
I
n
th
e
s
ec
o
n
d
s
tag
e,
r
o
u
n
d
k
e
y
s
ar
e
g
en
er
ated
f
r
o
m
th
e
in
itial
k
e
y
,
p
lay
in
g
a
k
e
y
r
o
le
in
th
e
en
cr
y
p
tio
n
p
r
o
ce
s
s
b
y
p
r
o
v
id
i
n
g
th
e
n
ec
ess
ar
y
tr
an
s
f
o
r
m
atio
n
at
ea
c
h
r
o
u
n
d
.
Fin
ally
,
th
e
th
ir
d
s
tag
e
f
o
cu
s
es
o
n
co
n
v
er
tin
g
th
e
in
p
u
t
d
ata
f
o
r
p
r
o
ce
s
s
in
g
an
d
en
s
u
r
in
g
its
p
r
o
p
er
in
v
e
r
s
e
co
n
v
er
s
io
n
,
en
ab
lin
g
co
r
r
ec
t d
ec
r
y
p
tio
n
an
d
r
etr
iev
al
o
f
th
e
o
r
ig
in
al
d
ata.
No
w,
le
t's
lo
o
k
at
th
e
s
tr
u
ctu
r
e
o
f
th
es
e
s
tep
s
.
T
h
e
f
ir
s
t
s
tag
e.
C
o
n
s
id
er
th
e
s
tag
e
o
f
s
elec
tio
n
th
e
wo
r
k
in
g
b
ases
.
L
et
th
e
n
u
m
b
e
r
o
f
d
eg
r
ee
s
o
f
th
e
b
in
ar
y
s
eq
u
e
n
ce
o
f
ir
r
ed
u
cib
le
p
o
ly
n
o
m
ials
ac
co
r
d
in
g
ly
1
eq
u
al
to
1
,
2
eq
u
al
to
2
,
eq
u
al
to
[
4
]
.
I
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
2
,
Ap
r
il
20
25
:
1
9
0
0
-
1
9
1
1
1904
th
is
ca
s
e
th
e
h
ig
h
est
d
eg
r
ee
o
f
wo
r
k
in
g
b
ases
is
eq
u
al
to
an
d
at
th
e
s
tag
es
o
f
s
elec
tio
n
o
f
wo
r
k
in
g
b
ases
with
d
eg
r
ee
,
u
p
to
=
1
,
we
f
in
d
all
th
e
p
o
s
s
ib
le
s
o
lu
tio
n
s
o
f
th
e
alg
eb
r
aic
eq
u
atio
n
th
at
s
atis
f
y
th
e
(
5
)
[
5
]
,
[
1
0
]
:
1
1
+
2
2
+
⋯
+
=
.
(
9
)
wh
er
e
0
≤
≤
,
=
1
,
:
u
n
k
n
o
wn
co
e
f
f
icien
t
,
:
th
e
n
u
m
b
er
o
f
ir
r
e
d
u
cib
le
p
o
ly
n
o
m
ials
with
s
elec
te
d
d
eg
r
ee
,
:
th
e
n
u
m
b
er
o
f
ir
r
ed
u
cib
le
p
o
ly
n
o
m
ials
with
all
d
eg
r
ee
,
wh
er
e
1
≤
≤
,
th
e
n
u
m
b
er
o
f
all
th
e
wo
r
k
in
g
b
ases
is
as
(
1
0
)
:
=
1
+
2
+
⋯
+
.
(
1
0
)
T
h
e
s
ec
o
n
d
s
tag
e.
Fo
r
th
e
im
p
lem
en
tin
g
th
e
tr
a
n
s
f
o
r
m
m
et
h
o
d
b
ased
o
n
th
e
o
p
er
atio
n
o
f
m
o
d
u
lar
ex
p
o
n
e
n
tiatio
n
in
th
e
ex
ten
d
ed
Galo
is
f
ield
,
th
e
v
alu
es
an
d
−
1
ar
e
o
b
tain
e
d
b
y
th
e
p
s
eu
d
o
r
a
n
d
o
m
s
eq
u
en
ce
g
en
er
ato
r
(
PS
G)
:
i)
th
e
co
n
s
tr
u
cti
o
n
o
f
s
eq
u
en
ce
,
ii)
d
iv
is
io
n
r
ec
eiv
ed
b
i
n
ar
y
s
eq
u
en
ce
b
y
s
elec
ted
wo
r
k
in
g
b
ases
in
ac
co
r
d
a
n
ce
with
th
e
d
eg
r
ee
,
iii)
s
u
b
s
tit
u
te
th
e
b
in
ar
y
s
eq
u
e
n
ce
s
y
s
tem
to
th
e
d
ec
im
al
s
y
s
tem
,
an
d
iv
)
s
elec
t th
e
v
al
u
e
o
b
tain
ed
as GCD
(
,
(
(
)
−
1
)
=1
.
T
h
e
th
ir
d
s
tag
e.
I
t
is
k
n
o
wn
th
at
th
e
d
ata
en
cr
y
p
tio
n
s
p
e
ed
r
eq
u
ir
es
a
lo
t
o
f
tim
e
b
ased
o
n
th
e
o
p
er
atio
n
o
f
m
o
d
u
lar
ex
p
o
n
en
tiatio
n
ac
co
r
d
in
g
to
th
e
f
o
r
m
u
la
(
1
5
)
.
Ho
wev
er
,
it
is
ad
v
is
ab
le
to
u
s
e
NPN
s
to
in
cr
ea
s
e
s
p
ee
d
o
f
th
e
ca
lc
u
latio
n
o
f
th
is
p
r
o
ce
d
u
r
e.
T
h
e
r
ef
o
r
e,
let
u
s
e
th
e
NPNs
f
o
r
d
ata
en
cr
y
p
tio
n
p
r
o
ce
d
u
r
e,
in
th
is
ca
s
e
in
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
w
o
r
k
in
g
b
ases
in
Galo
is
f
ield
(
2
)
s
elec
ted
in
ac
co
r
d
an
ce
with
t
h
e
f
o
r
m
u
la
(
9
)
.
I
n
th
e
p
r
o
p
o
s
ed
tr
an
s
f
o
r
m
m
e
th
o
d
,
in
p
u
t
d
ata
is
p
r
o
v
id
e
d
a
s
len
g
th
o
f
1
2
8
b
its
.
T
h
en
it
d
iv
id
ed
in
to
3
2
b
its
b
lo
ck
s
an
d
wo
r
k
s
with
ea
ch
b
lo
ck
.
E
ac
h
3
2
-
b
its
b
lo
ck
is
d
i
v
id
ed
in
to
p
ar
ts
ac
c
o
r
d
in
g
t
o
th
e
wo
r
k
in
g
b
ases
d
eg
r
ee
.
T
h
e
o
b
tain
e
d
p
a
r
t a
cc
o
r
d
in
g
to
th
e
f
o
r
m
u
la
(
1
)
s
h
o
wn
as a
s
eq
u
en
ce
o
f
r
e
m
ain
s
in
NPNs
:
(
)
=
1
(
)
,
2
(
)
,
3
(
)
,
…
,
(
)
.
(
1
1
)
wh
er
e
(
)
-
o
b
tain
ed
p
ar
ts
,
=
1
,
.
Fo
r
th
e
tr
an
s
f
o
r
m
atio
n
o
f
th
e
s
p
litt
ed
b
lo
ck
s
th
at
o
b
tain
ed
b
y
f
o
r
m
u
la
(
1
1
)
ex
p
r
ess
as
(
1
2
)
[
8
]
:
(
)
=
(
)
(
)
,
=
1
,
.
(
1
2
)
cip
h
er
tex
ts
s
y
s
tem
s
o
b
tain
ed
b
y
f
o
r
m
u
la
(
1
2
)
e
x
p
r
ess
as
(
1
3
)
:
(
)
=
1
(
)
,
2
(
)
,
3
(
)
,
…
,
(
)
.
(
1
3
)
I
n
th
is
ca
s
e,
th
e
in
v
e
r
s
e
tr
an
s
f
o
r
m
co
r
r
esp
o
n
d
s
to
f
o
r
m
u
la
(
8
)
is
eq
u
al
to
:
(
)
=
(
)
−
1
(
)
.
(
1
4
)
Ob
tain
ed
p
lain
tex
ts
(
1
1
)
b
y
f
o
r
m
u
la
ex
p
r
ess
as
(
1
5
)
:
(
)
=
1
(
)
,
2
(
)
,
2
(
)
,
…
,
(
)
.
(
1
5
)
I
n
th
e
p
r
o
p
o
s
ed
alg
o
r
it
h
m
f
o
r
ea
ch
b
lo
ck
ca
lcu
late
in
v
er
s
e
o
f
u
s
ed
k
ey
:
⋅
(
)
−
1
≡
1
(
(
(
)
−
1
)
,
=
1
,
.
(
1
6
)
I
t
is
k
n
o
wn
in
th
e
E
M
tr
an
s
f
o
r
m
m
eth
o
d
ca
lcu
latin
g
th
e
ex
p
o
n
e
n
tiatio
n
p
r
o
ce
s
s
tak
es
a
lo
n
g
tim
e.
Ho
wev
er
,
in
th
e
p
r
o
p
o
s
ed
al
g
o
r
ith
m
ca
lcu
latin
g
th
e
e
x
p
o
n
e
n
tiatio
n
b
y
cr
ea
tin
g
an
in
d
e
x
tab
le,
co
n
s
eq
u
en
tly
th
e
s
p
ee
d
o
f
ca
lcu
latio
n
i
n
cr
e
ases
.
I
n
th
e
E
M
tr
an
s
f
o
r
m
ac
c
o
r
d
in
g
to
s
elec
ted
wo
r
k
in
g
b
a
s
es
(
)
th
e
in
d
ex
tab
le
ar
e
f
illi
n
g
in
b
y
(
1
7
)
:
(
)
=
(
)
,
=
∞
,
2
(
(
)
)
−
1
(
1
7
)
-
p
r
im
itiv
e
elem
e
n
t o
f
a
m
u
lti
p
licativ
e
g
r
o
u
p
in
a
f
ield
(
)
;
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Dev
elo
p
men
t a
n
d
a
n
a
lysi
s
o
f
s
ymm
etr
ic
en
cryp
tio
n
a
lg
o
r
ith
m
(
A
r
d
a
b
ek
K
h
o
mp
ysh
)
1905
Fo
r
ex
am
p
le:
L
et
co
n
s
id
er
th
e
in
d
ex
tab
le
o
f
ir
r
ed
u
cib
le
p
o
ly
n
o
m
ial
wh
er
e
wo
r
k
in
g
b
as
es
eq
u
al
to
(
)
=
3
+
+
1
in
th
e
f
ield
(
2
3
)
as
s
h
o
wn
in
T
ab
l
e
1
.
T
h
is
p
o
ly
n
o
m
ial
is
s
elec
ted
f
r
o
m
th
e
f
in
ite
f
ield
(
2
3
)
,
wh
ich
allo
ws
f
o
r
e
f
f
icien
t
c
alcu
latio
n
o
f
th
e
m
o
d
u
lo
ex
p
o
n
en
tiatio
n
o
p
er
atio
n
.
An
d
th
e
u
s
e
o
f
an
in
d
ex
tab
le
ac
ce
ler
ated
th
e
e
n
cr
y
p
tio
n
a
n
d
d
ec
r
y
p
tio
n
p
r
o
ce
s
s
es.
Acc
o
r
d
in
g
to
th
e
in
d
ex
t
ab
le
o
f
th
e
s
elec
ted
wo
r
k
in
g
b
ases
,
we
in
tr
o
d
u
ce
th
e
f
o
llo
win
g
m
ath
em
atica
l e
q
u
atio
n
:
Acc
o
r
d
in
g
t
o
th
e
in
d
ex
tab
le
o
f
th
e
s
elec
ted
wo
r
k
in
g
b
ases
,
we
in
tr
o
d
u
ce
t
h
e
m
ath
em
atica
l e
q
u
atio
n
:
=
(
)
(
(
)
)
.
(
1
8
)
wh
er
e
-
d
eg
r
ee
o
f
(
)
by
o
r
in
d
e
x
(
)
.
T
h
en
we
m
o
d
if
y
th
e
f
o
r
m
u
la
(
1
2
)
as (
1
9
)
:
(
)
=
(
)
(
)
=
(
(
)
(
2
(
(
)
)
−
1
)
)
(
)
.
(
1
9
)
I
n
th
e
in
v
er
s
e
tr
an
s
f
o
r
m
in
s
tead
o
f
in
v
er
s
e
elem
en
t
(
)
−
1
is
u
s
ed
:
=
(
)
(
(
)
)
(
2
0
)
(
)
=
(
)
−
1
(
)
=
(
(
−
1
)
(
2
(
(
)
)
−
1
)
)
(
)
(
2
1
)
I
t is sh
o
wn
th
at
th
e
ca
lcu
latio
n
o
f
th
e
in
d
ex
b
y
(
1
2
)
w
o
r
k
s
f
a
s
ter
.
T
ab
le
1
.
(
)
=
3
+
+
1
th
e
in
d
ex
tab
le
o
f
wo
r
k
in
g
b
ases
I
n
t
h
e
f
o
r
m
o
f
i
n
d
e
x
(
)
I
n
t
h
e
f
o
r
m
o
f
p
o
l
y
n
o
m
i
a
l
(
)
∞
0
0
1
1
2
2
3
+
1
4
2
+
5
2
+
+
1
6
1
2
.
2
.
S
-
blo
c
k
s
ub
s
t
it
utio
n t
a
ble
T
h
e
u
s
ed
S
-
b
l
o
ck
is
u
s
ed
as
a
s
u
b
s
titu
tio
n
o
p
er
atio
n
in
s
y
m
m
etr
ic
en
cr
y
p
tio
n
alg
o
r
ith
m
s
.
T
h
e
tab
le
co
n
tain
s
n
-
b
it
in
p
u
t
d
ata
an
d
r
an
d
o
m
l
y
g
en
e
r
ated
o
u
t
p
u
t
d
ata
f
r
o
m
m
-
b
it
in
Fig
u
r
e
3
.
S
-
b
lo
ck
s
ar
e
u
s
u
ally
p
ar
t
o
f
th
e
co
n
v
e
r
s
io
n
m
eth
o
d
an
d
ar
e
o
f
g
r
ea
t
im
p
o
r
ta
n
ce
f
o
r
th
e
cr
y
p
to
b
ilit
y
o
f
t
h
e
b
lo
ck
en
cr
y
p
tio
n
alg
o
r
ith
m
.
W
h
en
ch
a
n
g
in
g
th
e
in
p
u
t
v
alu
es
in
clu
d
e
d
in
th
e
S
-
b
lo
ck
,
th
e
b
its
in
th
e
o
u
tp
u
t
v
alu
es
s
h
o
u
ld
b
e
s
elec
ted
as a
n
y
.
Fig
u
r
e
3
.
S
-
b
l
o
ck
s
u
b
s
titu
tio
n
tab
le
T
h
e
way
o
f
ch
o
s
en
th
e
S
-
b
lo
ck
m
ay
b
e
d
if
f
er
e
n
t.
B
u
t
its
r
eliab
ilit
y
is
d
eter
m
in
ed
b
y
its
cr
y
p
to
g
r
ap
h
ic
s
tr
en
g
t
h
.
I
t
is
k
n
o
wn
th
at
th
e
S
-
b
lo
ck
is
cu
r
r
en
tly
u
s
ed
in
m
an
y
s
y
m
m
etr
i
c
b
lo
ck
en
cr
y
p
tio
n
alg
o
r
ith
m
s
,
s
u
ch
as
B
elT
,
ad
v
an
ce
d
e
n
cr
y
p
ti
o
n
s
tan
d
ar
d
(
AE
S
)
,
Sh
an
g
Mi
4
(
SM4
)
,
G
OST2
8
1
4
7
-
8
9
,
d
ata
en
cr
y
p
tio
n
s
tan
d
ar
d
(
DE
S
)
,
an
d
T
W
OFI
SH
[
1
4
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
2
,
Ap
r
il
20
25
:
1
9
0
0
-
1
9
1
1
1906
I
n
th
e
b
lo
ck
en
cr
y
p
tio
n
alg
o
r
ith
m
u
s
in
g
th
e
E
M
tr
an
s
f
o
r
m
m
eth
o
d
,
th
e
s
elec
tio
n
o
f
th
e
S
-
b
lo
ck
is
d
eter
m
in
ed
b
y
a
m
ath
em
atica
l
tr
an
s
f
o
r
m
ati
o
n
.
An
i
r
r
ed
u
ci
b
le
p
o
ly
n
o
m
ial
o
f
th
e
m
u
ltip
li
ca
tiv
e
g
r
o
u
p
in
th
e
Galo
is
f
ield
(
2
)
is
ch
o
s
en
,
alo
n
g
with
an
y
p
o
ly
n
o
m
ial
r
e
f
er
r
e
d
to
as
b
ases
.
T
h
e
ch
o
s
en
p
o
ly
n
o
m
ial
is
th
en
ex
p
o
n
en
tiated
b
y
th
e
elem
en
ts
o
f
th
e
m
u
ltip
licativ
e
g
r
o
u
p
,
as sh
o
wn
in
f
o
r
m
u
la
(
2
2
)
.
=
(
)
(
)
(
)
(
)
,
=
0
,
2
(
(
)
)
−
1
.
)
(
2
2
)
W
h
er
e
is
S
-
b
lo
ck
,
(
)
is
p
o
ly
n
o
m
ial
ca
lled
b
ase,
(
)
is
m
u
ltip
lic
ativ
e
g
r
o
u
p
elem
en
ts
,
(
)
is
m
o
d
u
le
ir
r
ed
u
cib
le
p
o
ly
n
o
m
ial.
T
h
e
S
-
b
o
x
p
er
m
u
tatio
n
s
o
b
tain
ed
b
y
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
a
r
e
s
h
o
wn
in
T
ab
le
2
.
T
ab
le
2
.
S
-
b
o
x
u
s
ed
in
th
e
p
r
o
p
o
s
ed
en
cr
y
p
tio
n
alg
o
r
ith
m
SEA1
2
8
00
01
02
03
04
05
06
07
08
09
A
B
C
D
E
F
01
1B
34
5E
D4
65
13
EC
8F
C6
92
A8
74
C9
B
F5
8D
F0
FA
14
AD
03
2D
5C
E2
D
AF
35
45
E0
3B
C7
89
9C
2A
1D
6E
E6
61
7F
3C
86
05
77
E4
57
17
80
5F
CF
51
4D
38
EA
D5
7E
27
B2
5B
A3
81
44
FB
F
99
5D
F9
39
F1
E1
20
F3
D7
48
4F
E
82
69
A7
ED
94
F2
CC
7C
11
DA
E7
7A
4B
62
52
60
64
08
D8
D1
12
F7
BB
98
46
CD
67
25
84
33
1F
58
8E
DD
A6
F6
A0
AC
18
19
02
36
68
BC
D9
CA
26
A9
6F
FD
55
21
E8
E3
16
9B
6B
91
85
28
2B
06
5A
B8
B5
1A
2F
6A
8A
B1
76
FF
63
49
54
3A
DC
BD
C2
FE
78
7D
A
EE
B9
AE
2E
71
BE
EF
A2
9A
70
A5
DB
FC
4E
15
B6
37
73
88
87
1E
43
BA
83
72
93
B3
40
97
DF
90
9E
1C
75
D2
3F
AB
59
95
E9
F8
22
C5
BF
F4
96
C4
A4
C0
C8
10
C1
D3
24
9F
07
41
8C
EB
CE
4A
79
66
3E
B0
6D
CB
3D
9D
31
29
30
32
04
6C
D0
09
C3
E5
4C
23
DE
8B
AA
42
A1
B7
2C
47
D6
53
7B
50
56
C
B4
00
3.
E
NCRY
P
T
I
O
N
A
L
G
O
RI
T
H
M
S AN
A
L
YS
I
S
R
esear
ch
in
th
e
f
ield
o
f
b
lo
c
k
cip
h
e
r
alg
o
r
ith
m
s
is
co
n
d
u
cted
b
y
s
cien
tis
ts
wo
r
ld
wid
e
to
en
h
a
n
ce
s
ec
u
r
ity
an
d
ef
f
icien
c
y
,
a
n
d
d
ev
elo
p
n
ew
e
n
cr
y
p
tio
n
m
eth
o
d
s
.
On
e
way
t
o
d
ete
r
m
in
e
th
e
cr
y
p
to
g
r
ap
h
i
c
s
tr
en
g
th
o
f
b
lo
ck
cip
h
er
alg
o
r
ith
m
s
is
th
r
o
u
g
h
th
eir
s
tatis
t
ical
s
ec
u
r
ity
.
Stati
s
tical
s
ec
u
r
ity
(
o
r
s
tr
en
g
th
)
o
f
b
lo
ck
cip
h
er
alg
o
r
ith
m
s
is
r
el
ated
to
th
eir
ab
ilit
y
to
with
s
t
an
d
v
a
r
io
u
s
ty
p
es
o
f
cr
y
p
tan
a
ly
s
es
b
ased
o
n
th
e
s
tatis
t
ical
p
r
o
p
er
ties
o
f
th
e
cip
h
er
tex
t.
T
h
is
is
a
cr
itical
asp
ec
t
o
f
s
ec
u
r
ity
b
ec
a
u
s
e
ce
r
tain
s
tatis
tical
ch
ar
ac
ter
is
tics
o
f
th
e
cip
h
er
tex
t
ca
n
p
r
o
v
id
e
a
n
attac
k
er
with
in
f
o
r
m
atio
n
ab
o
u
t
th
e
k
ey
o
r
th
e
o
r
ig
i
n
al
m
ess
ag
e.
T
h
e
en
cr
y
p
tio
n
alg
o
r
ith
m
m
o
d
el
was
im
p
lem
en
ted
in
C
++
.
An
an
aly
s
is
an
d
ev
alu
atio
n
o
f
test
s
wer
e
co
n
d
u
cte
d
to
ass
ess
th
e
s
tat
i
s
tical
s
af
ety
o
f
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
.
Fo
r
test
in
g
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
:
i)
1
5
f
iles
o
f
d
if
f
e
r
en
t sizes
an
d
ii)
1
0
f
u
ll
-
k
ey
an
d
d
if
f
e
r
en
t
wo
r
k
in
g
b
ases
wer
e
u
s
ed
.
1
5
0
cip
h
er
tex
t o
b
tain
e
d
b
y
p
r
o
p
o
s
ed
alg
o
r
ith
m
wer
e
test
ed
to
s
ta
tis
tica
l
s
af
ety
te
s
t
s
.
On
e
o
f
th
e
p
r
im
ar
y
asp
ec
ts
in
ev
alu
atin
g
th
e
s
tr
en
g
th
o
f
cr
y
p
t
o
g
r
ap
h
ic
alg
o
r
ith
m
s
in
v
o
lv
es
ass
ess
in
g
th
eir
s
tati
s
tical
s
ec
u
r
ity
.
I
f
th
e
s
eq
u
en
ce
o
f
cip
h
er
tex
ts
g
e
n
er
ated
b
y
an
e
n
cr
y
p
tio
n
alg
o
r
ith
m
p
r
o
v
id
es
p
r
o
p
er
ties
o
f
r
an
d
o
m
n
ess
,
th
e
n
th
e
alg
o
r
ith
m
is
co
n
s
id
er
ed
s
tatis
tically
s
ec
u
r
e
[
1
5
]
.
Hen
ce
,
th
e
s
tatis
tical
p
r
o
p
er
ties
o
f
th
e
p
r
o
p
o
s
ed
en
c
r
y
p
tio
n
alg
o
r
ith
m
wer
e
ex
am
in
ed
u
s
in
g
D.
Kn
u
th
an
d
NI
ST
test
s
[
1
6
]
,
[
1
7
]
.
I
n
1
9
6
9
,
Kn
u
th
[
1
8
]
p
r
esen
ted
th
e
f
ir
s
t
s
et
o
f
s
tatis
tical
test
s
in
h
is
cla
s
s
ic
wo
r
k
“T
h
e
Ar
t
o
f
Pro
g
r
am
m
in
g
.
”
D.
Kn
u
t'
s
tes
ts
ar
e
b
ased
o
n
a
s
tatis
tical
cr
iter
io
n
:
ch
ec
k
f
o
r
u
n
co
u
p
led
r
u
n
s
,
c
h
ec
k
f
o
r
in
ter
v
als,
ch
ec
k
f
o
r
co
m
b
in
ati
o
n
s
,
test
f
o
r
co
u
p
o
n
co
llecto
r
,
ch
ec
k
f
o
r
p
e
r
m
u
tatio
n
s
,
ch
ec
k
f
o
r
m
o
n
o
to
n
y
a
n
d
ch
ec
k
f
o
r
co
r
r
elatio
n
.
T
h
e
test
s
ar
e
b
ased
o
n
a
s
tatis
tical
2
cr
iter
io
n
.
T
h
e
ca
lc
u
lated
v
alu
e
o
f
s
tatis
t
ics
i
s
2
with
tab
u
lar
r
esu
lts
an
d
,
d
ep
e
n
d
in
g
o
n
th
e
p
r
o
b
a
b
ilit
y
o
f
t
h
e
ap
p
ea
r
a
n
ce
o
f
s
u
ch
s
tatis
tics
,
a
co
n
clu
s
io
n
is
m
ad
e
ab
o
u
t
its
q
u
ality
[
1
9
]
.
D.
Kn
u
t'
s
test
s
u
s
e
g
r
ap
h
ic
al
an
d
ev
al
u
atio
n
test
s
to
s
tu
d
y
th
e
s
tatis
tical
p
r
o
p
er
ties
o
f
cip
h
er
tex
t.
Gr
ap
h
ic
test
s
r
e
s
u
lts
m
ay
n
o
t
b
e
ex
ac
t,
as
th
e
g
r
ap
h
ic
v
iewe
r
ca
n
n
o
t
h
av
e
an
y
ac
t
u
al
r
esu
lts
,
s
o
th
er
e
m
ay
b
e
v
ar
i
o
u
s
d
ev
iatio
n
s
.
T
h
e
n
u
m
b
er
o
f
s
u
cc
ess
f
u
lly
p
ass
ed
test
s
b
y
D.
Kn
u
th
s
h
o
wn
in
Fig
u
r
e
4
.
Gr
ap
h
ic
test
s
r
esu
lts
:
His
to
g
r
am
o
f
th
e
d
is
tr
ib
u
tio
n
o
f
elem
en
ts
,
d
is
tr
ib
u
tio
n
o
n
th
e
p
lan
e
,
ch
ec
k
i
n
g
th
e
s
er
ies,
ch
ec
k
in
g
f
o
r
m
o
n
o
to
n
y
,
b
y
te
a
u
to
co
r
r
elatio
n
f
u
n
ctio
n
(
AC
F),
b
it
au
to
c
o
r
r
elati
o
n
f
u
n
ctio
n
(
AC
F),
g
r
ap
h
ic
s
p
ec
tr
al
test
,
co
m
p
lex
ity
p
r
o
f
ile
was
test
ed
ac
co
r
d
in
g
ly
1
4
7
,
1
4
8
,
1
4
9
,
1
4
3
,
1
4
4
,
1
4
7
,
1
4
9
,
an
d
1
5
0
cip
h
er
tex
ts
.
Ass
ess
m
en
t
te
s
t
r
esu
lts
s
h
o
w
wh
ich
r
esu
lts
a
r
e
p
ass
ed
o
r
an
d
wh
ich
ar
e
n
o
t
as
s
h
o
wn
in
Fig
u
r
e
5
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Dev
elo
p
men
t a
n
d
a
n
a
lysi
s
o
f
s
ymm
etr
ic
en
cryp
tio
n
a
lg
o
r
ith
m
(
A
r
d
a
b
ek
K
h
o
mp
ysh
)
1907
Fig
u
r
e
4
.
Gr
a
p
h
ic
test
s
r
esu
lts
Fig
u
r
e
5
.
Ass
ess
m
en
t te
s
t r
esu
lts
Ass
es
s
m
en
t te
s
t r
esu
lt
s
: c
h
ec
k
in
g
u
n
c
o
u
p
led
s
er
ies,
ch
ec
k
in
g
f
o
r
m
o
n
o
t
o
n
y
,
i
n
ter
v
al
ch
ec
k
,
ch
ec
k
in
g
co
m
b
in
atio
n
s
,
co
u
p
o
n
co
llect
o
r
test
,
ch
ec
k
p
er
m
u
tatio
n
s
,
th
e
co
r
r
elatio
n
ch
e
ck
was
test
p
ass
ed
,
r
esp
ec
tiv
ely
,
1
4
4
,
1
4
8
,
1
3
9
,
1
4
4
,
1
1
4
,
1
4
5
,
1
4
2
,
an
d
1
5
0
cip
h
e
r
tex
ts
.
NI
ST
h
as
cr
ea
ted
s
ev
er
al
s
tatis
ti
ca
l
test
s
[
2
0
]
,
th
at
in
v
o
lv
e
ca
lcu
latin
g
a
s
tatis
tic
r
ep
r
esen
tin
g
a
p
ar
ticu
lar
p
r
o
p
er
ty
o
f
a
s
eq
u
e
n
ce
a
n
d
co
m
p
a
r
in
g
it
t
o
a
r
ef
e
r
en
ce
s
tatis
t
ic.
T
h
ese
r
ef
er
en
ce
s
tatis
tics
ar
e
d
er
iv
ed
m
ath
e
m
atica
lly
,
a
to
p
ic
ex
ten
s
iv
ely
c
o
v
er
ed
in
v
ar
io
u
s
th
eo
r
em
s
an
d
s
cien
tific
p
ap
er
s
in
th
e
f
ield
s
o
f
cr
y
p
to
g
r
a
p
h
y
,
p
r
o
b
a
b
ilit
y
th
eo
r
y
,
an
d
n
u
m
b
e
r
th
eo
r
y
.
T
o
in
v
esti
g
ate
t
h
e
s
tatis
tical
s
ec
u
r
ity
o
f
th
e
p
r
o
p
o
s
ed
SEA1
2
8
e
n
cr
y
p
tio
n
al
g
o
r
ith
m
,
th
e
f
o
llo
win
g
NI
ST
s
tati
s
tical
te
s
ts
[
2
1
]
wer
e
u
s
ed
:
f
r
eq
u
en
cy
(
M
o
n
o
b
i
t)
test
,
f
r
eq
u
en
cy
test
with
in
a
b
lo
ck
,
r
u
n
s
test
,
test
f
o
r
th
e
lo
n
g
est
r
u
n
o
f
o
n
e
s
in
a
b
lo
ck
,
b
in
ar
y
m
atr
i
x
r
a
n
k
test
,
d
is
cr
ete
Fo
u
r
ier
tr
an
s
f
o
r
m
(
s
p
ec
tr
al)
test
,
non
-
o
v
er
lap
p
in
g
tem
p
late
m
at
ch
in
g
test
,
o
v
er
lap
p
i
n
g
tem
p
l
ate
m
atch
in
g
test
,
Ma
u
r
er
’
s
Un
iv
er
s
al
s
tatis
tical
test
,
lin
ea
r
co
m
p
lex
ity
test
,
s
er
ial
test
,
ap
p
r
o
x
im
ate
en
tr
o
p
y
test
,
C
u
m
u
lativ
e
Su
m
s
(
C
u
s
u
m
)
test
,
r
an
d
o
m
ex
cu
r
s
io
n
s
test
,
r
an
d
o
m
ex
c
u
r
s
io
n
s
v
ar
ian
t te
s
t.
I
n
ea
ch
test
,
a
P
-
v
alu
e
is
ca
lc
u
lated
to
in
d
icate
th
e
lev
el
o
f
r
an
d
o
m
n
ess
.
A
P
-
v
alu
e
o
f
1
s
ig
n
if
ies
an
id
ea
lly
r
an
d
o
m
s
eq
u
en
ce
,
wh
i
le
a
P
-
v
alu
e
o
f
0
in
d
icate
s
a
co
m
p
letely
p
r
ed
ictab
le
s
eq
u
e
n
ce
.
T
h
e
P
-
v
alu
e
is
th
en
co
m
p
ar
ed
to
a
th
r
esh
o
ld
lev
el
o
f
α
(
r
an
d
o
m
n
ess
)
,
ty
p
ic
ally
s
et
at
0
.
0
1
.
I
f
th
e
P
-
v
alu
e
ex
ce
ed
s
α
,
th
e
n
u
ll
h
y
p
o
th
esis
is
ac
ce
p
ted
,
an
d
th
e
s
eq
u
en
ce
is
co
n
s
id
er
ed
r
a
n
d
o
m
;
o
t
h
er
wis
e,
it
is
d
ee
m
ed
n
o
n
-
r
an
d
o
m
.
T
h
is
p
r
o
ce
s
s
lead
s
to
th
e
f
o
llo
win
g
co
n
clu
s
io
n
s
[
2
2
]
:
i)
i
f
th
e
≥
0
.
01
s
atis
f
ies
th
e
co
n
d
itio
n
,
th
en
th
e
cip
h
er
tex
t
is
co
n
s
id
er
ed
r
an
d
o
m
with
a
tr
u
s
t
lev
el
o
f
9
9
%;
an
d
ii)
if
th
e
≤
0
.
01
s
atis
f
ie
s
t
h
e
co
n
d
itio
n
,
th
en
th
e
cip
h
er
te
x
t is co
n
s
id
er
ed
n
o
n
-
r
a
n
d
o
m
with
a
tr
u
s
t le
v
el
o
f
9
9
%.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
2
,
Ap
r
il
20
25
:
1
9
0
0
-
1
9
1
1
1908
T
h
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test
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l
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r
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ess
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y
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aly
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h
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r
o
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r
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ass
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s
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o
r
h
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eity
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am
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i
n
g
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e
d
is
tr
ib
u
tio
n
o
f
P
-
v
alu
es,
as
d
etailed
in
th
e
ar
ticle
[
2
3
]
.
T
h
is
to
o
l
ca
n
p
er
f
o
r
m
all
s
tatis
tical
test
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i
m
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ltan
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ly
.
I
n
th
is
ca
s
e,
p
a
r
am
eter
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m
m
o
n
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ar
e
s
eq
u
en
ce
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g
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d
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am
p
le
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ize,
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o
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e
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ir
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.
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s
eq
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en
ce
le
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o
f
1
,
0
0
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0
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0
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its
an
d
a
s
am
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le
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ize
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f
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2
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wer
e
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a
r
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er
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o
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d
f
r
o
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e
p
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ed
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cr
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o
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ith
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f
o
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o
m
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ess
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f
all
th
e
A
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d
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v
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es
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e
g
r
ea
ter
o
r
eq
u
al
th
an
C
an
d
D
r
esp
ec
tiv
ely
,
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e
test
r
esu
lt
is
PA
SS
.
T
h
e
r
esu
lt
s
o
b
tain
ed
ar
e
p
r
esen
ted
in
Fig
u
r
e
6
.
T
o
in
v
esti
g
ate
t
h
e
s
tatis
tical
s
ec
u
r
ity
o
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o
u
tp
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t
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eq
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en
ce
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o
f
th
e
SEA
1
2
8
en
cr
y
p
tio
n
alg
o
r
ith
m
u
s
in
g
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e
NI
ST
test
s
,
th
e
s
am
e
1
5
0
f
iles
wer
e
u
s
ed
as
f
o
r
th
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Kn
u
th
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h
e
n
u
m
b
er
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cc
ess
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l
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r
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lt o
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tu
d
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o
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e
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en
cr
y
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o
r
ith
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is
s
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o
wn
in
Fig
u
r
e
7
.
Fig
u
r
e
6
.
Descr
ip
tio
n
s
in
f
in
al
an
aly
s
is
r
ep
o
r
t
Fig
u
r
e
7
.
NI
ST
test
s
r
esu
lts
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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Dev
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en
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r
ith
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[
2
4
]
,
[
2
5
]
.
T
h
e
r
es
u
lts
o
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lin
ea
r
a
n
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er
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tial
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aly
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e
s
h
o
wn
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T
ab
le
3
,
an
d
th
e
r
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lts
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eb
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aic
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aly
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e
s
h
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wn
i
n
T
ab
le
4
a
n
d
Fig
u
r
e
8
.
W
e
u
s
ed
s
tan
d
ar
d
alg
eb
r
aic
an
aly
s
is
to
ev
alu
ate
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e
q
u
ality
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f
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-
b
o
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p
p
lied
to
th
e
NB
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en
cr
y
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tio
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o
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ith
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h
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clu
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it
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o
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r
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e
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tial
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d
lin
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r
a
p
p
r
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x
im
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s
[
2
6
]
.
At
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ex
am
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o
f
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lts
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tin
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ith
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u
n
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er
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im
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n
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,
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at
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ay
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with
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im
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l d
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it p
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tio
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.
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k
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p
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1
2
8
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n
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r
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9
T
ab
le
4
.
SAC
an
aly
s
is
o
f
S
-
b
o
x
(
SEA1
2
8
)
B
i
t
0
B
i
t
1
B
i
t
2
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i
t
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t
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Fig
u
r
e
8
.
Gr
a
p
h
ical
r
ep
r
esen
tatio
n
o
f
SAC
4.
CO
NCLUS
I
O
N
T
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
r
elies
o
n
e
x
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tiatio
n
m
o
d
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lo
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tin
g
lar
g
e
-
d
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it
n
u
m
b
er
s
in
r
esid
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class
es
wi
th
in
a
p
o
s
itio
n
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u
m
b
er
s
y
s
tem
as
s
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ets
o
f
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m
aller
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ig
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.
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e
n
ab
les
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g
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ta
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le
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ased
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.
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ased
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d
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e
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ed
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S
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1
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Evaluation Warning : The document was created with Spire.PDF for Python.