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e
v
a
lu
a
tin
g
th
e
s
tr
e
n
g
th
an
d
t
h
e
ef
f
icie
n
c
y
o
f
t
h
e
p
r
o
p
o
s
ed
s
ch
e
m
es.
E
v
e
n
th
e
c
r
y
p
to
g
r
ap
h
y
co
n
ce
r
n
is
s
ec
u
r
i
t
y
;
h
o
w
e
v
er
s
p
ee
d
an
d
s
p
ac
e
ar
e
also
th
e
f
ac
to
r
s
th
at
e
f
f
ec
ted
t
h
e
s
tr
en
g
t
h
o
f
t
h
e
s
ch
e
m
es
p
r
o
p
o
s
ed
.
T
h
is
p
ap
er
is
estab
li
s
h
ed
to
r
ev
ie
w
th
e
d
i
f
f
er
en
t
p
u
b
lic
k
e
y
cr
y
p
to
g
r
ap
h
y
s
ch
e
m
e
b
as
ed
o
n
p
er
f
o
r
m
a
n
ce
an
al
y
s
is
u
s
ed
to
s
ee
r
esear
ch
p
atter
n
s
f
o
r
th
e
last
4
0
y
ea
r
s
s
in
ce
t
h
e
y
w
er
e
in
v
en
ted
.
Me
an
w
h
ile,
th
is
s
t
u
d
y
h
ad
b
ee
n
co
n
d
u
cted
b
ased
o
n
s
ev
er
al
s
t
ep
s
w
h
ic
h
in
c
lu
d
es
g
ath
er
i
n
g
th
e
d
ata,
p
r
e
-
p
r
o
ce
s
s
in
g
d
ata
,
class
i
f
y
th
e
p
r
ev
io
u
s
s
t
u
d
y
b
ased
o
n
m
etr
ics
p
er
f
o
r
m
a
n
ce
,
ev
al
u
ate
d
ata
b
ased
o
n
m
etr
ic
s
p
er
f
o
r
m
an
ce
class
if
icatio
n
a
n
d
o
b
tain
th
e
r
esu
lts
.
2.
P
UB
L
I
C
K
E
Y
C
RYP
T
O
G
R
AP
H
Y
P
E
RF
O
RM
ANCE M
E
T
R
I
CS O
N
D
I
F
F
E
R
E
N
T
P
K
C
SCH
E
M
E
T
h
is
s
ec
tio
n
p
r
esen
t
s
t
h
e
p
er
f
o
r
m
a
n
ce
m
etr
ic
s
in
ev
a
lu
at
in
g
th
e
p
u
b
lic
k
e
y
cr
y
p
to
g
r
ap
h
y
s
ch
e
m
e
.
T
h
e
s
ch
e
m
e
s
co
n
s
i
s
t
o
f
Di
f
f
ie
-
Hell
m
a
n
Ke
y
E
x
ch
a
n
g
e,
R
S
A
,
Mc
E
liece
,
Go
ld
w
a
s
s
e
r
-
Mic
ali,
E
lGa
m
al,
E
llip
tic
C
u
r
v
e,
Di
g
ita
l
Si
g
n
a
tu
r
e,
L
a
ttices,
Fu
l
l
y
Ho
m
o
m
o
r
p
h
ic,
NT
R
U
an
d
GGH
.
Fi
g
u
r
e
1
s
h
o
w
s
th
e
s
ch
e
m
es
a
n
d
t
h
e
y
ea
r
t
h
e
y
w
er
e
p
r
o
p
o
s
ed
.
Fro
m
t
h
e
f
ig
u
r
e,
Dif
f
ie
-
Hell
m
a
n
,
R
S
A
a
n
d
Mc
E
liece
ar
e
th
e
ea
r
lies
t sc
h
e
m
e
s
in
tr
o
d
u
ce
d
co
m
p
ar
ed
to
o
th
er
s
.
Fig
u
r
e
1
.
T
h
e
tim
el
in
e
o
f
cr
y
p
to
g
r
ap
h
y
s
ch
e
m
es
Gen
er
all
y
,
ea
c
h
s
c
h
e
m
e
w
as
d
ev
elo
p
ed
to
o
f
f
er
f
ac
ili
ties
f
o
r
u
s
er
s
i
n
d
ata
co
m
m
u
n
ic
atio
n
a
n
d
tr
an
s
m
is
s
io
n
a
s
w
ell
as
to
s
a
v
e
th
e
ca
p
ac
it
y
,
th
e
co
m
p
u
tat
io
n
al
ti
m
e
an
d
to
en
s
u
r
e
t
h
e
d
ata
p
r
o
tectio
n
w
il
l
al
w
a
y
s
b
e
r
eliab
le.
T
h
u
s
,
p
u
b
l
ic
k
e
y
cr
y
p
to
g
r
ap
h
y
(
P
KC
)
i
s
ev
alu
a
ted
b
y
t
h
ese
p
er
f
o
r
m
an
ce
m
etr
ics
to
m
a
k
e
s
u
r
e
th
e
cr
y
p
ta
n
al
y
s
i
s
is
p
er
f
o
r
m
i
n
g
w
ell
i
n
d
eliv
er
i
n
g
s
ec
u
r
ed
d
ata
f
r
o
m
s
en
d
er
to
r
ec
eiv
er
th
r
o
u
g
h
p
u
b
lic
n
et
w
o
r
k
s
.
T
h
er
e
ar
e
th
r
ee
p
er
f
o
r
m
a
n
ce
m
etr
ics
o
f
P
KC
,
w
h
i
ch
ar
e
s
ec
u
r
i
t
y
,
s
p
ee
d
an
d
s
p
ac
e
[6
-
7]
.
A
cc
o
r
d
in
g
to
[
8
]
s
ec
u
r
it
y
is
d
ef
i
n
ed
as
al
l
ab
o
u
t
co
n
f
id
e
n
tialit
y
,
i
n
te
g
r
i
t
y
a
n
d
av
a
ilab
ilit
y
.
Ot
h
er
t
h
an
th
at
,
co
m
p
u
ter
an
d
n
et
w
o
r
k
s
ec
u
r
it
y
is
ab
o
u
t
co
n
ce
r
n
i
n
g
i
n
p
r
o
tectin
g
t
h
e
s
y
s
te
m
s
.
I
n
cr
ea
s
in
g
t
h
e
s
ec
u
r
it
y
u
s
u
all
y
w
il
l
als
o
in
cr
ea
s
e
th
e
s
ize
o
f
k
e
y
t
h
at
w
il
l
u
s
e
m
o
r
e
s
p
ac
e.
T
h
e
m
o
r
e
s
p
ac
e
u
s
ed
,
th
e
s
lo
w
er
th
e
alg
o
r
ith
m
.
I
n
li
n
e
w
it
h
[
2
]
an
e
f
f
icie
n
t
cr
y
p
to
g
r
a
p
h
y
a
lg
o
r
it
h
m
p
r
o
b
ab
ly
u
s
es
l
ess
s
p
ac
e
a
f
ter
t
h
e
e
n
cr
y
p
tio
n
p
r
o
ce
s
s
in
o
r
d
er
to
h
av
e
f
ast
p
r
o
ce
s
s
i
n
g
.
A
s
s
ta
te
d
b
y
[
9
]
f
ast
p
r
o
ce
s
s
i
n
g
i
s
ab
o
u
t
th
e
ti
m
e
n
ee
d
ed
in
g
e
n
er
atin
g
k
e
y
,
en
cr
y
p
t
in
g
an
d
d
ec
r
y
p
ti
n
g
p
r
o
ce
s
s
.
Ho
w
e
v
er
,
th
er
e
ar
e
al
s
o
in
te
g
r
ated
p
er
f
o
r
m
a
n
ce
m
etr
ics
th
a
t
h
ad
b
ee
n
h
i
g
h
lig
h
ted
b
y
th
e
p
r
ev
io
u
s
r
esear
ch
er
s
w
h
ic
h
ap
p
lied
f
o
r
d
if
f
er
e
n
t
s
ch
e
m
e
s
;
s
ec
u
r
it
y
a
n
d
s
p
ee
d
; secu
r
it
y
an
d
s
p
ac
e;
s
p
ee
d
an
d
s
p
ac
e;
a
n
d
s
ec
u
r
it
y
,
s
p
ee
d
an
d
s
p
ac
e.
T
h
ese
p
er
f
o
r
m
an
ce
m
etr
ic
s
ar
e
u
s
ed
to
e
v
al
u
ate
t
h
e
p
er
f
o
r
m
an
ce
o
f
t
h
e
P
KC
s
ch
e
m
es
a
s
s
h
o
w
n
i
n
Fi
g
u
r
e
2
.
I
t
also
s
h
o
w
s
t
h
at
m
o
s
t
o
f
th
e
s
c
h
e
m
es
i
n
cl
u
d
in
g
Di
f
f
ie
Hell
m
a
n
,
R
S
A
,
Mc
E
liece
,
E
lGa
m
al,
E
llip
tic
C
u
r
v
e
an
d
G
GH
ar
e
m
o
r
e
f
o
cu
s
ed
o
n
s
ec
u
r
it
y
.
Oth
er
t
h
a
n
th
a
t,
m
o
s
t
o
f
th
e
s
ch
e
m
e
also
s
h
o
w
s
at
ten
tio
n
o
n
th
e
i
n
te
g
r
atio
n
o
f
s
ec
u
r
it
y
an
d
s
p
ee
d
(
d
ig
ital
s
i
g
n
a
tu
r
e
a
n
d
h
y
b
r
id
s
c
h
e
m
e)
;
an
d
s
ec
u
r
it
y
an
d
s
p
ac
e
(
lattic
es
an
d
f
u
ll
y
h
o
m
o
m
o
r
p
h
ic
s
c
h
e
m
e)
.
O
n
l
y
a
f
e
w
o
f
t
h
e
s
c
h
e
m
e
s
f
o
c
u
s
ed
o
n
s
p
ee
d
an
d
s
p
ac
e
s
ep
ar
atel
y
.
On
t
h
e
o
th
er
h
a
n
d
,
GGH
a
n
d
lattices
p
aid
atten
t
io
n
o
n
s
p
a
ce
as
th
e
e
v
alu
a
tio
n
cr
iter
ia
f
o
r
th
e
s
c
h
e
m
e
p
er
f
o
r
m
a
n
ce
m
e
tr
ics
as
t
h
ese
s
ch
e
m
es
ap
p
lied
s
m
all
k
e
y
s
ize
a
n
d
s
m
all
cip
h
er
tex
t
[
1
0
-
1
1
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4752
I
n
d
o
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esia
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J
E
lec
E
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g
&
C
o
m
p
Sci,
Vo
l
.
1
2
,
No
.
1
,
Octo
b
er
201
8
:
3
8
6
–
3
9
3
388
Fig
u
r
e
2
.
P
er
f
o
r
m
a
n
ce
Me
tr
ics
o
n
Dif
f
er
en
t P
KC
Sch
e
m
es
3.
RE
L
AT
E
D
WO
RK
S O
N
P
E
RF
O
RM
ANCE
M
E
T
RIC
S
O
F
P
K
C
SCH
E
M
E
S
B
asicall
y
,
t
h
e
m
ai
n
co
n
ce
r
n
o
f
P
KC
i
s
t
h
e
s
ec
u
r
it
y
it
s
el
f
wh
er
e
it
m
u
s
t
m
a
k
e
s
u
r
e
t
h
at
d
a
ta
tr
an
s
m
it
s
ec
u
r
el
y
f
r
o
m
s
en
d
er
to
r
ec
ei
v
er
o
v
er
p
u
b
lic
n
et
w
o
r
k
s
.
A
cc
o
r
d
in
g
to
[
2
]
cr
y
p
to
g
r
ap
h
y
p
r
o
v
id
e
a
tec
h
n
iq
u
e
to
s
ec
u
r
e
p
er
s
o
n
al
d
ata
f
r
o
m
u
n
a
u
th
o
r
ized
u
s
er
s
.
Oth
er
th
a
n
th
at,
th
e
s
p
ee
d
also
p
lay
s
t
h
e
i
m
p
o
r
ta
n
t
r
o
les
as
to
en
s
u
r
e
u
s
er
s
ca
n
en
cr
y
p
t
a
n
d
d
ec
r
y
p
t
f
aster
.
Mo
r
eo
v
er
,
n
o
t
o
n
l
y
s
ec
u
r
i
t
y
a
n
d
s
p
ee
d
,
s
p
ac
e
also
s
h
o
u
ld
b
e
co
u
n
ted
i
n
t
h
e
co
n
ce
r
n
o
f
P
K
C
f
o
r
t
h
e
u
s
a
g
e
o
f
d
ev
ices
th
at
h
as
li
m
ited
s
p
ac
e
a
n
d
r
eso
u
r
ce
s
.
So
m
e
o
f
th
e
p
r
ev
io
u
s
s
t
u
d
ies
n
o
t
o
n
l
y
f
o
cu
s
ed
o
n
s
ec
u
r
it
y
,
s
p
ee
d
an
d
s
p
a
ce
s
ep
ar
atel
y
,
b
u
t
t
h
e
y
i
n
te
g
r
a
te
th
e
p
er
f
o
r
m
a
n
ce
m
etr
ics
f
o
r
t
h
eir
s
c
h
e
m
es
e
v
a
lu
atio
n
cr
iter
ia
f
o
r
e
x
a
m
p
le
s
ec
u
r
it
y
an
d
s
p
ee
d
;
s
ec
u
r
it
y
a
n
d
s
p
ac
e;
s
p
ee
d
an
d
s
p
ac
e;
an
d
s
ec
u
r
it
y
,
s
p
ee
d
an
d
s
p
ac
e.
T
ab
le
1
s
h
o
w
s
t
h
e
p
r
ev
io
u
s
r
esear
c
h
th
a
t
f
o
c
u
s
s
in
g
i
n
d
if
f
er
e
n
t
p
er
f
o
r
m
a
n
ce
m
etr
ics
th
at
ca
n
b
e
class
i
f
ied
as
s
i
n
g
le
p
er
f
o
r
m
an
ce
m
e
tr
ics
a
n
d
in
te
g
r
ated
p
er
f
o
r
m
an
ce
m
etr
ic
s
.
Oth
er
t
h
an
t
h
at,
it
al
s
o
s
h
o
w
s
th
e
s
c
h
e
m
es
t
h
at
ar
e
ar
e
d
iv
i
d
ed
in
to
th
r
ee
ca
teg
o
r
ies
w
h
ic
h
ar
e
co
n
v
e
n
tio
n
al
,
tr
an
s
-
co
n
te
m
p
o
r
ar
y
an
d
co
n
te
m
p
o
r
ar
y
s
ch
e
m
es
b
ased
o
n
t
h
e
y
ea
r
p
r
o
p
o
s
ed
.
T
ab
le
1
.
R
esear
ch
Fo
cu
s
ed
o
n
P
er
f
o
r
m
a
n
ce
Me
tr
ics
f
o
r
P
KC
Sch
e
m
e
C
la
s
s
i
f
icat
io
n
C
o
n
v
e
n
t
i
o
n
a
l
T
r
a
n
s
-
C
o
n
t
e
m
p
o
r
a
r
y
C
o
t
e
mp
o
r
a
r
y
P
e
r
f
o
r
man
c
e
M
e
t
r
i
c
s
/
Y
e
a
r
s
S
i
n
g
l
e
P
e
r
f
o
r
ma
n
c
e
M
e
t
r
i
c
s
S
e
c
u
r
i
t
y
[
1
2
-
16]
[
1
7
-
22]
[
2
3
]
–
5
3
]
S
p
e
e
d
[
5
4
]
[
5
5
]
[
5
6
]
[
5
7
]
[
5
8
]
S
p
a
c
e
[
1
0
]
[
5
9
]
I
n
t
e
g
r
a
t
e
d
P
e
r
f
o
r
ma
n
c
e
M
e
t
r
i
c
s
S
e
c
u
r
i
t
y
&
S
p
e
e
d
[
1
]
[
6
0
]
[
6
1
]
[
6
2
-
66]
[
6
7
-
76]
S
e
c
u
r
i
t
y
&
S
p
a
c
e
[
5
]
[
7
7
]
[
7
8
]
[
7
9
]
[
8
0
-
88]
S
p
e
e
d
&
S
p
a
c
e
[
8
9
]
[
9
0
]
[
9
1
-
93
]
S
e
c
u
r
i
t
y
,
S
p
e
e
d
&
S
p
a
c
e
[
9
4
]
[
9
5
]
[
9
6
]
[
9
7
-
99]
R
ef
er
r
i
n
g
to
T
ab
le
1
,
a
f
e
w
r
esear
ch
es
w
er
e
i
m
p
le
m
e
n
ted
in
t
h
e
co
n
v
en
tio
n
al
y
ea
r
s
a
n
d
al
m
o
s
t
n
o
d
if
f
er
e
n
ce
i
n
th
e
n
e
x
t
tr
an
s
-
c
o
n
te
m
p
o
r
ar
y
y
ea
r
s
.
Ho
w
ev
er
,
f
r
o
m
t
h
e
w
h
o
le
tab
le
it
s
h
o
w
s
th
a
t
m
o
s
t
o
f
t
h
e
s
tu
d
ie
s
w
er
e
co
n
ce
n
tr
ate
in
th
e
co
n
te
m
p
o
r
ar
y
y
ea
r
s
.
On
th
e
o
th
er
h
a
n
d
,
al
m
o
s
t a
ll t
h
e
r
ese
ar
ch
th
at
f
o
c
u
s
es o
n
s
in
g
le
p
er
f
o
r
m
a
n
ce
m
etr
ics
p
a
id
atten
tio
n
o
n
s
ec
u
r
it
y
.
O
n
l
y
a
f
e
w
o
f
t
h
e
r
esear
ch
lo
o
k
at
t
h
e
s
p
ee
d
an
d
s
p
ac
e
as
t
h
eir
p
er
f
o
r
m
a
n
ce
m
etr
ic
s
i
n
t
h
eir
p
r
o
p
o
s
ed
s
ch
e
m
es.
Fro
m
t
h
e
i
n
te
g
r
ated
p
er
f
o
r
m
an
ce
m
etr
ic
s
p
er
s
p
ec
tiv
e,
it
also
s
h
o
w
s
t
h
e
s
a
m
e
v
ie
w
w
h
er
e
m
o
s
t
o
f
th
e
r
esear
ch
w
er
e
d
o
n
e
ag
g
r
e
s
s
i
v
el
y
i
n
t
h
e
co
n
te
m
p
o
r
ar
y
y
ea
r
s
a
n
d
f
o
cu
s
ed
o
n
t
h
e
i
n
te
g
r
atio
n
w
it
h
t
h
e
s
ec
u
r
it
y
p
er
f
o
r
m
an
ce
m
e
tr
ics,
w
h
i
c
h
ar
e
s
ec
u
r
it
y
an
d
s
p
ee
d
; a
n
d
s
ec
u
r
it
y
an
d
s
p
ac
e.
2
0
2
0
2
0
0
0
2
0
1
0
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4752
R
ev
iew
o
n
P
u
b
lic
K
ey
C
r
yp
to
g
r
a
p
h
y
S
c
h
eme
-
B
a
s
ed
P
erfo
r
ma
n
ce
Metr
ics
(
Ja
s
min
I
lya
n
i A
h
ma
d
)
389
4.
P
RE
F
E
R
RE
D
P
E
RF
O
RM
ANCE M
E
T
RIC
S
Fro
m
t
h
e
s
ev
e
n
p
er
f
o
r
m
an
ce
-
m
etr
ics
d
i
s
cu
s
s
ed
p
r
ev
io
u
s
l
y
,
it
s
h
o
w
s
th
a
t
t
h
er
e
ar
e
t
h
r
e
e
h
i
g
h
est
p
er
f
o
r
m
a
n
ce
m
etr
ics
p
o
p
u
lar
in
th
e
p
r
ev
io
u
s
s
t
u
d
ies
w
h
ich
ar
e
s
ec
u
r
it
y
(
4
4
.
4
4
%
)
;
s
ec
u
r
ity
a
n
d
s
p
ee
d
(
2
0
%);
an
d
s
ec
u
r
it
y
a
n
d
s
p
ac
e
(
1
4
.
4
4
%).
Fro
m
th
e
to
p
th
r
ee
p
er
f
o
r
m
an
ce
m
etr
ics,
s
ec
u
r
it
y
s
h
o
w
s
th
e
h
ig
h
es
t
p
er
f
o
r
m
a
n
ce
m
etr
ic
s
t
h
at
ar
e
p
o
p
u
lar
a
m
o
n
g
r
esear
c
h
er
s
wh
ich
ta
k
e
4
4
.
4
%
o
u
t
o
f
to
tal
r
esear
ch
.
O
n
t
h
e
o
t
h
e
r
h
an
d
,
s
p
ac
e
(
2
.
2
2
%)
,
s
p
ee
d
(
5
.
5
6
%),
s
p
ee
d
an
d
s
p
ac
e
(
5
.
5
6
%)
an
d
s
ec
u
r
it
y
,
s
p
ee
d
an
d
s
p
ac
e
(
7
.
7
8
%)
s
h
o
w
s
th
e
lo
w
est
p
er
ce
n
ta
g
e
a
m
o
n
g
th
e
to
tal
p
r
ev
io
u
s
s
t
u
d
ies.
T
h
i
s
is
b
ec
au
s
e,
to
u
p
g
r
ad
e
th
e
s
e
cu
r
it
y
,
t
h
e
k
e
y
s
ize
an
d
th
e
cip
h
er
tex
t
s
ize
w
ill
e
x
p
an
d
.
T
h
u
s
,
it
w
ill
af
f
ec
t
t
h
e
s
p
ac
e.
A
cc
o
r
d
in
g
to
[
1
0
0
]
i
f
th
e
s
p
ac
e
u
s
ed
is
m
o
r
e
w
h
er
e
th
e
b
lo
ck
s
ize
a
n
d
k
e
y
s
ize
ar
e
lar
g
er
,
it
w
i
l
l
af
f
ec
t
th
e
s
p
ee
d
o
f
t
h
e
al
g
o
r
ith
m
an
d
b
ec
o
m
e
s
lo
w
er
.
Fro
m
liter
atu
r
e
s
u
r
v
e
y
,
in
p
u
b
lic
k
e
y
cr
y
p
to
g
r
ap
h
y
,
th
e
s
e
ar
e
th
e
s
ig
n
i
f
ica
n
t
f
i
n
d
in
g
s
t
h
at
ar
e
m
ad
e
b
ased
o
n
th
e
s
ev
e
n
-
p
er
f
o
r
m
a
n
ce
m
etr
ics
.
Fi
g
u
r
e
3
s
h
o
w
s
t
h
e
p
r
ef
er
r
ed
p
er
f
o
r
m
a
n
ce
m
etr
i
cs
o
f
P
KC
s
ch
e
m
e
w
h
ic
h
ar
e
s
ec
u
r
it
y
,
th
e
n
f
o
llo
w
ed
b
y
s
ec
u
r
it
y
an
d
s
p
ee
d
; a
n
d
s
ec
u
r
it
y
a
n
d
s
p
ac
e.
Fig
u
r
e
3
.
P
er
f
o
r
m
a
n
ce
Me
tr
ics
Fo
cu
s
ed
b
y
P
r
ev
io
u
s
S
tu
d
ie
s
5.
CO
NCLU
SI
O
N
T
h
is
p
ap
er
s
tu
d
ied
a
n
o
v
er
v
ie
w
o
f
s
e
v
en
p
er
f
o
r
m
a
n
ce
-
m
e
tr
ics
f
o
r
p
u
b
lic
k
e
y
e
n
cr
y
p
tio
n
;
s
ec
u
r
it
y
;
s
p
ee
d
;
s
p
ac
e
;
s
ec
u
r
it
y
an
d
s
p
ee
d
;
s
ec
u
r
it
y
an
d
s
p
ac
e;
s
p
ee
d
an
d
s
p
ac
e;
an
d
s
ec
u
r
it
y
,
s
p
ee
d
an
d
s
p
ac
e
.
T
h
ey
h
av
e
t
h
eir
o
w
n
s
tr
e
n
g
t
h
to
s
u
p
p
o
r
t
th
e
ac
h
iev
i
n
g
o
f
cr
y
p
to
g
r
ap
h
y
g
o
al
s
u
c
h
as
s
ec
u
r
ed
[
2
3
]
[
2
4
]
[
2
5
]
[
2
6
]
[
2
7
]
,
f
ast
[
5
7
]
[
5
8
]
an
d
ef
f
ici
en
t
[
5
9
]
.
Mo
s
t
o
f
t
h
e
p
r
ev
io
u
s
r
esear
ch
er
s
f
o
cu
s
o
n
s
ec
u
r
it
y
[
3
3
-
53]
;
s
ec
u
r
it
y
an
d
s
p
ee
d
[
6
7
-
76]
;
an
d
s
ec
u
r
it
y
an
d
s
p
ace
[
8
0
-
88]
as
th
eir
s
ch
e
m
e
p
er
f
o
r
m
a
n
ce
m
etr
ic
s
.
Oth
er
t
h
an
t
h
at,
f
r
o
m
t
h
e
p
r
ev
io
u
s
s
ec
tio
n
s
,
it
s
h
o
w
s
t
h
at
m
o
s
t
o
f
t
h
e
r
esea
r
ch
w
er
e
d
o
n
e
ag
g
r
es
s
i
v
el
y
i
n
th
e
co
n
te
m
p
o
r
ar
y
y
ea
r
s
.
Ho
w
ev
er
,
l
ac
k
o
f
r
esea
r
ch
f
o
c
u
s
o
n
s
p
ac
e
alo
n
e
b
ec
au
s
e
o
f
h
i
g
h
s
ec
u
r
it
y
an
d
s
p
ee
d
w
ill
lead
o
f
u
s
in
g
m
o
r
e
s
p
ac
e.
T
h
e
f
in
d
i
n
g
s
clea
r
l
y
s
h
o
w
ed
t
h
at
t
h
e
s
ec
u
r
it
y
;
s
ec
u
r
it
y
an
d
s
p
ee
d
;
s
ec
u
r
it
y
an
d
s
p
ac
e
ar
e
th
e
k
e
y
p
er
f
o
r
m
a
n
ce
m
etr
ics
w
h
ich
a
d
d
r
ess
ed
b
y
t
h
e
r
esear
c
h
er
s
i
n
p
r
ev
io
u
s
s
tu
d
ies
.
Ov
er
all,
t
h
is
p
ap
er
co
n
tr
ib
u
te
s
s
u
g
g
e
s
tio
n
s
a
n
d
g
u
id
eli
n
es
f
o
r
f
u
tu
r
e
r
esear
c
h
er
s
i
n
P
KC
f
ield
to
ch
o
o
s
e
a
n
d
u
s
e
t
h
e
ap
p
r
o
p
r
iate
s
ch
e
m
e
s
b
ased
o
n
th
e
p
er
f
o
r
m
an
ce
m
et
r
ics th
at
h
ad
b
ee
n
co
n
ce
n
tr
ate
d
b
y
t
h
e
p
r
ev
io
u
s
r
esear
c
h
er
s
.
RE
F
E
R
E
NC
E
S
[1
]
W
.
Di
ff
ie,
W
.
Di
ff
ie,
a
n
d
M
.
E.
He
ll
m
a
n
,
“
Ne
w
Dire
c
ti
o
n
s
in
Cr
y
p
to
g
ra
p
h
y
,
”
IEE
E
T
ra
n
s.
In
f.
T
h
e
o
ry
,
v
o
l.
2
2
,
n
o
.
6
,
p
p
.
6
4
4
–
6
5
4
,
1
9
7
6
.
[2
]
A
.
M
u
sh
taq
u
e
,
H.
Dh
im
a
n
,
S
.
Hu
ss
a
in
,
a
n
d
S
.
M
a
h
e
sh
w
a
ri,
“
Ev
a
lu
a
ti
o
n
o
f
DES
,
T
DES
,
A
E
S
,
Blo
w
f
ish
a
n
d
Tw
o
f
ish
En
c
r
y
p
ti
o
n
A
lg
o
rit
h
m
:
Ba
se
d
o
n
S
p
a
c
e
Co
m
p
lex
it
y
,
”
v
o
l.
3
,
n
o
.
4
,
p
p
.
2
8
3
–
2
8
6
,
2
0
1
4
.
[3
]
A
.
V
M
e
ier,
“
T
h
e
El
G
a
m
a
l
Cr
y
p
to
sy
st
e
m
,
”
p
p
.
1
–
1
3
,
2
0
0
5
.
[4
]
L
.
W
a
n
g
,
H.
Zh
a
o
t,
a
n
d
G
.
Ba
il
,
“
c
o
st
-
Eff
icie
n
t
Im
p
le
m
e
n
tatio
n
Cr
y
p
to
g
ra
p
h
y
o
n
Em
b
e
d
d
e
d
S
y
ste
m
s,” 2
0
0
7
.
[5
]
M
.
S
.
Hw
a
n
g
,
C.
C.
Ch
a
n
g
,
a
n
d
K.
F
.
Hw
a
n
g
,
“
A
n
El
Ga
m
a
l
-
li
k
e
c
r
y
p
to
s
y
ste
m
f
o
r
e
n
c
ip
h
e
rin
g
l
a
rg
e
m
e
ss
a
g
e
s,
”
IEE
E
T
ra
n
s.
K
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o
wl
.
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t
a
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n
g
.
,
v
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l.
1
4
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o
.
2
,
p
p
.
4
4
5
–
4
4
6
,
2
0
0
2
.
[6
]
A
.
L
u
to
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“
A
Re
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ie
w
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re
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t
Cry
p
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ic E
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m
,
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v
o
l.
6
,
p
p
.
1
–
5
,
2
0
1
6
.
[7
]
V
.
Ka
p
o
o
r,
“
A
H
y
b
rid
Cr
y
p
to
g
ra
p
h
y
Tec
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iq
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e
to
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u
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rt
Cy
b
e
r
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e
c
u
rit
y
In
f
ra
stru
c
tu
re
,
”
v
o
l.
4
,
n
o
.
1
1
,
p
p
.
3
9
9
5
–
4
0
0
2
,
2
0
1
5
.
[8
]
J.
M
.
A
n
d
e
rso
n
,
“
W
h
y
we
n
e
e
d
a
n
e
w
d
e
f
in
it
io
n
o
f
in
f
o
rm
a
ti
o
n
se
c
u
rit
y
,
”
Co
mp
u
t.
S
e
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u
r.
,
v
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l.
2
2
,
n
o
.
4
,
p
p
.
3
0
8
–
3
1
3
,
2
0
0
3
.
[9
]
J.
Bu
c
h
m
a
n
n
,
F
.
G
ö
p
f
e
rt,
T
.
G
ü
n
e
y
su
,
T
.
Od
e
r,
a
n
d
T
.
P
ö
p
p
e
lm
a
n
n
,
“
Hig
h
-
P
e
rf
o
rm
a
n
c
e
a
n
d
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ig
h
tw
e
i
g
h
t
L
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-
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se
d
P
u
b
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ic
-
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y
En
c
r
y
p
ti
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n
,
”
P
ro
c
.
2
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d
ACM
I
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W
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Priva
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,
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T
P
T
S
’1
6
,
p
p
.
2
–
9
,
2
0
1
6
.
Evaluation Warning : The document was created with Spire.PDF for Python.
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.
1
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201
8
:
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3
390
[1
0
]
S.
-
H.
P
a
e
n
g
,
B.
E.
Ju
n
g
,
a
n
d
K.
-
C
.
Ha
,
“
A
L
a
tt
ice
Ba
s
e
d
P
u
b
li
c
Ke
y
Cr
y
p
to
s
y
ste
m
Us
in
g
P
o
ly
n
o
m
ial
Re
p
re
se
n
tatio
n
s,”
L
n
c
s
,
p
p
.
2
9
2
–
3
0
8
,
2
0
0
3
.
[1
1
]
O.
G
o
ld
re
ich
,
S
.
G
o
ld
w
a
ss
e
r,
a
n
d
S
.
Ha
lev
i,
“
P
u
b
li
c
-
Ke
y
Cr
y
p
to
s
y
ste
m
s
f
ro
m
L
a
tt
ic
e
Re
d
u
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ti
o
n
P
r
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b
lem
s,”
Ad
v
.
Cry
p
to
l.
-
{CRY
PT
O}
’9
7
,
1
7
th
An
n
u
.
In
t.
Cry
p
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Co
n
f.
S
t
.
Ba
r
b
a
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Ca
li
fo
rn
ia
,
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A
,
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g
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1
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9
7
,
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c
.
,
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1
2
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4
,
p
p
.
1
1
2
–
1
3
1
,
1
9
9
7
.
[1
2
]
R.
L
.
Riv
e
st,
A
.
S
h
a
m
ir,
a
n
d
L
.
A
d
le
m
a
n
,
“
{A
}
m
e
th
o
d
f
o
r
o
b
t
a
in
in
g
d
ig
it
a
l
sig
n
a
tu
re
s
a
n
d
p
u
b
li
c
k
e
y
c
r
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p
to
s
y
ste
m
s,”
Co
mm
u
n
.
ACM
,
v
o
l.
2
1
,
n
o
.
2
,
p
p
.
1
2
0
–
1
2
6
,
1
9
7
8
.
[1
3
]
S
.
G
o
ld
w
a
ss
e
r
a
n
d
S
.
M
ica
li
,
“
P
r
o
b
a
b
i
li
stic e
n
c
ry
p
ti
o
n
,
”
J
.
C
o
mp
u
t.
S
y
st.
S
c
i.
,
v
o
l.
2
8
,
n
o
.
2
,
p
p
.
2
7
0
–
2
9
9
,
1
9
8
4
.
[1
4
]
T
.
El
g
a
m
a
l,
“
A
P
u
b
l
ic
Ke
y
Cr
y
p
to
sy
ste
m
a
n
d
a
S
ig
n
a
tu
re
S
c
h
e
m
e
Ba
se
d
o
n
Disc
re
te
L
o
g
a
rit
h
m
s,
”
IEE
E
T
ra
n
s.
In
f.
T
h
e
o
ry
,
v
o
l
.
3
1
,
n
o
.
4
,
p
p
.
4
6
9
–
4
7
2
,
1
9
8
5
.
[1
5
]
J.
Ho
f
fste
in
,
D.
L
iem
a
n
,
J.
P
i
p
h
e
r
,
a
n
d
J
.
H.
S
il
v
e
rm
a
n
,
“
Ntru
:
a
P
u
b
li
c
Ke
y
Cr
y
p
to
sy
ste
m
,
”
p
p
.
1
–
17.
[1
6
]
P
.
Ng
u
y
e
n
,
“
Cr
y
p
tan
a
l
y
sis
o
f
th
e
G
o
ld
re
ich
–
G
o
ld
wa
ss
e
r
–
H
a
lev
i
Cr
y
p
to
sy
ste
m
f
ro
m
Cr
y
p
to
‟
9
7
,
”
p
p
.
2
8
8
–
3
0
4
,
1
9
9
9
.
[1
7
]
P
.
L
o
id
re
a
u
a
n
d
N.
S
e
n
d
rier,
“
W
e
a
k
k
e
y
s
in
th
e
M
c
El
iec
e
p
u
b
li
c
-
k
e
y
c
r
y
p
to
s
y
ste
m
,
”
IEE
E
T
ra
n
s.
In
f.
T
h
e
o
ry
,
v
o
l.
4
7
,
n
o
.
3
,
p
p
.
1
2
0
7
–
1
2
1
1
,
2
0
0
1
.
[1
8
]
L
.
Ha
rn
,
M
.
M
e
h
ta,
S
.
M
e
m
b
e
r,
a
n
d
W
.
Hs
in
,
“
I
n
teg
ra
ti
n
g
Diff
ie
–
He
ll
m
a
n
Ke
y
Ex
c
h
a
n
g
e
i
n
to
th
e
Dig
it
a
l
S
ig
n
a
tu
re
A
lg
o
rit
h
m
(
DSA
),
”
v
o
l.
8
,
n
o
.
3
,
p
p
.
1
9
8
–
2
0
0
,
2
0
0
4
.
[1
9
]
O.
Re
g
e
v
,
“
N
e
w
Latti
c
e
Ba
se
d
Cry
p
to
g
ra
p
h
ic Co
n
stru
c
ti
o
n
s
,
”
p
p
.
1
–
4
3
,
2
0
0
4
.
[2
0
]
D.
Bo
n
e
h
a
n
d
G
.
Di
Cre
sc
e
n
z
o
,
“
P
u
b
l
ic k
e
y
e
n
c
r
y
p
ti
o
n
w
it
h
k
e
y
w
o
rd
se
a
rc
h
,
”
A
d
v
.
Cry
p
to
lo
g
y
-
…
,
2
0
0
4
.
[2
1
]
R.
A
lfaris,
M
.
R.
S
a
i
d
,
M
.
Ot
h
m
a
n
,
a
n
d
F
.
Ism
a
il
,
“
M
o
d
if
ied
Dif
f
ie
-
H
e
ll
m
a
n
P
r
o
to
c
o
l
By
Ex
ten
d
T
h
e
T
h
e
o
r
y
o
f
T
h
e
Co
n
g
ru
e
n
c
e
,
”
v
o
l.
2
,
n
o
.
1
1
,
p
p
.
8
4
2
–
8
4
8
,
2
0
0
8
.
[2
2
]
S
.
F
l
o
n
ta
a
n
d
L
.
M
icle
a
,
“
A
n
e
x
t
e
n
sio
n
o
f
th
e
El
G
a
m
a
l
e
n
c
r
y
p
ti
o
n
a
lg
o
rit
h
m
,
”
2
0
0
8
IEE
E
In
t
.
Co
n
f.
A
u
t
o
m.
Qu
a
l
.
T
e
stin
g
,
Ro
b
o
t
.
AQT
R
2
0
0
8
-
T
H
ET
A
1
6
t
h
Ed
.
-
Pr
o
c
.
,
v
o
l
.
3
,
p
p
.
4
4
4
–
4
4
6
,
2
0
0
8
.
[2
3
]
A
.
Kh
a
li
q
u
e
,
“
Im
p
le
m
e
n
tatio
n
o
f
El
li
p
ti
c
C
u
rv
e
Dig
it
a
l
S
ig
n
a
tu
re
A
l
g
o
rit
h
m
,
”
v
o
l.
2
,
n
o
.
2
,
p
p
.
2
1
–
2
7
,
2
0
1
0
.
[2
4
]
S
.
G
o
ld
w
a
ss
e
r,
Y.
Ka
lai,
C.
P
e
ik
e
rt,
a
n
d
V
.
V
a
ik
u
n
tan
a
t
h
a
n
,
“
Ro
b
u
stn
e
ss
o
f
th
e
L
e
a
rn
in
g
w
it
h
Err
o
rs
A
s
su
m
p
ti
o
n
,
”
2
0
1
0
.
[2
5
]
M
.
J.
Ka
k
ish
,
“
S
ECURIT
Y
IM
P
ROV
M
ENT
S
T
O
T
HE
DIFF
IE
-
HELL
M
AN
S
CHEM
ES
,
”
v
o
l.
8
,
n
o
.
J
u
ly
,
p
p
.
7
9
–
8
5
,
2
0
1
1
.
[2
6
]
A
.
S
.
A
p
p
ro
a
c
h
,
“
M
o
d
if
ied
RS
A
A
l
g
o
rit
h
m
,
”
p
p
.
5
5
2
–
5
5
5
,
2
0
1
1
.
[2
7
]
R.
T
h
a
n
u
ja
a
n
d
D.
K.
S
,
“
A
NEW
A
P
P
ROA
CH
T
O
DIFF
IE
-
HELL
M
AN
KEY
EX
CHA
N
G
E
ALG
ORI
T
HM,
”
v
o
l.
1
,
n
o
.
3
,
p
p
.
5
3
4
–
5
3
5
.
[2
8
]
P
.
S
h
a
rm
a
,
S
.
S
h
a
rm
a
,
a
n
d
R.
S
.
Dh
a
k
a
r,
“
M
o
d
if
ied
El
g
a
m
a
l
Cr
y
p
to
s
y
ste
m
A
l
g
o
rit
h
m
(M
ECA
),
”
2
0
1
1
2
n
d
I
n
t
.
Co
n
f.
Co
mp
u
t.
Co
mm
u
n
.
T
e
c
h
n
o
l
.
ICCCT
-
2
0
1
1
,
p
p
.
4
3
9
–
4
4
3
,
2
0
1
1
.
[2
9
]
M
.
Yo
sh
in
o
a
n
d
No
b
o
r
u
,
“
Im
p
ro
v
in
g
GG
H Cr
y
p
to
sy
ste
m
f
o
r
L
a
r
g
e
Err
o
r
V
e
c
to
r,
”
Isit
a
2
0
1
2
,
p
p
.
4
1
6
–
4
2
0
,
2
0
1
2
.
[3
0
]
G
.
M
o
ise
,
“
On
th
e
a
tt
a
c
k
s
o
v
e
r
th
e
e
ll
ip
ti
c
c
u
rv
e
-
b
a
se
d
c
r
y
p
to
s
y
st
e
m
s,”
Pro
c
.
-
3
rd
In
t.
Co
n
f.
Eme
rg
.
In
tell.
Da
t
a
W
e
b
T
e
c
h
n
o
l
.
EIDW
T
2
0
1
2
,
p
p
.
2
4
4
–
2
4
9
,
2
0
1
2
.
[3
1
]
P
.
S
e
h
g
a
l,
N.
A
g
a
r
w
a
l,
S
.
Du
tt
a
,
a
n
d
P
.
M
.
D.
R.
V
in
c
e
n
t,
“
M
o
d
if
ica
ti
o
n
o
f
Di
ff
ie
-
He
ll
m
a
n
A
l
g
o
rit
h
m
to
P
ro
v
id
e
M
o
re
S
e
c
u
re
Ke
y
Ex
c
h
a
n
g
e
,
”
v
o
l.
5
,
n
o
.
3
,
p
p
.
2
4
9
8
–
2
5
0
1
,
2
0
1
3
.
[3
2
]
M
.
P
.
Re
w
a
g
a
d
a
n
d
M
.
Y.
P
a
w
a
r,
“
Us
e
o
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l
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n
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p
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3
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–
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3
.
[3
3
]
A
.
Ka
u
sh
ik
,
“
Ex
ten
d
e
d
Dif
f
ie
-
H
e
ll
m
a
n
A
lg
o
rit
h
m
f
o
r
Ke
y
Ex
c
h
a
n
g
e
a
n
d
M
a
n
a
g
e
m
e
n
t,
”
v
o
l.
3
,
n
o
.
3
,
p
p
.
6
7
–
7
0
,
2
0
1
3
.
[3
4
]
G
.
M
a
tee
s
c
u
a
n
d
M
.
V
lad
e
sc
u
,
“
En
terp
rise
s : co
m
b
in
i
n
g
d
if
f
e
re
n
t
Cr
y
p
to
g
ra
p
h
y
tec
h
n
iq
u
e
s,”
p
p
.
6
5
9
–
6
6
2
,
2
0
1
3
.
[3
5
]
E.
F
u
ji
sa
k
i
a
n
d
T
.
Ok
a
m
o
to
,
“
S
e
c
u
re
in
teg
ra
ti
o
n
o
f
a
s
y
m
m
e
tri
c
a
n
d
sy
m
m
e
tri
c
e
n
c
r
y
p
ti
o
n
sc
h
e
m
e
s,”
J
.
Cry
p
to
l.
,
v
o
l.
2
6
,
n
o
.
1
,
p
p
.
8
0
–
1
0
1
,
2
0
1
3
.
[3
6
]
H.
A
rsh
a
d
a
n
d
M
.
Nik
o
o
g
h
a
d
a
m
,
“
T
h
re
e
-
F
a
c
to
r
A
n
o
n
y
m
o
u
s
A
u
th
e
n
ti
c
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ti
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n
a
n
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y
Ag
re
e
m
e
n
t
S
c
h
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m
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f
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le
c
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re
M
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d
icin
e
In
f
o
rm
a
ti
o
n
S
y
ste
m
s,” 2
0
1
4
.
[3
7
]
Z.
T
a
n
,
“
RES
EA
RCH
A
R
T
IC
L
E
A
U
se
r
A
n
o
n
y
m
it
y
P
re
se
rv
in
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Th
re
e
-
F
a
c
to
r
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u
th
e
n
ti
c
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ti
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n
S
c
h
e
m
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re
M
e
d
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e
I
n
f
o
rm
a
ti
o
n
S
y
ste
m
s,”
2
0
1
4
.
[3
8
]
M
.
S
h
a
n
k
a
r,
“
H YB
RID C
RY
P
T
OG
R
A
P
HIC T
ECHNIQ
UE
U S
ING
RS
A
,
”
v
o
l.
6
,
n
o
.
6
,
p
p
.
3
9
–
4
8
,
2
0
1
4
.
[3
9
]
S
.
De
sh
m
u
k
h
,
“
H
y
b
rid
c
ry
p
to
g
ra
p
h
y
tec
h
n
iq
u
e
u
sin
g
m
o
d
if
ied
,
”
v
o
l.
5
,
n
o
.
6
,
p
p
.
7
3
0
2
–
7
3
0
4
,
2
0
1
4
.
[4
0
]
M
.
T
h
a
n
g
a
v
e
l,
P
.
V
a
ra
lak
sh
m
i,
M
.
M
u
rra
li
,
a
n
d
K.
Nit
h
y
a
,
“
An
E
n
h
a
n
c
e
d
a
n
d
S
e
c
u
re
d
R
S
A
Ke
y
G
e
n
e
ra
ti
o
n
S
c
h
e
m
e
(ES
RK
G
S
),
”
J
.
In
f.
S
e
c
u
r.
Ap
p
l.
,
v
o
l.
2
0
,
p
p
.
3
–
1
0
,
2
0
1
5
.
[4
1
]
Y.
L
u
,
L
.
L
i,
H.
P
e
n
g
,
a
n
d
Y
.
Ya
n
g
,
“
A
n
En
h
a
n
c
e
d
Bio
m
e
tri
c
-
Ba
s
e
d
A
u
th
e
n
ti
c
a
ti
o
n
S
c
h
e
m
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f
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r
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e
l
e
c
a
re
M
e
d
icin
e
In
f
o
rm
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ti
o
n
S
y
ste
m
s Us
in
g
El
li
p
t
ic Cu
rv
e
Cry
p
to
s
y
s
te
m
,
”
J
.
M
e
d
.
S
y
st.
,
v
o
l.
3
9
,
n
o
.
3
,
p
.
3
2
,
2
0
1
5
.
[4
2
]
S
.
A
.
Ch
a
u
d
h
ry
,
K.
M
a
h
m
o
o
d
,
H.
Na
q
v
i,
a
n
d
M
.
K.
Kh
a
n
,
“
A
n
I
m
p
ro
v
e
d
a
n
d
S
e
c
u
re
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m
e
tri
c
A
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th
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c
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ti
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n
S
c
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m
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re
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e
In
f
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ti
o
n
S
y
ste
m
s
Ba
s
e
d
o
n
El
li
p
ti
c
Cu
rv
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Cry
p
to
g
ra
p
h
y
,
”
J
.
M
e
d
.
S
y
st.
,
v
o
l.
3
9
,
n
o
.
1
1
,
2
0
1
5
.
[4
3
]
R.
G
h
o
sh
,
“
A
N
EF
F
ICIENT
A
N
D
ROBU
S
T
M
OD
IF
IED
RS
A
BA
S
ED
S
ECURIT
Y,”
v
o
l.
6
,
n
o
.
2
,
p
p
.
1
5
–
2
2
,
2
0
1
6
.
[4
4
]
D.
B.
Kh
a
irn
a
r
a
n
d
P
.
S
.
Ka
d
a
m
,
“
S
e
c
u
re
RS
A
:
P
a
ir
W
ise
Ke
y
Di
strib
u
ti
o
n
u
sin
g
M
o
d
if
ied
RS
A
Alg
o
rit
h
m
,
”
v
o
l.
6
,
n
o
.
4
,
p
p
.
3
8
3
–
3
8
7
,
2
0
1
6
.
[4
5
]
K.
Dh
e
iaa
,
M
.
A
ls
a
b
ti
,
a
n
d
H.
R.
Ha
sh
i
m
,
“
A
N
e
w
A
p
p
ro
a
c
h
f
o
r
I
m
a
g
e
En
c
r
y
p
ti
o
n
in
t
h
e
M
o
d
if
ied
RS
A
Cr
y
p
to
sy
ste
m
Us
in
g
M
ATLA
B,
”
v
o
l.
1
2
,
n
o
.
4
,
p
p
.
3
6
3
1
–
3
6
4
0
,
2
0
1
6
.
Evaluation Warning : The document was created with Spire.PDF for Python.
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391
[4
6
]
H.
R.
Ha
sh
i
m
,
“
A
N
e
w
M
o
d
if
ica
ti
o
n
o
f
RS
A
Cr
y
p
to
s
y
ste
m
Ba
s
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n
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h
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m
b
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h
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P
riv
a
te
Ke
y
s,”
p
p
.
2
7
0
–
2
7
9
.
[4
7
]
Y.
W
a
n
g
,
W
.
Ba
o
,
Y.
Z
h
a
o
,
H.
Xio
n
g
,
a
n
d
Z.
Qi
n
,
“
A
n
El
G
a
m
a
l
En
c
ry
p
ti
o
n
w
it
h
F
u
z
z
y
Ke
y
wo
rd
S
e
a
rc
h
o
n
C
lo
u
d
En
v
iro
n
m
e
n
t,
”
v
o
l.
1
8
,
n
o
.
3
,
p
p
.
4
8
1
–
4
8
6
,
2
0
1
6
.
[4
8
]
I.
Co
n
f
e
re
n
c
e
a
n
d
C.
T
e
c
h
n
o
l
o
g
ies
,
“
S
e
c
u
re
M
u
lt
i
S
e
rv
e
r
A
u
t
h
e
n
ti
c
a
ti
o
n
S
y
ste
m
u
sin
g
El
li
p
ti
c
Cu
rv
e
Dig
it
a
l
S
ig
n
a
tu
re
,
”
p
p
.
0
–
3
,
2
0
1
6
.
[4
9
]
Y.
S
a
z
a
k
i,
“
T
h
e
De
v
e
lo
p
m
e
n
t
An
d
r
o
id
-
Ba
se
d
S
M
S
S
e
c
u
rit
y
S
o
f
tw
a
r
e
Us
in
g
ECDS
A
w
it
h
Bo
o
lea
n
P
e
rm
u
tatio
n
,
”
p
p
.
2
6
–
3
0
,
2
0
1
6
.
[5
0
]
D.
Ja
g
a
d
is
w
a
r
y
a
n
d
D.
S
a
ra
sw
a
d
y
,
“
Esti
m
a
ti
o
n
o
f
M
o
d
if
ied
RS
A
Cr
y
p
to
s
y
ste
m
w
it
h
H
y
p
e
r
I
m
a
g
e
En
c
r
y
p
ti
o
n
A
l
g
o
rit
h
m
,
”
v
o
l.
1
0
,
n
o
.
F
e
b
ru
a
ry
,
p
p
.
1
–
5
,
2
0
1
7
.
[5
1
]
K.
Zh
a
n
g
,
M
.
T
o
m
li
n
sin
,
a
n
d
M
.
Z.
A
h
m
e
d
,
“
A
M
o
d
if
ied
M
c
El
iec
e
P
u
b
li
c
Ke
y
En
c
r
y
p
ti
o
n
S
y
ste
m
w
it
h
a
Hig
h
e
r
S
e
c
u
rit
y
L
e
v
e
l,
”
p
p
.
9
9
1
–
9
9
6
,
2
0
1
3
.
[5
2
]
L
.
V
a
n
T
h
a
i,
“
M
c
El
iec
e
c
r
y
p
to
sy
ste
m
b
a
se
d
id
e
n
ti
f
ica
ti
o
n
a
n
d
si
g
n
a
tu
re
sc
h
e
m
e
u
sin
g
c
h
a
in
e
d
B
CH
c
o
d
e
s,”
p
p
.
122
–
1
2
7
,
2
0
1
5
.
[5
3
]
E.
Kro
u
k
a
n
d
A
.
Ov
c
h
in
n
ik
o
v
,
“
A
b
o
u
t
On
e
M
o
d
if
ica
ti
o
n
o
f
M
c
El
iec
e
Cry
p
to
s
y
ste
m
b
a
s
e
d
o
n
P
lo
tk
i
n
Co
n
stru
c
ti
o
n
,
”
p
p
.
7
–
1
0
,
2
0
1
6
.
[5
4
]
S
.
Bo
n
i,
“
Im
p
ro
v
in
g
th
e
Dif
f
ie
-
H
e
ll
m
a
n
Ke
y
Ex
c
h
a
n
g
e
A
l
g
o
rit
h
m
b
y
P
r
o
p
o
sin
g
t
h
e
M
u
lt
i
p
li
c
a
ti
v
e
Ke
y
Ex
c
h
a
n
g
e
A
l
g
o
rit
h
m
,
”
v
o
l.
1
3
0
,
n
o
.
1
5
,
p
p
.
7
–
1
0
,
1
9
7
6
.
[5
5
]
I.
In
tr
o
d
u
c
ti
o
n
,
“
F
a
st A
lg
o
rit
h
m
s f
o
r,
”
v
o
l.
2
8
,
n
o
.
1
,
p
p
.
2
1
0
–
2
3
6
,
1
9
8
5
.
[5
6
]
“
AN
EF
F
ICIENT
M
OD
IF
IED
EL
L
IP
T
IC
CURV
E
DIG
I
TAL
S
I
G
N
AT
URE
ALGO
RITHM
T
il
a
h
u
n
Kiro
s
De
p
a
rtme
n
t
o
f
Co
m
p
u
ter
S
c
ien
c
e
a
n
d
En
g
in
e
e
rin
g
M
e
k
e
ll
e
In
stit
u
te
o
f
T
e
c
h
n
o
lo
g
y
a
n
d
Ku
m
u
d
h
a
Ra
im
o
n
d
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l
a
n
d
Co
m
p
u
ter E
n
g
in
e
e
rin
g
,
”
v
o
l.
2
6
,
2
0
0
9
.
[5
7
]
D.
S
teh
lé
a
n
d
R.
S
tein
f
e
ld
,
“
F
a
ste
r
F
u
ll
y
Ho
m
o
m
o
rp
h
ic E
n
c
ry
p
ti
o
n
,
”
2
0
1
0
.
[5
8
]
H.
W
a
n
g
,
H.
Zh
a
n
g
,
a
n
d
S
.
T
a
n
g
,
“
Ke
y
re
c
o
v
e
r
y
o
n
se
v
e
ra
l
m
a
t
rix
p
u
b
li
c
-
k
e
y
e
n
c
r
y
p
ti
o
n
sc
h
e
m
e
s,”
v
o
l.
1
0
,
p
p
.
152
–
1
5
5
,
2
0
1
6
.
[5
9
]
V
.
L
y
u
b
a
sh
e
v
s
k
y
,
C.
P
e
ik
e
rt,
a
n
d
O.
Re
g
e
v
,
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On
Id
e
a
l
L
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tt
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c
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e
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rn
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it
h
Err
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rs Ov
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.
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5
8
4
8
,
p
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.
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–
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4
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2
0
1
3
.
[6
0
]
R.
J.
M
c
El
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e
,
“
A
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li
c
-
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y
Cr
y
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4
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6
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7
8
.
[6
1
]
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.
Blu
m
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n
d
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.
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o
ld
w
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ss
e
r,
“
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n
e
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ro
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a
b
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u
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li
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v
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.
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p
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8
5
.
[6
2
]
E.
Ra
m
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r
a
j,
S
.
Ka
rth
ik
e
y
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n
,
a
n
d
M
.
He
m
a
lath
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,
“
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De
s
i
g
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f
S
e
c
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rit
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ro
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(
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d
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l
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n
d
R
S
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),
”
p
p
.
7
8
–
8
6
.
[6
3
]
Q.
T
a
n
g
a
n
d
L
.
Ch
e
n
,
“
P
u
b
li
c
-
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e
c
t.
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mp
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t.
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in
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lu
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n
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tes
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f.
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n
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e
c
t.
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tes
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ti
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s)
,
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l
.
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1
L
NCS,
p
p
.
1
6
3
–
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8
,
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0
1
0
.
[6
4
]
B.
P
.
U.
Iv
y
,
P
.
M
a
n
d
iw
a
,
a
n
d
M
.
Ku
m
a
r,
“
A
m
o
d
if
ied
RS
A
c
r
y
p
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o
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st
e
m
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se
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„
n
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rim
e
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m
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e
rs,”
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l.
1
,
n
o
.
2
,
p
p
.
6
3
–
6
6
,
2
0
1
3
.
[6
5
]
A
.
H.
A
l
-
Ha
m
a
m
i
a
n
d
I.
A
.
A
ld
a
rise
h
,
“
En
h
a
n
c
e
d
m
e
th
o
d
f
o
r
R
S
A
c
r
y
p
to
s
y
ste
m
a
l
g
o
rit
h
m
,
”
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c
.
-
2
0
1
2
In
t.
Co
n
f.
Ad
v
.
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mp
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t.
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c
i.
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l.
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e
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AT
2
0
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2
,
p
p
.
4
0
2
–
4
0
8
,
2
0
1
3
.
[6
6
]
S
.
M
a
th
u
r,
“
A
M
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IF
IED
RS
A
A
P
P
ROA
CHFOR
ENCRYP
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IN
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ND
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ES
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K
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R
ALGO
RITHM
,
”
v
o
l.
1
,
2
0
1
6
.
[6
7
]
P
.
Ku
p
p
u
sw
a
m
y
,
“
ENRICHM
ENT
OF
S
ECURIT
Y
T
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CRYP
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P
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UBL
IC
KEY
ALG
ORI
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ON
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O
CK,”
v
o
l.
2
,
n
o
.
3
,
p
p
.
3
4
7
–
3
5
5
,
2
0
1
1
.
[6
8
]
A
.
M
.
S
a
g
h
e
e
r,
“
El
li
p
ti
c
c
u
rv
e
s
c
r
y
p
to
g
ra
p
h
ic
tec
h
n
i
q
u
e
s,”
6
th
In
t.
Co
n
f.
S
ig
n
a
l
Pro
c
e
ss
.
Co
mm
u
n
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S
y
st.
ICS
PCS
2
0
1
2
-
Pro
c
.
,
2
0
1
2
.
[6
9
]
P
.
Ku
p
p
u
sw
a
m
y
a
n
d
S
.
Q.
Y.
A
l
-
Kh
a
li
d
i,
“
Hy
b
rid
En
c
ry
p
ti
o
n
/De
c
r
y
p
ti
o
n
T
e
c
h
n
iq
u
e
Us
in
g
Ne
w
P
u
b
l
ic
Ke
y
a
n
d
S
y
m
m
e
tri
c
Ke
y
A
lg
o
rit
h
m
,
”
M
IS
Rev
.
,
v
o
l.
1
9
,
n
o
.
2
,
p
p
.
1
–
1
3
,
2
0
1
4
.
[7
0
]
C.
P
e
ik
e
rt,
“
L
a
tt
ice
Cr
y
p
to
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ra
p
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f
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th
e
In
ter
n
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t,
”
p
p
.
1
–
2
5
,
2
0
1
4
.
[7
1
]
S
.
A
.
Ja
ju
a
n
d
S
.
S
.
Ch
o
w
h
a
n
,
“
A
M
o
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if
ied
RS
A
a
l
g
o
rit
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m
to
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h
a
n
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u
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n
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tu
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2
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1
5
In
t
.
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n
f.
W
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rk
.
Co
mp
u
t.
Co
mm
u
n
.
I
EM
CON 2
0
1
5
,
2
0
1
5
.
[7
2
]
S
.
K.
Bh
o
w
m
ic
k
,
S
.
K.
Da
s,
a
n
d
T
.
Ch
a
k
r
a
b
o
rty
,
“
Av
a
il
a
b
le
On
li
n
e
th
ro
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g
h
IS
S
N :
0
9
7
5
-
7
6
6
X
C
OD
EN :
IJP
T
F
I
Re
se
a
rc
h
A
rti
c
le,” v
o
l.
8
,
n
o
.
4
,
p
p
.
2
6
5
7
8
–
2
6
5
8
3
,
2
0
1
6
.
[7
3
]
M
.
A
.
Ra
ji
,
F
.
Am
iri
,
a
n
d
M
.
A
h
m
a
d
ian
,
“
A
Ne
w
s
e
c
u
re
e
m
a
il
sc
h
e
m
e
Us
in
g
Di
g
it
a
l
S
ig
n
a
tu
re
w
i
th
S
/
M
IM
E
,
”
v
o
l.
4
,
n
o
.
3
,
p
p
.
5
6
–
6
2
,
2
0
1
6
.
[7
4
]
M
.
H.
A
z
a
i
m
,
D.
W
.
S
u
d
ih
a
rto
,
a
n
d
E.
M
.
Ja
d
ied
,
“
De
sig
n
a
n
d
I
m
p
le
m
e
n
tatio
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o
f
En
c
ry
p
ted
S
M
S
o
n
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n
d
ro
i
d
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m
a
rtp
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o
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m
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in
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g
ECDS
A
-
ECDH an
d
A
ES
,
”
p
p
.
1
8
–
2
3
,
2
0
1
6
.
[7
5
]
P
.
S
.
P
riy
a
n
k
a
,
“
ENH
A
NCED H
YBRID
CRYP
T
OG
R
A
P
HY
,
”
v
o
l.
1
9
,
n
o
.
2
,
p
p
.
1
0
8
–
1
1
3
,
2
0
1
6
.
[7
6
]
A
.
A
.
P
a
ti
l,
“
Hy
b
rid
Cry
p
to
g
ra
p
h
y
M
e
c
h
a
n
ism
f
o
r
S
e
c
u
rin
g
,
”
p
p
.
1
–
4
,
2
0
1
6
.
[7
7
]
N.
G
u
ra
,
A
.
P
a
tel,
A
.
W
a
n
d
e
r,
a
n
d
H.
E
b
e
rle,
“
Co
m
p
a
rin
g
El
li
p
ti
c
Cu
rv
e
Cr
y
p
to
g
ra
p
h
y
a
n
d
RS
A
o
n
8
-
b
it
C
P
Us
.
”
[7
8
]
D.
J.
Be
rn
ste
in
,
T
.
L
a
n
g
e
,
a
n
d
C.
P
e
ters
,
“
A
tt
a
c
k
in
g
a
n
d
d
e
f
e
n
d
in
g
t
h
e
M
c
El
iec
e
c
ry
p
to
s
y
ste
m
,
”
L
e
c
t.
No
tes
Co
mp
u
t
.
S
c
i.
(
in
c
lu
d
i
n
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u
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se
r.
L
e
c
t.
No
tes
Arti
f.
In
tell.
L
e
c
t.
No
tes
Bi
o
in
fo
rm
a
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c
s)
,
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l.
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p
.
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–
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.
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9
]
O.
Re
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e
v
,
“
On
L
a
tt
ice
s
,
Lea
rn
in
g
w
it
h
Err
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rs
,
Ra
n
d
o
m
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in
e
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r
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o
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e
s
,
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n
d
Cry
p
to
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ra
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h
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,
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n
o
.
1
5
8
4
8
,
p
p
.
1
–
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7
,
2
0
0
9
.
[8
0
]
M
.
V
a
n
Dijk
a
n
d
C.
G
e
n
try
,
“
F
u
ll
y
Ho
m
o
m
o
rp
h
ic E
n
c
ry
p
ti
o
n
o
v
e
r
th
e
In
teg
e
rs,” p
p
.
1
–
2
8
,
2
0
1
0
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
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J
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&
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p
Sci,
Vo
l
.
1
2
,
No
.
1
,
Octo
b
er
201
8
:
3
8
6
–
3
9
3
392
[8
1
]
A
.
M
a
n
d
a
l,
D.
Na
c
c
a
c
h
e
,
a
n
d
M
.
T
ib
o
u
c
h
i,
“
F
u
ll
y
Ho
m
o
m
o
rp
h
ic
En
c
ry
p
ti
o
n
o
v
e
r
th
e
I
n
te
g
e
rs
w
it
h
S
h
o
rter
P
u
b
li
c
Ke
y
s,” p
p
.
1
–
2
4
,
2
0
1
1
.
[8
2
]
Z.
Bra
k
e
rsk
i,
“
E
f
f
i
c
ien
t
F
u
ll
y
Ho
m
o
m
o
rp
h
ic E
n
c
ry
p
ti
o
n
f
ro
m
(
S
tan
d
a
rd
)
L
W
E.
”
[8
3
]
Q.
Zh
a
n
g
,
Z.
L
i,
a
n
d
C.
S
o
n
g
,
“
T
h
e
I
m
p
ro
v
e
m
e
n
t
o
f
d
ig
it
a
l
sig
n
a
tu
re
a
lg
o
rit
h
m
b
a
se
d
o
n
e
ll
ip
ti
c
c
u
rv
e
c
r
y
p
to
g
ra
p
h
y
,
”
201
1
2
n
d
I
n
t.
C
o
n
f.
Arti
f.
In
tell
.
M
a
n
a
g
.
S
c
i.
El
e
c
tro
n
.
C
o
mm
e
r.
,
p
p
.
1
6
8
9
–
1
6
9
1
,
2
0
1
1
.
[8
4
]
R.
L
in
d
n
e
r
a
n
d
C.
P
e
ik
e
rt,
“
Be
tt
e
r
Ke
y
S
ize
s (
a
n
d
A
tt
a
c
k
s )
f
o
r
LW
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-
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se
d
En
c
r
y
p
ti
o
n
,
”
p
p
.
3
1
9
–
3
2
0
,
2
0
1
1
.
[8
5
]
R.
Ho
o
s
h
m
a
n
d
,
M
.
K.
S
h
o
o
s
h
t
a
ri,
T
.
Eg
h
li
d
o
s,
a
n
d
M
.
R.
A
re
f
,
“
Re
d
u
c
in
g
th
e
Ke
y
L
e
n
g
th
o
f
M
c
El
iec
e
Cr
y
p
to
sy
ste
m
Us
in
g
P
o
lar Co
d
e
s,
”
n
o
.
9
2
,
p
p
.
1
0
4
–
1
0
8
,
2
0
1
4
.
[8
6
]
R.
J.
Hw
a
n
g
,
F
.
F
.
S
u
,
Y.
S
.
Ye
h
,
a
n
d
C
.
Y.
C
h
e
n
,
“
A
n
e
ff
icie
n
t
d
e
c
r
y
p
ti
o
n
m
e
th
o
d
f
o
r
RS
A
c
r
y
p
to
sy
ste
m
,
”
Pro
c
.
-
In
t.
C
o
n
f
.
Ad
v
.
In
f
.
Ne
tw.
A
p
p
l.
AI
NA
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5
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M
.
Ba
ld
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M
.
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.
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Ro
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c
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[8
8
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R.
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p
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(
HES
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[8
9
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Jo
sh
Be
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p
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.
1
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9
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[9
0
]
R.
Ra
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B
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Ý.
Ü.
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n
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.
1
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1
]
R.
Dh
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a
t,
“
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[9
2
]
I.
S
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p
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m
,
“
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p
p
.
3
4
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–
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8
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1
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[9
3
]
J.
G
.
F
il
h
o
,
G
.
P
.
S
il
v
a
,
D.
C.
C.
Im
,
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M
ice
li
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.
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.
Im
,
“
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lg
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m
s,”
1
9
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n
t.
C
o
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f.
In
f
.
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sio
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p
p
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1
9
9
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–
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8
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2
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1
6
.
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4
]
V
.
M
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r,
“
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e
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in
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ra
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v
.
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8
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[9
5
]
J.
Ho
ff
ste
in
,
J.
P
ip
h
e
r,
a
n
d
J.
H.
S
il
v
e
r
m
a
n
,
“
N
T
RU:
A
rin
g
-
b
a
se
d
p
u
b
li
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k
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y
c
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p
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ste
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mb
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p
p
.
2
6
7
–
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8
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1
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9
8
.
[9
6
]
T
.
P
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.
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.
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a
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A
.
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a
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“
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th
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M
c
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Cry
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m
.
”
[9
7
]
W
.
L
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o
a
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d
J.
T
a
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,
“
P
UBL
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ITH
KEY
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S
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ON
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,
”
p
p
.
6
–
8.
[9
8
]
R.
Rizk
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d
Y.
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lk
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,
“
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o
-
p
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so
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tw
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rk
s,”
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.
El
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c
tr.
S
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st
.
In
f.
T
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c
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,
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.
2
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3
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p
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9
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–
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,
2
0
1
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.
[9
9
]
V
.
Ka
p
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,
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,
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v
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1
4
1
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n
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.
1
1
,
p
p
.
2
5
–
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0
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2
0
1
6
.
[1
0
0
]
A
.
A
l
Ta
m
i
m
i,
“
P
e
rf
o
rm
a
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c
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a
n
a
l
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sis o
f
d
a
ta en
c
r
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p
ti
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lg
o
rit
h
m
s
,
”
Retrie
v
e
d
Oc
t.
,
v
o
l.
1
,
p
p
.
3
9
9
–
4
0
3
,
2
0
0
8
.
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