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c
h
as
to
en
s
u
r
e
th
e
s
ec
u
r
it
y
o
f
t
h
e
s
c
h
e
m
e
a
s
w
ell
as
to
s
a
v
e
s
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ac
e
a
n
d
ti
m
e
d
u
r
in
g
d
ata
co
m
m
u
n
icatio
n
.
Fig
u
r
e
1
s
h
o
w
s
t
h
e
class
i
f
icatio
n
o
f
P
KC
al
g
o
r
ith
m
s
w
i
th
t
h
e
r
elev
a
n
t sc
h
e
m
es
.
Fig
u
r
e
1
.
P
u
b
lic
Key
C
r
y
p
to
g
r
ap
h
y
al
g
o
r
ith
m
s
cla
s
s
i
f
icatio
n
Dis
cr
ete
L
o
g
ar
it
h
m
p
r
o
b
lem
i
s
a
m
at
h
e
m
atica
l
p
r
o
b
le
m
t
h
a
t
o
cc
u
r
s
i
n
m
a
n
y
s
ett
in
g
s
a
n
d
ex
p
lain
s
th
at
it
i
s
to
u
g
h
to
co
m
p
u
te
th
e
ex
p
o
n
en
t
g
i
v
e
n
a
p
o
w
er
i
n
a
k
n
o
w
n
m
u
l
tip
licati
v
e
g
r
o
u
p
[
3
]
.
T
h
e
s
ch
e
m
e
s
d
ev
elo
p
ed
u
n
d
er
Dis
cr
ete
L
o
g
ar
ith
m
al
g
o
r
ith
m
ar
e
Dif
f
ie
-
Hell
m
a
n
a
n
d
E
lGa
m
al
cr
y
p
to
s
y
s
te
m
.
Di
f
f
ie
-
Hell
m
a
n
w
a
s
i
n
v
e
n
ted
i
n
1
9
7
6
th
at
b
r
o
u
g
h
t
n
e
w
d
ir
ec
tio
n
o
f
cr
y
p
to
g
r
ap
h
y
t
h
at
i
n
tr
o
d
u
ce
d
k
e
y
e
x
ch
a
n
g
e
p
r
o
to
co
l
w
h
ich
b
ased
o
n
d
is
cr
ete
lo
g
ar
ith
m
p
r
o
b
le
m
[
6
]
.
E
v
en
t
h
e
s
c
h
e
m
e
is
s
ec
u
r
e
a
n
d
f
a
s
t,
h
o
w
e
v
er
,
it
w
as
d
if
f
ic
u
lt
to
r
ev
er
s
e
t
h
e
e
n
cr
y
p
tio
n
p
r
o
ce
s
s
.
Ma
n
y
r
esear
ch
er
s
h
ad
i
m
p
r
o
v
i
s
ed
t
h
e
o
r
ig
i
n
al
Dif
f
ie
-
Hel
l
m
a
n
to
in
cr
ea
s
e
s
p
ee
d
o
f
k
e
y
g
e
n
er
at
io
n
an
d
to
g
en
er
ate
a
n
d
ex
ch
an
g
e
k
e
y
s
o
v
er
an
i
n
s
ec
u
r
e
n
et
w
o
r
k
s
ch
e
m
e
b
y
u
s
i
n
g
s
i
m
p
le
ar
it
h
m
e
tic
eq
u
at
io
n
s
[
7
]
.
T
h
er
e
ar
e
also
s
ch
e
m
es
p
r
o
p
o
s
ed
to
i
m
p
r
o
v
is
e
t
h
e
s
ec
u
r
it
y
o
f
Dif
f
ie
-
Hell
m
a
n
cr
y
p
to
s
y
s
te
m
b
y
r
e
d
u
cin
g
p
o
s
s
ib
ilit
y
o
f
a
k
n
o
wn
p
lain
te
x
t
attac
k
s
[8
-
9]
an
d
m
an
-
in
-
th
e
-
m
id
d
le
attac
k
s
[
1
0
-
11]
.
Me
an
w
h
ile
,
f
r
o
m
th
e
s
ec
u
r
it
y
p
er
s
p
ec
ti
v
e
,
[
1
2
]
c
r
y
p
to
s
y
s
te
m
w
as
p
r
o
p
o
s
ed
to
in
tr
o
d
u
ce
d
ig
ital
s
ig
n
at
u
r
e
s
c
h
e
m
e
w
h
ich
is
als
o
b
ased
o
n
Di
f
f
ie
-
Hell
m
a
n
d
is
cr
ete
lo
g
ar
i
th
m
p
r
o
b
lem
a
n
d
k
e
y
d
is
tr
ib
u
tio
n
s
c
h
e
m
e.
Ho
w
e
v
er
,
th
e
k
e
y
s
ize
s
h
o
u
ld
b
e
lar
g
e
an
d
th
e
s
p
ee
d
b
ec
o
m
e
s
lo
w
er
.
Sev
er
al
r
esear
ch
er
s
h
ad
p
r
o
p
o
s
ed
th
eir
s
c
h
e
m
e
s
to
o
v
er
co
m
e
t
h
e
d
r
a
w
b
ac
k
o
f
E
lGa
m
al
cr
y
p
to
s
y
s
te
m
[
1
3
-
14]
an
d
to
s
ec
u
r
e
ag
ain
s
t
m
at
h
e
m
atica
l
a
n
d
b
r
u
t
e
-
f
o
r
ce
attac
k
s
[
1
5
]
.
On
th
e
o
th
er
h
a
n
d
,
R
S
A
[
1
6
]
an
d
Go
ld
w
a
s
s
er
-
Mic
ali
[
1
7
]
cr
y
p
to
s
y
s
te
m
ar
e
t
h
e
p
o
p
u
lar
s
ch
e
m
e
s
i
n
I
n
te
g
er
Facto
r
iz
atio
n
al
g
o
r
ith
m
.
R
S
A
is
b
as
ed
o
n
t
h
e
id
ea
o
f
f
ac
to
r
in
g
th
e
t
w
o
lar
g
e
p
r
i
m
e
n
u
m
b
er
s
.
T
h
e
s
ec
u
r
it
y
o
f
t
h
is
s
ch
e
m
e
i
s
d
ep
en
d
ed
o
n
th
e
d
if
f
icu
lties
to
f
ac
to
r
th
e
n
u
m
b
er
s
.
Se
v
er
al
p
r
ev
io
u
s
r
esear
ch
er
s
m
o
d
i
f
ied
th
e
o
r
ig
in
a
l
R
S
A
s
c
h
e
m
e
b
y
in
cr
ea
s
in
g
t
h
e
n
u
m
b
er
o
f
p
r
iv
ate
k
e
y
s
[
1
8
]
,
u
s
e
t
w
o
p
u
b
lic
k
e
y
s
[
1
9
]
,
u
s
e
th
r
ee
p
r
i
m
e
n
u
m
b
er
s
[
2
0
]
,
u
s
e
f
o
u
r
p
r
i
m
e
n
u
m
b
er
s
[
2
1
]
,
an
d
u
s
e
„
n
‟
p
r
i
m
e
n
u
m
b
er
s
i
n
s
tea
d
o
f
t
w
o
[
2
2
-
24]
.
T
h
e
m
o
d
if
ie
d
s
ch
e
m
e
s
w
er
e
p
r
o
p
o
s
ed
to
in
cr
ea
s
e
th
e
s
ec
u
r
it
y
as
w
ell
as
to
in
cr
ea
s
e
t
h
e
s
p
ee
d
o
f
en
cr
y
p
tio
n
an
d
d
ec
r
y
p
tio
n
ti
m
e.
Ho
w
e
v
er
,
w
h
en
t
h
e
k
e
y
s
ize
i
n
cr
ea
s
ed
,
it
co
n
s
u
m
e
s
m
o
r
e
ti
m
e
f
o
r
lar
g
e
f
iles
[
2
5
]
,
[
2
1
]
.
Oth
er
w
is
e,
Go
ld
w
as
s
er
-
Mic
al
i
cr
y
p
to
s
y
s
te
m
in
tr
o
d
u
ce
d
q
u
ad
r
atic
r
esid
u
o
s
it
y
m
o
d
u
lo
co
m
p
o
s
i
te
in
teg
er
s
w
h
er
e
f
ac
t
o
r
izatio
n
is
u
n
k
n
o
w
n
.
T
h
e
s
ec
u
r
it
y
o
f
t
h
e
s
c
h
e
m
e
r
elies
o
n
t
h
e
q
u
ad
r
atic
r
es
id
u
o
s
it
y
h
ar
d
en
.
Ne
v
er
th
e
less
,
o
n
e
m
o
s
t
i
m
p
o
r
tan
t
d
r
a
w
b
ac
k
o
f
th
is
s
ch
e
m
e
w
a
s
r
eq
u
ir
ed
lar
g
e
n
u
m
b
er
o
f
r
a
n
d
o
m
b
its
a
n
d
p
r
o
d
u
ce
lar
g
e
a
m
o
u
n
t
s
o
f
cip
h
er
te
x
t
[
1
7
]
.
I
n
o
r
d
er
to
o
v
er
co
m
e
th
e
p
r
o
b
lem
,
s
e
v
er
al
s
c
h
e
m
es
h
ad
b
ee
n
i
n
tr
o
d
u
ce
d
th
at
ar
e
ca
p
ab
le
o
f
en
cr
y
p
tin
g
o
n
e
b
it
at
a
ti
m
e
[
2
6
]
.
I
n
s
tead
,
th
e
tec
h
n
iq
u
e
u
s
ed
i
n
s
c
h
e
m
e
s
g
r
o
u
p
ed
i
n
C
o
d
in
g
T
h
eo
r
y
alg
o
r
ith
m
ar
e
b
ased
o
n
co
d
es
f
o
r
ex
a
m
p
le
P
o
lar
co
d
es
[
2
7
]
an
d
Go
p
p
a
co
d
es
[
2
8
]
.
On
e
o
f
th
e
s
ch
e
m
e
in
t
h
i
s
alg
o
r
ith
m
is
Mc
E
liece
cr
y
p
t
o
s
y
s
te
m
w
h
ic
h
w
a
s
f
aster
th
a
n
R
S
A
in
en
cr
y
p
tin
g
a
n
d
d
ec
r
y
p
tin
g
m
e
s
s
a
g
e
[
2
8
]
.
E
v
en
Mc
E
liece
h
a
s
a
f
a
s
t
p
o
l
y
n
o
m
ial
ti
m
e
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
A
n
a
lysi
s
R
ev
iew
o
n
P
u
b
lic
K
ey
C
r
yp
to
g
r
a
p
h
y
A
lg
o
r
ith
ms
(
Ja
s
min
I
lya
n
i A
h
ma
d
)
449
d
ec
o
d
in
g
al
g
o
r
ith
m
,
it
en
cr
y
p
t
s
s
a
m
e
m
e
s
s
a
g
e
m
o
r
e
th
a
n
o
n
ce
an
d
p
r
o
d
u
ce
lar
g
e
k
e
y
s
ize
w
h
ic
h
u
s
e
o
f
m
o
r
e
s
p
ac
e.
Ma
n
y
ea
r
lier
r
esear
c
h
er
s
i
m
p
r
o
v
is
ed
t
h
e
e
x
is
ti
n
g
s
ch
e
m
e
b
y
d
ec
r
ea
s
in
g
t
h
e
p
u
b
lic
an
d
p
r
iv
ate
k
e
y
len
g
th
s
[
2
7
]
,
[
2
9
]
,
r
ed
u
cin
g
th
e
co
m
p
le
x
it
y
o
f
t
h
e
s
c
h
e
m
e
[
3
0
-
32]
an
d
i
n
cr
ea
s
i
n
g
t
h
e
e
n
cr
y
p
tio
n
a
n
d
d
ec
r
y
p
tio
n
s
p
ee
d
[
3
1
]
.
A
lter
n
ati
v
el
y
,
lattices
al
g
o
r
ith
m
‟
s
te
c
h
n
iq
u
e
i
s
b
ased
o
n
lear
n
in
g
w
it
h
er
r
o
r
s
ass
u
m
p
tio
n
to
s
o
lv
e
s
h
o
r
test
v
ec
to
r
p
r
o
b
lem
(
SV
P
)
an
d
s
h
o
r
test
in
d
ep
en
d
en
t
v
ec
to
r
p
r
o
b
lem
[
3
3
]
.
T
h
e
s
ch
e
m
e
s
u
n
d
er
th
is
alg
o
r
ith
m
in
cl
u
d
es
L
a
ttice
-
b
as
ed
,
GGH,
NT
R
U
a
n
d
F
u
ll
y
H
o
m
o
m
o
r
p
h
i
c
cr
y
p
to
s
y
s
te
m
.
O
n
e
o
f
t
h
e
i
m
p
o
r
tan
t
cr
iter
ia
o
f
lattices
al
g
o
r
ith
m
is
it
ca
n
co
n
tr
ib
u
te
o
n
s
a
v
in
g
t
h
e
s
p
ac
e
b
y
r
ed
u
ci
n
g
th
e
p
u
b
li
c
k
e
y
s
ize
[
3
3
-
35]
.
T
h
u
s
,
b
ec
au
s
e
o
f
t
h
e
cr
ite
r
ia
i
t
is
al
s
o
s
u
itab
le
f
o
r
I
n
ter
n
et
o
f
T
h
in
g
s
(
I
o
T
)
d
ev
ices
[
5
]
w
h
ich
is
lig
h
t
w
e
ig
h
t
an
d
h
a
s
li
m
i
ted
s
p
ac
e.
Ot
h
er
th
a
n
t
h
at,
la
ttices
al
g
o
r
ith
m
also
h
as
h
i
g
h
s
ec
u
r
it
y
p
er
f
o
r
m
an
ce
w
h
er
e
it
i
s
s
u
itab
le
f
o
r
clo
u
d
co
m
p
u
ti
n
g
(
GGH
cr
y
p
to
s
y
s
te
m
[
3
6
]
,
Fu
ll
y
Ho
m
o
m
o
r
p
h
ic
[
3
7
-
39]
)
an
d
p
u
b
lic
n
et
w
o
r
k
w
h
ic
h
is
th
e
I
n
ter
n
et
(
GGH
c
r
y
p
to
s
y
s
te
m
[
4
0
]
,
L
attice
-
b
as
ed
[
4
1
]
)
.
Ho
w
e
v
er
,
s
e
v
er
al
r
esear
ch
er
s
s
tated
t
h
e
d
r
a
w
b
ac
k
o
f
t
h
eir
s
c
h
e
m
es
w
h
ich
ca
n
n
o
t
ac
h
iev
e
s
u
f
f
icie
n
t
s
ec
u
r
it
y
w
i
th
o
u
t
lar
g
e
p
ar
a
m
e
t
er
s
[
4
2
]
an
d
p
u
b
lic
k
e
y
w
as
to
o
lar
g
e
f
o
r
an
y
p
r
ac
tical
s
y
s
te
m
[
4
3
]
.
I
n
co
n
tr
ast,
b
asicall
y
E
llip
tic
C
u
r
v
e
alg
o
r
ith
m
w
a
s
d
ef
in
ed
d
is
cr
ete
lo
g
ar
ith
m
p
r
o
b
le
m
wh
ich
u
p
g
r
ad
e
Di
f
f
ie
-
Hell
m
an
Ke
y
E
x
c
h
an
g
e
p
r
o
to
co
l
an
d
p
r
o
v
id
e
s
m
all
k
e
y
s
ize
w
it
h
f
a
s
ter
i
m
p
le
m
e
n
tatio
n
[
4
4
]
.
T
h
en
,
s
ev
er
al
r
esear
c
h
er
s
i
m
p
r
o
v
is
ed
t
h
ei
r
s
c
h
e
m
es
o
n
s
ec
u
r
it
y
[
4
5
-
48]
.
Ho
w
e
v
er
,
th
e
s
ch
e
m
e
s
b
ec
o
m
e
s
m
o
r
e
s
o
p
h
is
t
icate
d
an
d
it
r
eq
u
ir
es
m
o
r
e
th
eo
r
et
ical
k
n
o
w
led
g
e
o
f
Ma
th
e
m
atics
[
4
9
]
.
Mo
r
eo
v
er
,
th
e
h
ig
h
er
t
h
e
s
ec
u
r
it
y
,
t
h
e
s
lo
w
er
t
h
e
en
cr
y
p
t
io
n
w
il
l
b
e
[
5
0
]
.
On
th
e
o
th
er
h
an
d
,
Di
g
ita
l
Si
g
n
at
u
r
e
also
o
n
e
o
f
th
e
p
u
b
lic
k
e
y
cr
y
p
to
g
r
ap
h
y
al
g
o
r
ith
m
s
p
u
r
p
o
s
e
ly
m
ak
in
g
t
h
e
r
ec
ei
v
er
b
eliev
es
t
h
e
m
ess
a
g
e
h
ad
b
ee
n
r
ec
eiv
ed
f
r
o
m
a
u
t
h
o
r
ized
s
en
d
er
w
i
th
o
u
t
an
y
m
o
d
if
icatio
n
d
u
r
i
n
g
tr
an
s
m
is
s
io
n
.
Dig
ital
s
ig
n
at
u
r
e
co
n
s
i
s
ts
o
f
s
ch
e
m
es
w
h
ich
ar
e
Dig
ital
Si
g
n
atu
r
e
Alg
o
r
it
h
m
(
DS
A
)
,
E
llip
tic
C
u
r
v
e
DS
A
,
Di
f
f
ie
Hel
l
m
a
n
DS
A
,
R
S
A
DS
A
,
NT
R
U
DS
A
a
n
d
H
y
b
r
id
DS
A
.
Mo
s
t
o
f
th
e
s
c
h
e
m
es
u
n
d
er
Dig
ital
Si
g
n
a
tu
r
e
al
g
o
r
ith
m
wer
e
co
n
ce
n
tr
ate
o
n
s
ec
u
r
it
y
an
d
s
p
ac
e
w
h
ic
h
al
s
o
s
u
itab
le
f
o
r
m
o
d
er
n
n
et
w
o
r
k
o
f
f
ice
a
n
d
li
n
k
i
n
o
n
l
in
e
tr
a
n
s
ac
tio
n
s
[
5
1
]
.
B
esid
es,
b
ec
au
s
e
th
e
s
c
h
e
m
es
h
av
e
s
m
aller
k
e
y
s
ize,
it
i
s
s
u
itab
l
e
f
o
r
co
n
s
tr
ai
n
ed
d
ev
ices
s
u
ch
as
p
ag
er
s
,
ce
ll
u
lar
p
h
o
n
es
a
n
d
s
m
ar
t
ca
r
d
s
[
5
2
]
.
Mo
r
eo
v
er
,
th
ese
s
ch
e
m
e
s
a
ls
o
ap
p
lied
in
d
i
f
f
er
e
n
t
ap
p
lica
tio
n
s
u
c
h
a
s
e
m
ail
[
5
3
]
,
s
h
o
r
t
m
e
s
s
a
g
e
s
er
v
ice
(
SMS
)
[
5
4
]
an
d
clo
u
d
co
m
p
u
ti
n
g
[
5
5
]
.
H
y
b
r
id
alg
o
r
ith
m
b
asical
l
y
p
r
o
v
id
e
th
e
i
n
teg
r
at
io
n
b
et
w
ee
n
p
u
b
lic
k
e
y
cr
y
p
to
g
r
ap
h
y
a
n
d
p
r
iv
ate
k
e
y
cr
y
p
to
g
r
ap
h
y
s
c
h
e
m
e
s
[
5
6
-
61]
;
b
et
w
ee
n
p
u
b
lic
k
e
y
cr
y
p
to
g
r
ap
h
y
s
c
h
e
m
e
s
[
6
2
]
o
r
b
et
w
ee
n
p
r
iv
ate
k
e
y
cr
y
p
to
g
r
ap
h
y
s
ch
e
m
es
[
6
3
]
.
Mo
s
t
o
f
t
h
e
s
c
h
e
m
es
in
H
y
b
r
id
alg
o
r
it
h
m
w
er
e
f
o
cu
s
ed
o
n
s
ec
u
r
it
y
an
d
,
s
ec
u
r
it
y
a
n
d
s
p
ee
d
b
ec
au
s
e
o
f
th
e
i
n
te
g
r
atio
n
o
f
d
if
f
er
en
t
cr
y
p
to
g
r
ap
h
y
s
c
h
e
m
es
w
il
l
s
tr
e
n
g
t
h
e
n
t
h
e
s
ec
u
r
it
y
m
ec
h
a
n
is
m
b
y
co
m
b
i
n
in
g
t
h
e
s
tr
e
n
g
th
s
o
f
e
n
cr
y
p
ti
o
n
o
f
ea
ch
f
o
r
m
[
5
8
]
,
[
6
0
]
,
[
6
3
]
.
Ho
w
e
v
er
,
h
y
b
r
id
cr
y
p
to
g
r
ap
h
y
s
c
h
e
m
es
h
av
e
ex
tr
a
s
tep
s
o
n
en
cr
y
p
tio
n
a
n
d
d
ec
r
y
p
tio
n
w
h
ic
h
g
i
v
e
i
m
p
ac
t
to
th
e
ti
m
e
r
eq
u
ir
ed
[
6
2
]
an
d
m
a
y
co
n
tai
n
p
r
o
b
lem
s
o
n
e
f
f
icien
t c
o
m
p
u
t
atio
n
an
d
p
o
w
er
f
u
l e
n
co
d
in
g
s
y
s
te
m
s
[
5
6
]
.
3.
F
I
NDIN
G
S AN
D
DI
SCUS
SI
O
N
T
h
e
liter
atu
r
e
s
u
r
v
e
y
w
as
d
o
n
e
o
n
th
e
p
r
ev
io
u
s
r
esear
c
h
w
it
h
in
last
f
o
u
r
d
ec
ad
es.
T
h
is
is
d
u
e
to
th
e
f
o
r
m
o
f
p
u
b
lic
k
e
y
cr
y
p
to
g
r
ap
h
y
w
h
ic
h
s
tar
ted
in
la
s
t
4
0
y
e
ar
s
w
it
h
Di
f
f
ie
-
Hell
m
a
n
an
d
R
S
A
s
c
h
e
m
es.
T
h
i
s
s
ec
tio
n
s
h
o
w
s
t
h
e
tr
e
n
d
s
o
f
p
r
ev
io
u
s
s
t
u
d
ies
i
n
P
KC
alg
o
r
i
th
m
.
Oth
er
t
h
a
n
th
a
t,
th
i
s
s
ec
tio
n
al
s
o
d
is
c
u
s
s
ed
ab
o
u
t
th
e
r
o
ad
m
ap
o
f
ea
c
h
al
g
o
r
ith
m
w
h
ich
s
h
o
w
s
th
e
p
o
p
u
lar
it
y
o
f
it
a
m
o
n
g
r
esear
c
h
er
s
.
Mo
r
eo
v
er
,
it
also
s
h
o
w
s
t
h
e
m
o
s
t c
h
o
s
en
al
g
o
r
it
h
m
a
m
o
n
g
t
h
e
r
esear
ch
er
s
w
i
t
h
in
la
s
t d
ec
ad
e.
3
.
1
.
Resea
rc
h T
re
n
ds
in
P
ub
lic
K
ey
Cry
pto
g
r
a
ph
y
Alg
o
rit
h
m
s
Gen
er
all
y
,
th
is
s
ec
tio
n
is
a
n
al
y
zin
g
th
e
r
e
s
ea
r
ch
f
r
o
m
all
ca
teg
o
r
y
o
f
P
KC
al
g
o
r
ith
m
w
it
h
in
t
he
la
s
t
f
o
u
r
d
ec
ad
es.
T
h
er
e
ar
e
a
lo
t
o
f
r
esear
c
h
er
s
‟
e
f
f
o
r
t
t
h
at
co
n
tr
ib
u
tes
i
n
cr
y
p
to
g
r
ap
h
y
f
ield
b
ased
o
n
t
h
e
a
m
o
u
n
t
o
f
r
esear
ch
.
T
ab
le
1
s
h
o
w
s
t
h
e
p
er
ce
n
tag
e
o
f
r
esear
ch
in
e
ac
h
P
KC
alg
o
r
ith
m
w
it
h
i
n
th
e
last
f
o
u
r
d
ec
ad
es.
Fro
m
t
h
e
to
tal
p
r
ev
io
u
s
r
ese
ar
ch
,
o
n
l
y
2
2
%
o
f
t
h
e
r
esear
ch
d
o
n
e
f
r
o
m
1
9
7
6
-
2
0
0
6
,
w
h
er
ea
s
7
8
%
o
f
t
h
e
r
esear
ch
ca
m
e
f
r
o
m
2
0
0
7
u
n
ti
l
n
o
w
a
s
s
h
o
w
n
i
n
t
h
e
tab
le
.
T
h
is
s
it
u
atio
n
s
h
o
w
s
t
h
at
th
er
e
is
a
n
i
n
cr
e
m
e
n
t
in
P
KC
r
esear
ch
w
o
r
k
f
o
r
th
e
las
t
ten
y
ea
r
s
co
m
p
ar
ed
to
3
0
y
ea
r
s
b
ef
o
r
e
i
t.
Fr
o
m
t
h
e
y
ea
r
1
9
7
6
u
n
til
to
d
ay
,
it
i
s
illu
s
tr
ated
th
at
m
o
s
t
o
f
t
h
e
p
r
ev
io
u
s
r
esear
ch
er
s
f
o
cu
s
ed
o
n
I
n
teg
er
F
ac
to
r
izatio
n
an
d
L
atti
ce
s
alg
o
r
ith
m
w
i
t
h
2
0
%
an
d
2
1
%
r
esp
ec
tiv
e
l
y
.
W
h
er
ea
s
th
e
p
er
ce
n
ta
g
e
o
f
r
esear
ch
d
o
n
e
in
D
is
cr
ete
L
o
g
ar
it
h
m
al
g
o
r
it
h
m
is
1
5
%
o
u
t
o
f
th
e
to
tal
r
esear
ch
w
it
h
i
n
th
e
last
f
o
u
r
d
ec
ad
es.
Oth
er
th
an
t
h
at,
r
esear
ch
d
o
n
e
in
H
y
b
r
id
an
d
D
ig
ital
S
ig
n
at
u
r
e
alg
o
r
ith
m
ta
k
e
o
n
l
y
1
3
%
ea
c
h
o
u
t
o
f
th
e
to
tal
p
ie
ch
ar
t.
Ho
w
ev
er
,
n
u
m
b
er
o
f
r
esear
ch
d
o
n
e
in
E
llip
tic
C
u
r
v
e
an
d
C
o
d
in
g
T
h
eo
r
y
a
lg
o
r
it
h
m
w
er
e
t
h
e
m
o
s
t
less
co
m
p
ar
ed
to
t
h
e
o
t
h
er
s
wh
ich
o
n
l
y
9
%
ea
ch
.
B
esid
es,
f
r
o
m
th
e
2
2
%
o
f
r
es
ea
r
ch
d
o
n
e
w
it
h
i
n
1
9
7
6
-
2
0
0
6
,
T
ab
le
1
s
h
o
w
s
t
h
at
t
h
er
e
i
s
n
o
s
tu
d
y
o
n
H
y
b
r
id
al
g
o
r
ith
m
d
u
r
in
g
th
a
t
ti
m
e
l
in
e
.
Mo
r
eo
v
er
,
n
u
m
b
er
o
f
r
esear
ch
in
D
ig
ital
S
i
g
n
at
u
r
e
also
less
w
h
ic
h
o
n
l
y
5
%
f
r
o
m
t
h
e
to
tal
r
esear
ch
.
Ho
w
e
v
er
,
d
u
r
in
g
t
h
at
ti
m
e,
r
es
ea
r
ch
er
s
h
ad
f
o
c
u
s
ed
o
n
L
a
ttices
an
d
I
n
teg
er
F
ac
to
r
izatio
n
w
h
ic
h
ta
k
e
3
2
%
an
d
2
3
%
r
esp
ec
ti
v
el
y
.
T
h
is
i
s
d
u
e
to
th
e
ad
v
a
n
tag
e
s
o
f
I
n
t
eg
er
Facto
r
izatio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4752
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
12
,
No
.
2
,
No
v
e
m
b
er
2
0
1
8
:
4
4
7
–
454
450
w
h
ic
h
h
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NC
E
S
[1
]
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
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c
e
Co
m
p
lex
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y
,
”
v
o
l.
3
,
n
o
.
4
,
p
p
.
2
8
3
–
2
8
6
,
2
0
1
4
.
[2
]
S
.
K.
Ra
k
e
sh
k
u
m
a
r,
“
P
e
rf
o
r
m
a
n
c
e
A
n
a
l
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sis
o
f
D
a
ta
En
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r
y
p
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t
a
n
d
a
rd
A
lg
o
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h
m
&
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ro
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d
D
a
ta
En
c
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y
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ti
o
n
S
tan
d
a
rd
A
lg
o
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h
m
,
”
v
o
l.
7
,
n
o
.
1
0
,
p
p
.
1
1
–
2
0
,
2
0
1
3
.
[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
]
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
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t
L
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tt
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-
Ba
se
d
P
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b
l
ic
-
Ke
y
En
c
r
y
p
ti
o
n
,
”
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ro
c
.
2
n
d
ACM
I
n
t.
W
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rk
.
I
o
T
Priva
c
y
,
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ru
st.
S
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r.
-
I
o
T
P
T
S
’1
6
,
p
p
.
2
–
9
,
2
0
1
6
.
[6
]
W
.
Di
ff
ie,
W
.
Di
ff
ie,
a
n
d
M
.
E.
He
ll
m
a
n
,
“
Ne
w
Dire
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ti
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n
s
in
Cr
y
p
to
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p
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y
,
”
IEE
E
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ra
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s.
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f.
T
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,
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l.
2
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o
.
6
,
p
p
.
6
4
4
–
6
5
4
,
1
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7
6
.
[7
]
S
.
Bo
n
i,
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Im
p
ro
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in
g
th
e
Dif
f
ie
-
H
e
ll
m
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y
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l
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o
sin
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e
M
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li
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Ke
y
Ex
c
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A
l
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m
,
”
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1
3
0
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o
.
1
5
,
p
p
.
7
–
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0
,
1
9
7
6
.
[8
]
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
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o
f
Di
ff
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-
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ll
m
a
n
A
l
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m
to
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ro
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id
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M
o
re
S
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c
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re
Ke
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Ex
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,
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l.
5
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.
3
,
p
p
.
2
4
9
8
–
2
5
0
1
,
2
0
1
3
.
[9
]
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
.
[1
0
]
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
.
[1
1
]
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
.
[1
2
]
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
3
]
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
.
[1
4
]
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
i
th
F
u
z
z
y
Ke
y
wo
rd
S
e
a
rc
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o
n
C
lo
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d
En
v
iro
n
m
e
n
t,
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l.
1
8
,
n
o
.
3
,
p
p
.
4
8
1
–
4
8
6
,
2
0
1
6
.
[1
5
]
P
.
S
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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
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rit
h
m
(M
ECA
),
”
2
0
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1
2
n
d
I
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t
.
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mp
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.
T
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.
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1
,
p
p
.
4
3
9
–
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3
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2
0
1
1
.
[1
6
]
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
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r
o
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t
a
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in
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ig
it
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l
sig
n
a
tu
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a
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k
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to
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s,”
Co
mm
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n
.
ACM
,
v
o
l.
2
1
,
n
o
.
2
,
p
p
.
1
2
0
–
1
2
6
,
1
9
7
8
.
[1
7
]
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
,
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o
.
2
,
p
p
.
2
7
0
–
2
9
9
,
1
9
8
4
.
[1
8
]
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
e
d
o
n
T
h
e
Nu
m
b
e
r
o
f
T
h
e
P
riv
a
te
Ke
y
s,”
p
p
.
2
7
0
–
2
7
9
.
[1
9
]
S
.
M
a
th
u
r,
“
A
M
OD
IF
IED
RS
A
A
P
P
ROA
CHFOR
ENCRYP
T
IN
G
A
ND
DECR
YP
T
ING
T
EX
T
A
N
D
IM
AG
ES
USING
M
U
LT
I
-
P
OW
ER
,
M
ULT
I
P
UBL
IC
KEYS
,
M
ULT
I
P
RIM
E
NU
M
BERS
A
ND
K
-
NEA
RES
T
NEIG
HBO
R
ALGO
RITHM
,
”
v
o
l.
1
,
2
0
1
6
.
[2
0
]
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
,
”
Pro
c
.
-
2
0
1
2
In
t.
Co
n
f.
Ad
v
.
Co
mp
u
t.
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.
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2
0
1
2
,
p
p
.
4
02
–
4
0
8
,
2
0
1
3
.
[2
1
]
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
.
[2
2
]
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
t
o
sy
st
e
m
b
a
se
d
o
n
„
n
‟
p
rim
e
n
u
m
b
e
rs,”
v
o
l.
1
,
n
o
.
2
,
p
p
.
6
3
–
6
6
,
2
0
1
3
.
[2
3
]
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.
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.
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5
9
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0
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.
[2
4
]
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.
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.
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l
,
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5
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6
.
[2
5
]
D.
B.
Kh
a
irn
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r
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n
d
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.
S
.
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d
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m
,
“
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re
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:
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ir
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ise
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strib
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m
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6
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o
.
4
,
p
p
.
3
8
3
–
3
8
7
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1
6
.
[2
6
]
Jo
sh
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n
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lo
h
,
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9
9
4
.
[2
7
]
R.
Ho
o
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m
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n
d
,
M
.
K.
S
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a
ri,
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.
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9
2
,
p
p
.
1
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–
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0
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4
.
Evaluation Warning : The document was created with Spire.PDF for Python.
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453
[2
8
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R.
J.
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,
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9
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0
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5
.
[3
1
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.
P
.
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Ca
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M
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.
”
[3
2
]
D.
J.
Be
rn
ste
in
,
T
.
L
a
n
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,
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n
d
C.
P
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ters
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3
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5
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[3
4
]
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“
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tt
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p
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3
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1
.
[3
5
]
V
.
L
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v
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P
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rs Ov
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5
8
4
8
,
p
p
.
1
–
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4
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2
0
1
3
.
[3
6
]
H.
W
.
Kim
a
n
d
D.
Ch
o
i,
“
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f
o
rm
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ti
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ted
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7
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E
.
Im
,
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.
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p
p
.
1
9
9
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–
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9
9
8
,
2
0
1
6
.
[3
8
]
D.
S
teh
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d
R.
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tein
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ld
,
“
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rp
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2
0
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0
.
[3
9
]
Z.
Bra
k
e
rsk
i,
“
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f
f
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t
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u
ll
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ro
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tan
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”
[4
0
]
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G
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ld
re
ich
,
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.
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o
ld
w
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ss
e
r,
a
n
d
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.
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lev
i,
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u
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li
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to
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f
ro
m
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Re
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r
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v
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to
l.
-
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7
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.
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1
]
C.
P
e
ik
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rt,
“
L
a
tt
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Cr
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p
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ra
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ter
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t,
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p
.
1
–
2
5
,
2
0
1
4
.
[4
2
]
P
.
Ng
u
y
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n
,
“
Cr
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tan
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o
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th
e
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ld
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r
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a
lev
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p
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7
,
”
p
p
.
2
8
8
–
3
0
4
,
1
9
9
9
.
[4
3
]
M
.
V
a
n
Dijk
a
n
d
C.
G
e
n
try
,
“
F
u
ll
y
Ho
m
o
m
o
rp
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ic E
n
c
ry
p
ti
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n
o
v
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r
th
e
In
teg
e
rs,” p
p
.
1
–
2
8
,
2
0
1
0
.
[4
4
]
V
.
M
i
ll
e
r,
“
Us
e
o
f
El
li
p
ti
c
Cu
rv
e
s
in
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p
to
g
ra
p
h
y
,
”
Ad
v
.
Cry
p
to
l.
–
CRY
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v
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l.
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NCS
2
1
8
,
p
p
.
4
1
7
–
4
2
6
,
1
9
8
6
.
[4
5
]
Y.
L
u
,
L
.
L
i,
H.
P
e
n
g
,
a
n
d
Y
.
Ya
n
g
,
“
A
n
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n
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Bio
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tri
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s Us
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,
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.
M
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d
.
S
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,
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l.
3
9
,
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o
.
3
,
p
.
3
2
,
2
0
1
5
.
[4
6
]
S
.
A
.
Ch
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ry
,
K.
M
a
h
m
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o
d
,
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Na
q
v
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a
n
d
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.
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Kh
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“
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”
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.
M
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3
9
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1
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2
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5
.
[4
7
]
H.
A
rsh
a
d
a
n
d
M
.
Nik
o
o
g
h
a
d
a
m
,
“
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In
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rm
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ti
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S
y
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m
s,” 2
0
1
4
.
[4
8
]
Z.
T
a
n
,
“
RES
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A
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n
f
o
rm
a
ti
o
n
S
y
ste
m
s,”
2
0
1
4
.
[4
9
]
G
.
M
o
ise
,
“
On
th
e
a
tt
a
c
k
s
o
v
e
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th
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c
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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
.
[5
0
]
R.
Ra
u
sc
h
e
r,
F
.
B
o
h
n
sa
c
k
,
Ý.
Ü.
Ý,
a
n
d
Ü.
Ý,
“
Re
su
lt
s
o
f
a
n
El
li
p
ti
c
-
Cu
rv
e
-
A
p
p
ro
a
c
h
f
o
r
Us
e
in
Cr
y
p
to
sy
ste
m
s
µ,”
n
o
.
1
.
[5
1
]
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
,
”
2
0
1
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
.
[5
2
]
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
.
[5
3
]
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
.
[5
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
n
o
f
En
c
ry
p
ted
S
M
S
o
n
A
n
d
ro
i
d
S
m
a
rtp
h
o
n
e
Co
m
b
in
i
n
g
ECDS
A
-
ECDH an
d
A
ES
,
”
p
p
.
1
8
–
2
3
,
2
0
1
6
.
[5
5
]
M
.
P
.
Re
w
a
g
a
d
a
n
d
M
.
Y.
P
a
w
a
r,
“
Us
e
o
f
d
ig
it
a
l
sig
n
a
tu
re
w
it
h
d
if
f
ie
h
e
ll
m
a
n
k
e
y
e
x
c
h
a
n
g
e
a
n
d
a
e
s
e
n
c
r
y
p
ti
o
n
a
lg
o
rit
h
m
to
e
n
h
a
n
c
e
d
a
ta
se
c
u
rit
y
in
c
lo
u
d
c
o
m
p
u
ti
n
g
,
”
Pro
c
.
-
2
0
1
3
I
n
t.
C
o
n
f.
C
o
mm
u
n
.
S
y
st.
Ne
tw.
T
e
c
h
n
o
l
.
CS
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2
0
1
3
,
p
p
.
4
3
7
–
4
3
9
,
2
0
1
3
.
[5
6
]
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
.
[5
7
]
V
.
Ka
p
o
o
r
,
“
A
H
y
b
rid
Cry
p
to
g
r
a
p
h
y
Tec
h
n
iq
u
e
f
o
r
Im
p
ro
v
in
g
Ne
tw
o
rk
S
e
c
u
rit
y
,
”
v
o
l.
1
4
1
,
n
o
.
1
1
,
p
p
.
2
5
–
3
0
,
2
0
1
6
.
[5
8
]
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
.
[5
9
]
R.
Rizk
a
n
d
Y.
A
lk
a
d
y
,
“
Tw
o
-
p
h
a
se
h
y
b
rid
c
r
y
p
to
g
ra
p
h
y
a
lg
o
rit
h
m
f
o
r
w
irele
ss
se
n
so
r
n
e
tw
o
rk
s,”
J
.
El
e
c
tr.
S
y
st
.
In
f.
T
e
c
h
n
o
l.
,
v
o
l
.
2
,
n
o
.
3
,
p
p
.
2
9
6
–
3
1
3
,
2
0
1
5
.
[6
0
]
P
.
Ku
p
p
u
sw
a
m
y
a
n
d
S
.
Q.
Y.
A
l
-
Kh
a
li
d
i,
“
Hy
b
r
id
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
.
[6
1
]
E.
Ra
m
a
r
a
j,
S
.
Ka
rth
ik
e
y
a
n
,
a
n
d
M
.
He
m
a
lath
a
,
“
A
De
si
g
n
o
f
S
e
c
u
rit
y
P
ro
to
c
o
l
u
sin
g
Hy
b
rid
En
c
ry
p
ti
o
n
T
e
c
h
n
iq
u
e
(
A
ES
-
Rij
n
d
a
e
l
a
n
d
R
S
A
),
”
p
p
.
7
8
–
8
6
.
[6
2
]
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
.
[6
3
]
R.
S
in
g
h
,
I.
P
a
n
c
h
b
h
a
iy
a
,
A
.
P
a
n
d
e
y
,
a
n
d
R.
H.
G
o
u
d
a
r,
“
H
y
b
rid
En
c
ry
p
ti
o
n
S
c
h
e
m
e
(HES
) :
An
A
p
p
ro
a
c
h
f
o
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
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5
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454
T
ra
n
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m
it
ti
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e
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u
re
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In
tern
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c
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o
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c
,
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p
.
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1
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5
.
[6
4
]
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
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y
p
e
r
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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
.
[6
5
]
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
.
[6
6
]
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
teg
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
.
[6
7
]
Z.
Bra
k
e
rs
k
i
a
n
d
G
.
S
e
g
e
v
,
“
Be
tt
e
r
se
c
u
rit
y
f
o
r
d
e
ter
m
in
isti
c
p
u
b
li
c
-
k
e
y
e
n
c
r
y
p
ti
o
n
:
T
h
e
a
u
x
il
iar
y
-
i
n
p
u
t
se
tt
in
g
,
”
J
.
Cry
p
to
l.
,
v
o
l.
2
7
,
n
o
.
2
,
p
p
.
2
1
0
–
2
4
7
,
2
0
1
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.