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e
y
cr
y
p
to
g
r
ap
h
y
f
o
cu
s
e
s
o
n
t
h
e
s
tr
u
ct
u
r
e
o
f
s
i
m
p
le
i
ter
ativ
e
cr
y
p
to
g
r
ap
h
i
c
o
p
er
atio
n
s
an
d
as
y
m
m
e
tr
ic
cr
y
p
to
g
r
ap
h
y
d
ep
en
d
s
o
n
t
h
e
d
if
f
icu
lt
y
o
f
a
m
a
th
e
m
atica
l
p
r
o
b
lem
[
3
]
.
I
f
n
et
w
o
r
k
d
es
ig
n
er
s
‟
p
r
io
r
it
y
i
s
en
er
g
y
co
n
s
er
v
at
io
n
,
t
h
e
n
s
y
m
m
etr
ic
k
e
y
c
ip
h
er
s
ar
e
p
r
ef
e
r
r
ed
f
o
r
u
s
e
i
n
th
e
en
cr
y
p
tio
n
o
f
d
ata
tr
an
s
m
it
te
d
b
y
a
s
e
n
s
o
r
n
o
d
e
[
3
]
T
h
e
tr
ad
itio
n
al
cr
y
p
to
g
r
ap
h
ic
alg
o
r
ith
m
s
ca
n
n
o
t
b
e
ap
p
lie
d
o
n
s
en
s
o
r
n
o
d
es
b
ec
au
s
e
o
f
t
h
eir
r
eso
u
r
ce
co
n
s
tr
ain
ts
.
Fo
r
th
es
e
ty
p
e
o
f
n
et
w
o
r
k
s
,
k
e
y
m
an
ag
e
m
e
n
t
s
c
h
e
m
e
is
b
est
s
u
ita
b
le
to
ac
h
iev
e
s
ec
u
r
it
y
.
Fo
r
s
ec
u
r
e
co
m
m
u
n
icatio
n
,
k
e
y
m
u
s
t
b
e
ex
c
h
a
n
g
e
s
ec
u
r
el
y
b
et
w
ee
n
t
h
e
n
o
d
es
b
ef
o
r
e
th
e
ex
ch
a
n
g
e
o
f
in
f
o
r
m
atio
n
.
T
h
e
k
e
y
m
a
n
a
g
e
m
e
n
t
is
m
u
lti
-
o
p
er
atio
n
al
tech
n
iq
u
e
i
n
w
h
i
ch
f
ir
s
t
k
e
y
is
g
en
er
ated
,
t
h
en
th
is
k
e
y
is
d
is
tr
ib
u
ted
a
n
d
ex
c
h
an
g
ed
a
m
o
n
g
th
e
n
o
d
es,
t
h
en
u
s
ed
b
y
t
h
e
s
e
n
d
er
an
d
r
ec
eiv
er
,
af
ter
s
u
cc
e
s
s
f
u
l
an
d
s
ec
u
r
e
tr
a
n
s
f
er
o
f
i
n
f
o
r
m
ati
o
n
k
e
y
s
ar
e
ab
o
lis
h
ed
an
d
t
h
en
r
e
f
r
es
h
ed
.
Hen
ce
,
w
e
ca
n
s
a
y
t
h
at
t
h
e
m
ai
n
s
tep
s
in
k
e
y
m
an
a
g
e
m
en
t
s
c
h
e
m
e
ar
e:
g
e
n
er
atio
n
,
d
is
tr
ib
u
ted
,
ex
ch
a
n
g
ed
,
u
s
ed
,
ab
o
lis
h
ed
an
d
r
ef
r
esh
ed
.
T
h
er
e
ar
e
m
an
y
k
e
y
m
a
n
a
g
e
m
e
n
t
s
ch
e
m
es
f
o
r
th
e
W
SNs
[
4
]
.
B
ased
o
n
t
h
e
e
n
cr
y
p
tio
n
al
g
o
r
ith
m
s
,
t
h
e
k
e
y
m
a
n
ag
e
m
e
n
t
s
ch
e
m
es
ar
e
ca
te
g
o
r
ized
in
to
th
r
e
e
t
y
p
es:
s
y
m
m
etr
ic
k
e
y
m
an
a
g
e
m
en
t,
as
y
m
m
etr
ic
m
a
n
ag
e
m
en
t
an
d
h
y
b
r
id
k
e
y
m
an
a
g
e
m
en
t
tec
h
n
iq
u
es.
S
y
m
m
etr
ic
k
e
y
(
o
r
p
r
iv
ate
k
e
y
)
m
a
n
ag
e
m
e
n
t
s
c
h
e
m
e
u
s
es
th
e
s
a
m
e
k
e
y
at
b
o
th
s
id
es
i
.
e.
s
en
d
er
an
d
r
ec
eiv
er
u
s
e
t
h
e
co
m
m
o
n
k
e
y
f
o
r
en
cr
y
p
tio
n
a
n
d
d
ec
r
y
p
tio
n
.
T
h
is
tech
n
iq
u
e
is
r
eliab
le
a
n
d
r
ap
id
f
ast,
b
u
t
it
lac
k
s
r
e
s
ilie
n
ce
,
s
ca
lab
ilit
y
an
d
co
n
n
ec
ti
v
it
y
.
T
h
e
m
ai
n
d
i
s
ad
v
an
tag
e
o
f
th
is
s
c
h
e
m
e
is
t
h
at
b
o
th
p
ar
ties
s
h
o
u
ld
ex
ch
a
n
g
e
th
e
k
e
y
s
ec
u
r
el
y
[
4
]
.
A
s
y
m
m
etr
ic
k
e
y
(
o
r
p
u
b
lic
k
e
y
)
m
a
n
ag
e
m
e
n
t
u
s
es
t
w
o
d
if
f
er
en
t
k
e
y
s
at
b
o
th
s
id
es.T
h
e
k
e
y
u
s
ed
f
o
r
en
cr
y
p
tio
n
i.e
.
o
n
s
en
d
er
s
id
e
is
ca
lled
as
p
u
b
li
c
k
e
y
a
n
d
f
o
r
d
ec
r
y
p
tio
n
i.e
.
o
n
r
ec
eiv
er
s
id
e
is
p
r
iv
at
e
k
e
y
.
T
h
e
w
ell
-
k
n
o
w
n
p
u
b
lic
k
e
y
cr
y
p
to
g
r
ap
h
y
t
ec
h
n
iq
u
es
ar
e:
R
o
n
R
i
v
est,
A
d
i
Sh
a
m
ir
a
n
d
L
eo
n
ar
d
A
d
le
m
a
n
(
R
S
A
)
,
E
llip
tic
C
u
r
v
e
C
r
y
p
to
g
r
ap
h
y
(
E
C
C
)
a
n
d
H
y
p
er
ellip
tic
C
u
r
v
e
C
r
y
p
to
g
r
ap
h
y
(
HE
C
C
)
[
4
]
.
R
ec
en
tl
y
m
an
y
r
esear
ch
er
s
p
r
o
v
ed
th
at
th
e
p
u
b
lic
k
e
y
cr
y
p
to
g
r
ap
h
y
i
s
s
u
itab
le
f
o
r
r
eso
u
r
ce
co
n
s
tr
ai
n
n
e
t
w
o
r
k
s
.
B
o
th
th
e
s
y
m
m
e
tr
ic
an
d
as
y
m
m
etr
ic
s
c
h
e
m
es
h
av
e
tr
ad
e
-
o
f
f
b
et
w
ee
n
t
h
e
s
ec
u
r
it
y
a
n
d
it
s
r
eso
u
r
ce
s
ar
e
co
n
s
tr
ai
n
t
[
4
]
.
T
h
e
m
ai
n
p
r
o
b
le
m
o
f
co
n
v
e
n
tio
n
al
P
u
b
lic
k
e
y
C
r
y
p
to
s
y
s
te
m
s
is
t
h
at
t
h
e
Ke
y
s
iz
e
h
a
s
to
b
e
s
u
f
f
icie
n
tl
y
lar
g
e
i
n
o
r
d
er
to
m
ee
t
th
e
h
ig
h
le
v
el
s
ec
u
r
it
y
r
eq
u
i
r
e
m
en
t,
r
es
u
lt
in
g
i
n
lo
w
er
s
p
ee
d
an
d
co
n
s
u
m
p
tio
n
o
f
m
o
r
e
b
an
d
w
id
th
[
5
]
.
T
h
e
th
ir
d
tech
n
iq
u
e
i.e
h
y
b
r
id
k
e
y
tec
h
n
iq
u
e
w
h
ic
h
is
t
h
e
co
m
b
i
n
atio
n
o
f
s
y
m
m
etr
ic
an
d
p
u
b
lic
k
e
y
cr
y
p
to
g
r
ap
h
y
.
I
t
m
er
g
e
s
t
h
e
ad
v
an
ta
g
es
o
f
b
o
th
s
c
h
e
m
es.
T
h
e
f
ea
s
ib
ilit
y
o
f
p
u
b
lic
-
k
e
y
cr
y
p
to
g
r
ap
h
y
(
P
KC
)
h
as
b
ee
n
p
r
o
v
e
n
[
6
]
.
PKC
is
g
et
tin
g
m
o
r
e
atten
tio
n
i
n
W
SNs
d
u
e
to
t
h
e
r
ea
s
o
n
th
a
t
it
ca
n
ea
s
il
y
r
eso
lv
e
t
w
o
f
u
n
d
a
m
en
t
a
l
an
d
d
if
f
ic
u
lt
p
r
o
b
lem
s
,
au
th
e
n
ticat
io
n
an
d
s
y
m
m
etr
ic
k
e
y
d
is
tr
ib
u
tio
n
,
w
it
h
t
h
e
h
elp
o
f
Di
g
ital
s
i
g
n
atu
r
e
alg
o
r
ith
m
(
DS
A
)
a
n
d
Di
f
f
ie
-
Hel
l
m
a
n
k
e
y
e
x
ch
a
n
g
e
[
7
]
[
8
]
.
Mo
s
t
r
esear
ch
e
s
ap
p
lied
E
C
C
w
h
ich
h
a
s
m
u
ch
s
m
aller
o
v
er
h
ea
d
t
h
an
R
S
A
,
b
u
t
E
C
C
p
r
o
ce
d
u
r
es
ar
e
s
till
h
ea
v
y
to
r
eso
u
r
ce
-
co
n
s
tr
ain
ed
s
e
n
s
o
r
n
o
d
es [
9
]
.
E
C
C
is
b
est as c
o
m
p
ar
ed
to
R
SA
[
10
].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
4
,
A
u
g
u
s
t
2
0
1
7
:
2
2
3
2
–
2
2
4
0
2234
T
h
e
p
ap
e
r
w
ill n
o
w
d
is
c
u
s
s
an
d
s
u
r
v
e
y
s
o
m
e
o
f
th
e
p
u
b
lic
k
e
y
cr
y
p
to
g
r
ap
h
y
s
c
h
e
m
es.
3.
P
UB
L
I
C
-
K
E
Y
CR
YP
T
O
G
R
AP
H
Y
AL
G
O
RI
T
H
M
S IN WSN
3
.
1
.
RSA
Alg
o
rit
h
m
R
S
A
is
o
n
e
o
f
t
h
e
tec
h
n
iq
u
es
f
o
r
p
u
b
lic
k
e
y
en
cr
y
p
tio
n
.
I
t
w
a
s
t
h
e
f
ir
s
t
alg
o
r
it
h
m
to
b
e
d
ev
elo
p
ed
in
p
u
b
lic
-
k
e
y
cr
y
p
to
g
r
ap
h
y
,
a
n
d
o
n
e
o
f
th
e
f
ir
s
t
g
r
ea
t
ac
h
iev
e
m
en
ts
i
n
p
u
b
lic
k
e
y
e
n
cr
y
p
tio
n
.
I
t
in
v
o
lv
e
s
th
r
ee
s
tep
s
: [
1
1
]
1.
Ke
y
Ge
n
er
atio
n
2.
E
n
cr
y
p
tio
n
3.
Dec
r
y
p
tio
n
P
ha
s
e
1
:
K
ey
G
ener
a
t
io
n
R
S
A
u
s
es
t
w
o
k
e
y
s
f
o
r
its
p
r
o
ce
s
s
.
E
n
cr
y
p
tio
n
is
d
o
n
e
w
i
th
r
ec
eiv
er
‟
s
p
u
b
lic
k
e
y
a
n
d
d
ec
r
y
p
t
io
n
is
d
o
n
e
w
it
h
r
ec
eiv
er
‟
s
p
r
iv
a
te
k
e
y
.
T
o
g
en
er
ate
a
k
e
y
,
it u
s
es
f
o
llo
w
i
n
g
s
tep
s
:
1.
C
h
o
o
s
e
t
w
o
d
is
ti
n
ct
a
n
d
lar
g
e
p
r
im
e
n
u
m
b
er
s
s
a
y
,
P
an
d
Q.
2.
C
alcu
late
N
s
u
ch
t
h
at,
N=
P
*
Q.
3.
C
alcu
late
z
s
u
c
h
t
h
at,
z=
(
P
-
1
)
*
(
Q
-
1
)
.
4.
C
h
o
o
s
e
p
u
b
lic
k
e
y
e
x
p
o
n
en
t s
a
y
,
E
s
u
c
h
th
a
t 1
<
E
<
z
an
d
E
an
d
z
s
h
ar
e
n
o
Di
v
is
o
r
s
o
th
e
r
th
an
1
.
5.
Dete
r
m
i
n
e
D
w
h
ich
s
atis
f
ie
s
t
h
e
co
n
g
r
u
e
n
ce
r
elatio
n
.
E
*
D
=
1
(
m
o
d
z)
.
E
is
d
iv
is
ib
le
b
y
s
m
a
lles
t
o
f
th
e
s
er
ies:
z+
1
,
2
z+
1
,
3
z+
1
,
4
z+
1
,
………….
.
s
o
o
n
.
No
w
,
P
u
b
lic
Ke
y
: (
E
,
N)
an
d
P
r
iv
ate
Ke
y
: (
D,
N)
.
P
ha
s
e
2
:
E
ncry
ptio
n
T
h
is
is
th
e
p
r
o
ce
s
s
o
f
co
n
v
er
t
in
g
P
lain
T
ex
t
i
n
to
C
ip
h
er
T
ex
t.
T
h
is
p
r
o
ce
s
s
r
eq
u
ir
e
s
t
w
o
th
i
n
g
s
:
a
k
e
y
an
d
e
n
cr
y
p
tio
n
al
g
o
r
ith
m
.
E
n
cr
y
p
tio
n
o
cc
u
r
s
s
e
n
d
er
s
id
e
an
d
it
u
s
es
th
e
f
o
llo
w
i
n
g
eq
u
atio
n
to
e
n
cr
y
p
t
a
m
es
s
ag
e;
C
=
M
^
E
m
o
d
(
N)
,
w
h
er
e
C
is
cip
h
er
tex
t a
n
d
M
is
p
lain
te
x
t o
r
m
es
s
ag
e.
P
ha
s
e
3
:
Dec
ry
ptio
n
T
h
is
is
t
h
e
p
r
o
ce
s
s
o
f
co
n
v
e
r
tin
g
C
ip
h
er
T
ex
t
in
to
P
lain
T
ex
t.
T
h
is
p
r
o
ce
s
s
r
eq
u
ir
e
tw
o
t
h
i
n
g
s
:
Dec
r
y
p
tio
n
al
g
o
r
ith
m
an
d
a
k
e
y
.
Dec
r
y
p
t
io
n
o
cc
u
r
s
r
ec
ei
v
er
s
id
e
an
d
it
u
s
es
t
h
e
f
o
ll
o
w
i
n
g
eq
u
a
tio
n
to
d
ec
r
y
p
t
a
m
e
s
s
a
g
e;
M
=
C
^
D
m
o
d
(
N)
.
E
n
cr
y
p
tio
n
a
n
d
Dec
r
y
p
tio
n
p
r
o
ce
s
s
e
s
ar
e
s
h
o
w
n
b
elo
w
i
n
t
h
e
F
ig
u
r
e
2
:
Fig
u
r
e
2
.
R
S
A
T
ec
h
n
iq
u
e
3
.
2
.
Dif
f
ie
-
H
ell
m
a
n Alg
o
rit
h
m
I
t
is
o
n
e
o
f
th
e
ea
r
lies
t
ex
a
m
p
les
o
f
k
e
y
e
x
ch
a
n
g
e
i
m
p
le
m
en
ted
i
n
t
h
e
f
ield
o
f
cr
y
p
to
g
r
ap
h
y
.
T
h
e
Dif
f
ie
–
Hell
m
a
n
al
g
o
r
ith
m
all
o
w
s
b
o
th
p
ar
ties
,
w
h
ich
h
av
e
n
o
p
r
io
r
k
n
o
w
led
g
e
o
f
ea
ch
o
th
er
,
to
m
u
t
u
all
y
estab
lis
h
a
s
h
ar
ed
s
ec
r
et
k
e
y
o
v
er
an
in
s
ec
u
r
e
co
m
m
u
n
icat
io
n
s
c
h
a
n
n
el.
Di
f
f
ie
–
Hell
m
an
k
e
y
e
x
ch
a
n
g
e
i
s
a
s
y
m
m
etr
ic
cr
y
p
to
g
r
ap
h
y
b
ec
au
s
e
t
h
e
s
h
ar
ed
s
ec
r
et
k
e
y
an
d
s
es
s
io
n
k
e
y
ar
e
u
s
ed
f
o
r
en
cr
y
p
tio
n
a
n
d
d
ec
r
y
p
tio
n
[
1
2
]
,
[
1
3
]
.
I
t
is
u
s
ed
b
y
m
a
n
y
p
r
o
to
co
ls
,
lik
e
SS
L
,
Secu
r
e
Sh
ell,
an
d
I
P
Sec.
Step
s
o
f
th
is
al
g
o
r
ith
m
ar
e
as f
o
llo
w
s
[
2
]
:
1.
Select
t
w
o
n
u
m
b
er
s
„
p
‟
(
p
r
i
m
e
n
u
m
b
er
)
an
d
„
g
‟
(
b
ase)
.
2.
Select
t
w
o
s
ec
r
et
n
u
m
b
er
s
„
x
‟
f
o
r
s
en
d
er
an
d
„
y
‟
f
o
r
r
ec
eiv
er
.
3.
C
alcu
late
p
u
b
lic
n
u
m
b
er
R
1
=
g
^x
m
o
d
p
,
A
n
d
R
2
=
g
^
y
m
o
d
p
.
4.
E
x
ch
a
n
g
e
th
eir
p
u
b
lic
n
u
m
b
er
s
.
5.
C
o
m
p
u
tes Fir
s
t ses
s
io
n
k
e
y
a
s
K
s
, K
s
= R
2
^x
m
o
d
p
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
A
S
u
r
ve
y
o
n
C
o
mp
a
r
is
o
n
s
o
f Cr
yp
to
g
r
a
p
h
ic
A
lg
o
r
ith
ms Usi
n
g
C
erta
in
P
a
r
a
mete
r
s
in
W
S
N
(
P
o
o
ja
S
in
g
h
)
2235
6.
C
o
m
p
u
tes s
ec
o
n
d
s
ess
io
n
k
e
y
as K
r
, K
r
= R
1
^
y
m
o
d
p
7.
Her
e
K
s
= K
r
=
K
Fig
u
r
e
3
.
Dif
f
ie
-
Hell
m
a
n
alg
o
r
ith
m
T
h
is
alg
o
r
ith
m
ca
n
b
e
ex
p
lai
n
ed
v
ia
d
iag
r
a
m
as
s
h
o
w
n
i
n
f
i
g
u
r
e
3
ab
o
v
e
.
Sen
d
er
A
a
n
d
R
ec
eiv
er
B
w
a
n
ts
to
s
h
ar
e
th
e
ir
s
ec
r
et
k
e
y
s
o
v
er
in
s
ec
u
r
e
ch
a
n
n
el.
T
h
e
y
ar
e
n
o
t sh
ar
i
n
g
i
n
f
o
r
m
atio
n
,
th
e
y
j
u
s
t s
h
ar
e
k
e
y
s
.
T
h
e
m
ai
n
d
is
ad
v
a
n
ta
g
e
in
t
h
is
alg
o
r
ith
m
is
t
h
at,
m
a
n
-
in
-
t
h
e
-
m
id
d
le
-
attac
k
o
cc
u
r
s
i
n
th
i
s
alg
o
r
ith
m
.
I
t
o
cc
u
r
s
at
th
e
ti
m
e
o
f
ex
ch
a
n
g
i
n
g
p
u
b
lic
n
u
m
b
er
s
,
i.e
.
R
1
an
d
R
2
.
I
n
tr
u
d
er
m
o
d
if
ies
t
h
e
v
alu
e
s
o
f
R
1
a
n
d
R
2
an
d
tr
an
s
f
er
s
it to
b
o
th
p
ar
ties
.
Du
e
to
th
i
s
r
ea
s
o
n
,
s
es
s
io
n
k
e
y
v
al
u
e
co
m
e
s
to
b
e
u
n
eq
u
a
l.
3
.
3
.
DSA
Alg
o
rit
h
m
Dig
ital
s
i
g
n
at
u
r
es
ar
e
o
n
e
o
f
th
e
b
est
to
o
ls
to
i
m
p
le
m
e
n
t
s
ec
u
r
it
y
.
A
d
i
g
ital
s
ig
n
at
u
r
e
is
elec
tr
o
n
ic
v
er
s
io
n
o
f
a
w
r
itte
n
s
ig
n
at
u
r
e.
I
t
is
a
p
u
b
lic
-
k
e
y
cr
y
p
to
g
r
ap
h
ic
al
g
o
r
ith
m
[
1
4
]
,
w
h
ich
en
s
u
r
es
a
u
t
h
en
t
icatio
n
,
au
th
o
r
izatio
n
an
d
n
o
n
r
e
p
u
d
i
atio
n
[
1
5
]
.
Dig
ital
ce
r
tif
icate
is
a
d
ig
ital
I
D
to
s
h
o
w
id
en
ti
t
y
in
t
h
e
n
et
w
o
r
k
.
E
n
cr
y
p
tio
n
tec
h
n
o
lo
g
y
a
s
t
h
e
co
r
e
o
f
d
ig
ital
ce
r
tif
icate
s
ca
n
d
o
en
cr
y
p
tio
n
a
n
d
d
ec
r
y
p
tio
n
,
an
d
d
ig
i
tal
s
ig
n
at
u
r
e
an
d
s
ig
n
at
u
r
e
v
er
i
f
i
ca
tio
n
f
o
r
th
e
i
n
f
o
r
m
atio
n
tr
an
s
m
itte
d
o
n
th
e
n
et
w
o
r
k
to
e
n
s
u
r
e
co
n
f
id
en
t
ialit
y
in
te
g
r
it
y
a
n
d
s
ec
u
r
i
t
y
o
f
t
h
e
i
n
f
o
r
m
atio
n
tr
an
s
m
i
tted
o
n
li
n
e
[
1
6
]
.
Dig
ital
Si
g
n
at
u
r
e
is
i
m
p
le
m
e
n
ted
b
y
p
u
b
lic
an
d
p
r
iv
ate
k
e
y
alg
o
r
ith
m
s
a
n
d
h
a
s
h
f
u
n
ctio
n
s
.
I
t
is
u
s
ed
at
r
ec
eiv
er
s
id
e
f
o
r
m
ess
a
g
e
v
er
if
ica
tio
n
an
d
s
e
n
d
er
‟
s
id
en
tit
y
.
T
h
e
w
h
o
le
p
r
o
ce
s
s
o
f
d
ig
ital
s
i
g
n
atu
r
e
is
s
h
o
w
n
in
F
i
g
u
r
e
4
.
Dig
ital
s
i
g
n
atu
r
e
s
m
a
y
also
b
e
g
en
er
ated
f
o
r
s
to
r
ed
d
ata
an
d
p
r
o
g
r
am
s
s
o
th
at
th
e
i
n
te
g
r
it
y
o
f
th
e
d
ata
an
d
p
r
o
g
r
a
m
s
m
a
y
b
e
v
er
if
ied
at
an
y
later
ti
m
e
[
1
7
]
.
Fig
u
r
e
4
.
DSA
p
r
o
ce
s
s
Hash
f
u
n
ct
io
n
f
o
llo
w
s
s
o
m
e
p
r
o
p
er
ties
,
w
h
ic
h
ar
e
g
i
v
en
b
el
o
w
:
1.
Hash
f
u
n
ctio
n
s
h
o
u
ld
d
estro
y
all
h
o
m
o
m
o
r
p
h
i
s
m
s
tr
u
ct
u
r
es
in
th
e
u
n
d
er
l
y
i
n
g
p
u
b
lic
k
e
y
cr
y
p
to
s
y
s
te
m
(
b
e
u
n
ab
le
to
co
m
p
u
te
h
a
s
h
v
a
lu
e
o
f
2
m
e
s
s
a
g
es
co
m
b
i
n
ed
g
iv
en
t
h
eir
i
n
d
iv
id
u
al
h
a
s
h
v
al
u
es)
[
1
8
].
2.
Hash
f
u
n
ct
io
n
s
h
o
u
ld
b
e
co
m
p
u
ted
o
n
th
e
e
n
tire
m
ess
a
g
e
[
1
8
].
3.
Hash
f
u
n
ct
io
n
s
h
o
u
ld
b
e
a
o
n
e
w
a
y
f
u
n
ctio
n
s
o
th
at
m
es
s
ag
e
s
ar
e
n
o
t d
is
clo
s
ed
b
y
th
eir
s
i
g
n
atu
r
e
s
[
1
8
]
.
4.
Hash
f
u
n
ctio
n
s
h
o
u
ld
b
e
co
m
p
u
tat
io
n
all
y
i
n
f
ea
s
ib
le
g
i
v
e
n
a
m
e
s
s
a
g
e
a
n
d
its
h
a
s
h
v
a
l
u
e
to
co
m
p
u
te
an
o
th
er
m
ess
a
g
e
w
it
h
t
h
e
s
a
m
e
h
as
h
v
al
u
e
[
1
8
].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
4
,
A
u
g
u
s
t
2
0
1
7
:
2
2
3
2
–
2
2
4
0
2236
T
h
is
alg
o
r
ith
m
w
o
r
k
s
o
n
“
.
d
o
c,
.
p
d
f
,
.
tx
t”
an
d
o
th
er
ty
p
es
o
f
f
i
les,
an
d
h
a
s
h
f
u
n
ctio
n
ca
n
b
e
u
s
ed
f
o
r
d
y
n
a
m
ic
s
ize
o
f
d
ata.
T
h
e
ter
m
d
y
n
a
m
ic
m
ea
n
s
,
r
es
u
lts
o
f
h
ash
f
u
n
ct
io
n
d
ep
en
d
s
o
n
s
ize
o
f
t
h
e
d
ata
[
1
8
]
[
1
9
]
.
A
p
p
licatio
n
s
o
f
Di
g
ital
s
ig
n
atu
r
es
ar
e
i
n
i
n
f
o
r
m
atio
n
s
e
cu
r
it
y
(
au
t
h
en
ticatio
n
,
d
ata
i
n
teg
r
i
t
y
,
a
n
d
n
o
n
r
ep
u
d
iatio
n
)
,
e
-
co
m
m
er
ce
,
b
an
k
i
n
g
,
s
o
f
t
w
ar
e
d
i
s
tr
ib
u
tio
n
an
d
i
n
j
u
r
is
d
ict
io
n
,
a
n
d
to
d
ete
ct
f
o
r
g
er
y
o
r
ta
m
p
er
in
g
i
n
d
ata
[
1
4
].
3
.
4
.
E
CC
Alg
o
rit
h
m
T
h
is
alg
o
r
ith
m
i
s
m
ain
l
y
d
ep
en
d
o
n
t
h
e
alg
eb
r
aic
s
tr
u
ct
u
r
e
o
f
ellip
tic
c
u
r
v
es
[
1
0
]
.
E
C
C
in
c
lu
d
es
th
r
ee
s
tep
s
in
its
o
p
er
atio
n
,
i.e
.
,
k
e
y
ag
r
ee
m
e
n
t,
en
cr
y
p
tio
n
,
an
d
d
ig
ital
s
ig
n
atu
r
e
alg
o
r
it
h
m
s
[
2
0
]
.
T
h
e
f
ir
s
t
s
tep
is
k
e
y
d
is
tr
ib
u
tio
n
al
g
o
r
it
h
m
,
w
h
ic
h
is
u
s
ed
to
s
h
ar
e
a
s
ec
r
et
k
e
y
,
s
ec
o
n
d
s
tep
is
t
h
e
en
cr
y
p
tio
n
al
g
o
r
it
h
m
th
at
en
ab
les
co
n
f
id
en
tial
co
m
m
u
n
icatio
n
,
an
d
last
is
th
e
d
ig
ital
s
ig
n
at
u
r
e
alg
o
r
ith
m
w
h
ich
is
u
s
ed
to
au
th
e
n
tica
te
t
h
e
s
i
g
n
er
,
i.e
.
s
e
n
d
er
an
d
v
alid
ate
th
e
i
n
te
g
r
it
y
o
f
th
e
m
ess
a
g
e
[
2
0
]
.
An
ellip
tic
cu
r
v
e
is
a
p
lan
e
cu
r
v
e
s
h
o
u
ld
s
at
is
f
ie
s
th
e
f
o
llo
w
i
n
g
eq
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atio
n
[
1
0
]
an
d
th
e
g
r
ap
h
o
f
th
e
eq
u
a
tio
n
is
s
h
o
w
n
i
n
F
i
g
u
r
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5
.
y
2
=x
3
+
ax
+
b
E
C
C
is
co
n
s
id
er
ed
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est
f
o
r
c
r
ea
tin
g
f
aster
,
s
m
al
ler
an
d
m
o
r
e
ef
f
ic
ien
t
k
e
y
s
[
2
1
]
.
E
C
C
o
f
f
er
s
a
n
eq
u
iv
ale
n
t
a
m
o
u
n
t
o
f
s
ec
u
r
it
y
f
o
r
a
f
ar
s
m
a
ller
k
e
y
s
ize
an
d
h
en
ce
,
it
r
ed
u
ce
s
p
r
o
ce
s
s
in
g
an
d
co
m
m
u
n
icatio
n
o
v
er
h
ea
d
.
Fo
r
ex
a
m
p
le,
R
S
A
-
1
0
2
4
is
eq
u
i
v
ale
n
t
in
s
tr
e
n
g
th
to
E
C
C
-
1
6
0
[
1
0
]
,
s
ec
o
n
d
ex
am
p
le
is
R
S
A
-
2048
is
eq
u
i
v
ale
n
t
to
E
C
C
-
2
2
4
[
1
0
]
an
d
th
ir
d
ex
a
m
p
le
is
R
S
A
-
3
0
7
2
is
eq
u
iv
a
len
t
to
E
C
C
-
2
5
6
[
1
0
]
.
E
C
C
is
co
n
s
id
er
ed
as
b
est
s
u
itab
le
te
ch
n
iq
u
e
f
o
r
s
en
s
o
r
n
et
w
o
r
k
s
w
h
ic
h
p
r
o
v
id
es
a
g
o
o
d
tr
ad
e
-
o
f
f
b
et
w
ee
n
k
e
y
s
ize
a
n
d
s
ec
u
r
it
y
[
1
0
]
.
I
t
o
f
f
er
s
th
e
m
a
x
i
m
u
m
s
ec
u
r
it
y
w
it
h
s
m
aller
b
it
k
e
y
s
izes
th
a
t
i
s
w
h
y
it
co
n
s
u
m
es
les
s
p
o
w
er
[
2
1
]
an
d
h
en
ce
,
E
llip
tic
cu
r
v
e
cr
y
p
to
g
r
ap
h
y
is
g
o
o
d
f
o
r
b
atter
y
b
ac
k
u
p
al
s
o
[
2
1
].
Fo
llo
w
i
n
g
ar
e
th
e
s
tep
s
f
o
r
E
C
C
cr
y
p
to
g
r
ap
h
y
[
2
1
]:
1.
T
h
e
u
s
er
m
u
s
t
f
ir
s
t e
n
co
d
e
an
y
m
e
s
s
a
g
e
M
as a
p
o
in
t o
n
t
h
e
ellip
tic
cu
r
v
e
P
m
.
2.
Select
s
u
itab
le
cu
r
v
e
&
p
o
in
t
G
as in
Di
f
f
ie
-
Hell
m
a
n
.
3.
E
ac
h
u
s
er
c
h
o
o
s
es p
r
iv
ate
k
e
y
n
A
<
n
a
n
d
co
m
p
u
te
s
p
u
b
lic
k
e
y
P
A
=n
A
G.
4.
Fo
r
en
cr
y
p
tio
n
en
cr
y
p
t P
m
,
C
m
={
k
G,
P
m
+k
P
b
},
w
h
er
e
k
is
a
r
an
d
o
m
n
u
m
b
er
.
5.
Fo
r
d
ec
r
y
p
tio
n
d
ec
r
y
p
t C
m
,
c
o
m
p
u
te:
P
m
+
k
P
b
–
n
B
(
k
G)
=
P
m
+k
(
nB
G
)
–
n
B
(
k
G)
=
P
m
Fig
u
r
e
5
.
E
llip
tic
C
u
r
v
e
3
.
5
.
H
y
brid Alg
o
rit
h
m
H
y
b
r
id
m
ea
n
s
t
h
e
co
m
b
i
n
ati
o
n
o
f
t
w
o
o
r
m
o
r
e
th
i
n
g
s
.
H
y
b
r
id
al
g
o
r
ith
m
ta
k
es
t
h
e
ad
v
an
ta
g
e
s
o
f
s
y
m
m
etr
ic
an
d
as
y
m
m
e
tr
ic
alg
o
r
ith
m
s
.
So
m
an
y
h
y
b
r
id
alg
o
r
ith
m
s
h
a
v
e
b
ee
n
p
r
o
p
o
s
ed
.
So
m
e
au
t
h
o
r
s
ta
k
e
o
n
l
y
s
y
m
m
etr
ic
al
g
o
r
it
h
m
s
,
s
o
m
e
u
s
es
o
n
l
y
as
y
m
m
e
tr
ic
al
g
o
r
ith
m
s
an
d
s
o
m
e
a
u
t
h
o
r
s
ta
k
e
co
m
b
i
n
atio
n
o
f
th
ese
t
w
o
.
Au
th
o
r
s
o
f
[
4
]
,
u
s
e
s
E
C
C
a
n
d
HE
C
C
tec
h
n
iq
u
e
s
an
d
in
c
u
lcate
w
it
h
Gen
e
tics
A
l
g
o
r
ith
m
.
Au
t
h
o
r
s
o
f
[
2
]
,
u
s
es
R
S
A
a
n
d
Di
f
f
ie
-
Hell
m
a
n
tec
h
n
iq
u
e
s
to
d
ev
elo
p
a
h
y
b
r
id
al
g
o
r
ith
m
.
Au
t
h
o
r
s
o
f
[
2
2
]
,
u
s
es
DE
S
an
d
I
DE
A
t
ec
h
n
iq
u
es
f
o
r
t
h
e
ir
p
r
o
p
o
s
ed
h
y
b
r
id
alg
o
r
it
h
m
.
Alg
o
r
it
h
m
w
h
ich
is
p
r
o
p
o
s
ed
b
y
[
2
]
is
s
i
m
p
le
a
m
o
n
g
all
t
h
r
ee
.
I
n
t
h
is
,
a
u
t
h
o
r
s
u
s
e
s
t
h
e
t
w
o
ti
m
es XO
R
o
p
er
atio
n
to
m
a
k
e
th
e
m
e
s
s
a
g
e
m
o
r
e
co
m
p
lex
.
S
tep
s
o
f
th
i
s
alg
o
r
it
h
m
ar
e
as
f
o
llo
ws:
1.
E
n
cr
y
p
t th
e
m
e
s
s
a
g
e
u
s
in
g
R
S
A
a
n
d
g
e
n
er
ate
cip
h
er
tex
t,
C
1
.
2.
A
p
p
l
y
XO
R
o
p
er
atio
n
b
et
w
e
en
C
1
an
d
K
r
.
(
K
r
is
th
e
s
e
s
s
io
n
k
e
y
ca
lc
u
late
b
y
s
e
n
d
er
u
s
in
g
D
if
f
ie
-
Hell
m
a
n
al
g
o
r
ith
m
)
.
T
h
is
s
tep
p
r
o
d
u
ce
s
cip
h
er
tex
t,
s
a
y
C
2
.
3.
Ag
ai
n
ap
p
l
y
XO
R
o
p
er
atio
n
b
et
w
ee
n
C
2
a
n
d
K
s
(K
s
is
th
e
s
e
s
s
io
n
k
e
y
ca
lcu
la
te
b
y
r
ec
eiv
e
r
u
s
i
n
g
Di
f
f
ie
-
Hell
m
a
n
al
g
o
r
ith
m
)
.
T
h
is
s
tep
p
r
o
d
u
ce
s
th
e
f
i
n
al
cip
h
er
te
x
t,
C
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
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C
E
I
SS
N:
2
0
8
8
-
8708
A
S
u
r
ve
y
o
n
C
o
mp
a
r
is
o
n
s
o
f Cr
yp
to
g
r
a
p
h
ic
A
lg
o
r
ith
ms Usi
n
g
C
erta
in
P
a
r
a
mete
r
s
in
W
S
N
(
P
o
o
ja
S
in
g
h
)
2237
4.
Dec
r
y
p
t th
e
cip
h
er
te
x
t u
s
i
n
g
R
S
A
al
g
o
r
ith
m
an
d
o
b
tain
t
h
e
o
r
ig
in
al
m
es
s
ag
e.
3
.
6
.
DNA
cr
y
pto
g
ra
ph
y
DN
A
is
a
p
r
o
lo
n
g
p
o
l
y
m
er
o
f
co
m
p
ac
t
u
n
i
ts
ca
lled
n
u
cleo
t
id
es.
E
ac
h
DN
A
s
tr
an
d
i
s
co
m
p
o
s
ed
o
f
f
o
u
r
n
u
cleo
b
ases
:
A
,
G
,
C
&
T
.
T
h
e
d
etail
o
f
an
y
li
v
i
n
g
t
h
i
n
g
i
s
s
to
r
ed
in
DN
A
b
ases
as
s
h
o
w
n
i
n
Fig
u
r
e
6
[
29
]
.
Fig
u
r
e
6
.
DNA
s
tr
u
ct
u
r
e
DN
A
cr
y
p
to
g
r
ap
h
y
u
s
e
s
DN
A
b
ase
p
air
s
a
s
t
h
e
i
n
f
o
r
m
at
io
n
ca
r
r
ier
.
B
ec
au
s
e
o
f
t
h
e
p
r
o
ce
s
s
in
g
p
o
w
er
o
f
DN
A
ch
ip
s
,
it
is
m
o
r
e
ad
v
an
ce
d
tech
n
iq
u
e.
As
w
e
k
n
o
w
tr
ad
itio
n
al
cr
y
p
to
g
r
ap
h
ic
alg
o
r
ith
m
s
(
li
k
e
DE
S,
R
S
A
etc.
)
m
a
y
b
e
b
r
ea
k
b
y
an
at
tack
er
,
s
o
t
h
er
e
is
a
n
ee
d
o
f
m
o
r
e
s
ec
u
r
e
cr
y
p
to
g
r
ap
h
ic
tec
h
n
iq
u
es.
DN
A
co
m
p
u
ti
n
g
al
g
o
r
ith
m
s
h
av
e
p
r
o
p
o
s
ed
f
o
r
cr
y
p
to
g
r
a
p
h
y
is
s
u
e
s
[
2
3
-
25
]
.
Sev
er
al
alg
o
r
ith
m
s
o
f
DN
A
cr
y
p
to
g
r
ap
h
y
h
av
e
b
ee
n
p
r
o
p
o
s
ed
w
h
ich
u
s
e
s
ec
r
et
a
n
d
p
u
b
lic
k
e
y
s
f
o
r
co
n
ce
alin
g
th
e
d
a
ta
[
2
6
-
28
].
Fo
r
p
r
o
v
id
in
g
t
h
e
s
ec
u
r
it
y
i
n
W
S
N,
th
e
k
e
y
p
air
s
(
i.e
.
p
u
b
lic
&
p
r
iv
ate
k
e
y
)
ar
e
u
s
ed
in
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
o
f
[
2
9
]
.
Fo
r
th
e
k
e
y
p
air
g
e
n
er
at
io
n
,
R
S
A
al
g
o
r
ith
m
is
u
s
ed
.
T
h
eir
alg
o
r
ith
m
h
a
s
t
h
r
ee
s
te
p
s
i.e
.
in
f
o
r
m
atio
n
,
co
m
p
u
tatio
n
an
d
b
io
lo
g
ical
[
2
9
]
.
I
n
th
eir
p
r
o
p
o
s
ed
w
o
r
k
,
s
e
cu
r
it
y
is
e
n
h
a
n
ce
d
b
y
u
s
i
n
g
f
a
ls
e
d
ata
in
c
u
lcate
d
in
th
e
o
r
i
g
in
a
l d
ata
in
th
e
f
o
r
m
o
f
n
u
c
leo
tid
e
b
ases
[
2
9
-
32
].
4.
CO
M
P
ARIS
O
N
USI
N
G
VA
RIOU
S P
ARAM
E
T
E
RS
T
h
e
au
th
o
r
s
h
a
v
e
ca
te
g
o
r
ized
th
e
al
g
o
r
ith
m
s
ac
co
r
d
in
g
to
t
h
eir
k
e
y
s
ize
r
eq
u
ir
e
m
en
t,
s
tr
en
g
t
h
a
n
d
we
a
k
n
ess
e
s
,
p
o
s
s
ib
le
a
ttack
s
w
h
ic
h
ca
n
o
cc
u
r
o
n
s
e
n
s
o
r
n
o
d
es
b
y
u
s
in
g
t
h
e
s
e
al
g
o
r
ith
m
s
a
n
d
t
h
en
th
e
ir
co
u
n
ter
m
ea
s
u
r
es.
A
l
g
o
r
ith
m
s
w
it
h
s
m
all
k
e
y
s
ize
s
ar
e
b
r
ea
k
ab
le
i
n
t
h
e
n
ea
r
f
u
t
u
r
e.
So
t
h
er
e
is
a
n
ee
d
to
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CO
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s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
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N:
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2239
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[1
]
S
.
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h
m
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G.
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.
[5
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.
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[6
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D.
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l
.
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S
e
n
so
r A
d
Ho
c
C
o
mm
u
n
ica
ti
o
n
Ne
tw
o
rk
,
p
p
.
7
1
-
8
0
,
2
0
0
4
.
[7
]
Y.
L
iu
,
e
t
a
l.
,
“
P
KC
b
a
se
d
b
ro
a
d
c
a
st
a
u
th
e
n
ti
c
a
ti
o
n
u
si
n
g
sig
n
a
tu
re
a
m
o
rti
z
a
ti
o
n
f
o
r
W
S
Ns
”
,
IEE
E
T
ra
n
s.
W
ire
les
s
Co
mm
u
n
ica
ti
o
n
s,
v
o
l
.
1
1
,
n
o
.
6
,
p
p
.
2
1
0
6
-
2
1
1
5
,
2
0
1
2
.
[8
]
P
.
P
o
ra
m
b
a
g
e
,
e
t
a
l.
,
“
P
a
u
t
h
k
e
y
:
A
p
e
rv
a
si
v
e
a
u
th
e
n
ti
c
a
ti
o
n
p
r
o
t
o
c
o
l
a
n
d
k
e
y
e
sta
b
li
sh
m
e
n
t
sc
h
e
m
e
f
o
r
w
irel
e
ss
se
n
so
r
n
e
tw
o
rk
s in
d
istr
ib
u
ted
a
p
p
li
c
a
ti
o
n
s”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
Distrib
u
ted
S
e
n
so
r
Ne
two
rk
,
v
o
l.
2
0
1
4
.
[9
]
D.
Kim
a
n
d
S
.
A
n
,
“
P
KC
-
b
a
se
d
Do
S
A
tt
a
c
k
s
-
Re
sista
n
t
S
c
h
e
m
e
in
W
irele
ss
S
e
n
so
r
Ne
t
w
o
rk
s”
,
IEE
E
S
e
n
so
rs
J
o
u
rn
a
l,
2
0
1
6
.
[1
0
]
M
.
P
a
n
d
a
,
“
S
e
c
u
r
it
y
in
W
irele
ss
S
e
n
so
r
Ne
tw
o
rk
s
u
sin
g
Cry
p
to
g
ra
p
h
ic
T
e
c
h
n
iq
u
e
s”
,
Ame
ric
a
n
J
o
u
rn
a
l
o
f
En
g
i
n
e
e
rin
g
Res
e
a
rc
h
(
AJER)
, v
ol
.
0
3
,
i
ss
.
0
1
,
p
p
-
50
-
5
6
,
2
0
1
4
.
[1
1
]
Al
-
Ha
m
a
m
i,
e
t
a
l.
,
“
En
h
a
n
c
e
d
M
e
th
o
d
f
o
r
RS
A
Cry
p
to
s
y
ste
m
A
lg
o
rit
h
m
”
,
IEE
E
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
Ad
v
a
n
c
e
d
Co
mp
u
ter
S
c
ien
c
e
A
p
p
l
ica
ti
o
n
s a
n
d
T
e
c
h
n
o
lo
g
ies
(
ACS
A
T
)
,
p
p
.
4
0
2
-
4
0
8
,
No
v
2
0
1
2
.
[1
2
]
h
tt
p
s:/
/en
.
w
ik
ip
e
d
ia.o
rg
/w
ik
i/
Diffie_
He
ll
m
a
n
_
k
e
y
_
e
x
c
h
a
n
g
e
.
[1
3
]
R.
S
.
Dh
a
k
a
r,
e
t
a
l.
,
“
M
o
d
if
ied
RS
A
En
c
r
y
p
ti
o
n
A
lg
o
rit
h
m
(M
RE
A
)”
,
S
e
c
o
n
d
IEE
E
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
Ad
v
a
n
c
e
d
Co
mp
u
ti
n
g
&
Co
mm
u
n
ica
ti
o
n
T
e
c
h
n
o
l
o
g
ies
(
ACCT
)
,
p
p
.
4
2
6
-
4
2
9
,
Ja
n
2
0
1
2
.
[1
4
]
C.
Du
tt
a
,
e
t
a
l.
,
“
A
n
Ef
f
icie
n
t
I
m
p
lem
e
n
tatio
n
o
f
Dig
it
a
l
S
ig
n
a
tu
re
”
,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Ad
v
a
n
c
e
d
Res
e
a
rc
h
in
Co
mp
u
ter
S
c
ien
c
e
a
n
d
S
o
f
twa
re
En
g
i
n
e
e
rin
g
,
v
ol
.
5
,
i
ss
.
2
,
p
p
.
4
5
2
-
4
5
7
,
F
e
b
2
0
1
5
.
[1
5
]
M
.
A
.
Nia
,
e
t
a
l.
,
“
A
n
In
tro
d
u
c
t
io
n
t
o
Dig
it
a
l
S
ig
n
a
tu
re
S
c
h
e
m
e
s”
,
In
P
r
o
c
e
e
d
in
g
o
f
Na
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
In
fo
rm
a
t
io
n
,
A
p
r
2
0
1
4
.
[1
6
]
Z.
Q.
M
i
n
g
,
“
S
e
c
u
re
Dig
it
a
l
Ce
rti
fica
te De
sig
n
b
a
se
d
o
n
th
e
P
u
b
l
icK
e
y
Cr
y
p
to
g
ra
p
h
y
A
lg
o
rit
h
m
”
,
TE
L
KO
M
NIK
A
,
v
o
l.
1
1
,
n
o
.
1
2
,
p
p
.
7
3
6
6
-
7
3
7
2
,
D
e
c
2
0
1
3
.
[1
7
]
V
o
c
a
l,
“
h
tt
p
:/
/w
ww
.
v
o
c
a
l.
c
o
m
/cr
y
p
to
g
ra
p
h
y
/d
sa
d
ig
it
a
l
sig
n
a
tu
re
a
lg
o
rit
h
m
.
[1
8
]
W
il
li
a
m
S
talli
n
g
s,
h
tt
p
:/
/w
il
li
a
m
st
a
ll
in
g
s.co
m
/E
x
tras
/S
e
c
u
rit
y
No
te
s/lec
tu
re
s/a
u
th
e
n
t.
h
tm
l.
[1
9
]
N.
Jirwa
n
,
e
t
a
l.
,
“
Re
v
ie
w
a
n
d
A
n
a
l
y
si
s
o
f
Cr
y
p
to
g
ra
p
h
y
Tec
h
n
iq
u
e
s”
,
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
S
c
ien
ti
f
ic
&
En
g
i
n
e
e
rin
g
Res
e
a
rc
h
,
v
o
l.
4
,
i
ss
.
3
,
M
a
r
2
0
1
3
.
[2
0
]
F
.
Am
in
,
e
t
a
l.
,
“
A
n
a
ly
sis
o
f
P
u
b
li
c
-
Ke
y
Cr
y
p
to
g
ra
p
h
y
f
o
r
W
ire
les
s
S
e
n
so
r
Ne
tw
o
rk
s
S
e
c
u
rit
y
”
,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Co
m
p
u
ter
,
E
lec
trica
l,
Au
to
m
a
ti
o
n
,
C
o
n
tro
l
a
n
d
I
n
fo
rm
a
ti
o
n
En
g
in
e
e
rin
g
,
v
o
l
.
2
,
n
o
.
5
,
2
0
0
8
.
[2
1
]
R.
Bh
a
n
o
t
a
n
d
R
.
Ha
n
s,
“
A
R
e
v
i
e
w
a
n
d
Co
m
p
a
ra
ti
v
e
A
n
a
l
y
sis
o
f
V
a
rio
u
s
En
c
ry
p
ti
o
n
A
lg
o
rit
h
m
s”
,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
S
e
c
u
rity
a
n
d
Its
A
p
p
li
c
a
ti
o
n
s
,
v
o
l
.
9
,
n
o
.
4
,
p
p
.
2
8
9
-
3
0
6
,
2
0
1
5
.
[2
2
]
M
.
Ja
in
,
“
Im
p
lem
e
n
tatio
n
o
f
Hy
b
rid
Cr
y
p
to
g
ra
p
h
y
A
lg
o
ri
th
m
”
,
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
Co
re
En
g
i
n
e
e
rin
g
&
M
a
n
a
g
e
me
n
t
(
IJ
CEM
),
v
ol
.
1
,
i
ss
.
3
,
Ju
n
2
0
1
4
.
[2
3
]
T
.
M
a
n
d
g
e
a
n
d
V
.
C
h
o
u
d
h
a
ry
,
“
A
DN
A
En
c
r
y
p
ti
o
n
T
e
c
h
n
iq
u
e
Ba
se
d
o
n
M
a
tri
x
M
a
n
i
p
u
lati
o
n
a
n
d
S
e
c
u
re
k
e
y
G
e
n
e
r
a
ti
o
n
S
c
h
e
m
e
”
,
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
I
n
fo
rm
a
ti
o
n
Co
mm
u
n
ica
ti
o
n
a
n
d
Em
b
e
d
d
e
d
S
y
st
e
ms
(
ICICES
),
p
p
.
4
7
-
5
2
,
2
0
1
3
.
[2
4
]
S
.
S
a
d
e
g
,
e
t
a
l
.
,
“
A
n
e
n
c
ry
p
ti
o
n
a
lg
o
r
it
h
m
in
sp
ired
f
ro
m
DN
A
”
,
In
ter
n
a
t
io
n
a
l
Co
n
fer
e
n
c
e
o
n
M
a
c
h
in
e
a
n
d
W
e
b
In
telli
g
e
n
c
e
(
ICM
W
I)
, p
p
.
3
4
4
–
3
4
9
,
2
0
1
0
.
[2
5
]
X
.
G
u
o
z
h
e
n
X
,
e
t
a
l.
,
“
Ne
w
f
ield
o
f
c
r
y
p
to
g
ra
p
h
y
:
DN
A
c
r
y
p
to
g
ra
p
h
y
”
,
Ch
in
.
S
c
i.
B
u
ll
.
,
2
0
0
6
.
[2
6
]
Y.
Zh
a
n
g
,
e
t
a
l.
,
“
On
th
e
se
c
u
rit
y
o
f
s
y
m
m
e
tri
c
c
ip
h
e
rs
b
a
se
d
o
n
DN
A
c
o
d
in
g
”
,
In
f
o
rm
a
ti
o
n
S
c
ie
n
c
e
s
,
p
p
.
2
5
4
–
2
6
1
,
2
0
1
4
.
[2
7
]
G
.
Cu
i,
e
t
a
l.
,
“
A
n
En
c
r
y
p
ti
o
n
S
c
h
e
m
e
Us
in
g
DN
A
T
e
c
h
n
o
lo
g
y
”
,
3
rd
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
Bi
o
-
I
n
sp
ire
d
Co
mp
u
t
in
g
:
T
h
e
o
rie
s a
n
d
Ap
p
li
c
a
ti
o
n
s (
BICT
A)
,
p
p
.
3
7
-
4
2
,
2
0
0
8
.
[2
8
]
S
.
P
.
N.
T
rip
a
th
i,
e
t
a
l.
,
“
S
e
c
u
ri
n
g
DN
A
In
f
o
rm
a
ti
o
n
t
h
ro
u
g
h
P
u
b
li
c
Ke
y
Cr
y
p
to
g
ra
p
h
y
”
,
M
IS
Rev
iew
,
v
o
l.
1
9
,
iss
.
1
,
p
p
.
4
5
-
5
9
,
2
0
1
3
.
[2
9
]
M
.
a
n
d
S
.
Up
a
d
h
y
a
y
a
,
“
S
e
c
u
re
c
o
m
m
u
n
i
c
a
ti
o
n
u
si
n
g
DN
A
c
r
y
p
to
g
ra
p
h
y
w
it
h
se
c
u
re
so
c
k
e
t
la
y
e
r
(S
S
L
)
p
ro
to
c
o
l
in
w
irele
ss
se
n
so
r
n
e
tw
o
rk
s”
,
4
th
In
ter
n
a
ti
o
n
a
l
C
o
n
fer
e
n
c
e
o
n
Eco
-
frien
d
ly
Co
m
p
u
ti
n
g
a
n
d
Co
mm
u
n
ica
ti
o
n
S
y
ste
ms
,
El
se
v
ier,
p
p
.
8
0
8
–
8
1
3
,
2
0
1
5
.
[3
0
]
M
.
a
n
d
S
.
Up
a
d
h
y
a
y
a
,
“
I
m
p
ro
v
e
d
S
e
c
u
rit
y
u
si
n
g
DN
A
Cr
y
p
to
g
ra
p
h
y
in
W
irele
ss
S
e
n
so
r
Ne
t
w
o
rk
s
”
,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Co
m
p
u
ter
A
p
p
l
ica
ti
o
n
s
, v
ol
.
1
5
5
,
n
o
.
1
3
,
De
c
2
0
1
6
.
[3
1
]
N.
S
a
in
i,
e
t
a
l.
,
“
En
h
a
n
c
e
m
e
n
t
o
f
se
c
u
rit
y
u
sin
g
c
r
y
p
to
g
ra
p
h
ic
tec
h
n
iq
u
e
s”
4
th
IEE
E
In
ter
n
a
ti
o
n
a
l
C
o
n
fer
e
n
c
e
,
p
p
.
1
-
5
,
2
0
1
5
.
[3
2
]
X
.
Re
n
,
“
S
e
c
u
rit
y
M
e
th
o
d
s
f
o
r
W
irele
ss
S
e
n
so
r
Ne
t
w
o
rk
s”
,
P
ro
c
e
e
d
in
g
s
o
f
th
e
IEE
E
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Evaluation Warning : The document was created with Spire.PDF for Python.