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Vo
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15
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Decem
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20
25
,
p
p
.
5
6
7
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~
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9
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CC B
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li
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C
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p
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:
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Fau
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Dip
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Un
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s
ity
Sem
ar
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g
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n
d
o
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esia
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m
ail: ir
za
n
u
r
f
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
r
ap
id
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v
a
n
ce
m
en
t
o
f
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i
g
ital
tech
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o
lo
g
y
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p
ar
ticu
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ly
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th
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ea
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o
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as
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m
ed
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ated
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.
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m
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tiv
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ty
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o
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ch
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ly
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is
k
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o
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ata
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h
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o
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r
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p
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n
,
an
d
u
n
au
th
o
r
ize
d
m
a
n
ip
u
latio
n
[
1
]
.
As
th
e
v
o
lu
m
e
o
f
s
en
s
itiv
e
in
f
o
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m
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ats.
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ely
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2
]
.
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to
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am
ewo
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s
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I
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I
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p
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,
Vo
l.
15
,
No
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6
,
Decem
b
e
r
20
25
:
5
6
7
9
-
5
6
8
9
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d
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th
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h
ash
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[
3
]
.
Ad
d
iti
o
n
ally
,
c
o
m
b
in
in
g
th
is
s
tr
u
ctu
r
e
with
estab
lis
h
ed
cr
y
p
to
s
y
s
tem
s
,
s
u
ch
as
R
SA
an
d
AE
S,
ca
n
c
r
ea
te
a
r
o
b
u
s
t
f
r
am
ewo
r
k
th
at
en
cr
y
p
ts
an
d
v
e
r
if
ies
d
ata
s
ec
u
r
ely
,
t
h
er
eb
y
s
ig
n
if
ican
tly
en
h
an
cin
g
tr
u
s
t a
n
d
r
eliab
ilit
y
in
d
ig
ital sy
s
tem
[
4
]
.
B
u
ild
in
g
o
n
ex
is
tin
g
liter
atu
r
e,
wh
ich
h
ig
h
lig
h
ts
th
e
v
u
ln
er
ab
ilit
ies
ass
o
ciate
d
with
co
n
v
en
tio
n
al
d
ata
s
to
r
ag
e
an
d
s
ec
u
r
ity
p
r
ac
tices
[
5
]
,
t
h
is
r
esear
ch
f
o
c
u
s
es
o
n
th
e
in
n
o
v
ativ
e
u
s
e
o
f
R
SA
an
d
AE
S
alg
o
r
ith
m
s
with
in
h
ash
ch
ai
n
f
r
am
ewo
r
k
s
.
B
y
lev
er
ag
in
g
th
e
s
tr
en
g
th
s
o
f
b
o
th
s
y
m
m
etr
ic
(
AE
S)
an
d
asy
m
m
etr
ic
(
R
SA)
en
cr
y
p
tio
n
m
eth
o
d
s
,
th
e
r
esear
ch
aim
s
to
d
ev
elo
p
a
s
o
p
h
is
ticated
cr
y
p
to
g
r
ap
h
ic
s
o
lu
tio
n
th
at
o
f
f
er
s
s
u
p
e
r
io
r
s
ec
u
r
ity
a
n
d
p
r
i
v
ac
y
.
C
o
m
p
ar
ed
t
o
o
th
er
co
m
b
in
ati
o
n
s
s
u
ch
as
T
wo
f
is
h
an
d
E
lGam
al,
R
SA
an
d
AE
S
p
r
o
v
id
e
a
m
o
r
e
r
o
b
u
s
t
h
y
b
r
id
a
p
p
r
o
ac
h
,
e
f
f
e
ctiv
ely
s
af
eg
u
ar
d
i
n
g
ag
ai
n
s
t
u
n
au
th
o
r
ize
d
ac
ce
s
s
wh
ile
m
ain
tain
in
g
ef
f
icien
t e
n
cr
y
p
tio
n
a
n
d
d
ec
r
y
p
tio
n
p
r
o
ce
s
s
es
[
6
]
.
T
h
e
p
r
o
p
o
s
ed
s
o
lu
tio
n
en
h
an
ce
s
cu
r
r
en
t
p
r
ac
tices
b
y
en
s
u
r
in
g
th
at
ea
ch
d
ata
b
lo
ck
is
cr
y
p
to
g
r
ap
h
ically
lin
k
ed
to
th
e
p
r
ev
io
u
s
o
n
e,
t
h
er
eb
y
s
tr
en
g
th
en
in
g
th
e
s
y
s
tem
’
s
r
esis
tan
ce
to
u
n
au
th
o
r
ized
tam
p
er
in
g
[
7
]
.
T
h
is
r
esear
c
h
co
n
tr
i
b
u
tes
a
n
o
v
el
m
et
h
o
d
o
lo
g
y
f
o
r
d
ata
p
r
o
tectio
n
,
p
ar
ticu
la
r
ly
in
en
v
ir
o
n
m
en
ts
ch
ar
ac
ter
ized
b
y
h
ig
h
d
ata
th
r
o
u
g
h
p
u
t,
an
d
lay
s
th
e
g
r
o
u
n
d
wo
r
k
f
o
r
f
u
t
u
r
e
in
n
o
v
atio
n
s
in
in
f
o
r
m
atio
n
s
ec
u
r
ity
s
y
s
tem
s
.
As
s
u
ch
,
it
h
o
ld
s
s
ig
n
if
ican
t
im
p
licatio
n
s
n
o
t
o
n
ly
f
o
r
th
e
ed
u
ca
tio
n
s
ec
to
r
,
wh
er
e
s
ec
u
r
e
d
ata
m
an
ag
em
e
n
t
is
cr
u
cial
b
u
t
also
f
o
r
a
n
y
i
n
d
u
s
tr
y
r
elian
t
o
n
t
h
e
in
teg
r
it
y
an
d
c
o
n
f
i
d
en
tiality
o
f
d
ig
ital in
f
o
r
m
atio
n
.
T
h
i
s
s
t
u
d
y
i
s
s
i
t
u
at
e
d
w
i
t
h
i
n
t
h
e
d
o
m
a
i
n
o
f
c
o
m
p
u
t
e
r
e
n
g
i
n
e
e
r
i
n
g
a
n
d
i
n
f
o
r
m
a
t
i
o
n
s
e
c
u
r
i
t
y
,
a
d
d
r
e
s
s
i
n
g
t
h
e
g
r
o
w
i
n
g
n
e
e
d
f
o
r
r
o
b
u
s
t
d
a
t
a
p
r
o
t
e
c
t
i
o
n
i
n
d
i
g
i
t
al
s
y
s
te
m
s
.
T
h
e
c
e
n
t
r
a
l
r
es
e
a
r
c
h
q
u
es
t
i
o
n
e
x
a
m
i
n
es
h
o
w
h
y
b
r
i
d
c
r
y
p
t
o
g
r
a
p
h
i
c
t
e
c
h
n
i
q
u
e
s
—
s
p
e
c
i
f
i
c
a
ll
y
,
t
h
e
i
n
t
e
g
r
a
t
i
o
n
o
f
R
S
A
a
n
d
A
E
S
w
i
t
h
i
n
a
h
a
s
h
c
h
a
i
n
f
r
a
m
e
w
o
r
k
e
n
h
a
n
c
e
d
b
y
Me
r
k
le
t
r
ee
s
t
r
u
c
t
u
r
e
s
—
c
a
n
e
f
f
e
ct
i
v
e
l
y
i
m
p
r
o
v
e
s
y
s
t
e
m
i
n
t
e
g
r
i
t
y
a
n
d
d
e
t
ec
t
u
n
a
u
t
h
o
r
i
z
e
d
d
at
a
m
o
d
i
f
i
c
a
t
i
o
n
s
.
T
h
e
m
a
i
n
o
b
j
ec
t
i
v
e
i
s
t
o
d
e
v
e
l
o
p
a
s
ec
u
r
e
a
n
d
e
f
f
i
c
i
e
n
t
e
n
c
r
y
p
t
i
o
n
s
y
s
t
em
t
h
a
t
c
a
n
d
e
t
e
c
t
u
n
a
u
t
h
o
r
i
z
e
d
d
a
t
a
m
o
d
i
f
ic
a
t
i
o
n
s
i
n
r
e
al
ti
m
e
.
T
h
is
a
p
p
r
o
a
ch
u
t
i
l
i
ze
s
t
h
e
s
t
r
e
n
g
t
h
s
o
f
i
n
d
iv
i
d
u
a
l
c
o
m
p
o
n
e
n
t
s
:
A
E
S
p
r
o
v
i
d
e
s
f
a
s
t
e
n
c
r
y
p
t
i
o
n
[
8
]
,
R
S
A
e
n
s
u
r
e
s
s
ec
u
r
e
k
e
y
m
a
n
a
g
e
m
e
n
t
[
9
]
,
a
n
d
Me
r
k
le
tr
ee
s
f
a
c
i
l
i
t
a
t
es
i
n
t
e
g
r
i
t
y
v
e
r
i
f
i
ca
t
i
o
n
,
c
o
ll
e
c
ti
v
e
l
y
r
e
s
u
l
ti
n
g
i
n
a
r
o
b
u
s
t
a
n
d
s
ca
l
a
b
l
e
s
o
l
u
t
i
o
n
[
1
0
]
.
T
h
i
s
w
o
r
k
c
o
n
t
r
i
b
u
te
s
a
n
o
v
e
l
m
e
t
h
o
d
o
l
o
g
y
t
h
a
t
e
n
h
a
n
c
e
s
cu
r
r
e
n
t
c
r
y
p
t
o
g
r
a
p
h
i
c
p
r
a
c
t
i
c
es
b
y
l
i
n
k
i
n
g
e
a
c
h
d
a
t
a
b
l
o
c
k
c
r
y
p
t
o
g
r
a
p
h
i
c
a
l
l
y
a
n
d
v
a
l
i
d
a
ti
n
g
i
ts
i
n
t
e
g
r
i
t
y
t
h
r
o
u
g
h
h
i
e
r
a
r
c
h
i
c
a
l
h
a
s
h
i
n
g
.
C
o
m
p
a
r
e
d
t
o
e
x
i
s
ti
n
g
m
o
d
e
l
s
,
t
h
e
p
r
o
p
o
s
e
d
s
y
s
te
m
d
e
m
o
n
s
t
r
a
t
es
s
u
p
e
r
i
o
r
p
e
r
f
o
r
m
a
n
c
e
i
n
b
o
t
h
e
x
e
c
u
t
i
o
n
t
i
m
e
a
n
d
a
n
o
m
a
l
y
d
e
t
e
c
t
i
o
n
,
as
e
v
i
d
e
n
c
e
d
b
y
e
m
p
i
r
i
c
a
l
t
e
s
t
i
n
g
.
T
h
e
f
i
n
d
i
n
g
s
e
x
p
a
n
d
e
x
i
s
ti
n
g
k
n
o
w
l
e
d
g
e
i
n
t
h
e
f
i
e
l
d
o
f
in
f
o
r
m
a
t
i
o
n
s
e
c
u
r
i
t
y
a
n
d
c
r
y
p
t
o
g
r
a
p
h
i
c
e
n
g
i
n
e
e
r
i
n
g
,
o
f
f
e
r
i
n
g
p
r
a
c
t
i
c
a
l
i
n
s
i
g
h
ts
f
o
r
i
m
p
l
e
m
e
n
t
at
i
o
n
i
n
s
e
c
t
o
r
s
s
u
c
h
as
e
d
u
c
a
t
i
o
n
,
cl
o
u
d
s
e
r
v
i
c
es
,
d
a
t
a
b
as
e
b
a
c
k
e
n
d
e
n
g
i
n
e
e
r
i
n
g
,
a
n
d
I
o
T
.
F
u
t
u
r
e
r
e
s
e
a
r
c
h
m
a
y
b
u
i
l
d
u
p
o
n
t
h
i
s
m
o
d
e
l
t
o
f
u
r
t
h
e
r
o
p
t
im
i
z
e
c
r
y
p
t
o
g
r
a
p
h
i
c
e
f
f
i
c
i
e
n
c
y
a
n
d
e
x
p
l
o
r
e
i
ts
a
d
ap
t
a
b
i
l
i
t
y
t
o
e
m
e
r
g
i
n
g
t
e
c
h
n
o
l
o
g
i
e
s
a
n
d
d
i
s
t
r
i
b
u
t
e
d
s
y
s
te
m
s
.
T
h
e
r
e
f
o
r
e
,
t
h
i
s
s
t
u
d
y
p
r
o
p
o
s
e
s
a
h
y
b
r
i
d
c
r
y
p
t
o
g
r
a
p
h
i
c
m
o
d
e
l
t
h
a
t
i
n
t
e
g
r
a
t
es
R
S
A
a
n
d
A
E
S
w
i
t
h
i
n
a
h
a
s
h
c
h
ai
n
s
y
s
te
m
e
n
h
a
n
c
e
d
b
y
Me
r
k
le
t
r
ee
s
t
r
u
c
t
u
r
e
s
,
a
i
m
i
n
g
t
o
e
n
s
u
r
e
r
e
a
l
-
t
i
m
e
d
a
t
a
i
n
te
g
r
i
t
y
v
e
r
i
f
i
c
a
t
i
o
n
a
n
d
s
e
c
u
r
e
e
n
c
r
y
p
t
i
o
n
i
n
h
i
g
h
-
t
h
r
o
u
g
h
p
u
t
d
i
g
i
t
a
l
e
n
v
i
r
o
n
m
e
n
ts
.
2.
L
I
T
E
R
AT
U
RE
R
E
VI
E
W
I
n
teg
r
atin
g
ad
v
a
n
ce
d
cr
y
p
to
g
r
ap
h
ic
tech
n
iq
u
es
is
cr
itical
f
o
r
im
p
r
o
v
in
g
s
y
s
tem
in
te
g
r
ity
an
d
d
at
a
s
ec
u
r
ity
.
T
h
is
r
ev
iew
ex
am
in
es
v
ar
io
u
s
s
tu
d
ies
th
at
f
o
cu
s
o
n
u
s
in
g
h
ash
ch
ain
s
,
Me
r
k
l
e
tr
ee
s
,
an
d
h
y
b
r
id
cr
y
p
to
g
r
ap
h
y
,
co
llectiv
ely
e
n
h
an
cin
g
d
ata
p
r
o
tectio
n
in
in
f
o
r
m
atio
n
s
y
s
tem
s
.
Nag
a
r
aj
an
d
Mo
h
an
r
aj
in
v
esti
g
ated
o
n
e
-
wa
y
h
ash
ch
ain
alg
o
r
it
h
m
s
f
o
r
s
elec
ti
v
e
d
ata
en
c
r
y
p
tio
n
,
em
p
h
asizin
g
th
eir
r
o
le
in
m
ain
tain
in
g
d
ata
in
teg
r
ity
.
W
h
ile
ef
f
ec
tiv
e,
o
n
e
-
wa
y
en
cr
y
p
tio
n
lim
its
d
ec
r
y
p
tio
n
ca
p
ab
i
liti
es,
u
n
d
er
s
co
r
in
g
th
e
n
ee
d
f
o
r
two
-
way
h
ash
ch
a
in
s
o
r
th
eir
co
m
b
in
ati
o
n
with
co
m
p
lem
en
tar
y
s
tr
ateg
ies,
p
ar
ticu
lar
ly
in
s
y
s
tem
s
em
p
lo
y
in
g
Me
r
k
le
tr
ee
s
f
o
r
r
o
b
u
s
t
v
er
if
icatio
n
[
1
1
]
.
Gau
r
et
a
l
.
[
1
2
]
c
o
n
d
u
cted
a
co
m
p
ar
ativ
e
a
n
aly
s
is
o
f
cr
y
p
t
o
g
r
ap
h
ic
alg
o
r
ith
m
s
,
id
en
tify
i
n
g
AE
S
as
p
ar
ticu
lar
ly
ef
f
icien
t
r
eg
a
r
d
in
g
m
em
o
r
y
an
d
ex
ec
u
tio
n
tim
e.
AE
S
’
s
ef
f
icien
cy
s
u
p
p
o
r
ts
its
in
teg
r
atio
n
with
R
SA
in
h
y
b
r
id
c
r
y
p
t
o
g
r
ap
h
ic
m
o
d
els,
wh
ich
a
r
e
well
-
s
u
ited
f
o
r
h
ash
ch
ai
n
s
y
s
tem
s
lev
er
ag
in
g
Me
r
k
le
tr
ee
s
f
o
r
en
h
an
ce
d
in
teg
r
ity
c
h
ec
k
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
E
n
h
a
n
cin
g
s
ystem
in
teg
r
ity
w
ith
Mer
kle
tr
ee
:
efficien
t h
yb
r
i
d
cryp
to
g
r
a
p
h
y
u
s
in
g
R
S
A
…
(
I
r
z
a
N
u
r
F
a
u
z
i
)
5681
J
in
tch
ar
ad
ze
an
d
I
av
ich
[
6
]
e
x
p
lo
r
ed
h
y
b
r
i
d
en
cr
y
p
tio
n
with
AE
S
an
d
R
SA,
h
ig
h
lig
h
tin
g
s
ig
n
if
ican
t
s
ec
u
r
ity
b
en
ef
its
an
d
e
f
f
icien
t
v
ital
ex
ch
an
g
es.
T
h
e
co
n
ju
n
ctio
n
o
f
t
h
ese
alg
o
r
ith
m
s
w
ith
in
a
h
ash
ch
ain
ar
ch
itectu
r
e
o
f
f
er
s
r
o
b
u
s
t
p
r
o
tectio
n
an
d
s
p
ee
d
,
with
Me
r
k
le
tr
ee
s
f
u
r
th
er
r
ein
f
o
r
cin
g
d
ata
v
er
if
icatio
n
b
y
estab
lis
h
in
g
a
s
ec
u
r
e
au
d
it tr
ai
l.
Sh
o
lik
h
atin
et
a
l.
[
1
3
]
e
x
a
m
in
ed
th
e
ex
ec
u
tio
n
tim
e
a
n
d
a
v
alan
ch
e
ef
f
ec
t
o
f
R
SA
an
d
AE
S,
d
em
o
n
s
tr
atin
g
AE
S
’
s
s
u
p
er
i
o
r
p
er
f
o
r
m
an
ce
.
Z
o
u
et
a
l.
[
1
4
]
f
u
r
th
e
r
n
o
ted
th
at
th
e
s
tab
ilit
y
o
f
h
y
b
r
id
alg
o
r
ith
m
s
f
o
r
p
r
o
ce
s
s
in
g
lar
g
e
f
iles
is
cr
u
cial
f
o
r
m
ain
ta
in
in
g
h
ig
h
in
teg
r
ity
with
in
h
ash
ch
ain
s
y
s
tem
s
en
r
ich
ed
b
y
Me
r
k
le
t
r
ee
s
tr
u
c
tu
r
es.
B
o
th
s
tu
d
ies
h
ig
h
lig
h
t
t
h
at
th
e
ef
f
icien
cy
a
n
d
s
tab
ilit
y
o
f
cr
y
p
to
g
r
ap
h
ic
alg
o
r
ith
m
s
ar
e
cr
itical
f
ac
to
r
s
in
p
r
eser
v
in
g
d
ata
in
teg
r
ity
,
es
p
ec
ially
wh
en
ap
p
lied
to
c
o
m
p
lex
an
d
lar
g
e
-
s
ca
le
h
ash
ch
ain
s
y
s
tem
s
en
h
an
ce
d
b
y
Me
r
k
le
t
r
ee
s
tr
u
ctu
r
es.
Hash
ch
ain
s
co
m
b
in
ed
with
Me
r
k
le
tr
ee
s
p
r
o
v
id
e
a
s
tr
o
n
g
au
th
e
n
ticatio
n
an
d
d
ata
in
teg
r
ity
f
r
am
ewo
r
k
.
Z
h
ao
et
a
l.
[
1
5
]
d
em
o
n
s
tr
ated
th
e
e
f
f
icac
y
o
f
h
ash
ch
ain
-
in
teg
r
ated
s
etu
p
s
.
Han
an
d
J
ian
g
[
1
6
]
p
r
o
p
o
s
ed
a
s
ec
u
r
e
c
o
m
m
u
n
icatio
n
m
eth
o
d
b
ased
o
n
m
ess
ag
e
h
ash
ch
ain
s
,
d
em
o
n
s
tr
atin
g
im
p
r
o
v
ed
m
ess
ag
e
in
teg
r
ity
,
n
o
n
-
r
ep
u
d
iatio
n
,
a
n
d
tr
an
s
m
is
s
io
n
ef
f
icien
cy
th
r
o
u
g
h
ch
ain
-
b
ased
au
th
e
n
ticatio
n
an
d
s
ig
n
atu
r
e
m
ec
h
an
is
m
s
.
T
h
ese
ap
p
r
o
ac
h
es
co
llectiv
ely
in
f
o
r
m
s
tr
ateg
i
es
to
en
h
an
ce
s
y
s
tem
in
teg
r
it
y
th
r
o
u
g
h
th
e
a
d
ep
t
u
s
e
o
f
h
y
b
r
id
c
r
y
p
to
g
r
ap
h
y
a
n
d
Me
r
k
le
tr
ee
s
.
3.
M
E
T
H
O
D
C
r
y
p
to
g
r
ap
h
ic
alg
o
r
ith
m
s
en
h
an
ce
d
ata
s
ec
u
r
ity
b
y
tr
an
s
f
o
r
m
in
g
in
p
u
t
in
t
o
s
ec
u
r
e
o
u
tp
u
t
th
r
o
u
g
h
d
ef
in
ed
s
tep
s
.
T
h
is
p
ap
er
e
x
a
m
in
es
R
SA
an
d
AE
S
en
cr
y
p
t
io
n
with
in
a
h
ash
ch
ain
f
r
am
ewo
r
k
en
r
ich
ed
b
y
Me
r
k
le
tr
ee
s
.
R
SA,
an
asy
m
m
etr
ic
alg
o
r
ith
m
,
s
ec
u
r
es
k
ey
ex
ch
an
g
es,
wh
ile
AE
S
o
f
f
er
s
ef
f
icien
t
s
y
m
m
etr
ic
en
cr
y
p
tio
n
.
Me
r
k
le
tr
ee
s
r
ein
f
o
r
ce
d
ata
in
teg
r
ity
an
d
v
er
if
ic
atio
n
.
T
o
g
eth
er
,
th
ese
tech
n
o
l
o
g
ies
f
o
r
m
a
r
o
b
u
s
t
ar
ch
itectu
r
e
th
at
s
tr
en
g
th
e
n
s
s
ec
u
r
ity
,
en
s
u
r
es
d
ata
in
teg
r
it
y
,
an
d
d
eliv
er
s
ef
f
icien
t
cr
y
p
to
g
r
ap
h
ic
s
o
lu
tio
n
s
ac
r
o
s
s
ap
p
licatio
n
s
.
3
.
1
.
AE
S
T
h
e
ad
v
an
ce
d
en
cr
y
p
tio
n
s
tan
d
ar
d
(
AE
S)
is
a
m
o
d
e
r
n
s
y
m
m
etr
ic
cr
y
p
t
o
g
r
ap
h
ic
alg
o
r
ith
m
in
tr
o
d
u
ce
d
b
y
NI
ST
in
2
0
0
1
t
o
r
ep
lace
th
e
d
ata
en
cr
y
p
tio
n
s
tan
d
ar
d
(
DE
S)
[
1
6
]
.
AE
S
was
d
ev
elo
p
e
d
b
y
J
o
an
Dae
m
en
an
d
Vin
ce
n
t
R
ijm
en
an
d
s
elec
ted
f
o
r
its
r
esis
tan
ce
to
cr
y
p
t
o
g
r
a
p
h
ic
attac
k
s
,
co
m
p
u
tatio
n
al
ef
f
icien
cy
,
an
d
d
esig
n
s
im
p
licity
[
1
7
]
.
AE
S
o
p
e
r
ates
with
a
b
lo
ck
len
g
th
o
f
1
2
8
b
its
an
d
k
ey
len
g
th
s
o
f
1
2
8
,
1
9
2
,
o
r
2
5
6
b
its
,
with
th
e
n
u
m
b
er
o
f
r
o
u
n
d
s
v
ar
y
in
g
b
ased
o
n
cr
u
cial
len
g
t
h
[
1
8
]
.
AE
S
em
p
lo
y
s
f
iv
e
d
ata
u
n
its
:
b
it,
b
y
te,
wo
r
d
,
b
lo
c
k
,
an
d
s
tate.
A
b
it
is
th
e
s
m
allest
d
ata
u
n
it,
p
ar
t
o
f
th
e
b
in
ar
y
s
y
s
tem
,
wh
ile
a
b
y
te
co
n
s
is
ts
o
f
8
b
its
.
A
wo
r
d
is
4
b
y
tes
(
3
2
b
its
)
,
an
d
a
b
lo
ck
is
1
6
b
y
tes
(
1
2
8
b
its
)
.
T
h
e
s
tate
is
a
b
l
o
ck
ar
r
an
g
ed
as
a
4
x
4
b
y
te
m
atr
ix
[
1
9
]
.
T
h
e
e
n
cr
y
p
tio
n
p
r
o
ce
s
s
in
v
o
lv
es
tr
an
s
f
o
r
m
in
g
th
e
s
tate
in
s
e
v
er
al
r
o
u
n
d
s
,
ea
c
h
co
m
p
r
is
in
g
f
o
u
r
t
r
an
s
f
o
r
m
atio
n
s
:
Su
b
B
y
tes,
Sh
if
tR
o
ws,
Mix
C
o
lu
m
n
s
,
an
d
Ad
d
R
o
u
n
d
Key
.
T
h
e
n
u
m
b
e
r
o
f
r
o
u
n
d
s
d
ep
en
d
s
o
n
th
e
k
e
y
len
g
th
,
a
n
d
Mix
C
o
lu
m
n
s
is
o
m
itted
in
th
e
f
i
n
al
r
o
u
n
d
[
1
9
]
.
Dec
r
y
p
tio
n
i
n
AE
S
is
th
e
r
e
v
er
s
e
o
f
t
h
e
en
c
r
y
p
tio
n
p
r
o
ce
s
s
,
with
ea
ch
tr
an
s
f
o
r
m
atio
n
h
av
in
g
its
in
v
er
s
e:
I
n
v
Su
b
B
y
tes,
I
n
v
Sh
if
tR
o
ws,
an
d
I
n
v
Mix
C
o
lu
m
n
s
.
T
h
e
p
r
o
ce
d
u
r
es
en
s
u
r
e
th
e
s
e
cu
r
e
co
n
v
er
s
io
n
o
f
en
cr
y
p
ted
d
ata
b
ac
k
t
o
its
o
r
ig
in
al
f
o
r
m
,
m
ain
tain
i
n
g
d
ata
in
teg
r
ity
an
d
c
o
n
f
id
e
n
tiality
th
r
o
u
g
h
o
u
t
th
e
tr
an
s
f
o
r
m
atio
n
[
2
0
]
.
T
h
is
r
e
v
e
r
s
al
p
r
o
ce
s
s
n
o
t
o
n
ly
r
esto
r
es
t
h
e
o
r
i
g
in
al
d
ata
b
u
t
also
r
ein
f
o
r
ce
s
th
e
r
eliab
ilit
y
o
f
AE
S in
s
ec
u
r
e
co
m
m
u
n
icati
o
n
s
y
s
tem
s
wh
er
e
d
ata
ac
cu
r
a
cy
an
d
p
r
o
tectio
n
ar
e
p
a
r
am
o
u
n
t.
3
.
2
.
RSA
R
SA
is
a
wid
ely
r
ec
o
g
n
ized
p
u
b
lic
-
k
ey
al
g
o
r
ith
m
,
in
tr
o
d
u
ce
d
in
1
9
7
6
b
y
M
I
T
r
esear
ch
er
s
R
o
n
R
iv
est,
Ad
i
Sh
am
ir
,
an
d
L
eo
n
ar
d
Ad
lem
an
[
2
1
]
.
I
ts
s
ec
u
r
ity
is
r
o
o
ted
in
th
e
co
m
p
lex
ity
o
f
f
ac
to
r
in
g
lar
g
e
n
u
m
b
er
s
in
t
o
p
r
im
e
f
ac
to
r
s
.
R
SA
’
s
co
m
p
u
tatio
n
s
r
ely
o
n
E
u
ler
’
s
th
eo
r
em
,
with
E
u
ler
’
s
to
t
ien
t
f
u
n
ctio
n
,
Φ
(
n
)
,
r
ep
r
esen
tin
g
th
e
c
o
u
n
t
o
f
n
u
m
b
er
s
less
th
an
n
th
at
a
r
e
co
p
r
i
m
e
to
n
.
Fo
r
p
r
im
e
n
u
m
b
er
s
,
Φ
(
n
)
e
q
u
als
n
-
1
,
a
n
d
if
n
eq
u
als th
e
p
r
o
d
u
ct
o
f
two
p
r
im
es (
p
an
d
q
)
,
th
en
Φ
(
n
)
is
(
p
-
1
)
(
q
-
1)
[
2
2
]
.
R
SA
’
s
en
cr
y
p
tio
n
a
n
d
d
ec
r
y
p
tio
n
p
r
o
ce
s
s
es
h
in
g
e
o
n
s
elec
t
in
g
two
lar
g
e
r
a
n
d
o
m
p
r
im
e
n
u
m
b
er
s
,
p
an
d
q
.
T
h
ese
p
r
im
es
g
en
er
ate
th
e
m
o
d
u
lu
s
=
,
wh
ich
is
u
s
ed
i
n
th
e
p
u
b
lic
k
ey
.
T
h
e
R
SA
k
e
y
g
en
er
atio
n
in
v
o
lv
es
ca
lcu
latin
g
Φ
(
n
)
an
d
s
elec
tin
g
an
in
teg
er
e
as
th
e
p
u
b
lic
k
ey
,
wh
er
e
1
<
e
<
Φ
(
n
)
an
d
e
is
co
p
r
im
e
with
Φ
(
n
)
.
T
h
e
d
ec
r
y
p
tio
n
k
ey
,
d
,
is
d
eter
m
in
e
d
b
y
th
e
r
elati
o
n
s
h
ip
ed
≡
1
(
m
o
d
Φ
(
n
)
)
[
2
1
]
.
R
SA
’
s
en
cr
y
p
tio
n
in
v
o
lv
es
co
n
v
er
tin
g
th
e
p
lain
tex
t
m
ess
ag
e
in
to
b
lo
ck
s
,
ap
p
ly
in
g
th
e
f
o
r
m
u
la
c
≡
m
e
m
o
d
n
to
tr
an
s
f
o
r
m
it
in
to
cip
h
er
tex
t.
Dec
r
y
p
tio
n
r
ev
er
s
es
th
is
u
s
in
g
m
≡
c
d
m
o
d
n
,
r
ev
ea
lin
g
th
e
p
lain
tex
t.
T
h
is
p
r
o
ce
s
s
em
p
h
a
s
izes
s
ec
u
r
e
v
ital
ex
ch
an
g
es
a
n
d
en
s
u
r
es
d
ata
co
n
f
i
d
en
tiality
,
m
ak
in
g
R
SA
an
in
teg
r
al
p
ar
t
o
f
m
o
d
er
n
cr
y
p
t
o
g
r
ap
h
ic
p
r
o
to
c
o
ls
[
2
3
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
6
,
Decem
b
e
r
20
25
:
5
6
7
9
-
5
6
8
9
5682
3
.
3
.
H
a
s
h
c
ha
in
A
h
ash
c
h
ain
is
a
cr
y
p
to
g
r
ap
h
i
c
tech
n
iq
u
e
f
o
r
s
ec
u
r
in
g
d
ata
b
y
s
u
cc
ess
f
u
lly
g
en
er
atin
g
a
s
eq
u
en
ce
o
f
r
elate
d
h
ash
v
alu
es.
I
t
p
r
o
tect
s
d
ata
tr
an
s
m
itted
o
v
er
c
o
m
m
u
n
icatio
n
n
etwo
r
k
s
b
y
e
n
cr
y
p
tin
g
it
u
s
in
g
h
ash
v
alu
es
as
en
cr
y
p
tio
n
k
e
y
s
[
2
4
]
.
T
h
e
h
ash
f
u
n
ctio
n
H
is
a
n
alg
o
r
ith
m
th
at
ac
ce
p
ts
an
i
n
p
u
t
m
ess
ag
e
an
d
a
f
ix
ed
-
len
g
th
k
e
y
,
p
r
o
d
u
ci
n
g
a
n
o
u
tp
u
t m
ess
ag
e
o
f
a
f
ix
ed
le
n
g
th
r
e
f
er
r
ed
to
as th
e
d
ig
est
[
4
]
.
3
.
4
.
M
er
k
le
t
re
e
T
h
e
Me
r
k
le
T
r
ee
,
in
tr
o
d
u
ce
d
b
y
Me
r
k
le
i
n
1
9
7
9
,
is
a
m
eth
o
d
f
o
r
o
r
g
an
izin
g
d
ata
in
t
o
b
lo
ck
s
,
co
m
p
u
tin
g
h
ash
v
alu
es
f
o
r
ea
ch
b
lo
c
k
,
a
n
d
in
s
er
tin
g
t
h
em
i
n
to
leaf
n
o
d
es
[
2
5
]
.
T
h
is
p
r
o
c
ess
is
r
ep
ea
ted
in
a
b
in
ar
y
tr
ee
s
tr
u
ctu
r
e
u
n
til
a
s
in
g
le
h
ash
v
alu
e,
k
n
o
wn
as
th
e
h
ash
r
o
o
t,
is
cr
ea
ted
.
T
h
e
h
ash
r
o
o
t
s
er
v
es
as
a
s
ig
n
atu
r
e
f
o
r
v
er
if
y
in
g
t
h
e
i
n
teg
r
ity
o
f
th
e
d
ata
b
lo
ck
s
.
I
n
b
lo
c
k
ch
ain
tech
n
o
l
o
g
y
,
th
e
Me
r
k
le
t
r
ee
is
co
m
m
o
n
l
y
u
s
ed
to
v
er
if
y
th
e
i
n
teg
r
ity
o
f
b
lo
c
k
d
ata
[
2
6
]
.
A
Me
r
k
le
t
r
ee
is
p
ar
ticu
lar
ly
ef
f
ec
tiv
e
at
h
an
d
lin
g
lar
g
e
d
at
asets
b
y
d
iv
id
in
g
th
em
in
to
b
l
o
ck
s
o
f
a
s
p
ec
if
ic
s
ize
an
d
p
lacin
g
th
e
m
in
co
r
r
esp
o
n
d
in
g
leaf
n
o
d
e
s
.
W
h
en
s
y
n
ch
r
o
n
izin
g
d
ata
t
o
an
o
th
er
n
o
d
e
,
th
e
Me
r
k
le
r
o
o
t
is
ex
tr
ac
ted
,
allo
win
g
f
o
r
a
th
o
r
o
u
g
h
in
teg
r
i
ty
ch
ec
k
.
E
v
en
a
s
in
g
le
-
b
y
te
er
r
o
r
d
u
r
in
g
d
ata
tr
an
s
m
is
s
io
n
ca
n
b
e
q
u
ick
ly
id
en
tifie
d
b
y
co
m
p
ar
in
g
Me
r
k
le
r
o
o
ts
,
as
ev
e
r
y
d
ata
b
lo
c
k
’
s
h
ash
v
alu
e
is
co
m
p
ar
ed
with
o
th
er
s
,
e
n
s
u
r
in
g
d
ata
in
teg
r
ity
in
b
lo
ck
ch
ain
en
v
ir
o
n
m
en
ts
[
2
6
]
.
As
an
ess
en
tial
co
m
p
o
n
en
t
o
f
b
lo
ck
c
h
ain
tec
h
n
o
l
o
g
y
,
th
e
Me
r
k
le
t
r
ee
en
ab
les
s
ec
u
r
e
d
a
ta
s
tab
ilit
y
an
d
co
n
ten
t
v
er
if
icatio
n
.
I
t
is
in
teg
r
al
to
b
lo
ck
ch
ain
ar
ch
itectu
r
es,
f
ac
ilit
atin
g
th
e
s
ec
u
r
e
d
ata
ex
ch
an
g
e
b
etwe
en
u
s
er
s
b
y
en
s
u
r
in
g
t
h
at
all
d
ata
r
em
ain
s
co
n
s
is
ten
t
an
d
er
r
o
r
-
f
r
ee
ac
r
o
s
s
th
e
n
etwo
r
k
[
2
7
]
.
T
h
is
m
ec
h
an
is
m
en
s
u
r
es
th
at
an
y
tam
p
er
in
g
o
r
in
co
n
s
is
ten
cy
with
in
th
e
d
ata
b
lo
ck
s
ca
n
b
e
s
wif
tly
id
en
tifie
d
,
m
ak
in
g
Me
r
k
le
tr
ee
s
a
co
r
n
er
s
to
n
e
o
f
t
r
u
s
t a
n
d
r
eliab
ilit
y
in
d
ec
en
tr
alize
d
s
y
s
tem
s
.
3
.
5
.
M
et
ho
do
lo
g
ic
a
l
f
o
un
da
t
io
n a
nd
pro
ce
du
ra
l desig
n
T
h
e
p
r
o
p
o
s
ed
cr
y
p
to
g
r
ap
h
ic
m
o
d
el
is
d
esig
n
ed
to
en
h
an
ce
d
ata
in
teg
r
ity
an
d
s
ec
u
r
ity
b
y
co
m
b
in
in
g
s
y
m
m
etr
ic
an
d
asy
m
m
etr
ic
e
n
cr
y
p
tio
n
tech
n
iq
u
es
with
in
a
h
ash
-
b
ased
f
r
am
ewo
r
k
.
T
h
is
s
ec
tio
n
o
u
tlin
es
th
e
th
eo
r
etica
l
b
asis
u
n
d
er
ly
in
g
t
h
e
m
eth
o
d
s
elec
tio
n
an
d
ex
p
lain
s
th
e
p
r
o
ce
d
u
r
al
s
tep
s
tak
en
d
u
r
in
g
th
e
r
esear
ch
.
B
y
lev
er
ag
in
g
th
e
co
m
p
lem
en
tar
y
s
tr
en
g
th
s
o
f
AE
S,
R
SA,
an
d
Me
r
k
le
t
r
ee
s
tr
u
ctu
r
es,
t
h
e
m
o
d
el
estab
lis
h
es
a
r
esil
ien
t
cr
y
p
to
g
r
ap
h
ic
f
o
u
n
d
atio
n
ca
p
a
b
le
o
f
d
etec
tin
g
tam
p
er
in
g
an
d
e
n
s
u
r
in
g
s
ec
u
r
e
d
ata
t
r
an
s
m
is
s
io
n
ac
r
o
s
s
d
is
tr
ib
u
ted
en
v
ir
o
n
m
e
n
ts
.
T
h
e
m
o
d
el
u
tili
ze
s
two
f
o
u
n
d
atio
n
al
cr
y
p
to
g
r
ap
h
ic
alg
o
r
ith
m
s
:
AE
S
an
d
R
SA.
AE
S
i
s
a
s
y
m
m
etr
ic
en
cr
y
p
tio
n
alg
o
r
ith
m
wid
ely
r
ec
o
g
n
ized
f
o
r
its
h
ig
h
c
o
m
p
u
tatio
n
al
ef
f
icien
cy
,
s
ca
lab
ilit
y
,
an
d
s
u
itab
ilit
y
f
o
r
s
ec
u
r
in
g
lar
g
e
v
o
lu
m
es
o
f
d
ata
in
r
ea
l
-
tim
e
ap
p
licatio
n
s
.
I
t
o
p
er
ates
o
n
f
ix
ed
-
s
ize
b
lo
ck
s
an
d
s
u
p
p
o
r
ts
m
u
ltip
le
k
ey
len
g
th
s
,
m
ak
i
n
g
it
s
u
itab
le
f
o
r
h
ig
h
-
s
p
ee
d
d
ata
en
cr
y
p
tio
n
[
2
8
]
.
R
SA,
o
n
th
e
o
th
er
h
an
d
,
is
an
asy
m
m
etr
ic
en
cr
y
p
tio
n
alg
o
r
i
th
m
th
at
p
r
o
v
id
es
s
ec
u
r
e
k
ey
ex
ch
an
g
e
an
d
d
ig
ital
s
ig
n
atu
r
e
ca
p
ab
ilit
ies.
I
ts
s
ec
u
r
ity
is
b
ased
o
n
th
e
m
at
h
em
atica
l
d
if
f
icu
lty
o
f
p
r
im
e
f
ac
to
r
izatio
n
,
wh
ich
en
s
u
r
es
r
o
b
u
s
tn
ess
in
k
ey
m
an
ag
em
en
t
[
2
9
]
.
T
o
f
u
r
th
e
r
s
tr
en
g
th
en
th
e
i
n
teg
r
ity
v
er
if
icatio
n
p
r
o
ce
s
s
,
th
e
m
o
d
el
in
co
r
p
o
r
ates
Me
r
k
le
t
r
ee
s
tr
u
ctu
r
es
in
to
a
h
ash
ch
ain
s
y
s
tem
.
A
Me
r
k
le
t
r
ee
is
a
b
i
n
ar
y
tr
ee
o
f
h
ash
v
alu
es
th
at
e
n
ab
les
ef
f
icien
t
an
d
s
ca
lab
le
v
er
if
icatio
n
o
f
d
ata
b
l
o
ck
s
.
E
ac
h
leaf
n
o
d
e
r
e
p
r
esen
t
s
th
e
h
ash
o
f
a
d
ata
b
lo
ck
,
a
n
d
in
ter
n
al
n
o
d
es
ar
e
d
er
iv
ed
f
r
o
m
th
e
h
ash
es
o
f
th
eir
ch
ild
n
o
d
es.
T
h
e
r
o
o
t
o
f
th
e
tr
ee
,
k
n
o
wn
as
th
e
Me
r
k
le
r
o
o
t
,
s
er
v
es
as
a
cr
y
p
to
g
r
ap
h
ic
s
u
m
m
ar
y
o
f
th
e
en
tire
d
ataset
[
1
0
]
.
An
y
m
o
d
if
icatio
n
to
a
s
in
g
le
d
ata
b
lo
c
k
r
esu
lts
in
a
ch
an
g
e
in
th
e
co
r
r
esp
o
n
d
in
g
h
ash
,
wh
ich
p
r
o
p
ag
ates
th
r
o
u
g
h
t
h
e
t
r
ee
an
d
alter
s
th
e
Me
r
k
le
r
o
o
t
,
th
er
eb
y
en
a
b
lin
g
im
m
ed
iate
d
etec
tio
n
o
f
tam
p
er
in
g
.
T
h
e
m
eth
o
d
o
lo
g
ical
r
atio
n
al
e
f
o
r
th
is
in
teg
r
atio
n
lies
in
th
e
co
m
p
lem
e
n
tar
y
s
tr
en
g
th
s
o
f
th
e
co
m
p
o
n
en
ts
.
AE
S e
n
s
u
r
es r
ap
id
en
cr
y
p
tio
n
an
d
d
ec
r
y
p
tio
n
,
R
SA
s
ec
u
r
es th
e
tr
an
s
m
is
s
io
n
o
f
en
cr
y
p
tio
n
k
ey
s
,
an
d
Me
r
k
le
tr
ee
s
p
r
o
v
id
e
a
r
eliab
le
m
ec
h
an
is
m
f
o
r
v
er
if
y
i
n
g
d
ata
in
teg
r
it
y
ac
r
o
s
s
d
is
tr
ib
u
ted
s
y
s
tem
s
.
T
h
e
h
ash
ch
ain
s
tr
u
ctu
r
e
lin
k
s
ea
c
h
d
ata
b
lo
c
k
to
its
p
r
ed
ec
ess
o
r
,
cr
ea
tin
g
a
s
eq
u
en
tial
d
e
p
e
n
d
en
cy
t
h
at
f
u
r
t
h
er
r
ein
f
o
r
ce
s
th
e
s
y
s
tem
’
s
r
esis
tan
ce
to
u
n
au
th
o
r
ized
alter
atio
n
s
.
T
h
e
r
esear
ch
p
r
o
ce
d
u
r
e
is
im
p
lem
en
ted
as f
o
llo
ws
.
a.
I
n
itializatio
n
o
f
em
p
ty
ar
r
a
y
s
to
s
to
r
e
en
cr
y
p
ted
d
ata
b
lo
ck
s
an
d
Me
r
k
le
tr
ee
leaf
h
ash
es.
b.
I
ter
ativ
e
p
r
o
ce
s
s
in
g
o
f
ea
ch
d
a
ta
b
lo
ck
:
−
C
o
m
p
u
te
th
e
h
ash
o
f
th
e
b
lo
ck
.
−
E
n
cr
y
p
t t
h
e
b
lo
c
k
u
s
in
g
AE
S
with
a
g
en
er
ated
s
y
m
m
etr
ic
k
e
y
.
−
E
n
cr
y
p
t t
h
e
AE
S k
ey
u
s
in
g
R
SA w
ith
th
e
p
u
b
lic
k
e
y
.
−
Ap
p
en
d
th
e
en
cr
y
p
ted
b
lo
ck
a
n
d
en
cr
y
p
ted
k
ey
to
th
e
d
ata
c
h
ain
.
−
Gen
er
ate
a
n
ew
AE
S k
ey
f
o
r
t
h
e
n
ex
t
b
lo
ck
u
s
in
g
th
e
cu
r
r
en
t b
lo
ck
’
s
h
ash
.
−
Sto
r
e
th
e
b
lo
ck
h
ash
in
t
h
e
Me
r
k
le
tr
ee
leaf
ar
r
ay
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
E
n
h
a
n
cin
g
s
ystem
in
teg
r
ity
w
ith
Mer
kle
tr
ee
:
efficien
t h
yb
r
i
d
cryp
to
g
r
a
p
h
y
u
s
in
g
R
S
A
…
(
I
r
z
a
N
u
r
F
a
u
z
i
)
5683
c.
C
o
n
s
tr
u
ctio
n
o
f
t
h
e
Me
r
k
le
tr
e
e
f
r
o
m
t
h
e
co
llected
leaf
h
ash
e
s
.
d.
C
o
m
p
u
tatio
n
o
f
th
e
Me
r
k
le
r
o
o
t
to
r
ep
r
esen
t th
e
in
teg
r
ity
o
f
th
e
d
ataset.
e.
Gen
er
atio
n
o
f
v
er
if
icatio
n
p
r
o
o
f
s
f
o
r
ea
c
h
b
lo
c
k
h
ash
a
n
d
v
a
lid
atio
n
ag
ain
s
t th
e
Me
r
k
le
r
o
o
t
.
f.
Fin
al
o
u
tp
u
t in
clu
d
es th
e
Me
r
k
le
r
o
o
t
a
n
d
th
e
e
n
cr
y
p
ted
d
at
a
ch
ain
.
T
h
is
p
r
o
ce
d
u
r
e
e
n
s
u
r
es
th
at
th
e
cr
y
p
t
o
g
r
a
p
h
ic
o
p
er
atio
n
s
ar
e
b
o
th
s
ec
u
r
e
an
d
r
ep
r
o
d
u
cib
le.
B
y
co
m
b
in
in
g
AE
S,
R
SA,
an
d
Me
r
k
le
tr
ee
s
tr
u
ctu
r
es
with
in
a
h
ash
ch
ain
f
r
am
ewo
r
k
,
th
e
m
o
d
el
lev
er
ag
es
th
e
s
tr
en
g
th
s
o
f
ea
ch
co
m
p
o
n
e
n
t.
As
a
r
esu
lt,
it
o
f
f
er
s
a
co
m
p
r
eh
e
n
s
iv
e
s
o
lu
tio
n
f
o
r
m
ain
tain
in
g
d
ata
co
n
f
id
en
tiality
a
n
d
in
teg
r
ity
in
d
ig
ital e
n
v
ir
o
n
m
en
ts
.
4.
P
RO
P
O
SE
D
M
O
D
E
L
T
h
e
p
r
o
p
o
s
ed
m
o
d
el
em
p
l
o
y
s
h
y
b
r
id
cr
y
p
t
o
g
r
a
p
h
y
,
c
o
m
b
in
in
g
s
y
m
m
etr
ic
an
d
a
s
y
m
m
etr
ic
en
cr
y
p
tio
n
tech
n
i
q
u
es
to
b
o
ls
ter
d
ata
s
ec
u
r
ity
with
in
a
h
ash
ch
ain
s
y
s
tem
,
f
u
r
th
er
r
ein
f
o
r
ce
d
b
y
Me
r
k
le
t
r
ee
s
tr
u
ctu
r
es.
T
h
is
s
tr
ateg
y
h
a
r
n
ess
es
th
e
s
p
ee
d
o
f
s
y
m
m
etr
i
c
k
ey
e
n
cr
y
p
tio
n
alo
n
g
s
id
e
t
h
e
r
o
b
u
s
t
s
ec
u
r
ity
p
r
o
v
id
e
d
b
y
asy
m
m
etr
ic
k
e
y
cr
y
p
to
g
r
ap
h
y
an
d
Me
r
k
le
tr
ee
s
.
W
h
ile
h
y
b
r
id
cr
y
p
to
g
r
ap
h
y
is
ty
p
ically
s
ec
u
r
e,
it
m
ay
en
co
u
n
ter
c
h
allen
g
es lik
e
s
lo
wer
p
r
o
ce
s
s
in
g
s
p
ee
d
s
with
lar
g
e
d
atasets
.
As
s
h
o
wn
in
Fig
u
r
e
1
,
th
is
m
o
d
el
co
m
b
i
n
es
f
ast
d
ata
en
cr
y
p
tio
n
u
s
in
g
AE
S
with
s
ec
u
r
e
k
ey
ex
ch
an
g
e
th
r
o
u
g
h
R
SA,
all
w
ith
in
a
h
ash
ch
ain
s
tr
u
ctu
r
e
.
E
ac
h
d
ata
b
lo
ck
in
clu
d
es
a
“
Nex
t
k
ey
”
,
wh
ich
is
g
en
er
ated
f
r
o
m
th
e
h
ash
o
f
th
e
cu
r
r
e
n
t
b
lo
ck
a
n
d
u
s
ed
to
en
cr
y
p
t
th
e
n
e
x
t
o
n
e
—
cr
e
atin
g
a
s
ec
u
r
e
lin
k
b
etwe
en
b
lo
c
k
s
.
T
h
e
AE
S
k
e
y
u
s
ed
to
en
c
r
y
p
t
ea
ch
d
ata
b
l
o
ck
is
s
ec
u
r
ely
wr
ap
p
e
d
u
s
in
g
R
SA
en
cr
y
p
tio
n
—
r
ef
er
r
ed
to
in
th
e
m
o
d
el
as
“
R
SA
E
n
c
”
—
wh
ich
en
s
u
r
es
a
cc
ess
an
d
d
ec
r
y
p
tio
n
ar
e
r
estricte
d
to
au
th
o
r
ized
u
s
er
s
.
T
o
f
u
r
th
er
en
h
a
n
ce
th
e
s
y
s
tem
’
s
r
eliab
ili
ty
,
ea
ch
b
lo
ck
is
v
er
if
ied
th
r
o
u
g
h
Me
r
k
le
t
r
ee
v
alid
atio
n
,
en
ab
lin
g
q
u
ick
an
d
ac
cu
r
ate
d
etec
tio
n
o
f
an
y
u
n
a
u
th
o
r
ize
d
ch
an
g
es
to
th
e
d
ata.
T
h
is
lay
e
r
ed
ap
p
r
o
ac
h
y
ield
s
a
cr
y
p
to
g
r
a
p
h
ic
f
r
am
ewo
r
k
th
at
is
n
o
t
o
n
l
y
s
ec
u
r
e
b
u
t
also
r
esil
ien
t
an
d
s
ca
lab
le
in
e
n
v
ir
o
n
m
en
ts
wh
er
e
d
ata
in
teg
r
ity
is
cr
u
cial.
Fig
u
r
e
1
.
Pro
p
o
s
ed
m
o
d
el
o
f
h
ash
ch
ain
b
lo
c
k
W
ith
in
th
is
f
r
am
ewo
r
k
,
d
ata
is
en
cr
y
p
ted
u
s
in
g
a
s
y
m
m
etr
ic
k
ey
,
wh
ich
is
th
en
s
ec
u
r
ed
with
th
e
s
en
d
er
’
s
p
r
iv
ate
asy
m
m
etr
ic
k
ey
.
T
h
e
r
ec
eiv
er
d
ec
r
y
p
ts
th
e
s
y
m
m
etr
ic
k
ey
to
ac
ce
s
s
th
e
d
ata.
Me
r
k
le
t
r
ee
v
alid
atio
n
en
s
u
r
es
in
teg
r
ity
b
y
v
er
if
y
i
n
g
ea
c
h
b
lo
c
k
an
d
d
etec
tin
g
u
n
a
u
th
o
r
ize
d
ch
an
g
es.
T
h
is
p
r
o
ce
s
s
is
d
etailed
in
th
e
ac
co
m
p
an
y
in
g
p
s
eu
d
o
co
d
e
b
elo
w.
BEGIN
1. Initialize:
-
EncryptedDataChain[] ← []
-
MerkleLeaves[] ← []
2. FOR each block in Data[], DO
3. Compute the hash of the data block:
BlockHash ← Hash(block)
4. Encrypt data block with AES:
EncryptedBlock ← AES_Encrypt(AES_Key, block)
5. Encrypt AES key with RSA:
EncryptedAESKey ← RSA_Encrypt(RSA_PublicKey, AES_Key)
6. Append the encrypted block and encrypted AES key to the chain:
EncryptedDataChain.append({EncryptedBlock, EncryptedAESKey})
7. Generate a new AES key for the next block:
AES_Key ← Hash(BlockHash)
8. Append BlockHash to MerkleLeaves:
MerkleLeaves.append(BlockHash)
END FOR
9. Construct Merkle Tree from MerkleLeaves:
MerkleRoot ← ConstructMerkleTree(MerkleLeaves)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
6
,
Decem
b
e
r
20
25
:
5
6
7
9
-
5
6
8
9
5684
10. Verify Merkle Tree:
FOR each BlockHash in MerkleLeaves, DO
VerificationProof ←
GenerateProof(MerkleLeaves, BlockHash)
ASSERT MerkleTree_Verify(MerkleRoot, VerificationProof, BlockHash) == True
END FOR
11. Return MerkleRoot and EncryptedDataChain
END
T
h
e
p
r
o
v
id
ed
p
s
eu
d
o
co
d
e
o
u
t
lin
es
a
s
ec
u
r
e
d
ata
en
cr
y
p
tio
n
an
d
v
er
if
icatio
n
p
r
o
ce
s
s
u
s
in
g
h
y
b
r
id
cr
y
p
to
g
r
ap
h
y
,
i
n
teg
r
atin
g
A
E
S,
R
SA,
an
d
Me
r
k
le
tr
e
es
.
I
n
itially
,
it
s
ets
u
p
t
wo
em
p
ty
ar
r
a
y
s
,
EncryptedDataChain
f
o
r
s
to
r
in
g
en
cr
y
p
te
d
d
ata
an
d
k
e
y
s
an
d
MerkleLeaves
f
o
r
s
to
r
in
g
h
ash
v
alu
e
s
o
f
ea
ch
d
ata
b
lo
ck
.
Fo
r
ea
ch
d
ata
b
lo
ck
,
t
h
e
p
r
o
ce
s
s
b
eg
in
s
b
y
co
m
p
u
tin
g
its
h
ash
.
T
h
e
d
ata
b
lo
ck
is
th
en
en
cr
y
p
ted
u
s
in
g
AE
S
with
a
s
p
ec
if
ied
k
ey
,
en
s
u
r
in
g
d
ata
c
o
n
f
id
en
tiality
.
T
h
e
AE
S
k
ey
is
f
u
r
th
er
e
n
cr
y
p
te
d
with
R
SA,
s
ec
u
r
in
g
th
e
k
e
y
its
elf
.
T
h
e
en
c
r
y
p
ted
b
lo
ck
an
d
th
e
AE
S
k
ey
ar
e
ap
p
en
d
e
d
to
t
h
e
EncryptedDataChain
.
A
n
ew
AE
S
k
ey
f
o
r
t
h
e
n
e
x
t
b
lo
ck
is
g
en
er
ate
d
b
y
h
ash
in
g
th
e
cu
r
r
e
n
t
b
lo
c
k
’
s
h
ash
,
cr
ea
tin
g
a
ch
ain
o
f
lin
k
e
d
en
cr
y
p
tio
n
k
ey
s
.
Fo
llo
win
g
th
is
,
th
e
h
ash
o
f
ea
ch
d
ata
b
lo
c
k
is
ad
d
ed
to
MerkleLeaves
,
wh
ich
ar
e
u
s
ed
to
co
n
s
tr
u
ct
a
Me
r
k
le
T
r
ee
.
T
h
e
r
o
o
t
o
f
t
h
is
tr
ee
,
MerkleRoot
,
r
ep
r
esen
ts
th
e
cr
y
p
t
o
g
r
a
p
h
ic
s
u
m
m
ar
y
o
f
all
th
e
b
lo
ck
s
,
en
s
u
r
in
g
in
teg
r
it
y
v
er
if
icatio
n
o
f
th
e
en
tire
d
ata
s
et.
T
o
v
er
if
y
th
e
in
teg
r
i
ty
o
f
th
e
d
ata,
th
e
p
s
eu
d
o
co
d
e
g
en
er
ates
a
v
er
if
i
ca
tio
n
p
r
o
o
f
f
o
r
ea
ch
b
l
o
ck
h
ash
an
d
co
n
f
ir
m
s
it
ag
ain
s
t
th
e
Me
r
k
le
r
o
o
t
.
T
h
is
co
n
f
ir
m
atio
n
en
s
u
r
es
th
at
n
o
u
n
au
th
o
r
ized
ch
an
g
es
h
av
e
o
cc
u
r
r
ed
to
t
h
e
d
ata
b
lo
c
k
s
.
F
in
ally
,
th
e
p
r
o
ce
s
s
r
etu
r
n
s
th
e
Me
r
k
le
r
o
o
t
an
d
th
e
EncryptedDataChain
,
p
r
o
v
i
d
in
g
d
ata
s
ec
u
r
ity
t
h
r
o
u
g
h
en
c
r
y
p
tio
n
an
d
d
ata
in
teg
r
ity
th
r
o
u
g
h
th
e
Me
r
k
le
t
r
ee
s
tr
u
ctu
r
e.
5.
RE
SU
L
T
S
AND
D
I
SCU
SS
I
O
N
T
h
is
s
ec
tio
n
p
r
esen
ts
th
e
o
u
tco
m
es
o
f
th
e
co
m
p
r
eh
en
s
i
v
e
ev
alu
atio
n
o
f
th
e
p
r
o
p
o
s
ed
h
y
b
r
i
d
cr
y
p
to
g
r
ap
h
y
m
o
d
el
in
te
g
r
ate
d
with
Me
r
k
le
tr
ee
s
.
T
h
e
ev
a
lu
atio
n
is
s
tr
u
ctu
r
e
d
ac
r
o
s
s
s
ev
er
al
s
u
b
-
s
ec
tio
n
s
,
in
clu
d
in
g
p
r
elim
in
ar
y
test
s
,
co
m
p
lex
ity
ass
ess
m
en
ts
,
an
d
ex
ec
u
tio
n
tim
e
an
al
y
s
es.
T
h
e
p
r
elim
in
ar
y
test
s
f
o
cu
s
o
n
v
alid
atin
g
th
e
m
o
d
e
l
’
s
r
o
b
u
s
tn
ess
an
d
ab
ilit
y
to
m
ain
tain
d
ata
i
n
teg
r
ity
u
n
d
e
r
v
ar
io
u
s
c
o
n
d
itio
n
s
.
Fo
llo
win
g
th
is
,
th
e
co
m
p
lex
it
y
an
aly
s
is
o
f
th
e
cr
y
p
to
g
r
ap
h
ic
alg
o
r
ith
m
s
is
ex
p
lo
r
ed
,
o
f
f
er
in
g
in
s
ig
h
ts
in
to
th
eir
co
m
p
u
tatio
n
al
ef
f
icien
c
y
.
Fin
ally
,
e
x
ec
u
tio
n
tim
es
ar
e
ass
es
s
ed
to
d
eter
m
in
e
th
e
m
o
d
el
’
s
p
er
f
o
r
m
an
ce
in
r
ea
l
-
tim
e
ap
p
licatio
n
s
,
en
s
u
r
in
g
b
o
th
s
ec
u
r
ity
an
d
ef
f
icien
c
y
ar
e
u
p
h
el
d
.
5
.
1
.
I
nte
g
rit
y
t
esting
T
h
e
Me
r
k
le
t
r
ee
s
u
p
p
o
r
ts
d
a
ta
co
n
s
is
ten
cy
test
in
g
th
r
o
u
g
h
its
h
ier
ar
ch
ical
s
tr
u
ctu
r
e.
E
ac
h
n
o
d
e
co
n
tain
s
th
e
h
ash
o
f
its
ch
ild
n
o
d
es,
wh
ile
th
e
Me
r
k
le
r
o
o
t
s
er
v
es
as
th
e
o
v
er
all
in
t
eg
r
ity
m
ar
k
er
.
T
h
is
s
tr
u
ctu
r
e
is
ess
en
tial
f
o
r
m
ain
tain
in
g
d
ata
in
teg
r
ity
in
c
o
m
p
lex
an
d
d
is
tr
ib
u
ted
s
y
s
tem
s
,
en
s
u
r
in
g
th
at
in
f
o
r
m
atio
n
r
em
ain
s
in
tact
f
r
o
m
o
r
ig
in
t
o
d
esti
n
atio
n
[
3
]
.
T
h
is
ap
p
r
o
ac
h
en
s
u
r
es
im
m
e
d
iate
d
etec
tio
n
o
f
c
h
an
g
es
a
n
d
o
f
f
er
s
h
ig
h
v
er
i
f
icatio
n
ef
f
icie
n
cy
,
ev
e
n
with
lar
g
e
d
atasets
.
I
n
itially
,
a
test
u
s
in
g
en
tire
ly
v
alid
d
ata
co
n
f
ir
m
e
d
th
e
s
y
s
tem
’
s
b
aselin
e
in
teg
r
ity
ch
ec
k
s
.
Su
b
s
eq
u
en
tly
,
a
s
ec
o
n
d
test
in
v
o
lv
e
d
alter
in
g
o
n
e
o
f
t
h
e
d
ata
b
lo
ck
s
to
ass
ess
th
e
s
y
s
te
m
’
s
ab
ilit
y
to
d
etec
t
d
is
cr
ep
an
cies.
B
ased
o
n
th
e
r
e
s
u
lts
,
th
e
s
y
s
tem
s
u
cc
ess
f
u
lly
id
en
tifie
d
in
co
n
s
is
ten
cies,
p
r
o
v
id
in
g
o
u
tp
u
ts
th
at
m
atch
th
o
s
e
illu
s
tr
ated
in
th
e
f
ig
u
r
es.
T
h
is
test
ev
alu
ates
th
e
s
y
s
tem
’
s
r
eliab
ilit
y
in
a
n
o
m
aly
d
etec
tio
n
,
en
s
u
r
in
g
co
n
s
is
ten
t
an
d
ac
cu
r
ate
s
y
s
tem
f
u
n
ctio
n
s
.
An
aly
zin
g
th
e
test
r
esu
lts
p
r
o
v
id
es
in
s
ig
h
ts
in
to
th
e
s
y
s
tem
’
s
ef
f
ec
tiv
en
ess
in
p
r
eser
v
in
g
d
ata
in
teg
r
ity
.
Fig
u
r
e
2
d
em
o
n
s
tr
ates
th
e
cr
y
p
to
g
r
a
p
h
ic
s
tr
en
g
t
h
o
f
th
e
Me
r
k
le
t
r
ee
,
wh
ich
s
ec
u
r
es
d
ata
b
lo
ck
s
th
r
o
u
g
h
h
ier
ar
c
h
ical
h
ash
in
g
.
T
h
is
s
tr
u
ctu
r
e
allo
ws f
o
r
p
r
ec
is
e
d
etec
tio
n
o
f
ev
en
m
in
o
r
d
ata
m
o
d
if
icatio
n
s
.
As
a
r
esu
lt,
th
e
in
teg
r
ity
o
f
th
e
en
tire
d
ata
ch
ain
is
p
r
eser
v
e
d
,
p
r
o
tectin
g
it f
r
o
m
u
n
a
u
th
o
r
ize
d
alter
atio
n
s
.
F
i
g
u
r
e
2
(
a
)
r
e
f
l
e
ct
s
t
h
e
v
a
li
d
a
ti
o
n
r
e
s
u
l
ts
o
f
t
e
n
d
at
a
b
l
o
c
k
s
,
a
l
l
d
e
e
m
e
d
“
V
a
li
d
”
b
y
t
h
e
Me
r
k
l
e
t
r
e
e
v
e
r
i
f
i
c
a
t
i
o
n
p
r
o
c
e
s
s
.
T
h
i
s
c
o
n
s
is
t
e
n
t
s
t
a
t
u
s
i
n
d
i
c
a
t
es
t
h
a
t
e
ac
h
b
l
o
c
k
’
s
h
a
s
h
v
a
l
u
e
a
l
i
g
n
s
p
r
e
c
i
s
e
l
y
wi
t
h
t
h
e
e
x
p
e
c
t
e
d
v
a
l
u
e
s
,
c
o
n
f
i
r
m
i
n
g
th
a
t
t
h
e
d
a
t
a
r
e
m
a
i
n
s
u
n
a
l
t
e
r
ed
a
n
d
s
e
c
u
r
e
.
T
h
e
u
n
i
f
o
r
m
i
t
y
a
c
r
o
s
s
al
l
e
n
t
r
i
e
s
d
e
m
o
n
s
t
r
a
t
es
t
h
e
s
y
s
te
m
’
s
e
f
f
e
c
t
i
v
e
n
e
s
s
i
n
m
a
i
n
t
a
i
n
i
n
g
d
a
t
a
i
n
t
e
g
r
i
t
y
t
h
r
o
u
g
h
e
n
c
r
y
p
t
i
o
n
a
n
d
v
e
r
i
f
i
c
a
t
i
o
n
m
e
c
h
a
n
i
s
m
s
.
T
h
e
M
e
r
k
le
t
r
e
e
p
l
a
y
s
a
c
r
i
t
i
ca
l
r
o
l
e
h
e
r
e
,
e
n
s
u
r
i
n
g
t
h
a
t
e
v
e
n
t
h
e
s
li
g
h
t
e
s
t
d
a
t
a
m
o
d
i
f
i
c
a
t
i
o
n
w
o
u
ld
t
r
i
g
g
e
r
a
d
i
s
c
r
e
p
a
n
c
y
,
t
h
e
r
e
b
y
h
i
g
h
l
i
g
h
t
i
n
g
t
h
e
r
o
b
u
s
t
n
es
s
o
f
th
i
s
c
r
y
p
t
o
g
r
a
p
h
i
c
t
e
c
h
n
i
q
u
e
i
n
s
a
f
e
g
u
a
r
d
i
n
g
d
a
t
a
.
I
n
Fig
u
r
e
2
(
b
)
,
a
m
o
d
i
f
icatio
n
in
b
lo
ck
6
tr
ig
g
e
r
s
a
r
ip
p
le
e
f
f
ec
t,
r
esu
ltin
g
in
an
“
I
n
v
alid
”
s
tatu
s
f
o
r
b
lo
ck
s
ix
an
d
all
s
u
b
s
eq
u
en
t
b
lo
ck
s
.
T
h
is
illu
s
tr
ates
th
e
Me
r
k
le
T
r
ee
’
s
ef
f
ec
tiv
e
n
ess
in
m
ain
tain
in
g
d
ata
in
teg
r
ity
,
as
ev
en
a
s
in
g
le
a
lter
atio
n
d
is
r
u
p
ts
th
e
h
ash
v
er
if
icatio
n
f
o
r
all
d
ep
en
d
e
n
t
b
lo
ck
s
.
T
h
e
h
ash
in
co
n
s
is
ten
cy
b
e
g
in
s
with
th
e
alter
ed
b
lo
c
k
a
n
d
p
r
o
p
ag
ates
t
h
r
o
u
g
h
th
e
c
h
ain
,
em
p
h
asizin
g
th
e
r
o
b
u
s
tn
ess
o
f
th
is
cr
y
p
to
g
r
a
p
h
ic
m
eth
o
d
in
d
etec
tin
g
an
d
p
r
ev
en
ti
n
g
u
n
au
t
h
o
r
ized
c
h
an
g
es.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
E
n
h
a
n
cin
g
s
ystem
in
teg
r
ity
w
ith
Mer
kle
tr
ee
:
efficien
t h
yb
r
i
d
cryp
to
g
r
a
p
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y
u
s
in
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R
S
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(
I
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a
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a
u
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)
5685
(
a)
(
b
)
Fig
u
r
e
2
.
R
esu
lts
o
f
s
y
s
tem
test
in
g
: (
a)
all
v
alid
d
ata
s
ce
n
ar
io
an
d
(
b
)
alter
ed
d
ata
b
lo
c
k
s
ce
n
ar
io
T
h
e
in
teg
r
ity
test
in
g
r
esu
lts
u
n
d
er
s
co
r
e
th
e
s
y
s
tem
’
s
ab
ilit
y
to
d
etec
t
ev
en
m
in
im
al
d
ata
alter
atio
n
s
,
wh
ich
is
ess
en
tial
f
o
r
m
ain
tain
in
g
tr
u
s
t
in
d
is
tr
ib
u
ted
e
n
v
ir
o
n
m
en
ts
.
T
h
is
b
eh
a
v
io
r
r
ef
lec
ts
th
e
Me
r
k
le
T
r
ee
’
s
s
tr
en
g
th
in
an
o
m
aly
d
etec
tio
n
,
wh
er
e
a
s
in
g
le
b
lo
ck
ch
a
n
g
e
in
v
alid
ates
th
e
en
tire
c
h
ain
.
C
r
itically
,
th
is
im
p
lies
th
at
th
e
p
r
o
p
o
s
ed
m
o
d
el
is
n
o
t
o
n
ly
ef
f
ec
tiv
e
in
p
r
eser
v
in
g
d
ata
in
te
g
r
ity
b
u
t
also
s
er
v
es
as
a
p
r
o
ac
tiv
e
m
ec
h
an
is
m
f
o
r
id
e
n
tify
in
g
tam
p
er
in
g
in
r
ea
l
-
ti
m
e.
I
n
ter
p
r
etatio
n
o
f
th
ese
r
esu
lts
s
u
g
g
ests
th
at
h
ier
ar
ch
ical
h
ash
in
g
is
a
r
elia
b
le
s
tr
ateg
y
f
o
r
en
s
u
r
in
g
d
ata
co
n
s
is
ten
cy
.
T
h
e
im
p
licatio
n
s
ar
e
s
ig
n
if
ican
t
f
o
r
ap
p
licatio
n
s
in
b
lo
ck
ch
ai
n
-
b
a
s
ed
ed
u
ca
tio
n
s
y
s
tem
s
an
d
s
ec
u
r
e
clo
u
d
p
latf
o
r
m
s
,
wh
er
e
d
ata
au
th
en
ticity
is
p
ar
am
o
u
n
t.
5
.
2
.
E
f
f
icient
t
esting
T
h
is
s
ec
tio
n
p
r
esen
ts
a
co
m
p
ar
ativ
e
an
aly
s
is
o
f
th
e
ef
f
icien
cy
o
f
d
if
f
e
r
en
t
cr
y
p
t
o
g
r
ap
h
i
c
alg
o
r
ith
m
co
m
b
in
atio
n
s
,
ex
p
licitly
f
o
cu
s
in
g
o
n
AE
S+R
SA,
T
wo
f
is
h
+E
l
-
Gam
al,
AE
S+E
l
-
Gam
al,
an
d
T
wo
f
is
h
+RS
A.
B
y
em
p
lo
y
in
g
B
ig
O
No
tatio
n
alo
n
g
s
id
e
ex
ec
u
tio
n
tim
e
m
etr
ics
[
3
0
]
.
T
h
e
an
aly
s
is
aim
s
to
ev
alu
ate
ea
c
h
alg
o
r
ith
m
p
air
’
s
c
o
m
p
u
tatio
n
a
l
ef
f
icien
cy
an
d
p
er
f
o
r
m
a
n
ce
s
p
ee
d
,
as
s
h
o
wn
in
T
ab
les
1
a
n
d
2
an
d
Fig
u
r
e
3
.
T
h
is
ap
p
r
o
ac
h
allo
ws
f
o
r
a
co
m
p
r
eh
en
s
iv
e
ass
ess
m
en
t
o
f
th
eir
s
u
itab
ilit
y
f
o
r
s
ec
u
r
e
d
ata
p
r
o
ce
s
s
in
g
an
d
r
ea
l
-
tim
e
ap
p
licatio
n
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
6
,
Decem
b
e
r
20
25
:
5
6
7
9
-
5
6
8
9
5686
T
ab
le
1
.
C
o
m
p
a
r
ativ
e
co
m
p
le
x
ity
o
n
a
d
if
f
er
e
n
t a
lg
o
r
ith
m
A
l
g
o
r
i
t
h
m
K
e
y
P
r
e
p
a
r
a
t
i
o
n
En
c
r
y
p
t
i
o
n
D
e
c
r
y
p
t
i
o
n
A
ES+R
S
A
O
(
k
3
)
(
R
S
A
)
O(r
⋅
n
2
)
(
A
ES)
O(r
⋅
n
2
)
+
O
(
k
3
)
O
(
r
⋅
n
2
)
+
O
(
k
3
)
Tw
o
f
i
s
h
+
E
l
G
a
m
a
l
O
(
k
3
)
(
El
G
a
mal
)
O
(
n
2
)
(
Tw
o
f
i
sh
)
O
(
n
2
)
+
O
(
k
3
)
O
(
n
2
)
+
O
(
k
3
)
T
ab
le
2
.
C
o
m
p
a
r
ativ
e
tim
e
ex
ec
u
tio
n
o
n
d
if
f
e
r
en
t a
lg
o
r
ith
m
s
B
l
o
c
k
Ti
me
E
x
e
c
u
t
i
o
n
(
ms)
A
ES+R
S
A
Tw
o
f
i
s
h
+
E
l
-
G
a
m
a
l
1
0
,
2
6
6
7
,
1
2
0
2
0
,
6
4
4
6
,
7
2
5
3
0
,
9
8
1
7
,
7
5
8
4
1
,
3
4
0
1
1
,
2
0
9
5
1
,
7
5
8
1
2
,
6
1
4
6
2
,
2
0
5
1
2
,
7
2
1
7
2
,
6
7
1
1
6
,
3
9
0
8
3
,
0
1
6
1
5
,
1
8
1
9
3
,
6
6
8
1
6
,
5
4
4
10
3
,
9
9
5
2
0
,
3
0
9
Fig
u
r
e
3
.
C
o
m
p
a
r
is
o
n
o
f
ex
ec
u
tio
n
tim
e
b
etwe
en
AE
S+R
SA a
n
d
T
wo
f
is
h
+E
lGam
al
alg
o
r
ith
m
s
B
ased
o
n
T
ab
le
s
1
an
d
2
an
d
Fig
u
r
e
3
,
th
e
a
n
aly
s
is
ev
alu
ates
b
o
th
alg
o
r
ith
m
ic
c
o
m
p
l
ex
ity
an
d
ex
ec
u
tio
n
tim
e
ac
r
o
s
s
d
if
f
er
en
t
cr
y
p
t
o
g
r
ap
h
ic
co
m
b
i
n
at
io
n
s
.
T
h
is
co
m
p
ar
is
o
n
h
ig
h
lig
h
ts
th
e
r
elativ
e
ef
f
ec
tiv
en
ess
an
d
ef
f
icien
c
y
o
f
ea
ch
ap
p
r
o
ac
h
.
E
ac
h
alg
o
r
ith
m
ex
h
ib
its
d
is
tin
ct
ch
ar
ac
ter
i
s
tics
,
m
ak
in
g
th
em
s
u
itab
le
f
o
r
v
a
r
y
in
g
s
ec
u
r
ity
r
e
q
u
ir
em
en
ts
an
d
ap
p
licatio
n
co
n
tex
ts
.
AE
S+R
S
A
d
em
o
n
s
tr
ates
a
well
-
b
alan
ce
d
ap
p
r
o
ac
h
with
e
f
f
icien
t
ex
ec
u
tio
n
tim
es
r
an
g
in
g
f
r
o
m
0
.
2
6
6
to
3
.
9
9
5
m
s
ac
r
o
s
s
d
if
f
er
en
t
b
lo
ck
s
.
T
h
e
co
m
p
lex
ity
o
f
O(
k
³)
f
o
r
R
SA
en
s
u
r
es
s
ec
u
r
e
v
ital
ex
c
h
an
g
es,
wh
ile
O(
r
·
n
²)
f
o
r
AE
S
f
ac
ilit
ates
f
ast
en
cr
y
p
tio
n
an
d
d
e
cr
y
p
tio
n
.
T
h
is
co
m
b
in
atio
n
en
s
u
r
es
r
ap
id
d
ata
p
r
o
ce
s
s
in
g
,
m
ak
i
n
g
it h
ig
h
ly
s
u
itab
le
f
o
r
a
p
p
licatio
n
s
r
eq
u
ir
i
n
g
b
o
t
h
s
p
ee
d
a
n
d
s
ec
u
r
ity
.
T
wo
f
is
h
+E
lGam
al
s
h
o
ws
h
ig
h
ex
ec
u
tio
n
tim
es,
n
o
tab
ly
p
ea
k
in
g
at
2
0
.
3
0
9
m
s
,
wh
ich
r
ef
lects
it
s
s
ig
n
if
ican
t
co
m
p
u
tatio
n
al
o
v
e
r
h
ea
d
d
u
e
to
O(
k
³)
c
o
m
p
lex
it
y
ass
o
ciate
d
with
E
lGam
al
’
s
k
ey
m
a
n
ag
em
en
t
.
Alth
o
u
g
h
s
ec
u
r
e,
t
h
is
co
m
b
i
n
atio
n
m
ay
n
o
t
b
e
o
p
tim
al
f
o
r
en
v
ir
o
n
m
en
ts
d
em
a
n
d
in
g
q
u
i
ck
d
ata
p
r
o
ce
s
s
in
g
.
T
h
e
ef
f
icien
cy
an
aly
s
is
r
ev
ea
l
s
th
at
AE
S+R
SA
ac
h
iev
es
o
p
tim
al
p
er
f
o
r
m
an
ce
co
m
p
ar
ed
to
o
th
e
r
alg
o
r
ith
m
p
air
s
,
with
s
ig
n
if
ican
tly
lo
wer
ex
ec
u
tio
n
tim
es.
Fro
m
a
cr
iti
ca
l
s
tan
d
p
o
in
t,
th
e
r
esu
lts
v
alid
ate
th
e
f
ea
s
ib
ilit
y
o
f
h
y
b
r
id
c
r
y
p
to
g
r
ap
h
y
in
r
ea
l
-
tim
e
s
y
s
tem
s
.
5
.
3
.
Dis
cus
s
io
n o
f
f
ind
ing
s
a
nd
co
ntr
ibu
t
io
n t
o
t
he
f
ield
T
h
e
f
in
d
in
g
s
o
f
th
is
s
tu
d
y
c
o
n
f
ir
m
th
at
in
teg
r
atin
g
AE
S
an
d
R
SA
with
in
a
h
ash
ch
ai
n
s
y
s
tem
,
s
u
p
p
o
r
ted
b
y
Me
r
k
le
t
r
ee
s
tr
u
ctu
r
es,
s
ig
n
if
ican
tly
e
n
h
an
ce
s
b
o
th
d
ata
in
te
g
r
ity
an
d
en
c
r
y
p
tio
n
e
f
f
icien
cy
.
T
h
is
alig
n
s
with
p
r
io
r
r
esear
ch
th
at
h
ig
h
li
g
h
ts
th
e
in
d
iv
id
u
al
s
tr
en
g
th
s
o
f
th
ese
c
r
y
p
to
g
r
ap
h
ic
co
m
p
o
n
en
ts
[
6
]
,
[
1
2
]
,
b
u
t th
is
s
tu
d
y
a
d
v
an
c
es th
e
f
ield
b
y
d
em
o
n
s
tr
atin
g
th
ei
r
co
m
b
in
e
d
ef
f
ec
tiv
e
n
ess
in
a
u
n
if
ied
f
r
am
ewo
r
k
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
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&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
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E
n
h
a
n
cin
g
s
ystem
in
teg
r
ity
w
ith
Mer
kle
tr
ee
:
efficien
t h
yb
r
i
d
cryp
to
g
r
a
p
h
y
u
s
in
g
R
S
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…
(
I
r
z
a
N
u
r
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a
u
z
i
)
5687
T
h
e
r
ip
p
le
ef
f
e
ct
o
b
s
er
v
ed
i
n
th
e
Me
r
k
le
t
r
ee
v
alid
atio
n
—
wh
er
e
a
s
in
g
le
d
ata
b
lo
ck
alter
atio
n
in
v
alid
ates
s
u
b
s
eq
u
en
t
b
lo
ck
s
—
illu
s
tr
ate
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th
e
m
o
d
el
’
s
r
o
b
u
s
tn
ess
in
an
o
m
aly
d
etec
tio
n
[
3
]
,
[
1
6
]
.
T
h
is
b
eh
av
io
r
is
p
ar
ticu
lar
ly
v
alu
ab
le
in
d
is
tr
ib
u
ted
s
y
s
tem
s
wh
er
e
r
ea
l
-
tim
e
in
teg
r
ity
v
er
if
icati
o
n
is
cr
itical.
C
o
m
p
ar
ed
to
o
th
er
alg
o
r
ith
m
p
air
s
,
s
u
ch
as
T
wo
f
is
h
+
E
lGam
al,
th
e
AE
S+R
SA
co
m
b
in
atio
n
co
n
s
is
ten
tly
o
u
tp
er
f
o
r
m
s
in
e
x
ec
u
tio
n
tim
e
an
d
co
m
p
lex
ity
.
T
h
ese
r
esu
lts
n
o
t
o
n
ly
s
u
p
p
o
r
t
ea
r
lier
f
in
d
i
n
g
s
b
u
t
also
ex
ten
d
th
eir
im
p
licatio
n
s
to
h
ig
h
-
th
r
o
u
g
h
p
u
t
en
v
ir
o
n
m
e
n
ts
s
u
ch
as
ed
u
ca
tio
n
al
p
latf
o
r
m
s
,
I
o
T
n
etwo
r
k
s
,
an
d
s
ec
u
r
e
clo
u
d
in
f
r
astru
ctu
r
es.
C
o
llectiv
ely
,
th
ese
in
s
ig
h
ts
u
n
d
er
s
co
r
e
t
h
e
p
r
ac
tical
r
ele
v
an
ce
an
d
tec
h
n
ical
s
o
u
n
d
n
ess
o
f
th
e
p
r
o
p
o
s
ed
m
o
d
el.
I
t
ac
h
ie
v
es
a
b
alan
ce
d
tr
a
d
e
-
o
f
f
b
etwe
en
s
p
ee
d
,
s
ec
u
r
ity
,
a
n
d
in
te
g
r
it
y
,
th
er
eb
y
lay
in
g
a
s
tr
o
n
g
f
o
u
n
d
atio
n
f
o
r
f
u
tu
r
e
r
esear
ch
aim
ed
at
o
p
tim
izin
g
h
y
b
r
id
en
cr
y
p
tio
n
s
y
s
tem
s
an
d
ad
ap
tin
g
th
em
to
em
er
g
in
g
tec
h
n
o
lo
g
ies an
d
d
is
tr
ib
u
ted
ar
c
h
itectu
r
es.
Mo
r
eo
v
er
,
th
e
f
in
d
in
g
s
o
f
th
is
s
tu
d
y
h
av
e
th
e
p
o
te
n
tial to
co
n
tr
ib
u
te
m
ea
n
i
n
g
f
u
lly
to
th
e
s
co
p
e
o
f
I
n
f
o
r
m
ati
o
n
T
ec
h
n
o
lo
g
y
an
d
I
n
f
o
r
m
atio
n
Sy
s
tem
s
,
p
ar
ticu
lar
ly
in
th
e
d
o
m
ain
s
o
f
s
ec
u
r
ity
an
d
cr
y
p
to
g
r
ap
h
.
I
ts
em
p
h
asis
o
n
alg
o
r
ith
m
ic
p
er
f
o
r
m
an
ce
,
d
ata
in
t
eg
r
ity
,
an
d
s
y
s
tem
s
ca
lab
ilit
y
d
ir
ec
tly
ad
d
r
ess
es
k
ey
co
n
ce
r
n
s
in
m
o
d
e
r
n
d
i
g
ital
in
f
r
astru
ctu
r
e,
m
a
k
in
g
it
h
ig
h
ly
r
elev
an
t
to
b
o
th
ac
ad
em
ic
r
esear
ch
er
s
a
n
d
i
n
d
u
s
tr
y
p
r
o
f
ess
io
n
als
s
ee
k
in
g
r
o
b
u
s
t
s
o
lu
tio
n
s
in
cy
b
e
r
s
ec
u
r
ity
an
d
i
n
f
o
r
m
atio
n
s
y
s
tem
s
.
6.
CO
NCLU
SI
O
N
T
h
is
s
tu
d
y
ex
p
lo
r
ed
h
y
b
r
i
d
c
r
y
p
to
g
r
ap
h
y
with
R
SA
an
d
AE
S
to
en
h
an
ce
s
y
s
tem
in
te
g
r
ity
with
in
h
ash
ch
ain
f
r
a
m
ewo
r
k
s
au
g
m
en
ted
b
y
Me
r
k
le
tr
ee
s
.
A
E
S+R
SA
was
id
en
tifie
d
as
th
e
m
o
s
t
ef
f
icien
t
co
m
b
in
atio
n
,
p
r
o
v
i
d
in
g
s
wif
t
p
r
o
ce
s
s
in
g
an
d
r
o
b
u
s
t
s
ec
u
r
ity
id
ea
l
f
o
r
d
ata
-
in
ten
s
iv
e
en
v
ir
o
n
m
en
ts
.
T
h
e
in
teg
r
atio
n
o
f
h
ash
ch
ain
s
an
d
Me
r
k
le
tr
ee
s
s
ig
n
if
ican
tly
b
o
l
s
ter
ed
d
ata
in
teg
r
ity
,
en
s
u
r
i
n
g
r
ap
id
d
etec
tio
n
o
f
in
co
n
s
is
ten
cies
o
r
u
n
au
th
o
r
iz
ed
ch
an
g
es.
W
h
ile
o
th
er
co
m
b
in
atio
n
s
lik
e
T
wo
f
is
h
+E
lGam
al
r
em
ain
r
o
b
u
s
t,
th
eir
lo
n
g
er
p
r
o
ce
s
s
in
g
tim
es
h
ig
h
lig
h
t
th
e
s
u
p
e
r
io
r
ef
f
ici
en
cy
o
f
AE
S+R
SA.
Fu
tu
r
e
wo
r
k
s
h
o
u
ld
f
u
r
th
e
r
o
p
tim
ize
cr
y
p
to
g
r
ap
h
ic
s
tr
ateg
ies
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