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Vo
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2
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A
p
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20
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p
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2455
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An impro
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s k
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ims
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t
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Key
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Natio
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ts
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u
n
d
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Dep
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T
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T
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ab
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I
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s
titu
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Stan
d
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T
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lau
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tan
d
ar
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AE
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co
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to
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Dae
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2
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d
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[
1
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[
2
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.
B
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tili
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d
in
clo
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p
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[
3
]
,
[
4
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.
I
t
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y
m
m
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lo
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g
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ar
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s
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in
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o
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s
ec
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es
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y
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u
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1
6
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y
tes
d
ata
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izes
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k
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g
th
s
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f
1
6
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2
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a
n
d
3
2
b
y
tes
[
5
]
.
T
h
e
th
r
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e
s
s
en
tial
co
m
p
o
n
en
ts
o
f
AE
S
ar
e
k
ey
ex
p
an
s
io
n
,
d
ec
r
y
p
tio
n
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an
d
en
cr
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p
tio
n
.
An
XOR
o
p
er
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p
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f
o
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m
e
d
at
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r
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etwe
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ay
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ata
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r
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n
d
k
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u
r
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p
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r
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ate
r
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n
d
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m
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ess
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d
d
if
f
u
s
io
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[
6
]
–
[
8
]
.
A
well
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k
ey
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lin
g
alg
o
r
ith
m
(
KSA)
ca
n
p
r
ev
en
t
co
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p
u
tatio
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g
u
ess
in
g
o
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Desp
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,
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k
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p
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co
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f
u
s
io
n
a
n
d
d
if
f
u
s
io
n
[
9
]
,
[
1
0
]
.
E
n
cr
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p
tio
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g
ar
n
er
s
m
o
r
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ar
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,
wh
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,
v
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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:
2
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8
8
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8
I
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t J E
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&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
2
,
Ap
r
il
20
25
:
2
4
5
5
-
2
4
6
7
2456
f
o
r
alg
o
r
ith
m
s
lik
e
AE
S,
is
co
n
s
id
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ed
an
a
u
x
iliar
y
co
m
p
o
n
en
t
[
1
1
]
,
[
1
2
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.
Fin
ite
n
o
n
lin
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ity
in
th
e
AE
S
k
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ch
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k
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clu
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elate
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k
ey
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s
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Du
e
to
th
ese
f
laws
,
th
er
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ar
e
s
ig
n
if
ican
t
s
ec
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as
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p
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u
s
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n
,
an
d
m
an
ip
u
late
s
u
b
k
ey
s
[
1
3
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,
[
1
4
]
.
T
o
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cr
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s
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th
e
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it
tr
a
n
s
itio
n
b
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k
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KSA
s
h
o
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l
d
g
en
e
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s
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b
k
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th
at
ar
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in
d
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d
en
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o
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n
e
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o
th
er
a
n
d
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d
o
m
.
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o
n
s
eq
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en
tly
,
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is
s
tu
d
y
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s
to
im
p
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o
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th
e
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l
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o
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th
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n
cr
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e
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v
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s
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f
A
E
S KSA.
Ma
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esear
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s
h
av
e
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o
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d
u
cted
ex
te
n
s
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e
r
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d
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d
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m
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r
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s
s
v
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s
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cr
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n
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g
o
r
ith
m
s
.
Ham
m
o
d
et
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l
.
[
1
5
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s
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g
g
est
an
im
p
r
o
v
ed
ap
p
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o
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h
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KSA
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s
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g
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o
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MCF
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o
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e.
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m
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d
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,
an
d
p
er
f
o
r
m
a
n
ce
f
o
r
a
r
an
g
e
o
f
k
ey
le
n
g
th
s
.
R
ey
es
et
a
l.
[
1
6
]
u
s
ed
s
im
p
le
o
p
e
r
atio
n
s
lik
e
XOR
an
d
m
o
d
u
lo
ar
it
h
m
etic
to
m
o
d
if
y
th
e
AE
S
cip
h
er
r
o
u
n
d
a
n
d
KSA
to
f
ix
lo
w
d
if
f
u
s
io
n
r
ates
in
ea
r
ly
r
o
u
n
d
s
.
T
h
ey
im
p
r
o
v
ed
t
h
e
KSA
b
y
ad
d
in
g
b
y
te
s
u
b
s
titu
tio
n
an
d
r
o
u
n
d
c
o
n
s
tan
t
ad
d
itio
n
.
I
n
r
o
u
n
d
s
1
an
d
3
,
t
h
e
m
o
d
if
ied
AE
S
in
c
r
ea
s
ed
d
if
f
u
s
io
n
r
ate
an
d
im
p
r
o
v
e
d
e
n
cr
y
p
tio
n
o
u
t
p
u
t
r
a
n
d
o
m
n
ess
.
Peh
liv
an
o
g
l
u
et
a
l.
[
1
7
]
ex
p
lo
r
e
b
lo
ck
ci
p
h
er
s
an
d
th
ei
r
k
e
y
s
ch
ed
u
le
alg
o
r
ith
m
,
in
s
p
ir
ed
b
y
AE
S,
with
d
esira
b
le
p
r
o
p
er
t
ies
lik
e
g
o
o
d
av
alan
c
h
e
ef
f
ec
t
an
d
b
it
co
n
f
u
s
io
n
.
Similar
ly
,
C
ao
et
a
l.
[
1
8
]
o
p
tim
ize
th
e
AE
S
KSA
u
s
in
g
th
r
ee
i
m
p
r
o
v
em
en
t
s
tr
at
eg
ies:
ir
r
ev
er
s
ib
le
im
p
r
o
v
em
e
n
t,
wo
r
d
s
h
if
t,
a
n
d
r
an
d
o
m
n
u
m
b
er
s
tr
ateg
y
,
to
r
ed
u
ce
r
o
u
n
d
-
k
e
y
co
r
r
elatio
n
,
im
p
r
o
v
e
s
ec
u
r
ity
,
an
d
en
s
u
r
e
ef
f
icien
t
o
p
er
atio
n
.
Ku
m
ar
et
a
l.
[
1
9
]
p
r
o
p
o
s
ed
a
n
d
s
im
u
lated
a
n
ew
s
u
b
k
ey
g
e
n
er
atio
n
alg
o
r
ith
m
f
o
r
AE
S
o
n
th
e
FP
GA
Vir
tex
5
XC
5
VL
X5
0
T
,
e
n
h
an
ci
n
g
its
s
p
ee
d
,
m
ain
tain
in
g
w
o
r
d
d
i
f
f
u
s
io
n
,
an
d
m
in
im
izin
g
tim
e
co
n
s
u
m
p
tio
n
.
De
L
eo
n
et
a
l.
[
2
0
]
m
o
d
if
ied
th
e
tin
y
e
n
cr
y
p
tio
n
alg
o
r
ith
m
(
T
E
A)
,
a
lig
h
tweig
h
t
en
cr
y
p
tio
n
m
eth
o
d
,
to
im
p
r
o
v
e
s
ec
u
r
ity
b
y
r
o
tati
n
g
s
u
b
k
e
y
s
an
d
s
h
if
tin
g
k
ey
s
,
o
u
tp
er
f
o
r
m
in
g
th
e
o
r
ig
in
al
T
E
A.
B
y
ad
d
in
g
a
s
altin
g
alg
o
r
ith
m
t
o
th
e
s
u
b
k
e
y
,
Gala
s
an
d
Ger
ar
d
o
[
2
1
]
en
h
an
ce
d
t
h
e
s
ec
u
r
ity
o
f
th
e
c
o
r
r
ec
ted
b
l
o
ck
tin
y
en
cr
y
p
tio
n
alg
o
r
ith
m
,
XXT
E
A,
an
d
im
p
r
o
v
e
d
its
r
an
d
o
m
n
ess
an
d
av
alan
ch
e
e
f
f
ec
t.
T
h
is
ap
p
r
o
ac
h
was
m
o
r
e
ef
f
ec
tiv
e
th
an
th
e
o
r
ig
in
al
ap
p
r
o
ac
h
,
wh
ich
f
ailed
th
e
f
r
eq
u
en
c
y
test
.
T
h
e
k
ey
ex
p
an
s
io
n
p
r
o
ce
s
s
o
f
PR
E
SENT
-
1
2
8
is
en
h
a
n
ce
d
b
y
I
m
d
ad
et
a
l.
[
2
2
]
with
im
p
r
o
v
ed
r
an
d
o
m
n
ess
,
av
ala
n
ch
e
ef
f
ec
t,
an
d
Ham
m
i
n
g
d
is
tan
ce
b
etwe
en
r
o
u
n
d
k
ey
s
th
r
o
u
g
h
ex
p
er
im
en
tal
test
s
with
r
an
d
o
m
,
lo
w,
a
n
d
h
i
g
h
-
d
en
s
ity
in
itial
s
ec
r
et
k
ey
s
.
Z
ak
ar
ia
et
a
l.
[
2
3
]
im
p
r
o
v
ed
th
e
R
E
C
T
ANGL
E
k
ey
s
ch
ed
u
le
alg
o
r
ith
m
b
y
in
c
r
ea
s
in
g
r
an
d
o
m
izatio
n
an
d
co
n
f
u
s
io
n
p
r
o
p
er
ties
,
s
p
ee
d
,
an
d
t
h
r
o
u
g
h
p
u
t.
T
h
is
ar
ticle
ar
r
an
g
es
its
s
ec
ti
o
n
s
as
f
o
llo
ws,
s
ec
tio
n
2
p
r
o
v
id
es
a
co
m
p
r
eh
e
n
s
iv
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d
escr
ip
tio
n
o
f
th
e
s
tan
d
ar
d
an
d
im
p
r
o
v
ed
AE
S
k
ey
ex
p
an
s
io
n
p
r
o
ce
d
u
r
es.
T
h
is
s
ec
tio
n
also
d
e
s
cr
ib
es
th
e
s
tati
s
tical
test
s
an
d
k
ey
e
x
p
an
s
io
n
p
r
o
ce
s
s
ass
ess
m
en
t
p
ar
a
m
eter
s
to
e
v
alu
ate
t
h
e
r
o
b
u
s
tn
ess
o
f
th
e
s
tan
d
a
r
d
an
d
im
p
r
o
v
e
d
AE
S
k
ey
ex
p
an
s
io
n
alg
o
r
ith
m
s
.
Sec
tio
n
4
co
n
clu
d
es with
th
e
f
in
d
i
n
g
s
an
d
d
is
cu
s
s
io
n
s
f
r
o
m
s
ec
tio
n
3.
2.
M
E
T
H
O
D
2
.
1
.
Sta
nd
a
rd
AE
S K
S
A
T
h
is
ar
ticle
co
n
s
id
er
s
AE
S
-
1
2
8
KSA
an
d
Fig
u
r
e
1
d
ep
icts
i
ts
d
etailed
k
ey
s
ch
ed
u
lin
g
p
r
o
ce
s
s
.
T
h
e
r
o
u
n
d
-
k
ey
g
en
er
atio
n
p
r
o
ce
s
s
wo
r
k
s
at
th
e
wo
r
d
lev
el
(
3
2
b
i
ts
)
.
So
,
th
e
p
r
o
ce
d
u
r
e
s
tar
ts
b
y
d
iv
id
in
g
th
e
in
itial
s
ec
r
et
k
ey
o
f
len
g
th
1
2
8
b
its
in
to
f
o
u
r
wo
r
d
s
(
W
0
,
W
1
,
W
2
,
W
4
)
.
T
h
e
f
ir
s
t f
o
u
r
wo
r
d
s
o
f
t
h
e
k
ey
s
ch
ed
u
le
ar
e
th
e
s
am
e
as
t
h
e
f
o
u
r
wo
r
d
s
o
f
th
e
in
itial
s
ec
r
et
k
ey
.
KSA
d
er
iv
es
th
e
r
e
m
ain
in
g
4
0
wo
r
d
s
it
er
ativ
ely
th
r
o
u
g
h
a
s
eq
u
en
ce
o
f
t
r
an
s
f
o
r
m
atio
n
s
,
as
AE
S
-
1
2
8
en
cr
y
p
tio
n
an
d
d
ec
r
y
p
tio
n
n
ec
ess
itate
th
e
g
en
e
r
atio
n
o
f
1
0
r
o
u
n
d
k
ey
s
f
r
o
m
th
e
in
itial
s
ec
r
et
k
e
y
.
T
h
ese
4
0
wo
r
d
s
ar
e
f
u
r
th
e
r
d
iv
id
e
d
in
to
1
0
r
o
u
n
d
k
ey
s
.
I
n
(
1
)
–
(
1
0
)
g
en
e
r
ate
th
e
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r
d
s
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wh
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d
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le
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as f
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8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
2
,
Ap
r
il
20
25
:
2
4
5
5
-
2
4
6
7
2458
Ps
eu
d
o
co
d
e
o
f
s
tan
d
ar
d
AE
S KSA
ASE128KeyExpansion (byte initial_secretkey [16], word w [44])
{
word tmp_word;
Round_constants
=
[0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x04, 0x80, 0x1b, 0x36]
for (x=0; x<4; x++)
w[x]
=
(initial_secretkey[4*x],
initial_secr
etkey
[4*x+1],
initial_se
cretkey
[4*x+2],
initial_secretkey [4*x+3]);
for (x=4; x<44; x++)
{
tmp_word
=
w[x
-
1];
if (x mod 4
=
0)
tmp_word
=
SubWord (RotateWord(tmp_word))
⊕
Round_constants [x/4];
w[x]=tmp_word
⊕
w[x
-
4];
}
}
2
.
2
.
E
nh
a
nced
AE
S K
SA
2
.
2
.
1
.
E
nh
a
nced
k
ey
ex
pa
ns
io
n us
ing
S
-
B
o
x
ba
s
ed
ex
pa
n
ded r
o
un
d c
o
n
s
t
a
nts
T
h
e
AE
S
k
ey
s
ch
ed
u
lin
g
tech
n
iq
u
e
u
s
es
an
im
p
lem
en
tatio
n
o
f
cy
clic
r
o
tatio
n
,
S
-
b
o
x
,
an
d
XOR
wit
h
r
o
u
n
d
co
n
s
tan
ts
to
f
in
d
t
h
e
te
m
p
o
r
ar
y
wo
r
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s
(
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3
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,
W
7
’
,
W
1
1
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,
.
.
.
,
W
3
9
’
)
.
All
th
e
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em
ain
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g
r
o
u
n
d
k
ey
s
ca
n
b
e
p
r
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d
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ce
d
f
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m
th
e
o
r
i
g
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al
k
ey
u
s
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g
th
ese
tem
p
o
r
ar
y
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ar
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les.
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wev
e
r
,
t
h
e
r
o
u
n
d
co
n
s
tan
ts
(
,
0
,
0
,
0
)
in
AE
S
leav
e
th
r
ee
b
y
tes
as
ze
r
o
s
,
as
s
h
o
wn
i
n
Fig
u
r
e
1
,
wh
ich
less
en
s
th
e
am
o
u
n
t
o
f
c
o
n
f
u
s
io
n
an
d
d
if
f
u
s
io
n
in
th
e
r
o
u
n
d
k
e
y
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e
n
er
atio
n
p
r
o
ce
s
s
.
Attack
er
s
ca
n
e
x
p
lo
it
c
h
o
s
en
,
k
n
o
wn
,
an
d
r
elate
d
k
e
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ass
au
lts
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ec
au
s
e
o
f
th
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f
law.
T
o
p
u
t
it
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o
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,
XORi
n
g
with
ze
r
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t
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ea
te
m
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e
co
n
f
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wh
ich
m
ak
es it e
asier
f
o
r
ad
v
er
s
ar
ies
to
d
ed
u
ce
p
ar
ts
o
f
th
e
k
e
y
.
As s
h
o
wn
in
Fig
u
r
e
2
,
t
h
e
s
tr
etch
ed
r
o
u
n
d
co
n
s
tan
ts
(
R
C
j,
S
-
B
o
x
[
R
C
j]
,
S
-
B
o
x
[
S
-
B
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x
[
R
C
j]
]
,
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o
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[
S
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[
S
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R
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ar
e
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ed
in
p
lace
o
f
th
e
r
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n
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n
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ts
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,
0
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0
,
0
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in
th
e
p
r
o
p
o
s
ed
AE
S
KSA.
T
h
e
ex
p
a
n
d
ed
r
o
u
n
d
co
n
s
tan
ts
u
s
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g
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-
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x
a
r
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g
iv
en
in
T
ab
le
2
.
T
h
ese
ex
p
an
d
ed
r
o
u
n
d
co
n
s
tan
ts
ar
e
g
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er
ate
d
b
y
ap
p
ly
i
n
g
S
-
B
o
x
o
n
t
h
e
r
o
u
n
d
c
o
n
s
tan
ts
R
C
j
iter
ativ
ely
.
Fig
u
r
e
2
.
E
n
h
an
ce
d
AE
S k
ey
ex
p
an
s
io
n
p
r
o
ce
s
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
A
n
imp
r
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ve
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ch
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.
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a
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)
2459
T
ab
le
2
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E
x
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r
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2
.
2
.
2
.
E
nh
a
nced
k
ey
ex
pa
ns
io
n us
ing
cubic
po
ly
no
m
ia
l f
un
ct
io
n
AE
S
KSA
u
s
e
s
cir
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lar
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t
s
h
if
t
o
f
o
n
e
b
y
te,
S
-
b
o
x
s
u
b
s
titu
tio
n
s
,
an
d
XOR
o
p
er
atio
n
with
r
o
u
n
d
co
n
s
tan
ts
.
Ho
wev
er
,
r
o
u
n
d
k
e
y
s
s
till
s
h
o
w
s
o
m
e
lev
el
o
f
c
o
r
r
elatio
n
,
b
ec
au
s
e
ea
ch
r
o
u
n
d
k
e
y
is
g
e
n
er
ated
s
eq
u
en
tially
,
with
ea
ch
s
u
b
s
eq
u
en
t
r
o
u
n
d
k
ey
b
ei
n
g
d
er
iv
ed
f
r
o
m
th
e
p
r
e
v
io
u
s
o
n
e.
T
h
is
o
p
er
atio
n
is
p
er
f
o
r
m
ed
wo
r
d
-
wis
e,
m
ea
n
in
g
th
at
ea
ch
co
r
r
esp
o
n
d
in
g
wo
r
d
f
r
o
m
th
e
p
r
ev
io
u
s
ly
g
e
n
er
ated
r
o
u
n
d
k
ey
is
XORed
with
th
e
cu
r
r
en
t
wo
r
d
to
g
en
er
ate
th
e
n
ex
t
wo
r
d
.
Fo
r
in
s
tan
ce
,
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5
(
6
th
wo
r
d
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is
g
en
er
ated
f
r
o
m
W
4
an
d
W
1
,
W
6
(
7
th
wo
r
d
)
f
r
o
m
W
5
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d
W
2
,
an
d
W
7
(
8
th
wo
r
d
)
f
r
o
m
W
6
an
d
W
3
a
n
d
s
o
o
n
.
So
,
AE
S
n
ee
d
s
im
p
r
o
v
em
e
n
ts
to
r
ed
u
ce
c
o
r
r
elatio
n
s
b
etwe
en
r
o
u
n
d
k
ey
s
,
wh
ich
m
ak
es
th
e
k
ey
s
ch
ed
u
le
s
tr
o
n
g
er
.
Su
c
h
im
p
r
o
v
em
e
n
ts
ca
n
c
o
n
s
is
t
o
f
r
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in
in
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th
e
d
er
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n
tec
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n
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d
e
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n
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li
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ea
r
p
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s
s
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h
th
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,
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c
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p
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ly
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o
m
ial
f
u
n
ctio
n
is
u
s
ed
in
th
e
p
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p
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s
ed
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to
in
tr
o
d
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c
h
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s
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r
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n
d
k
ey
s
.
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h
e
g
en
e
r
ic
f
o
r
m
o
f
th
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s
ty
p
e
o
f
p
o
ly
n
o
m
ial
is
(
)
:
3
+
2
+
+
,
wh
e
r
e
m
d
o
es
n
o
t
eq
u
al
ze
r
o
.
T
h
e
b
e
h
av
io
r
o
f
th
ese
c
u
r
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es
is
d
eter
m
i
n
ed
b
y
t
h
e
v
a
lu
es
o
f
th
e
r
ea
l
c
o
ef
f
icien
ts
(
,
,
,
an
d
)
.
A
cu
b
ic
p
o
ly
n
o
m
ial
f
u
n
ctio
n
,
f
o
r
ex
am
p
le,
h
as
co
e
f
f
icien
ts
m
=
1
,
n
=
-
3
,
o
=
2
,
an
d
p
=
-
1
as
s
h
o
wn
in
Fig
u
r
e
3
.
T
h
e
en
h
a
n
ce
d
AE
S
KSA
u
s
es
th
ese
co
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f
icien
t
v
alu
es
b
ec
au
s
e
it
im
p
r
o
v
es
th
e
co
m
p
lex
ity
o
f
t
h
e
k
ey
ex
p
an
s
io
n
p
r
o
ce
s
s
.
T
h
ese
f
u
n
ctio
n
s
ca
n
b
e
em
p
lo
y
ed
as
a
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wer
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s
u
b
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h
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i
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e
to
im
p
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e
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if
f
u
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io
n
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n
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co
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f
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e
r
ties
o
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th
e
r
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u
n
d
k
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en
er
ati
o
n
m
ec
h
a
n
is
m
s
u
s
ed
in
b
lo
c
k
cip
h
er
s
.
Fig
u
r
e
3.
Gr
a
p
h
ical
r
ep
r
esen
tatio
n
o
f
f
(
x
)
I
n
AE
S
KSA,
f
o
r
ea
ch
wo
r
d
g
en
er
atio
n
,
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ch
c
o
r
r
esp
o
n
d
i
n
g
wo
r
d
f
r
o
m
th
e
p
r
e
v
io
u
s
ly
g
en
er
ated
r
o
u
n
d
k
ey
is
XORed
with
th
e
cu
r
r
en
t
wo
r
d
to
g
e
n
er
ate
th
e
n
ex
t
wo
r
d
.
T
h
e
p
r
o
p
o
s
ed
KSA
ap
p
lies
th
e
f
(
x
)
m
o
d
2
5
6
(
⊗
)
o
p
e
r
atio
n
o
n
e
ac
h
cu
r
r
en
t
wo
r
d
wh
ich
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ir
e
ctly
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ar
ticip
ates
in
th
e
XOR
o
p
er
atio
n
with
th
e
co
r
r
esp
o
n
d
in
g
wo
r
d
f
r
o
m
th
e
p
r
ev
io
u
s
k
e
y
.
Fo
r
in
s
tan
ce
,
th
e
wo
r
d
W
5
is
g
en
er
ated
eq
u
al
to
(
f
(
W
4
)
m
o
d
2
5
6
⨁
W
1
)
in
s
tead
o
f
W
4
⨁
W
1
.
I
n
th
e
p
r
o
p
o
s
ed
KSA,
th
e
k
ey
s
ch
ed
u
le
is
g
en
er
ated
as f
o
llo
ws:
W4
=
W
3
’
⨁
W
0
,
W
5
=
f
(
W
4
)
m
o
d
2
5
6
⨁
W1
,
W
6
=
f
(
W
5
)
m
o
d
2
5
6
⨁
W2
,
W
7
=
f
(
W
6
)
m
o
d
2
5
6
⨁
W3
,
W8
=
W
7
’
⨁
W
4
,
W
9
=
f
(
W
8
)
m
o
d
2
5
6
⨁
W5
,
W
1
0
=
f
(
W
9
)
m
o
d
2
5
6
⨁
W6
,
W
1
1
=
f
(
W
1
0
)
m
o
d
2
5
6
⨁
W
7
,
W
1
2
=
W
1
1
’
⨁
W
8
,
W
1
3
=
f
(
W
1
2
)
m
o
d
2
5
6
⨁
W9
,
W
1
4
=
f
(
W
1
3
)
m
o
d
2
5
6
⨁
W
1
0
,
W
1
5
=
f
(
W
1
4
)
m
o
d
2
5
6
⨁
W
1
1
,
W
1
6
=
W
1
5
’
⨁
W
1
2
,
W
1
7
=
f
(
W
1
6
)
m
o
d
2
5
6
⨁
W
1
3
,
W
1
8
=
f
(
W
1
7
)
m
o
d
2
5
6
⨁
W
1
4
,
W
1
9
=
f
(
W
1
8
)
m
o
d
2
5
6
⨁
W
1
5
,
W
2
0
=
W
1
9
’
⨁
W
1
6
,
W
2
1
=
f
(
W
2
0
)
m
o
d
2
5
6
⨁
W
1
7
,
W
2
2
=
f
(
W
2
1
)
m
o
d
2
5
6
⨁
W
1
8
,
W
2
3
=
f
(
W
2
2
)
m
o
d
2
5
6
⨁
W
1
9
,
W
2
4
=
W
2
3
’
⨁
W
2
0
,
W
2
5
=
f
(
W
2
4
)
m
o
d
2
5
6
⨁
W
2
1
,
W
2
6
=
f
(
W
2
5
)
m
o
d
2
5
6
⨁
W
2
2
,
W
2
7
=
f
(
W
2
6
)
m
o
d
2
5
6
⨁
W
2
3
,
W
2
8
=
W
2
7
’
⨁
W
2
4
,
W
2
9
=
f
(
W
2
8
)
m
o
d
2
5
6
⨁
W
2
5
,
W
3
0
=
f
(
W
2
9
)
m
o
d
2
5
6
⨁
W
2
6
,
W
3
1
=
f
(
W
3
0
)
m
o
d
2
5
6
⨁
W
2
7
,
W
3
2
=
W
3
1
’
⨁
W
2
8
,
W
3
3
=
f
(
W
3
2
)
m
o
d
2
5
6
⨁
W
2
9
,
W
3
4
=
f
(
W
3
3
)
m
o
d
2
5
6
⨁
W
3
0
,
W
3
5
=
f
(
W
3
4
)
m
o
d
2
5
6
⨁
W
3
1
,
W
3
6
=
W
3
5
’
⨁
W
3
2
,
W
3
7
=
f
(
W
3
6
)
m
o
d
2
5
6
⨁
W
3
3
,
W
3
8
=
f
(
W
3
7
)
m
o
d
2
5
6
⨁
W
3
4
,
W
3
9
=
f
(
W
3
8
)
m
o
d
2
5
6
⨁
W
3
5
,
W
4
0
=
W
3
9
’
⨁
W
3
6
,
W
4
1
=
f
(
W
4
0
)
m
o
d
2
5
6
⨁
W
3
7
,
W
4
2
=
W
4
1
⨁
W
3
8
,
W
4
3
=
f
(
W
4
2
)
m
o
d
2
5
6
⨁
W
3
9
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
2
,
Ap
r
il
20
25
:
2
4
5
5
-
2
4
6
7
2460
T
h
e
o
u
tp
u
t
o
f
th
e
wo
r
d
to
b
e
XORed
with
co
r
r
esp
o
n
d
in
g
w
o
r
d
s
f
r
o
m
t
h
e
p
r
ev
i
o
u
s
k
ey
is
d
eter
m
in
ed
b
y
th
e
cu
b
ic
p
o
ly
n
o
m
ial
f
u
n
c
tio
n
’
s
m
o
d
u
lu
s
o
f
2
5
6
.
On
ce
it
h
as
g
e
n
er
ated
all
th
e
wo
r
d
s
o
r
r
o
u
n
d
k
e
y
s
,
it
co
m
p
letes
th
e
k
ey
s
ch
e
d
u
lin
g
p
r
o
ce
s
s
.
As
s
h
o
wn
in
Fig
u
r
e
2
,
th
e
f
u
n
ctio
n
(
f
(
x
)
m
o
d
2
5
6
)
is
d
en
o
ted
b
y
t
h
e
s
y
m
b
o
l
⊗
.
T
h
e
r
elatio
n
s
h
ip
b
etwe
en
th
e
i
n
p
u
t
(
x
)
o
f
t
h
e
o
p
er
atio
n
(
⊗
)
a
n
d
its
o
u
tp
u
t
is
s
h
o
wn
i
n
Fig
u
r
e
4
.
A
co
m
p
lex
r
elatio
n
s
h
ip
ca
n
b
e
s
ee
n
b
y
an
al
y
zin
g
th
e
b
ac
k
tr
ac
k
in
g
o
f
t
h
e
in
p
u
t
(
)
v
alu
e
f
r
o
m
th
e
f
(
x
)
m
o
d
2
5
6
(
⊗
)
o
p
e
r
atio
n
o
u
tp
u
t,
wh
ich
h
as
s
ev
er
al
b
en
d
s
an
d
o
s
cillatio
n
s
as
illu
s
tr
ated
in
Fig
u
r
e
4
.
T
h
er
e
ar
e
ir
r
e
g
u
lar
s
h
if
ts
in
th
e
o
u
tp
u
ts
d
u
e
t
o
th
e
n
o
n
lin
e
ar
r
elatio
n
s
h
ip
b
etwe
en
in
p
u
ts
(
x
)
an
d
th
e
o
u
tp
u
ts
o
f
⊗
;
th
is
r
e
d
u
ce
s
th
e
co
r
r
elatio
n
b
etwe
en
wo
r
d
s
an
d
r
o
u
n
d
k
ey
s
in
th
e
k
e
y
s
c
h
ed
u
le.
Du
e
to
th
is
n
o
n
-
lin
ea
r
b
eh
a
v
io
r
,
attac
k
er
s
o
f
ten
f
i
n
d
it
ch
allen
g
i
n
g
to
i
n
f
er
th
e
in
p
u
t
k
e
y
f
r
o
m
th
e
r
o
u
n
d
k
ey
s
,
as
th
e
s
am
e
o
u
tp
u
t
m
ay
n
o
t
alwa
y
s
co
r
r
esp
o
n
d
to
th
e
s
am
e
in
p
u
t
in
th
e
o
p
er
atio
n
.
I
t
d
ep
e
n
d
s
o
n
th
e
r
ea
l
co
ef
f
icien
t
v
alu
es
u
s
ed
in
th
e
cu
b
ic
p
o
ly
n
o
m
ial
f
u
n
ctio
n
.
T
h
e
b
ac
k
tr
ac
k
in
g
p
r
o
ce
s
s
is
m
o
r
e
i
n
tr
icate
an
d
u
n
p
r
e
d
ictab
le,
wh
ich
m
ak
es
th
e
f
u
n
ctio
n
m
o
r
e
r
esil
ien
t to
cr
y
p
to
g
r
ap
h
i
c
attac
k
s
.
Fig
u
r
e
4
.
R
elatio
n
s
h
ip
b
etwe
e
n
in
p
u
t
(
x
)
a
n
d
⊗
o
p
er
atio
n
Ps
eu
d
o
co
d
e
o
f
en
h
a
n
ce
d
AE
S
KSA
EnhancedAES128KeyExpansion (byte initial_secretkey [16], word w [44], int m, int n, int o,
int p)
{
word tmp_word;
Round_constants
=
(0x017c10ca, 0x0277f5e6, 0x04f289a7, 0x083004f2, 0x10ca7492, 0x20b7a9d3,
0x4009017c, 0x80cdbd7a, 0x1baf79b6, 0x
36056b7f
);
for (x=0; x<4; x++)
w[x]
=
(initial_secretkey [4*x], initial_secretkey [4*x+1], initial_secretkey [4*x+2],
initial_secretkey [4*x+3]);
for (x=4; x<44; x++)
{
tmp_word
=
w[x
-
1];
if (x mod 4
=
0)
{
tmp_word =SubWord (RotateWord(tmp_word))
⊕
Round_constants[x/4];
w[x]=tmp_word
⊕
w[x
-
4];
}
else
{
for (y=0; y<4; y++)
{
tmp_word[y]
=
(m
*
tmp_word[y]
^
3
+
n
*
tmp_word[y]
^
2
+
o
*
tmp_word[y]
+
p) % 256
}
tmp_word
=
[tmp_word [0], tmp_word [1], tmp_word [2], tmp_word [3]];
w[k]
=
tmp_word
⊕
w[k
-
4];
}
}
}
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
A
n
imp
r
o
ve
d
ke
y
s
ch
ed
u
lin
g
f
o
r
a
d
va
n
ce
d
en
cryp
tio
n
s
ta
n
d
a
r
d
w
ith
.
.
.
(
Mu
th
u
Meen
a
ksh
i G
a
n
esa
n
)
2461
2
.
3
.
E
v
a
lua
t
i
o
n
T
h
is
s
ec
tio
n
d
is
cu
s
s
es
th
e
ev
alu
atio
n
m
eth
o
d
to
m
ea
s
u
r
e
t
h
e
s
tr
en
g
th
o
f
t
h
e
en
h
an
ce
d
AE
S
KSA.
Hig
h
d
en
s
ity
,
lo
w
d
e
n
s
ity
,
a
n
d
r
a
n
d
o
m
d
e
n
s
ity
in
p
u
t
k
ey
s
ets
wer
e
u
s
ed
f
o
r
th
e
ev
al
u
atio
n
p
r
o
ce
s
s
.
T
h
e
h
ig
h
-
d
e
n
s
ity
k
ey
(
HDK)
,
with
its
lar
g
e
n
u
m
b
er
o
f
‘
1
’
b
its
an
d
a
s
m
all
n
u
m
b
er
o
f
‘
0
’
b
its
(
at
m
o
s
t
two
)
,
p
o
s
es
a
ch
allen
g
e
to
alg
o
r
ith
m
s
wit
h
ex
tr
em
e
b
iases
to
war
d
s
th
e
‘
1
’
b
its
.
On
th
e
o
th
er
h
a
n
d
,
t
h
e
lo
w
-
d
en
s
ity
k
e
y
(
L
DK)
,
with
its
lar
g
e
n
u
m
b
e
r
o
f
‘
0
’
b
its
a
n
d
a
s
m
all
n
u
m
b
er
o
f
‘
1
’
b
its
(
at
m
o
s
t
two
)
,
p
o
s
es
a
ch
allen
g
e
to
alg
o
r
ith
m
s
with
ex
tr
em
e
b
ia
s
es
to
war
d
s
th
e
‘
0
’
b
its
.
R
an
d
o
m
d
en
s
ity
k
ey
s
(
R
DK)
co
n
s
is
t
o
f
r
an
d
o
m
s
eq
u
en
ce
s
o
f
‘
0
’
an
d
‘
1
’
b
its
,
s
er
v
in
g
as
a
b
aselin
e
f
o
r
m
o
r
e
ty
p
ical
k
ey
d
is
tr
ib
u
tio
n
s
.
T
h
e
f
o
llo
win
g
test
s
wer
e
u
s
ed
to
ev
alu
ate
th
e
p
r
o
p
o
s
ed
an
d
s
tan
d
ar
d
AE
S
KSA
s
:
f
r
eq
u
en
cy
test
,
av
alan
ch
e
e
f
f
ec
t,
b
it
d
if
f
er
en
ce
b
etwe
en
s
u
cc
ess
iv
e
s
u
b
k
ey
s
,
a
n
d
r
elate
d
k
ey
an
al
y
s
is
.
2
.
3
.
1
.
F
re
qu
ency
t
est
T
h
e
in
d
eter
m
in
ac
y
o
f
r
o
u
n
d
k
ey
s
g
en
er
ated
f
r
o
m
KSA
in
b
lo
ck
cip
h
er
s
ca
n
b
e
ev
alu
ated
u
s
in
g
th
e
f
r
eq
u
e
n
cy
test
,
w
h
ich
is
in
te
n
d
ed
to
e
v
alu
ate
th
e
r
a
n
d
o
m
n
ess
o
f
r
a
n
d
o
m
n
u
m
b
e
r
g
en
e
r
ato
r
s
(
R
NGs).
B
y
ass
es
s
in
g
th
e
d
is
tr
ib
u
tio
n
o
f
‘
0
’
a
n
d
‘
1
’
b
its
in
th
e
b
in
ar
y
s
eq
u
en
ce
o
f
r
o
u
n
d
k
ey
s
,
th
e
t
est
d
eter
m
in
es
if
it
d
is
p
lay
s
th
e
ess
en
tial
r
an
d
o
m
n
ess
f
o
r
s
ec
u
r
e
en
cr
y
p
tio
n
o
p
er
atio
n
s
[
2
5
]
.
Pas
s
in
g
th
e
test
in
d
icate
s
an
e
q
u
al
d
is
tr
ib
u
tio
n
o
f
0
s
an
d
1
s
,
r
ev
e
alin
g
th
e
s
tr
en
g
t
h
o
f
th
e
KSA;
f
ailu
r
e
im
p
lies
p
o
ten
tial
b
ias o
r
n
o
n
-
r
a
n
d
o
m
n
ess
.
T
o
co
n
d
u
ct
th
e
f
r
eq
u
e
n
cy
test
,
th
e
f
o
llo
win
g
s
tep
s
a
th
r
o
u
g
h
s
tep
d
ar
e
f
o
llo
we
d
:
a.
C
o
n
v
er
tin
g
th
e
b
in
ar
y
s
eq
u
en
ce
p
atter
n
(
ε)
i
n
to
±
1
:
T
h
is
p
r
o
ce
d
u
r
e
c
o
n
v
e
r
ts
th
e
s
eq
u
en
c
e
in
to
v
alu
es
-
1
an
d
+1
.
T
h
e
f
o
r
m
u
la
=
2
−
1
r
ep
r
esen
ts
a
co
n
v
er
s
io
n
o
f
th
is
ty
p
e.
T
h
at
is
,
if
=
0
,
th
en
=
-
1
,
an
d
if
=
1
,
th
en
=
1
.
b.
T
h
e
o
v
e
r
all
co
m
p
u
tatio
n
o
f
Su
m
(
S
n
):
1
+
2
+
.
.
.
+
=
wh
er
e
n
is
th
e
to
tal
n
u
m
b
er
o
f
b
its
.
c.
Dete
r
m
in
e
th
e
test
s
tatis
tic
e
s
ti
m
ato
r
(
):
=
|
|
⎷
d.
P
-
v
alu
e
ass
ess
m
en
t:
T
h
e
p
-
v
a
lu
e
is
co
m
p
u
te
d
an
d
in
v
esti
g
ated
u
s
in
g
th
e
co
m
p
lem
en
tar
y
er
r
o
r
f
u
n
ctio
n
(
)
as g
iv
en
b
elo
w.
−
=
(
⎷2
)
(
1
1
)
T
o
ev
alu
ate
th
e
s
tr
en
g
t
h
o
f
b
o
th
e
x
is
tin
g
an
d
p
r
o
p
o
s
ed
KSA,
1
0
,
0
0
0
in
itial
r
a
n
d
o
m
s
ec
r
et
k
ey
s
wer
e
g
en
er
ated
a
n
d
s
to
r
ed
in
a
s
in
g
le
f
ile.
Usi
n
g
th
ese
in
itial
s
ec
r
et
k
ey
s
1
0
r
o
u
n
d
k
e
y
s
wer
e
g
en
er
ated
an
d
s
to
r
ed
in
1
0
d
if
f
er
en
t
f
iles
f
o
r
e
x
is
tin
g
an
d
p
r
o
p
o
s
ed
KSAs
.
E
v
er
y
f
ile
is
ex
am
in
ed
s
ep
ar
ately
.
T
h
e
o
u
tco
m
es
o
f
th
e
p
r
o
p
o
s
ed
an
d
ex
is
tin
g
o
n
es we
r
e
co
m
p
ar
e
d
.
T
h
e
f
r
eq
u
e
n
cy
t
est ev
alu
ates th
e
r
an
d
o
m
n
ess
o
f
a
b
it seq
u
en
ce
b
y
ca
lcu
latin
g
th
e
p
-
v
alu
e
u
s
in
g
(
1
1
)
an
d
an
aly
zi
n
g
th
e
o
u
tco
m
es.
I
f
th
e
p
-
v
alu
e
is
m
o
r
e
th
an
o
r
eq
u
al
to
0
.
0
1
,
a
s
eq
u
en
ce
is
co
n
s
id
er
ed
p
s
eu
d
o
-
r
an
d
o
m
; if
n
o
t,
it is
co
n
s
id
er
e
d
n
o
n
-
r
an
d
o
m
[
2
5
]
.
2
.
3
.
2
.
Av
a
la
nche
ef
f
ec
t
o
f
r
o
un
d k
ey
s
I
n
cr
y
p
to
g
r
ap
h
y
,
th
e
p
h
e
n
o
m
e
n
o
n
k
n
o
wn
as
th
e
“
a
v
alan
ch
e
ef
f
ec
t
(
AE
)
”
o
cc
u
r
s
wh
en
a
n
alter
atio
n
o
f
a
s
in
g
le
b
it
in
th
e
in
p
u
t
(
p
la
in
tex
t
in
e
n
cr
y
p
ti
o
n
o
r
s
ec
r
et
k
ey
in
KSA)
ca
u
s
es
a
n
o
ticea
b
ly
d
if
f
er
en
t
o
u
tp
u
t
(
cip
h
er
tex
t
in
en
cr
y
p
tio
n
o
r
r
o
u
n
d
k
ey
s
in
KSA)
.
T
h
e
AE
t
est
f
o
r
th
e
KSA
ca
n
b
e
ca
r
r
ie
d
o
u
t
b
y
c
o
m
p
ar
i
n
g
two
k
ey
s
ch
e
d
u
les
g
en
e
r
ated
b
ef
o
r
e
an
d
af
ter
c
o
m
p
lem
en
ti
n
g
o
n
e
b
it
o
f
t
h
e
o
r
i
g
in
al
s
ec
r
et
k
ey
[
2
6
]
–
[
2
8
]
.
T
o
d
o
th
is
,
it is
n
ec
ess
ar
y
to
f
in
d
th
e
Ham
m
in
g
d
is
tan
ce
(
n
u
m
b
e
r
o
f
b
its
f
lip
p
ed
)
b
etwe
en
t
h
e
two
Key
s
ch
ed
u
les,
g
en
er
ated
b
ef
o
r
e
f
lip
p
in
g
an
y
b
its
o
f
th
e
o
r
ig
in
al
s
ec
r
et
k
e
y
an
d
af
ter
f
lip
p
in
g
a
s
in
g
le
b
it
o
f
th
e
o
r
ig
in
al
s
ec
r
et
k
ey
—
t
h
e
n
ex
t b
it
o
f
th
e
o
r
ig
in
al
k
e
y
ch
an
g
es with
ea
ch
iter
atio
n
to
d
ete
r
m
in
e
th
e
A
E
.
T
h
e
co
m
p
u
tatio
n
o
f
th
e
av
e
r
ag
e
AE
f
o
r
th
e
ex
is
tin
g
an
d
p
r
o
p
o
s
ed
KSA
is
g
iv
e
n
b
elo
w.
ℎ
=
100
(
1
2
)
2
.
3
.
3
.
B
it
diff
er
ence
bet
wee
n r
o
un
d k
ey
s
T
h
e
Ham
m
in
g
d
is
tan
ce
b
etwe
en
two
s
u
cc
ess
iv
e
s
u
b
k
ey
s
w
as
ca
lcu
lated
u
s
in
g
th
e
XOR
f
u
n
ctio
n
in
th
is
test
to
as
s
es
s
th
eir
co
r
r
elatio
n
.
T
h
e
s
tatis
tical
r
elatio
n
s
h
ip
b
etwe
en
th
e
r
o
u
n
d
k
ey
s
b
ec
o
m
es
ex
tr
em
el
y
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
2
,
Ap
r
il
20
25
:
2
4
5
5
-
2
4
6
7
2462
co
m
p
licated
wh
e
n
th
e
r
eliab
le
KSA
o
f
f
er
s
a
b
it
d
if
f
er
e
n
ce
o
f
m
o
r
e
th
an
5
0
%
[
2
2
]
,
[
2
7
]
.
T
o
ev
alu
ate
t
h
is
,
1
0
0
R
DK,
1
0
0
L
DK,
an
d
1
0
0
HD
K
wer
e
u
s
ed
.
Sin
ce
th
e
AE
S
KSA
alg
o
r
ith
m
g
en
er
ates
1
0
r
o
u
n
d
k
ey
s
f
r
o
m
an
in
itial
s
ec
r
et
k
ey
,
in
ea
ch
r
o
u
n
d
,
th
e
k
ey
s
g
en
e
r
ated
f
r
o
m
th
e
ex
is
tin
g
an
d
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
ar
e
also
wr
itten
to
s
ep
ar
ate
f
iles
,
an
d
th
ese
1
0
r
o
u
n
d
k
ey
s
,
in
clu
d
in
g
th
e
i
n
itial
s
ec
r
et
k
ey
,
i.e
.
,
1
1
s
ep
ar
ate
f
iles
f
o
r
b
o
th
alg
o
r
ith
m
s
,
wer
e
tak
e
n
f
o
r
test
in
g
.
T
h
e
Ham
m
in
g
d
is
tan
ce
b
etwe
en
two
s
u
cc
ess
iv
e
f
ile
co
n
ten
ts
was
d
eter
m
in
ed
iter
ativ
el
y
.
T
h
is
test
was
p
er
f
o
r
m
ed
f
o
r
b
o
th
e
x
is
tin
g
an
d
p
r
o
p
o
s
ed
KSA
wi
th
all
th
r
ee
ty
p
es
o
f
k
ey
s
,
an
d
av
e
r
ag
e
Ham
m
in
g
d
is
tan
ce
s
b
etwe
en
r
o
u
n
d
k
ey
s
wer
e
u
s
ed
to
m
ea
s
u
r
e
th
e
c
o
r
r
elatio
n
b
etwe
en
r
o
u
n
d
k
ey
s
.
2
.
3
.
4
.
Rela
t
ed
k
e
y
a
na
ly
s
is
T
h
e
r
elate
d
k
e
y
an
aly
s
is
id
en
tifie
s
k
ey
s
ch
ed
u
le
v
u
ln
e
r
ab
ilit
ies
an
d
ev
alu
ates
cr
y
p
to
g
r
ap
h
ic
p
r
o
tectio
n
.
I
t
p
r
ev
e
n
ts
k
ey
r
ec
o
v
er
y
b
y
attac
k
er
s
a
n
d
en
h
a
n
c
es
cr
y
p
to
g
r
ap
h
ic
d
esig
n
b
y
ex
p
o
s
in
g
wea
k
n
ess
es.
T
o
p
e
r
f
o
r
m
r
elate
d
k
ey
an
aly
s
is
,
g
iv
en
an
o
r
ig
i
n
al
k
e
y
an
d
p
lain
tex
t
with
a
p
r
e
d
eter
m
in
e
d
d
if
f
er
en
ce
Δ
,
th
e
r
elate
d
k
ey
K’
is
g
e
n
er
at
ed
as
’
=
⊕
an
d
th
e
r
elate
d
p
lain
t
ex
t
X’
is
g
en
er
ated
as
’
=
⊕
,
wh
er
e
⊕
d
en
o
tes
th
e
b
itwis
e
XOR
o
p
er
atio
n
.
T
o
f
in
d
th
e
c
ip
h
er
tex
t
C
,
en
cr
y
p
t
th
e
p
lain
t
ex
t
X
with
th
e
k
ey
K
u
s
in
g
=
(
)
.
Fo
r
th
e
r
elate
d
cip
h
er
tex
t
C
’
,
en
cr
y
p
t
th
e
r
elate
d
p
lain
tex
t
X’
with
th
e
r
elate
d
k
ey
K
’
u
s
in
g
’
=
′
(
’
)
.
I
f
th
e
o
u
tp
u
t
d
if
f
e
r
en
c
e
d
is
tr
ib
u
tio
n
(
⊕
’
)
is
n
o
t
u
n
i
f
o
r
m
,
an
attac
k
e
r
co
u
ld
u
s
e
th
is
ir
r
eg
u
lar
ity
to
d
ed
u
ce
th
e
k
ey
f
o
r
en
cr
y
p
tin
g
m
ess
ag
es
with
th
e
in
p
u
t
d
if
f
e
r
en
ce
b
etwe
e
n
in
p
u
t
d
if
f
er
e
n
ce
s
(
⊕
’
)
.
T
h
e
Ham
m
in
g
d
is
tan
ce
m
ea
s
u
r
es
th
e
b
it
d
i
f
f
er
en
ce
b
etwe
en
C
an
d
C
′
[
2
9
]
,
[
3
0
]
.
T
h
e
m
ea
n
Ham
m
in
g
d
is
tan
ce
(
μ
)
b
etwe
en
cip
h
er
tex
ts
is
ca
lcu
lated
as
(
1
3
)
:
μ
=
1
∑
(
,
′
)
=
1
(
1
3
)
wh
er
e
is
th
e
n
u
m
b
er
o
f
b
y
tes
in
⊕
’
.
T
h
e
v
ar
ian
ce
o
f
th
e
Ham
m
in
g
d
is
tan
ce
(
σ
d
2
)
is
ca
lcu
lated
as
th
e
av
er
ag
e
o
f
th
e
s
q
u
ar
e
d
d
if
f
er
en
ce
s
b
etwe
en
ea
ch
Ham
m
in
g
d
is
tan
ce
,
(C
i
,
C
i
′)
an
d
th
e
m
ea
n
Ham
m
in
g
d
is
tan
ce
,
g
iv
en
b
y
(
1
4
)
:
σ
d
2
=
1
∑
(
(
,
′
)
−
μ
)
−
1
2
(
1
4
)
T
h
e
v
a
r
ian
ce
o
f
th
e
Ham
m
i
n
g
d
is
tan
ce
is
u
s
ed
to
ass
ess
th
e
u
n
i
f
o
r
m
ity
in
th
e
d
is
tr
ib
u
tio
n
o
f
th
e
o
u
tp
u
t
d
if
f
er
en
ce
s
⊕
’
.
L
o
w
v
ar
ian
ce
i
n
d
icate
s
co
n
s
is
ten
t
an
d
u
n
if
o
r
m
b
e
h
av
io
r
,
r
ed
u
cin
g
th
e
li
k
elih
o
o
d
o
f
ex
p
lo
itab
le
p
atter
n
s
in
r
elate
d
k
ey
an
aly
s
is
.
T
o
f
in
d
th
e
m
ea
n
Ham
m
in
g
d
is
tan
ce
b
etwe
en
cip
h
er
tex
ts
an
d
r
elate
d
cip
h
er
tex
ts
,
1
0
0
0
r
an
d
o
m
k
ey
s
an
d
p
lain
tex
ts
wer
e
u
s
ed
.
T
h
e
m
ea
n
Ham
m
in
g
d
is
tan
ce
was
ca
lcu
lated
b
y
av
er
a
g
in
g
th
e
Ham
m
i
n
g
d
is
tan
ce
s
b
etwe
en
N
b
y
tes
o
f
cip
h
er
tex
ts
C
i
an
d
th
eir
co
r
r
esp
o
n
d
i
n
g
r
elate
d
cip
h
er
tex
ts
C
i
’
u
s
in
g
(
1
3
)
an
d
its
v
ar
ian
ce
was
ca
lcu
lated
u
s
in
g
(
1
4
)
.
T
h
e
o
v
er
all
m
ea
n
Ham
m
in
g
d
is
tan
ce
an
d
th
e
v
ar
ian
ce
wer
e
ca
lcu
la
ted
b
y
tak
i
n
g
th
e
av
er
a
g
e
o
f
in
d
iv
id
u
al
Ham
m
in
g
d
is
tan
ce
s
an
d
th
eir
v
ar
ian
ce
s
r
esp
ec
tiv
ely
f
r
o
m
1
0
0
0
d
if
f
er
e
n
t tr
ials
.
2
.
3
.
5
.
E
x
ec
utio
n t
im
e
E
x
ec
u
tio
n
tim
e
is
a
cr
u
cial
f
a
cto
r
in
ev
alu
atin
g
th
e
ef
f
icien
cy
o
f
an
alg
o
r
ith
m
,
as
f
aster
ex
ec
u
tio
n
lead
s
to
im
p
r
o
v
e
d
u
s
er
ex
p
e
r
ien
ce
an
d
m
o
r
e
ef
f
icien
t
r
eso
u
r
ce
u
tili
za
tio
n
.
T
o
g
et
th
e
e
x
ec
u
tio
n
tim
e,
o
n
e
m
u
s
t
r
ec
o
r
d
th
e
s
tar
t
an
d
co
m
p
letio
n
tim
es
o
f
th
e
alg
o
r
ith
m
an
d
s
u
b
tr
ac
t
th
e
s
tar
t
f
r
o
m
th
e
co
m
p
letio
n
tim
e
[
3
1
]
.
T
h
e
ex
ec
u
tio
n
tim
e
f
o
r
b
o
th
KSAs
was c
alcu
lated
an
d
co
m
p
ar
ed
in
th
is
way
.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
3
.
1
.
F
re
qu
ency
t
est
T
ab
le
3
d
is
p
lay
s
th
e
f
r
eq
u
e
n
c
y
test
p
-
v
alu
es
f
o
r
1
0
r
o
u
n
d
k
ey
s
g
en
er
ated
b
y
t
h
e
s
tan
d
ar
d
AE
S
KS
A
an
d
th
e
en
h
an
ce
d
AE
S
KSA.
T
h
e
s
tan
d
ar
d
v
er
s
io
n
o
f
AE
S
KSA
h
as
an
av
er
ag
e
p
-
v
alu
e
o
f
0
.
5
1
0
3
9
2
1
7
4
,
b
u
t
th
e
im
p
r
o
v
ed
AE
S
KSA
h
as
a
n
av
er
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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