Indonesi
an
Journa
l
of El
ect
ri
cal Engineer
ing
an
d
Comp
ut
er
Scie
nce
Vo
l.
24
,
No.
1
,
Octo
be
r
20
21
,
pp.
548
~
553
IS
S
N:
25
02
-
4752, DO
I: 10
.11
591/ijeecs
.v
2
4
.i
1
.
pp
548
-
553
548
Journ
al h
om
e
page
:
http:
//
ij
eecs.i
aesc
or
e.c
om
Linea
r
eq
uation fo
r text
crypt
ogra
ph
y using lett
er
s'
coordin
at
es
Thamir
A.
Ja
rjis,
Yahya
Q.
I.
Al
-
F
ad
hil
i
Depa
rtment
o
f
C
om
pute
r
Scie
n
ce,
Col
le
ge
of
Edu
ca
t
ion
for
Pure
S
ci
en
ce,
Unive
rsit
y
of
Mos
ul, Mosul,
Ir
aq
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
Dec
16
,
202
0
Re
vised
A
ug
10
,
2021
Accepte
d
Aug
23
,
2021
T
h
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l
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.
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h
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p
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f
o
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m
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h
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d
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o
w
e
d
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e
t
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r
a
n
d
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o
b
u
s
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s
u
l
t
s
b
y
a
p
p
l
yi
n
g
t
h
e
f
r
e
q
u
e
n
c
y
a
n
a
l
ys
i
s
t
e
s
t
f
o
r
t
h
i
s
p
r
o
p
o
s
e
d
a
l
g
o
r
i
t
h
m
e
v
a
l
u
a
t
i
n
g
.
Ke
yw
or
ds:
Ci
ph
er
text
Fr
e
qu
e
ncy a
naly
sis
Linear
-
dec
rypt
ion
Linear
-
enc
rypt
ion
Secret
key
This
is an
open
acc
ess arti
cl
e
un
der
the
CC
B
Y
-
SA
l
ic
ense
.
Corres
pond
in
g
Aut
h
or
:
Tham
ir A
. J
a
rj
i
s
Dep
a
rtm
ent o
f C
om
pu
te
r
Scie
nce,
C
ollege
of
Educat
io
n
f
or
Pu
r
e Scie
nce
Un
i
ver
sit
y o
f M
os
ul
Al
-
Ma
j
m
oa
Al
-
Tha
qa
feya, M
os
ul
, Ira
q
Em
a
il
: t
ha
m
ir@uom
os
ul.edu
.iq
1.
INTROD
U
CTION
Crypto
gr
a
phy
is
a
te
rm
fo
r
t
he
sec
ret
w
riti
ng
w
hich
is
de
rive
d
f
r
om
a
Gr
ee
k
wor
d.
Nowa
days
it
ref
e
rs
to
the
sc
ie
nce
and
a
rt
of
m
essages
transf
e
r
to
secu
re
the
m
fr
om
att
acks.
It
’s
a
te
chn
i
qu
e
for
m
es
sages
encr
y
ption
a
nd
decr
ypti
on
[1
]
.
The
refor
e
,
cr
yptogra
p
hy
is
need
e
d
to
e
nc
r
ypt
the
m
essage
at
the
send
e
r
side
and
decr
ypt
it
at
the
receiver
side
[2
]
.
Fig
ure
1
si
m
plifie
s
t
he
te
chn
i
qu
e
s
of
cry
ptogra
phy
are
sy
m
m
et
ri
c
and
asym
m
e
tric
key
cryptography
[3
]
.
Sy
m
m
et
ri
c
key
cryptogr
aph
y
is
a
sh
are
d
key
betwee
n
sen
der
an
d
rec
ei
ver
.
T
h
e
s
e
n
d
e
r
u
s
e
s
t
h
e
k
e
y
a
n
d
t
h
e
e
n
c
r
y
p
t
i
o
n
a
l
g
o
r
i
t
hm
t
o
e
nc
r
y
p
t
t
h
e
m
e
s
s
a
g
e
.
W
h
e
r
e
a
s
t
h
e
s
a
m
e
k
e
y
a
n
d
t
h
e
d
e
c
r
y
p
t
i
o
n
a
l
go
r
i
t
hm
a
r
e
u
s
e
d
b
y
t
h
e
r
e
c
e
i
ve
r
t
o
d
e
c
r
y
pt
t
he
s
a
m
e
m
e
s
s
a
ge
.
W
h
i
l
e
a
p
u
b
l
i
c
k
e
y
i
s
u
s
e
d
b
y
t
h
e
s
e
n
d
e
r
u
s
i
n
g
a
s
y
m
m
e
t
r
i
c
k
e
y
c
r
y
p
t
o
g
r
a
p
h
y
[
4
]
,
[
5
]
.
B
u
t
a
p
r
i
v
a
t
e
s
e
c
r
e
t
k
e
y
i
s
a
s
s
i
g
n
e
d
t
o
t
h
e
r
e
c
e
i
v
e
r
o
nl
y
[
6]
.
The
public
key
of
th
e
receive
r
is
us
ed
by
the
sen
der
to
e
nc
r
ypt
the
m
essage,
w
hilst
the
own
receive
r'
s
pri
vate
key is
us
ed
to decry
pt the m
essage
by the
r
e
cei
ver
[7
]
-
[
9]
.
T
h
e
s
u
b
s
t
i
t
u
t
i
o
n
a
n
d
t
r
a
n
s
p
o
s
i
t
i
o
n
c
i
p
h
e
r
i
n
t
r
a
d
i
t
i
o
n
a
l
c
i
p
h
e
r
a
l
g
o
r
i
t
h
m
s
a
r
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s
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d
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n
s
y
m
m
e
t
r
i
c
k
e
y
c
r
y
p
t
o
g
r
a
p
h
y
[
1
]
,
[
1
0
]
.
I
n
s
u
b
s
t
i
t
u
t
i
o
n
c
i
p
h
e
r
,
a
s
y
m
b
o
l
i
s
r
e
p
l
a
c
e
d
b
y
a
n
o
t
h
e
r
s
y
m
b
o
l
w
i
t
h
s
u
c
h
e
a
s
e
.
I
t
h
a
s
t
w
o
t
y
p
e
s
;
t
h
e
m
o
n
o
a
l
p
h
a
b
e
t
i
c
s
u
b
s
t
i
t
u
t
i
o
n
c
i
p
h
e
r
a
n
d
p
o
l
y
a
l
p
h
a
b
e
t
i
c
s
u
b
s
t
i
t
u
t
i
o
n
c
i
p
h
e
r
.
T
h
e
m
o
n
o
a
l
p
h
a
b
e
t
i
c
c
i
p
h
e
r
,
i
n
w
h
i
c
h
a
l
e
t
t
e
r
i
s
a
l
w
a
y
s
r
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p
l
a
c
e
d
b
y
e
x
a
c
t
s
a
m
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l
e
t
t
e
r
i
n
t
h
e
c
i
p
h
e
r
t
e
x
t
.
C
a
e
s
a
r
c
i
p
h
e
r
i
s
t
h
e
w
e
l
l
-
k
n
o
w
n
e
x
a
m
p
l
e
o
f
m
o
n
o
a
l
p
h
a
b
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t
i
c
s
u
b
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i
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u
t
i
o
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c
i
p
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r
w
h
i
c
h
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a
l
w
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y
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p
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a
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b
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d
[
1
1
]
.
W
h
e
r
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a
s
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n
p
o
l
y
a
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p
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w
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w
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a
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[
1
2
]
-
[
1
4
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci
IS
S
N:
25
02
-
4752
Linear e
quatio
n
fo
r text
cry
pto
gra
phy
us
in
g l
et
te
rs'
c
oord
i
nate
s
(
Tha
mir A
. Jarj
is
)
549
Figure
1. Ty
pe
s of c
rypto
gr
a
phy
[
3]
In
tra
nspo
sit
io
n
ci
pher,
th
e
le
tt
ers
in
the
plainte
xt
kee
p
their
plainte
xt
fo
rm
bu
t
sw
app
e
d
thei
r
po
sit
io
ns
t
o
ge
t
the
ci
pherte
xt.
T
he
plaint
ext
is
c
om
po
sed
int
o
tw
o
dim
ension
al
ta
bl
e
and
by
us
i
ng
the
pr
e
def
i
ned
key
the
col
um
ns
are
exc
ha
ng
e
d
accor
dingly
[
15
]
,
[
16]
.
F
r
om
the
above
previe
w,
c
rypto
gr
a
phy
us
es
m
at
he
m
atical
op
e
rati
ons
to
e
ncr
y
pt
an
d
dec
rypt
se
ns
it
ive
data
an
d
i
nfor
m
at
ion
f
or
ei
ther
t
o
be
sto
re
d
or
to
be
tra
ns
m
i
tt
ed
acr
os
s
ne
tworks
sec
ur
el
y.
The
refore
,
these
data/
inf
or
m
at
ion
are
unrea
dab
le
bu
t
the
auth
or
iz
e
d
reci
pient
[
17
]
,
[
18
]
.
Un
li
ke
cry
pto
gra
ph
y,
c
rypt
analy
sis
is
the
sci
ence
that
stud
ie
s
the
e
ncry
pted
te
xt
then
a
naly
ses
an
d
brea
ks
it
to
gain
the
pl
ai
ntext
il
le
gally
.
People
w
ho
sp
eci
al
ist
with
su
c
h
sci
ence
nam
ed
as
cryptanaly
s
ts
bu
t
they
m
uch
m
or
e
cal
le
d
at
ta
ckers.
Cryptolo
gy
co
ns
ist
s
of
both
crypto
gr
a
phy
a
nd
cryptanaly
sis
[
19
]
-
[
2
3
].
T
he
pr
opos
e
d
al
go
r
it
h
m
ov
erc
om
e
s
the
pro
blem
of
e
ncr
y
pting
t
he
sam
e
le
t
te
r
from
the
plainte
xt
into
the
sam
e
corres
pondin
g
le
tt
er
in
the
ci
ph
e
r
te
xt.
T
his
pro
blem
fo
un
d
in
t
he
tr
aditi
on
al
crypto
gr
a
phy a
lgorit
hm
s.
-
Fr
e
qu
e
ncy a
naly
sis t
est
f
or e
va
luati
ng
t
he pr
opos
e
d
al
gorithm
T
h
e
r
e
d
u
n
d
a
n
c
y
o
f
e
a
c
h
l
e
t
t
e
r
,
e
a
c
h
l
e
t
t
e
r
’
s
c
o
o
r
d
i
n
a
t
e
s
a
nd
t
h
e
p
o
l
y
a
l
p
ha
b
e
t
i
c
i
n
t
hi
s
a
l
g
o
r
i
t
hm
h
a
s
b
e
e
n
a
n
a
l
y
z
e
d
.
T
h
i
s
a
n
a
l
y
s
i
s
w
a
s
i
m
pl
e
m
e
nt
e
d
u
s
i
n
g
t
h
e
F
r
e
q
u
e
n
c
y
l
e
t
t
e
r
’
s
p
r
e
s
e
n
t
a
t
i
o
n
a
n
a
l
y
s
i
s
t
e
s
t
.
F
i
g
u
r
e
2
il
lustrate
s
the
fr
e
qu
e
ncy
a
naly
sis
wh
ic
h
is
the
ap
proac
h
t
hat
at
tem
pt
to
revea
l
the
m
essage.
T
his
r
eveal
dep
e
nds
on
t
he
fr
e
qu
e
ncy
of
le
tt
ers
in
a
ci
ph
e
rtext
[2
4
]
.
The
le
tt
ers
in
En
glish
la
ng
ua
ge
ap
pea
r
in
di
ff
ere
nt
fr
e
qu
e
ncies
[
2
5
]
.
T
he
a
ppear
ance
of
the
m
os
t
c
omm
on
le
tt
e
r
in
E
ngli
sh
la
ngua
ge
"e
"
is
ab
out
12%.
T
he
seco
nd
c
ommon
le
tt
er
is
"t
"
is
about
9%
[21]
,
[2
6
]
.
T
hi
s
fr
e
qu
e
ncy
a
naly
sis
te
st
is
us
e
d
to
eval
ua
te
the
ou
tc
om
es o
f
th
e pro
posed
alg
or
it
hm
.
Figure
2. Fr
e
quency
of E
ng
li
sh
let
te
rs [24]
2.
METHO
DOL
OGY
In
this
pap
e
r
a
new
e
ncr
ypti
on
an
d
dec
rypti
on
al
gorithm
based
on
sym
metri
c
key
is
design
e
d
an
d
i
m
ple
m
ented.
This
al
gorithm
read
s
the
plainte
xt,
the
n
co
nsi
der
s
the
posi
ti
on
s
of
each
le
tt
er
in
the
plainte
xt
body
as
a
n
el
e
m
ent
of
2
-
D
m
at
rix
.
Lat
er,
it
ob
ta
ins
the
encr
y
ption
a
nd
dec
ryptio
n
ke
y
accor
ding
to
th
e
coor
din
at
es
of
each
le
tt
er
’s
i
th
an
d
j
th
i
n
the
2
-
D
m
at
rix.
T
hese
c
oor
din
at
es
re
pr
ese
nt
th
e
le
tt
er'
s
local
i
ty
;
in
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on
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n
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E
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c Eng
&
Co
m
p
Sci,
Vo
l.
2
4
, N
o.
1
,
Oct
o
ber
20
21
:
548
-
553
550
wh
ic
h
li
ne
(ro
w
/i
th
)
the
le
tt
er
is
and
in
w
hi
ch
inde
x
(c
ol
um
n
/j
th
)
it
is
wi
thin
this
li
ne.
Thes
e
c
oord
i
na
te
s
are
fu
lfil
li
ng
the
K
erckh
offs'
pr
in
ci
ple
for
key
s
ecrecy
[
27
]
.
Finall
y,
the
ci
ph
ertext
is
se
nt.
The
ai
m
of
usi
ng
thes
e
coor
din
at
es
as
the
key
in
the
ci
ph
e
rtext
is
for
ov
e
rc
om
ing
t
he
pro
blem
of
rep
la
c
in
g
the
le
tt
er
in
the
plainte
xt
by
the
exac
t
s
a
m
e
le
tt
er
in
the
ci
ph
e
rtext
.
Also
,
to
ove
rc
om
e
the
pro
bl
e
m
of
distri
buti
ng
t
he
tra
diti
on
al
encr
y
ption
/
dec
ryptio
n key an
d
to
m
ake th
is
al
gorithm
u
nbr
eakab
le
.
The
m
ai
n
two
adv
a
ntage
s
of
this
al
go
rithm
wh
ic
h
are
re
presented
in
the
si
m
plici
t
y
of
com
pu
ta
ti
on
and
secu
rity
le
vel.
Co
ns
e
qu
ently
,
the
e
xperim
ental
resu
lt
s
hav
e
bee
n
dem
on
strat
ed
t
hat
it
is
dif
ficult
to
disco
ver
t
he
use
d
ke
y.
Fig
ure
3
e
xpla
ins
the
crypt
os
yst
e
m
of
the
al
gorithm
has
be
en
di
vid
e
d
int
o
tw
o
m
od
ules [2
8
]
,
[
29
]
,
which
are
;
i)
d
at
a enc
rypt
ion
m
odule
a
nd ii
) d
at
a
decr
y
ption m
od
ule
.
Figure
3. Crypt
os
yst
em
o
f
the
pro
po
se
d
al
gor
it
h
m
[
28]
2.1.
Data
enc
rypti
on mo
dul
e
In
t
his
m
od
ule
any
data
or
pl
ai
ntext
to
be
sent
to
t
he
rec
ei
ver
is
e
ncr
y
pt
ed
pri
or
to
be
trans
ferred
us
in
g
t
he
c
oor
din
at
es'
le
tt
er
by
co
ns
i
der
i
ng
the
plainte
xt
a
s
a
2
-
D
m
at
rix.
Eac
h
le
tt
er
w
il
l
hav
e
it
s'
i
th
and
j
th
po
sit
io
ns
in
t
his
m
at
rix.
Final
ly
,
the
c
iph
e
rtext
will
be
ge
ne
rated
a
nd
se
nt
to
the
desti
nation.
Th
e
m
ai
n
s
te
ps
of the e
ncr
y
ption al
gorithm
are
as
f
ollow
s:
St
ep
1
: R
ea
d
t
he plai
ntext.
St
ep
2
: T
ra
ns
f
er
plainte
xt to
2
-
dim
ension
al
m
at
rix.
St
ep
3
:
O
btain
the
key
fo
r
ea
ch
le
tt
er
fr
om
i
ts
coo
r
din
at
es
into
the
m
a
trix
accord
i
ng
to
t
he
encr
y
ptio
n
li
near
equ
at
io
n: C =
a *
P +
b
wh
e
re
P: is t
he
p
la
intext
, C: is
the cip
he
rtext,
a: is t
he
i
th
c
oord
i
nate,
b: is th
e j
th
c
oor
din
at
e
St
ep
4
:
Use
t
he
k
ey
s a
bove
to
e
ncr
y
pt the wh
ole
plainte
xt
to
obta
in t
he c
iph
e
rtex
t.
St
ep
5
:
Send t
he
ci
phe
rtext t
o
the
inten
de
d recei
ver.
In
th
e
previ
ous
third
ste
p
w
hi
ch
in
vo
l
ves
the
ob
ta
ini
ng
of
e
ncr
y
ption
key,
there
are
t
wo
c
oeffici
ents
of
the let
te
r'
s co
or
din
at
es (
a a
nd
b)
wh
ic
h
m
ake th
e enc
rypt
ion
key
ch
an
ge
s af
te
r
eve
ry let
te
r
be
ing
e
ncry
pted,
as sho
wn in
F
igure
4
(
a
).
2.2.
Data
dec
rypti
on mo
dul
e
Wh
e
n
t
he
e
ncry
pted
data
(Ci
ph
e
rtext)
reac
he
s
the
receive
r,
it
cannot
be
re
ad.
I
n
order
to
be
read,
th
e
decr
y
ption
key
sh
ould
be
gra
bb
e
d
f
r
om
the
le
tt
ers’
po
sit
ion
s
within
t
he
ci
ph
erte
xt.
T
hen
t
he
ci
ph
e
r
te
xt
is
decr
y
pted
a
nd
conve
rted
to
it
s
or
i
gin
al
f
orm
us
in
g
the
dec
r
ypti
on
key
us
i
ng
t
he
le
tt
ers'
coor
din
at
es,
i
th
and
j
th
.
At the
receive
r
side t
he
f
ollo
wing ste
ps
s
ho
uld
be d
on
e
in or
der to
get t
he
original
plaint
ext.
St
ep
1
: R
ea
d
t
he
ci
p
he
rtext.
St
ep
2
: T
ra
ns
f
er cip
her
te
xt to
2
-
D
m
at
rix.
St
ep
3
:
O
btain
the
dec
ryptio
n
key
from
eac
h
le
tt
er'
s
coo
r
di
nates
into
the
m
at
rix
accor
di
ng
t
o
the
decry
ption
li
near
e
qu
at
io
n:
P
=
(C
–
b)/
a
wh
e
re: a,
b are
the co
e
ff
ic
ie
nts of th
e
li
near e
qu
at
io
n.
St
ep
4
:
Decr
y
pt
the cip
her
te
xt u
si
ng the
decry
ption
key.
St
ep
5
:
O
btain
the origi
nal tex
t.
The
decr
y
ptio
n
pa
rt
nee
ds
t
o
fin
d
the
m
od
inv
e
rse
of
the
encr
y
pted
le
tt
er
as
s
how
n
in
Figure
4
(
b).
Figures
4 sh
ows the
ps
e
udo
c
odes
for b
oth
e
nc
ryptio
n
a
nd dec
ryptio
n
al
go
r
it
h
m
s.
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Ind
on
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n
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E
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Sci
IS
S
N:
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02
-
4752
Linear e
quatio
n
fo
r text
cry
pto
gra
phy
us
in
g l
et
te
rs'
c
oord
i
nate
s
(
Tha
mir A
. Jarj
is
)
551
(a)
(b)
Figure
4. The
s
e figure
s ar
e;
(
a) P
se
udo co
de
for
t
he
e
ncr
y
ption
al
gorithm
an
d
(b)
Pse
udo c
ode f
or
t
he decry
ption al
gorith
m
3.
RESU
LT
S
AND DI
SCUS
S
ION
S
The
pr
opos
e
d
al
gorithm
is
tested
on
a
set
of
plainte
xts
of
dif
fer
e
nt
le
ngths
.
The
re
sul
ts
sh
owe
d
diff
e
re
nt
re
pr
e
sentat
ion
s
f
or
each
le
tt
er
suf
fici
ently
.
Each
le
tt
er
was
en
crypted
t
o
a
di
ff
ere
nt
le
tt
ers
in
the
ci
ph
e
rtext
acco
rd
i
ng
to
it
s'
coo
r
din
at
es
in
th
e
plainte
xt.
Fig
ur
e
5
sho
wing
the
sam
ple
of
the
ap
plied
plai
ntext
,
the obtai
ne
d
ci
ph
e
rtext a
nd th
e d
ec
ryptio
n
te
xt af
te
r
ru
nn
i
ng the
alg
or
it
hm
u
si
ng
MATL
AB
.
Figure
5. The
a
pp
li
ed
p
la
i
ntex
t, the
ob
ta
i
ned
ci
ph
e
rtext a
nd
decr
y
ption t
ext
The
le
tt
er
"o"
i
n
the
w
ord
"
m
on
oalph
a
beti
c"
in
the
plai
nt
ext
hav
e
bee
n
encr
y
pted
in
t
wo
dif
fer
e
nt
le
tt
ers
"y
"
an
d
"a"
in
the
ci
pherte
xt
resp
ect
ively
.
In
ad
diti
on,
the
wor
d
"t
he"
has
bee
n
m
entioned
in
t
he
first
li
ne
twic
e a
nd
had b
ee
n
e
nc
rypted
i
n diff
e
re
nt wo
rd
s
"ivz"
and
"gt
x" resp
ect
ively
.
Fu
rt
her
m
or
e,
f
reque
ncy
analy
sis
te
st
is
app
li
ed
to
both
t
he
plainte
xt
an
d
t
he
res
ulted
ci
pherte
xt.
The
fr
e
qu
e
ncies
of
the
le
tt
ers
in
th
e
ci
ph
e
rtext
ar
e
total
ly
diff
er
ent
f
ro
m
bo
th
t
he
sta
nda
rd
fr
e
qu
e
ncies
of
En
gli
s
h
la
nguag
e
le
tt
ers
an
d
the
plain
te
xt
as
sho
wn
in
T
a
ble
1.
In
Table
1,
the
pe
rcen
ta
ge
of
eac
h
le
tt
er
f
reque
ncy
i
n
the p
la
intext a
nd
the ci
ph
e
rtext w
as cal
culat
ed
by d
i
vid
in
g t
his f
re
qu
e
ncy o
f
ea
c
h
le
tt
er b
y t
he
total
n
umber o
f
le
tt
ers
in
the
t
ext.
This
was
done
by
a
le
tt
er
-
co
un
t
sc
ript.
The
ob
ta
in
ed
fr
e
que
ncy
of
the
le
tt
ers
in
the
ci
ph
e
rtext
us
i
ng
the
propose
d
al
go
rit
hm
is
e
ntirel
y
diff
e
rent
fr
om
the
fr
e
quency
of
bo
t
h
the
sam
ple
plainte
xt
and
t
he
sta
nda
r
d
E
ng
li
sh
la
ng
uag
e
le
tt
ers
.
T
his
pro
ves
t
hat
the
res
ults
of
the
pr
opos
e
d
al
gorithm
are
dif
ficult
to b
e
d
et
ect
e
d usin
g fr
e
quenc
y analy
sis t
ech
niques.
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n
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E
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c Eng
&
Co
m
p
Sci,
Vo
l.
2
4
, N
o.
1
,
Oct
o
ber
20
21
:
548
-
553
552
Table
1.
Res
ults o
f propose
d
a
lgorit
hm
ev
al
uation usin
g
t
he fre
qu
e
ncy a
nal
ysi
s test
Eng
lish
alph
ab
e
t
Frequ
en
cy
of
E
n
g
lish
letter
s
Sa
m
p
le of
the p
lai
n
tex
t
Cip
h
ertext
a
8
.17
6
.99
4
.55
b
1
.49
0
.91
3
.34
c
2
.78
4
.55
5
.77
d
4
.25
4
.25
3
.34
e
1
2
.7
1
3
.9
8
3
.34
f
2
.23
1
.21
4
.55
g
2
.02
1
.21
3
.64
h
6
.09
3
.95
2
.43
i
6
.97
6
.99
4
.25
j
0
.15
0
.00
3
.03
k
0
.77
0
.30
1
.82
l
4
.03
3
.64
2
.73
m
2
.41
2
.43
3
.34
n
6
.75
7
.59
3
.64
o
7
.51
7
.90
2
.73
p
1
.93
4
.25
4
.25
q
0
.10
0
.30
3
.64
r
5
.99
6
.99
3
.95
s
6
.33
7
.29
3
.34
t
9
.06
7
.29
4
.25
u
2
.76
2
.43
3
.95
v
0
.98
1
.21
0
.67
w
2
.36
2
.12
5
.16
x
0
.15
0
.00
5
.16
y
1
.97
2
.21
1
.51
z
0
.07
0
.00
5
.77
4.
CONCL
US
I
O
N
The
enc
ryptio
n
an
d
decr
y
ption
al
gorit
hm
s
us
in
g
li
near
eq
uation
base
d
on
le
tt
er'
s
coo
rdi
nates
in
the
plain
te
xt
body
are
r
obus
t
,
a
nd
their
res
ults
ar
e
diff
ic
ult
to
be
rev
eal
e
d.
Co
ns
ide
rin
g
the
ke
y
of
the
e
ncr
y
ptio
n
and
decr
y
ptio
n
proce
sses
f
r
om
the
le
t
te
r'
s
coord
i
nates
in
the
2
-
D
m
a
trix
w
hich
is
represe
nted
f
r
om
the
plainte
xt
body
is
for
overc
omi
ng
the
pro
ble
m
of
distri
bu
ti
ng
t
he
s
ecret
ke
y
and
to
m
ak
e
the
al
gorithm
s
m
or
e
secur
e
a
nd
un
br
ea
ka
ble.
Th
e
resu
lt
s
of
the
im
ple
m
entat
ion
al
gorith
m
s
sh
owed
t
ha
t
the
sa
m
e
l
et
te
rs
in
diff
e
re
nt
posit
ion
s
i
n
the
plai
ntext
are
e
ncr
y
pted
to
diff
e
re
nt
le
tt
ers
in
cip
he
rtext.
T
his
m
akes
the
al
gorithm
s
ov
e
rc
om
e
the
pro
blem
of
the
cl
assic
al
go
rit
hm
s
wh
ic
h
is
a
lway
s
encr
y
pt
the
le
tt
er
to
one
exact
corres
po
nd
i
ng
le
tt
er.
ACKN
OWLE
DGE
MENTS
The
a
uthors
a
ckno
wled
ge
th
e
su
pp
or
t
f
r
om
Un
ive
rsity
of
M
os
ul,
C
ol
le
ge
of
Ed
ucat
ion
f
or
P
ur
e
Scie
nce,
a
nd t
he
y gr
at
ef
ully
a
ppreciat
e.
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NCE
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f
f
i
c
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n
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r
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n
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r
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f
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r
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v
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n
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1
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on
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a
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J
E
le
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m
p
Sci
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gra
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ase
d
adv
anc
ed
en
cr
y
pti
o
n
standa
rd
for
s
ec
uring
te
x
t
and
image
fi
le
s
,
”
In
donesian
Journa
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of
El
e
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BIOGR
AP
HI
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A
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Dr
Th
amir
Ab
d
ulh
afe
dh
Jarj
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B.
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from
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p.
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r
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m
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Coll
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ti
on,
Univer
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of
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osul,
Mos
ul
-
Ira
q
in
1988.
M.Sc.
from
Co
m
p.
Depa
rtment
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g
e
of
MIP
A,
Gaja
m
ada
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,
Indonisi
ai
n
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Ph.D.
deg
ree
from
El
e
ct
r
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n
ee
r
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,
Coll
ege
of
Eng
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nee
ring
,
Gaja
m
a
da
Univer
sit
y
,
I
ndonisia
in
200
5.
Fiel
ds
of
int
e
rest:
sec
uri
t
y
,
al
gorit
hm
s a
nd
sim
ula
ti
on
.
Dr
Yah
y
a
Qasi
m
Ib
rahim
Al
-
Fadh
il
i:
B.
Sc
.
f
rom
Math.
/Com
p.
D
epa
rtment
,
Coll
ege
of
Educ
a
ti
on,
Univ
ersity
of
Mos
ul,
Mos
ul
-
Ira
q
in
1989.
M.Sc.
from
Com
p.
depa
rtment,
Co
ll
eg
e
of
Scie
nce,
Univer
sit
y
of
Mos
ul,
Mos
ul
-
Ira
q
in
2002.
Ph.D.
degr
ee
from
Com
p.
depa
rtment
,
School
of
Scie
n
ce
,
Loughborou
gh
Univer
sit
y
,
UK
in
2018.
Fiel
ds
of
int
er
est:
al
gorit
hm
s,
par
allel algorit
h
m
s,
sim
ula
ti
on,
i
m
age
proc
essing,
3D sim
ulation and
AI.
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