Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 2
,
A
p
r
il
201
6, p
p
.
60
2
~
61
0
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
2.9
267
6
02
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Implementation of Hi
gh Secu
ri
ty Cryptographic System with
Improved Error Correction a
nd Detection Rate using FPGA
Nare
ndr
a B
a
b
u
T*,
F
a
z
a
l Noor
bas
h
a*,
Le
enendr
a
Ch
owdary Gu
nn
am**
* Department of
Electronics and
Co
mmunication Engineering,
K L
Univers
ity
, Guntur, Andhr
a Pradesh, India
** Departm
e
n
t
o
f
El
ectron
i
cs
and
Com
m
unication
Engin
eering
,
Sasi Institut
e
of
T
e
chnolog
y
and
En
gineer
ing, India
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Oct 27, 2015
Rev
i
sed
D
ec 14
, 20
15
Accepte
d Ja
n
8, 2016
In this
arti
cl
e,
a
n
encr
yp
tion
alg
o
rith
m
with
an
error d
e
te
ction
t
echniqu
e i
s
pres
ented
for h
i
ghl
y s
e
cured
r
e
li
able
data
transmission over unreliable
communication channels.
In this
algorith
m,
an
input d
a
ta is
mapped into
orthogonal code
first. After
that the cod
e
is
encr
ypted with th
e h
e
lp of Linear
F
eedback S
h
if
t
Regis
t
er (LF
S
R). The
techn
i
que has
been
s
u
cces
s
f
ull
y
verified and s
y
nthesized using Xilinx b
y
Spartan-
3E FPGA. The results show
that the error
detection rate
has been increased to 100%
b
y
proposed
encr
ypt
i
on s
c
h
e
m
e
is
eff
ect
ive
a
nd improves ban
d
width eff
i
ciency
.
Keyword:
En
cry
p
tio
n
FPGA
LFSR
Ort
h
o
g
onal
c
o
de
Copyright ©
201
6 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
N
a
r
e
nd
r
a
Babu T,
Depa
rt
em
ent
of El
ect
r
oni
cs
a
n
d
C
o
m
m
uni
cat
i
on E
n
gi
nee
r
i
n
g
,
K
L Un
iv
er
sity, Gun
t
ur
,
An
dhr
a Pr
ad
esh, India.
1.
INTRODUCTION
1.
1. Cr
ypt
o
gr
aph
y
C
r
y
p
t
o
gra
p
hy
i
s
a process
of t
r
ansm
i
t
t
i
ng st
o
r
ed dat
a
i
n
a pa
rt
i
c
ul
ar f
o
rm
i
.
e. ci
phe
rs t
e
xt
whe
r
e o
n
l
y
th
e p
e
rm
itted
p
e
rson
can
access it. Si
m
p
ly
we can
say th
at it
is th
e p
r
o
c
ess o
f
secu
ri
n
g
d
a
ta b
y
scramb
lin
g
i
n
t
o
an i
n
c
o
m
p
rehe
nsi
b
l
e
ar
ra
ngem
e
nt
, cal
l
e
d ci
phe
r t
e
xt
(e
ncry
pt
i
o
n
)
. Ju
s
t
t
h
e i
ndi
vi
d
u
al
s wh
o ha
ve a secret
key
can
deco
d
e
t
h
e m
e
ssage i
n
t
o
pl
ai
n c
o
nt
ent
(
d
ecry
p
t
i
o
n
)
. E
n
c
r
y
p
t
i
o
n can
be
defi
ned a
s
cha
n
gi
ng t
h
e
ori
g
i
n
al
m
e
ssage i
n
t
o
ot
he
r f
o
rm
whi
c
h ca
n
be agai
n
ret
a
i
n
ed
by
usi
n
g t
h
e key
.
Decry
p
t
i
on i
s
t
h
e
pr
ocess o
f
con
v
e
r
t
i
ng
ci
p
h
er t
e
xt
bac
k
t
o
pl
ai
nt
e
x
t
.
T
h
e
ori
g
i
n
at
o
r
of a
enc
r
y
p
t
e
d m
e
ssage i
m
part
e
d
t
h
e
dec
odi
ng
proce
d
ure e
x
pe
cted to rec
o
up
the fi
rst
data just with
propose
d be
neficiaries,
accord
i
ngly bl
ocki
ng undesirable
pers
o
n
s t
o
d
o
si
m
i
l
a
r. Enco
de
d m
e
ssages ca
n he
re a
n
d t
h
e
r
e be
br
ok
en
by
cry
p
t
a
nal
y
si
s,
l
i
k
ewi
s
e cal
l
e
d
cod
e
brea
ki
n
g
.
C
r
y
p
t
og
rap
h
er
s are
t
h
e nam
e
gi
ve
n
t
o
t
h
ose
w
h
o
p
r
act
i
ce t
h
i
s
t
y
p
e
o
f
cry
p
t
o
gra
p
hi
c sy
st
em
.
Cryp
tog
r
aph
y
co
n
c
ern
s
m
a
in
ly
with
four ch
aracteristics t
h
ey
are co
nfi
d
en
tiality, in
teg
r
ity, non
-
rep
u
d
i
a
t
i
on, a
nd a
u
t
h
e
n
t
i
cat
i
o
n
.
O
n
l
y
t
hos
e sy
st
em
s and
p
r
ot
ocol
s
whi
c
h sat
i
s
fy
al
l
the ab
o
v
e m
e
n
t
i
one
d
characte
r
istics are known as
cryptosystem
s. Crypto
systems are
o
f
ten
thou
gh
t to
refer
on
ly to
m
a
th
e
m
atical
proce
d
ures a
nd com
puter
program
s
. Cryptosyste
m
s are cl
assified int
o
two categories they are symmetric key
an
d asymmetr
i
c
k
e
y
o
r
pub
lic k
e
y cr
yp
tog
r
ap
h
i
c
syste
m
s.
1.2. Err
o
r
Detection Codes
Err
o
r
det
ect
i
o
n
and co
rrect
i
o
n
are t
h
e
m
e
t
hods t
h
at
en
hanc
e t
h
e secure
d d
e
l
i
v
ery
of di
gi
t
a
l
dat
a
ov
e
r
uns
ecu
red
com
m
uni
cat
i
on ch
annel
s
. I
n
t
h
e
f
i
el
d o
f
i
n
fo
rm
at
i
on t
h
e
o
ry
an
d c
odi
ng
w
h
e
r
e t
h
e a
ppl
i
cat
i
ons
o
f
com
put
er sci
e
nce an
d t
e
l
ecom
m
uni
cat
i
ons pl
ay
an im
port
a
nt
rol
e
i
n
usi
ng t
h
ese e
r
r
o
r
det
ect
i
on t
ech
ni
q
u
es
.
During
tran
sm
i
ssio
n
m
o
st o
f
th
e co
mm
u
n
i
catio
n
ch
an
n
e
ls ad
d
o
n
to
so
m
e
ad
d
ition
a
l d
a
ta to
th
e o
r
ig
in
al
d
a
ta
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
60
2 – 6
1
0
60
3
whi
c
h i
s
pre
d
om
i
n
ant
l
y
kno
wn as n
o
i
s
e.
Due t
o
t
h
i
s
m
a
ny
unwa
n
t
e
d dat
a
or e
r
r
o
rs
occu
r d
u
ri
ng t
h
e
transm
ission of data
from
sende
r
t
o
receiver. In order
to lim
it this problem
we ha
ve
error
detection a
n
d
cor
r
ect
i
on t
e
c
hni
que
s. The
err
o
r d
e
t
ect
i
n
g
m
e
t
hod i
s
us
ed t
o
det
ect
t
h
at
part
i
c
ul
a
r
err
o
r w
h
i
l
e
t
h
e erro
r
co
rrectio
n
m
e
t
h
od
s are
u
s
ed
to
recon
s
tru
c
t th
e orig
in
al
d
a
t
a
. Gen
e
rally th
e d
e
fin
ition
of th
ese term
s
is
g
i
ven
bel
o
w.
Err
o
r
det
ect
i
o
n
:
i
s
defi
ne
d as t
h
e m
e
t
hod o
f
d
e
t
ect
i
ng t
h
e er
r
o
rs
w
h
i
c
h a
r
e c
a
use
d
d
u
e t
o
e
x
t
e
r
n
al
n
o
i
s
e o
r
any
ot
he
r s
o
u
r
ces.
Err
o
r c
o
r
r
ect
i
o
n:
i
s
defi
ne
d as t
h
e
m
e
t
hod of
recon
s
t
r
u
c
t
i
n
g
t
h
e ori
g
i
n
al
da
t
a
and t
r
ansm
i
t
s t
h
e erro
r fr
ee
dat
a
to the
receive
r.
Som
e
of t
h
e exi
s
t
i
ng E
D
C
c
ode
s are Ham
m
i
ng co
de an
d I
nve
rse
Gra
y
C
ode are si
ngl
e
bi
t
err
o
r
cor
r
ect
i
ng c
o
d
e
. A
dva
nce
d
h
a
m
m
i
ng co
de i
s
si
ngl
e
bi
t
err
o
r c
o
r
r
ect
i
n
g c
ode a
n
d d
o
ubl
e bi
t
err
o
r
det
e
ct
i
on.
Residue
num
b
er system
is a single
bit erro
r
correcting c
o
de use
d
i
n
DSP
process
o
rs
.
Pro
p
o
se
d E
D
C
co
de i
s
ort
h
o
g
onal
c
o
de.
These
c
odes
are
bi
na
ry
val
u
ed
co
des
w
h
i
c
h
has e
q
ual
num
ber
of
0’
s
and
1
’
s.t
h
ere
f
o
r
e al
l
ort
h
o
g
o
n
a
l
code
ge
nera
t
e
s zero
pari
t
y
bi
t
s
. I
f
t
h
e
r
e i
s
t
r
ansm
i
ssi
on e
r
r
o
r
,
then
we ca
n
fi
nd the e
r
ror
by ge
nerating t
h
e
pa
rity bits
at the
receive
r e
n
d.
The
pa
rity generation m
e
thod can
det
ect
onl
y
5
0
%
er
ro
rs.
Si
nc
e pa
ri
t
y
bi
t
d
o
e
s
not
ef
fect
fo
r
t
h
e
e
v
en
num
ber
of
er
r
o
rs
.
M
y
ap
pr
oach
i
s
t
o
com
p
are t
h
e i
n
com
i
ng ort
h
og
onal
c
o
de
w
ith th
e all th
e
o
r
t
h
o
gon
al cod
e
s
wh
ich
are stored
in th
e look
up
tab
l
e
at the recei
ver
end for
the pos
s
ible
m
a
tch.
Thi
s
c
o
r
r
el
at
i
o
n
pr
ocess
i
s
gi
ven
by
R(x
,
y) =
∑
1
T
h
e
av
e
r
ag
e nu
mb
e
r
of
er
ro
rs
th
a
t
ca
n
be c
o
r
r
ect
ed i
s
gi
v
e
n
by
,
1
Th
e
b
e
low tab
l
e sho
w
s th
e erro
r correction
cap
a
b
ilities.
Tab
l
e
1
.
Shows th
e erro
r correctio
n
cap
a
b
ilit
ies
S.
no
a-
bit data
b = 2^
(
a
-
1
)
t = (
b
/4)
-
1
1
4-
bit data
8-
bit code
1
2
5-
bit data
16-
bit code
3
3
6-
bit data
32-
bit code
7
4
7-
bit data
64-
bit code
15
5
8-
bit data
128-
bit code
31
1.
3. En
cryption Technics
The existing Encry
p
tion technics are Data Encry
p
t
i
on St
a
nda
r
d
(
D
ES
) w
h
ere i
t
uses a 64
bi
t
pri
v
at
e
k
e
y, Adv
a
n
c
ed en
cr
yp
tion
stan
d
a
rd
wh
er
e it u
s
es var
i
ab
le l
e
n
g
t
h
128
, 196, 2
5
6
b
it k
e
ys,
D
E
S4
0
wh
er
e
k
e
y is
pre
-
p
r
ocesse
d t
o
pr
o
v
i
d
e
4
0
bi
t
key
,
M
D
5
w
h
ere i
t
i
s
u
s
ed
t
o
enc
r
y
p
t
one
t
i
m
e passw
o
r
ds
,
i
t
uses
12
8
bi
t
key
.
In t
h
e
pr
op
ose
d
e
n
cry
p
t
i
o
n t
e
chni
que
,
dat
a
e
n
cry
p
t
i
on i
s
ba
sed
on
ra
nd
om
n
u
m
b
er w
h
i
c
h
i
s
ge
nerat
e
d b
y
t
h
e
Linear
Feedba
ck Shift Regis
t
er (LFS
R). LFSR is a sh
ift
reg
i
ster who
s
e in
pu
t is a lin
ear
fu
n
c
tion
o
f
its
pre
v
ious state. There
f
ore
t
h
e f
eedbac
k
p
o
l
y
n
o
m
i
al
deci
des t
h
e
pse
u
d
o
ra
n
d
o
m
pat
t
e
rn
of
t
h
e L
FSR
.
Th
e ch
aracteristic p
o
l
yno
m
i
al
o
f
th
e LFSR is
g
--
--
The rem
a
i
nder
of t
h
i
s
pape
r i
s
or
gani
ze
d as f
o
l
l
o
w
s
:
In sect
i
on
2 we
ha
ve r
e
vi
ewe
d
t
h
e re
fere
nces o
n
t
h
e err
o
r
det
ect
i
on an
d co
rrec
t
i
on an
d o
n
va
ri
o
u
s cry
p
t
o
graphic techniques. Section
3 presents the
propos
ed
desi
g
n
m
e
t
hodol
ogy
f
o
r err
o
r
det
ect
i
on/
c
o
r
r
ect
i
on a
n
d encry
p
t
i
on
usi
ng L
FSR
. Se
ct
i
on 4
prese
n
t
s
t
h
e
im
pl
em
ent
a
t
i
o
n a
n
d
res
u
l
t
s
of
t
h
e
pr
o
pose
d
d
e
si
gn
.
2.
RELATED WORK
Ped
r
o R
e
vi
ri
eg
o
et al
p
r
op
o
s
ed
an
altern
ative sch
e
m
e
to
ac
hieve single error co
rrectio
n (SEC)
c
o
de
in m
e
m
o
ries. The a
p
proach
is based on the use
of
pa
r
ity sh
ari
n
g
wh
ich is also
fo
rm
ed
b
y
a co
m
b
inatio
n
o
f
two c
o
des. In t
h
is case, the c
o
des
use a
pa
rity bit and a
SE
C code [1].
R
ukm
ani
R
an
d M
Ja
gadees
wari
pr
op
ose
d
a desi
g
n
fo
r E
r
ro
r det
ect
i
o
n a
nd c
o
rrect
i
o
n a
r
chi
t
ect
u
r
e t
o
d
e
tect th
e m
u
lt
ip
le erro
rs and
recov
e
r t
h
e d
a
t
a
in
m
o
tio
n
esti
m
a
t
i
o
n
.
It is th
e process of
describ
i
ng
th
e
m
o
t
i
o
n
vect
o
r
s i
n
t
h
e
t
r
ans
f
orm
a
t
i
on of
o
n
e
2
D
i
m
age t
o
ot
her
.
T
h
e desi
gn
i
s
ba
s
e
d
on
t
h
e
resi
d
u
e-a
n
d-
qu
ot
i
e
n
t
[2]
.
Jayar
a
n
i
M.A
an
d Jag
a
d
eeswar
i
M pr
opo
sed
a
d
e
sign
of
Maj
o
r
ity lo
g
i
c d
e
tector
/d
ecod
er
fo
r
f
a
u
lty
det
ect
i
o
n
al
o
n
g
wi
t
h
c
o
rrect
i
o
n
of
m
e
m
o
ry
appl
i
cat
i
o
ns.
Th
i
s
i
s
d
one
by
o
n
e st
e
p
l
o
gi
c
d
ecodi
ng
[
3
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Im
pl
eme
n
t
a
t
i
o
n
of
Hi
gh
Sec
u
ri
t
y
C
r
ypt
o
gra
phi
c
Syst
e
m
w
i
t
h
I
m
prove
d
Er
ror C
o
rrect
i
o
n
…
(
N
aren
dra
B.T.)
60
4
C
onst
a
nt
i
n
A
n
t
on an
d hi
s t
eam
present
a so
l
u
t
i
on f
o
r t
h
e e
r
r
o
rs c
o
r
r
ect
i
o
n usi
n
g re
g
u
l
a
r
LDPC
an
d
Ho
pfi
e
l
d
net
w
or
k base
d ass
o
ci
at
i
v
e
m
e
m
o
ri
es. Thei
r s
o
l
u
t
i
on sol
v
es t
h
i
s
pr
obl
em
by
usi
n
g an ass
o
c
i
at
i
v
e
m
e
m
o
ry
based
on t
h
e H
o
pfi
e
l
d
net
w
o
r
k
o
n
t
h
e dec
odi
n
g
st
age,
whi
c
h s
t
ores t
h
e c
o
rre
ct
code
wo
r
d
s.
Thi
s
me
m
o
ry tends
to tra
n
sform
the code
words
receive
d
with errors i
n
errors
free code
words
[4].
Lui
s
-J Sai
z
-A
dal
i
d
p
r
o
p
o
sed
t
h
e use o
f
H
a
m
m
i
ng co
des
m
odi
fi
ed t
o
d
e
t
ect
2-bi
t
and
3-
bi
t
bur
s
t
er
ro
r
s
, m
a
in
tai
n
ing
th
e sing
le er
ro
r cor
r
ecti
o
n
(SEC) f
eature, w
ith no
ex
tra r
e
dund
an
cy
an
d h
a
v
i
ng
t
h
e same
en
cod
e
r an
d
deco
d
e
r laten
c
ies. Th
e cod
e
s
propo
sed ad
d the ab
ility to
d
e
tect sho
r
t
bu
rst
errors, m
a
in
ta
in
ing
th
e sam
e
red
und
an
cy and
laten
c
y, an
d with a slig
h
t
i
n
crease in
th
e co
m
p
lex
ity o
f
th
e
d
e
co
d
e
r circu
it [5
]
.
S.B
a
ska
r
,
pr
o
p
o
se
d a schem
e
fo
r fa
ul
t
-
det
e
ct
i
on an
d c
o
r
r
ect
i
on m
e
t
hod
si
gni
fi
ca
nt
l
y
m
a
kes area
o
v
e
rh
ead
m
i
n
i
mal an
d
to
r
e
du
ce th
e d
e
cod
i
n
g
tim
e
th
r
ough
D
C
cod
e
s than
th
e ex
isting
tech
n
i
qu
e an
d
i
t
g
i
v
e
s
pr
om
i
s
i
ng o
p
t
i
o
n
f
o
r
m
e
m
o
ry ap
pl
i
cat
i
ons
[
6
]
.
B
o
Dai
an
d Z
h
en
sen
Gao
pr
op
ose
d
a com
m
uni
cat
i
on sy
st
em
based o
n
t
h
e ort
h
o
g
ona
l
di
ffere
nt
i
a
l
p
h
a
se sh
i
f
t k
e
yin
g
with pub
lic k
e
y cryp
tograph
y
. Th
e
p
r
i
v
acy of tran
smitted
d
a
ta is dou
b
l
ed
gu
aran
teed
b
y
th
is cryp
t
o
graph
y
[7
].
Lam
o
n
i
ca M p
r
opo
sed
a cr
ypto
g
r
a
ph
y techniq
u
e
w
h
er
e w
e
u
s
e qu
irk
y
law
s
of
qu
an
tu
m
p
h
y
sics to
encry
p
t
t
h
e
dat
a
. T
h
i
s
cry
p
t
o
g
r
ap
hy
ca
n sec
u
re
poi
nt
-t
o
-
p
o
i
n
t
co
n
n
ect
i
o
ns
onl
y
a
b
o
u
t
10
0
km
[8]
.
Su
kal
y
an som
and Say
a
ni
sen p
r
o
p
o
sed a
No
n-
ada
p
tiv
e
Partial En
cryptio
n
of
Gray scale I
m
ages
B
a
sed
o
n
C
h
a
o
s.
I
n
t
h
i
s
t
e
c
hni
que
t
h
e
g
r
a
y
scal
e i
m
ag
es
are
dec
o
m
pos
ed i
n
to
bina
ry
8 bit
planes
a
n
d the
decry
p
t
e
d
usi
n
g c
o
u
p
l
e
t
e
nt
m
a
p
base
d
pseu
d
o
ra
n
dom
bi
nar
y
num
ber
ge
ne
rat
o
r
[
9
]
.
Hos
s
ein Rahm
ani proposed t
h
e techni
que used is to create
,
XaaS c
once
p
t
,
we de
si
g
n
an
Encry
p
t
i
o
n
as a Serv
ice in o
r
d
e
r t
o
g
e
t
rid
of th
e secu
rity risk
s
of
cl
o
ud pr
o
v
i
d
e
r’s encry
p
t
i
on a
nd the inefficiency of
cl
i
e
nt
-si
d
e e
n
cr
y
p
t
i
on
[
10]
.
Mar
i
u
s
Iu
lian
an
d
Mi
h
a
ilescu
cam
e o
u
t
w
i
th
th
e techn
i
qu
e used
is to
cr
eate a str
ong an
d
un
iqu
e
au
th
en
ticatio
n
p
r
o
cess of th
e
b
i
o
m
etric te
m
p
lates an
d
t
o
g
u
a
rant
ee t
h
e sa
f
e
t
y
of t
h
e
bi
om
et
ri
c dat
a
[1
1]
.
Xi
aot
i
a
n
Wu,
Wei
S
u
n
pr
op
ose
d
a x
o
r
bas
e
d vi
sual
c
r
y
p
t
o
g
r
a
phy
(VC
)
whi
c
h
i
s
use
d
t
o
s
o
l
v
e
t
h
e
poor visual quality
problem
,
two
XOR base
d VC’s
are pro
posed, XOR based VC for
ge
neral acce
ss structure
and
ada
p
t
i
v
e
re
gi
o
n
i
n
c
r
em
ent
i
ng
X
O
R
base
d
VC
[
1
2]
.
Syed
Rizv
i,
Katie Co
v
e
r prop
o
s
ed
a En
cry
p
tio
n t
echnique especially for
clou
d serv
ice p
r
ov
id
er
s
wh
ere t
h
e en
cryp
tion
sch
e
me co
m
b
in
es
bo
th symmetric
and a
s
ymmetric cry
p
togra
p
hic algorit
h
m
s
which
p
r
ov
id
es strong
d
a
ta
confid
en
tiality
p
r
eservi
n
g
secret k
e
y en
cry
p
tio
n
fu
nctio
n
a
lities
[13].
Xua
n
xi
a Yao
and Z
h
i
C
h
en
pr
o
pose
d
t
h
e t
echni
que
use
d
i
s
a
l
i
ght
wei
g
ht
no
-p
ai
ri
n
g
AB
E schem
e
b
a
sed
on
ellip
t
i
c cu
rv
e cry
p
tog
r
aph
y
(ECC). Th
is sch
e
m
e
p
r
opo
sed to
ad
dress th
e security an
d
priv
acy i
ssu
es
in
Io
T [1
4
]
.
Gilles Brassard
p
r
op
osed
the tech
n
i
qu
e used
is
to
create a rad
i
cally
d
i
fferen
t
fo
un
d
a
tion
for
cry
p
t
o
gra
p
hy
and
t
h
e
u
n
cert
a
i
n
t
y
pri
n
ci
pl
e
o
f
qua
nt
um
phy
si
cs.
I
n
c
o
nve
nt
i
o
nal
i
n
f
o
rm
at
i
on t
h
e
o
r
y
and
cry
p
t
o
gra
p
hy
[
15]
.
Zha
ng
Qi
m
i
ng pr
o
pose
d
t
h
e t
echni
que
p
r
ese
n
t
s
a di
gi
t
a
l
cert
i
f
i
cat
e whi
c
h
i
s
an el
ect
ro
ni
c
doc
um
ent
t
h
at
pr
o
v
i
d
es s
ecuri
t
y
ser
v
i
ces usi
n
g
pu
bl
i
c
key
,
t
h
i
s
key
i
s
used
f
o
r e
n
cry
p
t
i
on
o
r
aut
h
en
t
i
cat
i
on of si
gn
at
ur
e
t
o
t
h
e
pri
v
at
e
key
.
T
h
i
s
pa
per
uses
a t
o
ol
cal
l
e
d C
l
a
ng
ua
ge
gene
ra
t
i
on
pu
bl
i
c
ke
y
al
gori
t
hm
for t
h
e
authe
n
tication of
the pri
v
ate key
[16].
P.K
.
Da
s p
r
o
pos
ed c
o
r
r
ect
i
ng t
h
e er
r
o
rs
i
n
co
des
whi
c
h are t
o
be t
r
ansm
i
t
t
e
d fr
o
m
source
t
o
d
e
stin
ation
u
s
i
n
g
p
a
rity b
its. Add
i
ng
th
e
p
a
rity b
its to
th
e ex
istin
g
cod
e
s wh
ich
is in
d
i
fferen
t
o
r
d
e
rs
u
s
i
ng
th
eor
e
m
s
, w
h
ich
g
i
v
e
s a
b
ound
o
n
th
e
r
e
q
u
i
re
m
e
n
t
n
u
m
b
e
r
o
f
p
a
r
ity b
its [1
7
]
.
3.
R
E
SEARC
H M
ETHOD
Sin
ce LFSR g
e
n
e
r
a
tes pseudo r
a
n
d
o
m
n
u
m
b
e
r
s
wh
er
e each n
u
m
b
e
r
is u
s
ed
to
en
cr
y
p
t th
e a-
b
it in
pu
t
d
a
ta.
Our ap
pro
ach is no
t on
l
y
to
en
cryp
t the in
pu
t d
a
ta
but also
to
en
code th
e d
a
ta
b
e
fore th
e en
co
d
i
ng
in
t
o
ort
h
o
g
onal
c
o
de.
O
n
ce t
h
e
i
n
p
u
t
dat
a
i
s
e
n
co
de
d, t
h
e e
n
co
de
d
dat
a
i
s
X
O
R
’
e
d
wi
t
h
t
h
e
ran
d
o
m
num
ber
gene
rat
e
d
by
LFSR
m
e
t
hod
. Thi
s
f
o
l
l
o
wi
ng
app
r
oac
h
i
s
t
o
im
prove t
h
e e
r
r
o
r
det
ect
i
on r
a
t
e
by
i
n
creasi
ng i
t
s
reliability. Orthogonal c
o
de techni
que
invol
ves m
a
j
o
r
bloc
ks i.e. t
r
ansm
it
ter and recei
ve
r which a
r
e
describe
d
bel
o
w.
Tran
smitter:
An
en
co
d
e
r, en
cry
p
to
r and
a sh
ift reg
i
ster th
e
entire t
h
ree blocks c
o
m
b
in
e to
fo
rm th
e b
a
sic
tran
sm
it
ter in
th
is m
e
th
o
d
. The o
u
t
pu
t of en
co
d
e
r is set to
b=2
a-1
b
its wh
ere th
e in
pu
t is a-b
it d
a
ta wh
ich is fed
to
th
e en
cod
e
r. Th
is b
-
b
it d
a
ta is sen
t
to
th
e en
cryp
t
o
r wh
ere it is XOR’ed
with
th
e p
s
eu
do
ran
d
o
m
n
u
m
b
e
r
gene
rat
e
d
by
t
h
e LFSR
.
In
or
der t
o
t
r
a
n
sm
i
t
t
h
i
s
code nee
d
t
o
be cha
nge
d
as a seri
al
. For t
h
i
s
t
r
ans
f
o
r
m
a
t
i
on
we
use t
h
e
shi
f
t
regi
st
er a
s
s
h
ow
n i
n
t
h
e
fi
g
u
r
e 1
.
T
h
u
s
by
u
s
i
ng
rai
s
i
n
g e
d
ge
of t
h
e cl
oc
k
p
u
l
s
e t
h
e
ge
ne
rat
e
d
o
r
t
h
ogo
n
a
l code is transm
i
tted
u
s
i
n
g th
e sh
ift
reg
i
ster.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
60
2 – 6
1
0
60
5
Fi
gu
re
1.
B
l
oc
k
di
ag
ram
of t
r
ansm
i
t
t
e
r
Receiver:
The inverse a
r
rangem
ent of the tr
ansm
itter
acts as a receiver i.e. a shift register, dec
r
yptor a
nd
decode
r com
b
ine to
form
the basic recei
ver
com
pone
nt.
T
h
e receive
d c
o
de is processe
d t
h
rough the
followi
ng
sequ
en
tial steps as shown
i
n
figu
re
2
.
Th
e i
n
co
m
i
n
g
serial b
it d
a
ta is con
v
e
rted
i
n
to
r-b
it p
a
rallel cod
e
s
b
y
u
s
ing
a sh
ift
reg
i
ster. Th
e r-b
it d
a
ta is
g
i
v
e
n
to
th
e d
e
cr
y
p
t
o
r. In
the
decry
p
to
r
the
r-b
it data is XOR’ed
with
t
h
e ra
nd
om
nu
m
b
er gene
rat
e
d
by
t
h
e LF
SR
i
n
sy
nc
hr
o
n
o
u
s
wi
t
h
cl
ock
a
n
d
ge
nerat
e
s
a
n
out
put
of
b
-
b
i
t
dat
a
.
Th
e b-b
it d
a
ta is g
i
v
e
n
t
o
th
e
d
ecod
e
r wh
ere it is co
m
p
ared with
all th
e co
d
e
s sto
r
ed
in
th
e lo
oku
p
tab
l
e for
erro
r d
e
tection. Th
is is
do
n
e
b
y
co
un
ting
the nu
m
b
er
of ones i
n
t
h
e si
gnal res
u
lting
from
‘XOR’
operation
b
e
tween
th
e b-b
it d
a
ta an
d
each
co
m
b
in
ation
of th
e orthog
o
n
a
l co
d
e
s i
n
th
e loo
kup
tab
l
e. A coun
ter is u
s
ed
to
count the num
b
er
of
ones i
n
the re
sulting data and searc
h
es for the m
i
nim
u
m
count.
Howe
ve
r a value rathe
r
than zero shows an error in
the recei
ve
d code
. The
orthogonal code in th
e lookup table which is ass
o
ciated
with the
m
i
nim
u
m
count is the closest m
a
tch for the
corrupte
d
receive
d code. T
h
e m
a
tched orthogonal code
in
th
e loo
kup
tab
l
e is th
e corrected
cod
e
,
which
is th
en
d
e
co
d
e
d
to
a-b
it data. Th
e receiver is ab
le to
correct
up to
(b/
4
)-1
bits in the received im
paired c
o
de. Howeve
r,
i
f
the minim
u
m count is a
ssociated with m
o
re than
one
com
b
i
n
at
i
o
n
o
f
ort
h
o
g
o
n
a
l
code
t
h
e
n
a
si
gnal
,
R
E
Q
,
g
o
es
hi
g
h
.
Fi
gu
re
2.
B
l
oc
k
di
ag
ram
of re
cei
ver
4.
R
E
SU
LTS AN
D ANA
LY
SIS
In
or
der t
o
t
e
st
t
h
e code I
S
E Xi
l
i
nx s
o
f
t
ware an
d a h
a
rd
ware
bo
ar
d
of S
p
art
a
n-
3
were u
s
ed
.
Mo
d
e
lsim
XE software is
used
t
o
p
e
rform sim
u
lat
i
o
n
.
Th
e
o
u
t
pu
t of t
h
e sim
u
latio
n
o
r
th
e
fin
a
l
resu
lts is
checke
d
for most
of t
h
e
5-bi
t com
b
in
at
i
ons
o
f
i
n
p
u
t
an
d
16
-
b
i
t
ort
h
og
o
n
al
co
de
. T
h
e
pr
ocess
o
f
s
o
ft
ware
sim
u
lation along with the
worki
n
g of cloc
k
cycles is
briefe
d
furthe
r for
both tra
n
sm
itter and recei
ver.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISS
N
:
2088-8708
Im
pl
eme
n
t
a
t
i
o
n
of
Hi
gh
Sec
u
ri
t
y
C
r
ypt
o
gra
phi
c
Syst
e
m
w
i
t
h
I
m
prove
d
Er
ror C
o
rrect
i
o
n
…
(
N
aren
dra
B.T.)
60
6
Tran
smitter:
Th
e i
n
ternal pro
cess
of tran
smit
ter and
th
e
si
m
u
latio
n
resu
lts can b
e
ob
serv
ed
i
n
fi
g
u
re 3
.
Th
e
5
-
b
it
t_
d
a
ta inp
u
t
si
g
n
a
l for th
e enco
d
e
r is 010
01 wh
ere th
e
o
r
t
h
ogo
n
a
l co
d
e
works on
it and
a 16
-b
it ou
tpu
t
i.e.
b=5
o
r
t
h
o
g
o
n
a
l
co
de
out
put
2
b-1
= 2
4
=
1
6
is ob
tain
ed
.
Th
e
t_
ortho
si
g
n
a
l
as show
n in the f
i
gur
e
3
r
e
presen
ts
the out
put of t
h
e enc
o
der “AAAA H”
(1010101010101
010)
whic
h is fed as input to
the
encrypt
o
r. The output
o
f
t
h
e en
cry
p
to
r t
_
ou
t “AAAB H” is
o
b
t
ained
for th
e
resp
ectiv
e in
pu
t.
To
en
ab
le t
h
e
tran
sm
issio
n
of serial
bi
t
dat
a
reset
si
gnal
i
s
use
d
f
o
r
eve
r
y
ri
si
n
g
e
dge
o
f
t
h
e cl
oc
k.
Receiver:
Once t
h
e data is obtaine
d at the recei
ver t
h
e
serial
data is trans
f
orm
e
d into pa
rallel data. The r_data
si
gnal
re
pres
en
t
s
t
h
e i
nput
si
g
n
al
of re
cei
ver
.
Thi
s
dat
a
i
s
decry
p
t
e
d a
nd a
n
ort
h
o
g
o
n
al
co
de i
s
obt
ai
ne
d
whi
c
h
is represente
d
by r_ortho signal. T
h
is data
acts as an
inpu
t to
th
e
d
e
cod
e
r
un
it. A cou
n
t
er v
a
riab
le
is u
s
ed
whic
h
c
o
unts
t
h
e num
ber of 1’s
in
the res
u
lt obtaine
d,
whe
n
the
receive
d c
ode
is
XOR
’d
with all the
possible
com
b
i
n
at
i
ons
of
o
r
t
h
og
o
n
al
code
. T
h
e
ori
g
i
n
al
dat
a
i
s
obt
ai
ne
d
by
c
h
ecki
n
g
t
h
e m
i
nim
u
m
cou
n
t
of
t
h
e
receive
d data.
There
woul
d be 4 cases for a
ll the sim
u
la
tion
results available. In t
h
e fi
rst case the re
ceived
d
a
ta r
_
d
a
ta=1
01
010
101
010
101
1. Th
e
r
_
d
a
ta is g
i
v
e
n
as th
e
in
pu
t to
th
e decryp
tor, th
e
ou
tpu
t
o
f
d
ecry
p
tor is
r
_
o
r
t
h
o
=
10
1010
101
010
100
0. I
t
is g
i
v
e
n
as in
pu
t to
th
e d
e
co
d
e
r
,
th
e d
e
cod
e
r
ch
eck
s
fo
r
th
e clo
s
est
m
a
t
c
h
to
the r_ort
ho by
perform
i
ng XOR ope
ration betwee
n r_orth
o and each and every value in the lookup table and
gi
ves t
h
e m
i
nim
u
m
count
=
0
00
0
0
. T
h
e v
a
l
u
e at
t
h
e si
gnal
cou
n
t
re
pre
s
en
t
s
num
ber o
f
e
r
r
o
rs
pre
s
ent
e
d
i
n
t
h
e
receive
d data.
In this case num
b
er of errors is zero.
The
value ass
o
ciated with
the m
i
nim
u
m
count is the
o
r
i
g
in
al
d
a
ta is r
e
p
r
esen
ted b
y
a sign
al r_o
u
t
=0
100
1 as show
n in
t
h
e
f
i
gu
re 4
.
In
the second case
the received da
ta r_data
=1000101010
101011. T
h
e
r_data is
give
n a
s
the i
n
put t
o
the dec
r
yptor,
the output of
decry
p
tor is r_ortho=
8aacH
. It is give
n as
input to the
decode
r, the
decode
r
check
s f
o
r t
h
e
cl
osest
m
a
t
c
h t
o
t
h
e r
_
o
r
t
h
o
by
per
f
o
rm
i
ng X
O
R
o
p
e
r
at
i
on
bet
w
ee
n r
_
o
r
t
h
o a
nd ea
ch an
d
ev
er
y
v
a
lu
e in th
e l
o
oku
p tab
l
e an
d g
i
v
e
s t
h
e m
i
n
i
m
u
m
co
un
t=000
10
. In
t
h
is case num
b
e
r
o
f
err
o
r
s
is two
.
The val
u
e ass
o
ciated with the
m
i
nim
u
m
co
un
t is th
e o
r
i
g
inal d
a
ta is rep
r
esen
ted
b
y
a sign
al r_ou
t=01
00
1
as
sho
w
n i
n
t
h
e
fi
gu
re
5.
In the third cas
e the receive
d
data
r_data=
1
001101010101011. The r_data
is give
n as the
input to the
d
ecr
y
p
to
r, th
e
o
u
t
p
u
t
of
d
e
cryp
to
r
is r_
or
tho
=
100
110
101
01
011
00
.
I
t
is
g
i
v
e
n
as in
pu
t
to
th
e d
ecod
e
r
,
th
e
decode
r chec
ks for the closes
t
m
a
tch to the r_ort
ho
by pe
rform
i
ng XOR operation betwe
e
n r_ortho and each
and e
v
ery
val
u
e i
n
t
h
e l
ook
u
p
t
a
bl
e and
gi
ves t
h
e m
i
nimum
count
=0
00
11
. In t
h
i
s
case num
ber of e
r
r
o
rs i
s
t
h
ree.
T
h
e
va
l
u
e ass
o
ci
at
ed
wi
t
h
t
h
e
m
i
ni
m
u
m
count
i
s
t
h
e
o
r
i
g
i
n
al
dat
a
i
s
re
p
r
esent
e
d
by
a
si
g
n
al
r
_ou
t=01
001
as show
n in
t
h
e
f
i
gu
r
e
6
.
In
t
h
e fou
r
th case th
e r_d
a
ta= 1
001
110
010
10
101
1
is
ob
tain
ed
as inp
u
t
. Bu
t th
ere is
no
clo
s
est m
a
tch
obt
ai
ne
d f
o
r t
h
e respect
i
v
e
or
t
h
o
g
o
n
al
co
de
and t
h
e c
o
unt
val
u
e i
s
m
o
re than t
h
e
num
be
r of e
r
r
o
rs
pr
o
duce
d
.
In t
h
i
s
case t
h
e out
put
i
s
n
o
t
obt
ai
ne
d an
d
t
h
e r_
req
g
o
e
s
hi
g
h
w
h
i
c
h
req
u
est
s
t
h
e s
e
nde
r t
o
re
sen
d
t
h
e
m
e
ssage.
Fig
u
re
3
.
Sim
u
latio
n
resu
lt
o
f
tran
sm
it
ter with
en
cry
p
tio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
60
2 – 6
1
0
60
7
Figure
4. Sim
u
lation res
u
lt
of
receiver wit
h
z
e
ro errors
Figure 5.
Sim
u
lation
res
u
lt of receiver
wit
h
2-bit
error
Figure 6.
Sim
u
lation
res
u
lt of receiver
wit
h
3-bit
error
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Im
pl
eme
n
t
a
t
i
o
n
of
Hi
gh
Sec
u
ri
t
y
C
r
ypt
o
gra
phi
c
Syst
e
m
w
i
t
h
I
m
prove
d
Er
ror C
o
rrect
i
o
n
…
(
N
aren
dra
B.T.)
60
8
Fi
gu
re
7.
I
n
p
u
t
dat
a
i
n
bi
t
s
Vs
enc
ode
r
& e
n
c
r
y
p
t
o
r
del
a
y
Fi
gu
re
8.
I
n
p
u
t
dat
a
i
n
bi
t
s
Vs
dec
ode
r
&
dec
r
y
p
t
o
r
del
a
y
Th
e sim
u
latio
n
resu
lts show th
at for an a-b
it d
a
ta enco
d
e
d
in
t
o
b-b
it o
r
thog
on
al
d
a
ta an
d
is
en
cry
p
ted
i
n
to
a cip
h
e
r tex
t
.
A
v
a
rying
n
u
m
b
e
r
of
o
r
thog
on
al cod
e
co
m
b
in
atio
ns are ob
t
a
in
ed
wh
ich
is
ab
le to
detect any fa
ul
ty com
b
ination. 2
a
i
s
t
h
e t
o
t
a
l
num
ber
of
o
r
t
h
o
g
onal
c
o
de
com
b
i
n
at
i
ons
obt
ai
ne
d.
Th
e
err
o
r
det
ect
i
on a
nd
cor
r
ect
i
on
pe
rc
ent
a
ge = (
2
b
-2b
)
/2
b
. Th
e t
o
tal syste
m
can
d
e
tect an
d
correct til
l (b
/4
)-1
b
it error
and sim
i
larly the
num
b
er of c
l
ock cycles ne
cessary
for
the
data received
to get processe
d is (2b+
2). Conside
r
an exam
pl
e l
i
k
e 5-
bi
t
dat
a
t
h
eref
ore t
h
e t
o
t
a
l
num
ber ort
h
og
o
n
al
code
bi
t
l
e
ngt
h i
s
2
b
=2
5-1
=16
,
and
the to
ta
l
num
ber
of
ort
h
og
o
n
al
co
de co
m
b
i
n
at
i
ons are
2
16
. In
ord
e
r t
o
en
cryp
t th
e
data, th
e k
e
y leng
th
sh
ou
l
d
b
e
o
f
the
sam
e
size as th
at of t
h
e data
obtained from
the e
n
code
r i.e. 1
6
-b
it k
e
y is req
u
i
red
t
o
en
cryp
t th
e d
a
ta. Hen
ce
0
2
4
6
8
10
12
456
78
Delay
in
ns
Input
data
in
bits
Encryptor
delay
Encoder
delay
0
10
20
30
40
50
60
70
80
45678
Delay
in
ns
Input
data
in
bits
Decryptor
delay
Decoder
delay
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
60
2 – 6
1
0
60
9
each 5-bit data
has a unique 16-bit or
thogonal code so a 16-b
it key requi
r
ed e
n
cry
p
tin
g that data. The
16-bi
t
key
i
s
o
b
t
a
i
n
e
d
usi
n
g a pse
u
do
ra
nd
om
generat
o
r L
FSR
.
The
del
a
y
t
i
m
e
for e
n
cry
p
t
i
on an
d
decry
p
t
i
on i
s
6
.
8
40n
s
wh
en
th
e inp
u
t
b
it len
g
t
h
is
5
,
sim
i
larly wh
en
t
h
e in
pu
t is a
6-b
i
t d
a
ta th
e
d
e
lay ti
m
e
s are 7
.
0
42n
s
wh
ich
sho
w
s t
h
at th
ere is
an in
crease in the d
e
lay tim
es
as the i
n
put
data increas
es
.
So, as t
h
e i
n
put data
increases t
h
e
orthogonal bit lengt
h also
increases which
re
sults in m
o
re s
ecu
rity as th
ere is an
in
crease o
f
k
e
y
len
g
t
h to en
cryp
t th
e
d
a
ta.
Th
ere b
y
as inp
u
t
i
n
cr
eases
the e
n
cry
p
tion tim
e also increases
for i
n
dividua
l
sy
st
em
s and t
h
e sy
nt
hesi
s
re
p
o
rt
s
f
o
r t
h
e
del
a
y
t
i
m
e
are sh
o
w
n
i
n
Tabl
e
I
I
.
The
pe
rce
n
t
a
g
e
o
f
e
r
r
o
r
co
rre
ct
i
on
and det
ect
i
on obt
ai
ne
d
i
s
(2
16
-
2
*
16)
/2
16
=99
.
9
5
% with
error co
rrecting
ab
ility an
d
th
e n
u
m
b
e
r erro
rs it
can
d
e
tect is 3
.
Similar
l
y
th
e er
ro
r
co
rr
ectio
n
an
d
d
e
tectio
n
per
cen
tag
e
fo
r
32
b
it o
r
t
h
o
gonal co
d
e
is 99
.99
%
and
the num
b
er of
errors
that can be
detected a
r
e 5.
He
nce the
possible
num
ber
of com
b
inations
receive
d at the
receiver will
be able to detect the c
o
rrect
c
o
de
with the
ort
h
ogonal c
o
de a
v
ailable.
Tab
l
e 2
sho
w
s th
e
erro
r
correctio
n
and
d
e
tectio
n
rates
fro
m
th
e
sim
u
latio
n
resu
lts
ob
tain
ed
for 4
-
b
it,
5-bit, 6-bit, 7-bit,
8-bit data as input. Table 3 shows the de
lay
tim
ings for both tra
n
sm
itter and receive
r along
with
th
e in
ternal b
l
o
c
k
d
e
lays ob
tain
ed du
ri
n
g
syn
t
h
e
sis.
We can
o
b
s
erve th
e as t
h
e inp
u
t
b
it leng
th
an
d th
e
k
e
y leng
th
t
o
en
cry
p
t th
e
d
a
ta in
creases th
e dela
y tim
e
s for t
h
e indivi
dual s
y
ste
m
s also inc
r
eases.
Tab
l
e
2
.
Su
mmary of
resu
lts an
d th
eir error co
rrectio
n and
detectio
n
resu
lts
I
nput Bits (
a
)
Or
tho code output
bit length (
b
)
No
o
f
erro
rs( t
)
% o
f
erro
rs d
e
tect
e
d
and corrected
4 8
1
93.
75
5 16
3
99.
95
6 32
7
99.
99
7 64
15
99.
99
8 128
31
100
A b
=
2
^
(a-1
)
t=(b
/4
)-1
%=(2
^b
-2
^b
)/2
^
b
Table 3. Summary
of
tra
n
sm
itter
and receive
r delay
tim
e
s
obtained from
the sy
nthesis
re
ports for 4-bit, 5-bit,
6-
bi
t
,
7-
bi
t
an
d
8
-
bi
t
I
nput data in bits
E
n
code
delay
(
ns)
En
cryp
to
r
delay
(
ns)
Trans
m
itt
er
delay
(
ns)
Decr
yptor
delay
(
ns)
Decoder
delay
(
ns)
Receiver
delay
(
ns)
4 4.
283
6.
054
6.
054
6.
054
16.
786
14.
898
5 4.
283
6.
840
6.
840
6.
840
19.
133
18.
766
6 4.
283
7.
032
7.
032
7.
032
23.
853
24.
089
7 4.
283
7.
062
7.
062
7.
062
44.
163
45.
478
8 4.
283
7.
082
7.
082
7.
082
63.
718
64.
238
5.
CO
NCL
USI
O
N
Th
e resu
lts o
f
th
e p
r
esen
t work
sh
ow th
at th
e erro
r det
ect
i
on a
nd c
o
r
r
ect
i
on rat
e
ha
s bee
n
i
n
crease
d
to
100
%
when
th
e inp
u
t
len
g
t
h
is an
8
-
b
it d
a
ta. Th
e en
cryptio
n
an
d d
e
cry
p
tio
n ti
m
e
delays are als
o
inc
r
ease
d
w
h
en
th
e input d
a
ta is in
cr
eased
as ob
ser
v
ed
fr
o
m
th
e r
e
su
lts o
f
4
-
b
it,
5
-
b
it, 6-
b
it, 7-b
it an
d
8
-
b
it data as
in
pu
t. Fu
tu
re
work
i
n
clud
es
main
tain
in
g
con
s
tan
t
ti
m
e
del
a
y
s
for
vary
i
n
g
i
n
p
u
t
l
e
ngt
h
b
y
usi
ng c
r
y
p
t
a
n
al
y
s
i
s
t
echni
q
u
es
an
d
ba
nd
wi
dt
h l
i
m
i
t
a
t
i
on.
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