Inter
national
J
our
nal
of
Electrical
and
Computer
Engineering
(IJECE)
V
ol.
8,
No.
5,
October
2018,
pp.
3594
–
3603
ISSN:
2088-8708
3594
I
ns
t
it
u
t
e
o
f
A
d
v
a
nce
d
Eng
ine
e
r
i
ng
a
nd
S
cie
nce
w
w
w
.
i
a
e
s
j
o
u
r
n
a
l
.
c
o
m
Steganographic
Scheme
Based
on
Message-Co
v
er
matching
Y
oussef
T
aouil
and
El
Bachir
Ameur
Department
of
Computer
Sciences,
F
aculty
of
Sciences,
Uni
v
ersity
Ibn
T
of
ail,
Morocco
Article
Inf
o
Article
history:
Recei
v
ed
No
v
ember
15,
2017
Re
vised
May
25,
2018
Accepted
July
1,
2018
K
eyw
ord:
Ste
g
anograph
y
Data
hiding
Permutation
Least
significant
bit
F
aber
-Schauder
D
WT
ABSTRA
CT
Ste
g
anograph
y
is
one
of
the
techniques
that
enter
into
the
field
of
information
security
,
it
is
the
art
of
dissimulating
data
into
digital
files
in
an
imperceptible
w
ay
that
does
not
arise
the
suspicion.
In
this
paper
,
a
ste
g
anographic
method
based
on
the
F
aber
-
Schauder
discrete
w
a
v
elet
transform
is
proposed.
The
embedding
of
the
secret
data
is
performed
in
Least
Significant
Bit
(
LSB
)
of
the
inte
ger
part
of
the
w
a
v
elet
coef
ficients.
The
secret
message
is
decomposed
into
pairs
of
bits,
then
each
pair
is
transformed
into
another
based
on
a
permutation
that
allo
ws
to
obtain
the
most
matches
possible
between
the
message
and
the
LSB
of
the
coef
ficients.
T
o
assess
the
performance
of
the
proposed
method,
e
xperiments
were
carried
out
on
a
lar
ge
set
of
images,
and
a
com-
parison
to
prior
w
orks
i
s
accomplished.
Results
sho
w
a
good
le
v
el
of
imperceptibility
and
a
good
trade-of
f
imperceptibility-capacity
compared
to
literature.
Copyright
c
2018
Institute
of
Advanced
Engineering
and
Science
.
All
rights
r
eserved.
Corresponding
A
uthor:
Y
oussef
T
aouil
LaRIT
Laboratory
,
Department
of
Computer
Sciences,
F
aculty
of
Sciences,
Ibn
T
of
ail
Uni
v
ersity
,
14000
K
enitra,
Morocco.
taouilysf@gmail.com
1.
INTR
ODUCTION
Among
the
grounds
discussed
in
t
h
e
field
of
information
security
is
the
cryptograph
y
and
data
hiding.
Cryptograph
y
protects
information
by
coding
its
content
to
become
incomprehensible
to
unauthorized
people.
But,
e
v
en
an
incomprehensible
message
may
attract
the
attention
of
ea
v
esdroppers.
T
o
o
v
ercome
this
hindrance,
ste
g
anograph
y
of
fers
the
aspect
of
”secrec
y”
rather
than
”incomprehensibilit
y”,
it
is
the
technique
of
concealing
information
through
digital
media.
Its
main
objecti
v
e
is
the
secrec
y
of
the
information’
s
e
xistence
so
that
no
one
aside
the
authorized
recipient
may
suspect
it.
In
ste
g
anograph
y
,
v
arious
media
files
ha
v
e
been
utilized
as
co
v
er
file
such
as
audio,
image,
video
and
plain
te
xt,
b
ut
among
these
media,
the
most
popular
one
to
dissimulate
secret
information
is
image
since
it
is
shared
e
v
eryday
on
netw
orks
and
also
because
the
human
visual
system
can
not
detect
slight
changes
done
on
the
image
intensity
.
Generally
,
there
are
tw
o
approaches
of
ste
g
anograph
y:
the
spatial
domain
and
the
frequenc
y
domain.
In
the
spatial
domain
approach,
data
is
hidden
directly
in
the
pix
els
of
the
co
v
er
image,
such
as
the
Least
Significant
Bit
(
LSB
)
Substitution”
[1],
[2].
Ho
we
v
er
,
this
technique
is
vulnerable
to
statistical
attacks,
to
protect
the
hidden
message,
authors
in
[3]
proposed
to
encode
it
using
the
Hung
arian
puzzle.
There
is
also
the
interpolation
based
techniques
[4],
[5],
[6]
where
data
is
hidden
in
the
error
between
the
initial
pix
els
and
the
interpolated
pix
els,
and
the
Pix
el
V
alue
Dif
ferencing
(
PVD
)
[7],
[8],
[9]
where
data
is
hidden
in
the
dif
ference
between
each
neighbouring
pix
els.
In
[10],
authors
proposed
a
ste
g
anographic
algorithm
based
on
Ant
Colon
y
Optimization
(A
CO),
the
A
CO
algorithm
is
used
to
select
the
comple
x
re
gions
of
the
co
v
er
image,
then
data
is
hidden
using
the
LSB
substitution
in
the
selected
areas.
In
the
frequenc
y
domain
based
techniques,
data
is
hidden
in
the
coef
ficients
of
the
transform
domain,
such
as
Discrete
Cosinus
T
ransform
(
DCT
)
and
Discrete
W
a
v
elet
T
ransform
(
D
WT
).
In
[11],
a
re
v
ersible
data
hiding
for
JPEG
images
is
proposed,
the
quantization
table
is
modified
through
di
viding
some
of
its
elements
by
an
inte
ger
while
multiplying
the
corresponding
quantized
DCT
coef
ficients
by
the
same
inte
ger
in
order
to
create
space
for
the
dissimulation.
In
[12],
authors
proposed
a
ste
g
anographic
scheme
for
JPEG
that
preserv
es
J
ournal
Homepage:
http://iaescor
e
.com/journals/inde
x.php/IJECE
I
ns
t
it
u
t
e
o
f
A
d
v
a
nce
d
Eng
ine
e
r
i
ng
a
nd
S
cie
nce
w
w
w
.
i
a
e
s
j
o
u
r
n
a
l
.
c
o
m
,
DOI:
10.11591/ijece.v8i5.pp3594-3603
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
3595
the
DCT
coef
ficients
histogram
in
order
to
resist
ste
g
analysis
based
attacks.
The
scheme
distinguishes
sensiti
v
e
pix
els
and
protects
them
from
the
e
xtra
bit
embedding
to
reduce
the
distortions
in
the
histogram.
In
[13],
the
Inte
ger
W
a
v
elet
T
ransform
(
IWT
)
is
applied
to
each
8
x
8
blocks
of
the
co
v
er
image,
then
the
zero
tree
method
is
utilized
to
select
the
proper
location
where
data
can
be
embedded.
In
[14],
a
ste
g
anographic
scheme
based
on
the
Haar
D
WT
is
proposed,
data
is
hidden
in
the
first
LSB
of
the
D
WT
coef
ficients,
the
algorithm
is
generalized
on
K-LSB
with
the
use
of
the
Optima
Pix
el
Adjustment
OP
A
procedure
in
[15].
In
[16],
the
edge
IWT
coef
ficients
are
classified
based
on
their
Most
Signifi
cant
bit
(
MSB
),
the
size
of
data
to
be
hidden
in
the
coef
ficient
is
determined
based
on
the
v
alue
of
the
coef
ficient’
s
MSB
s.
In
this
paper
,
we
propose
a
ste
g
anographic
scheme
based
on
the
F
aber
Schauder
D
WT
,
this
transform
allo
ws
us
to
hide
data
in
the
inte
ger
part
without
w
orrying
about
the
problem
of
the
floating
point
(the
pix
els
of
the
ste
go
image
are
guaranteed
to
be
inte
gers).
Data
is
hidden
in
the
LSB
s
of
the
transform
details.
The
mess
age
and
the
coef
ficients
LSBs
are
decomposed
to
pairs
of
bits
m
k
and
z
k
,
and
based
on
the
matrix
that
illustrates
the
dif
ference
of
distance
between
m
k
and
z
k
,
we
search
for
the
permutation
that
transforms
the
message
into
the
binary
sequence
that
has
the
most
possible
matches
with
z
k
.
The
selection
order
of
the
coef
ficients
where
to
dissimulate
data
is
gi
v
en
aleatory
by
a
random
k
e
y
.
Experiments
were
performed
on
a
lar
ge
set
of
a
v
ariety
of
images
to
assess
the
perfomance
of
the
proposed
w
ork,
and
comparison
to
prior
w
orks
is
accomplished.
Results
indicate
good
le
v
el
of
imperceptibility
and
trade-of
f
capacity-imperceptibility
.
The
remaining
of
the
paper
is
or
g
anized
as
follo
ws:
Section
2
details
the
algorithms
of
decompos
ition
and
reconstruction
of
the
F
aber
-Schauder
D
WT
.
In
section
3,
the
proposed
ste
g
anograph
y
method
is
e
xplained.
In
section
4,
e
xperimental
results
of
the
test
and
comparison
are
discussed.
Section
5
concludes
the
paper
.
2.
F
ABER-SCHA
UDER
D
WT
The
F
aber
-Schauder
W
a
v
elet
transform
is
a
multi-scale
transform,
the
multi-scale
analysis
is
formu-
lated
based
on
the
study
of
compactly
supported
w
a
v
elet
bases,
it
is
the
main
theory
in
w
a
v
elets
that
analyzes
in
detail
a
signal
in
the
frequenc
y
domain.
Multi-Scale
Analysis
of
L
2
(
R
)
is
a
sequence
of
nested
v
ector
spaces
(
V
j
)
j
2
Z
(
V
j
+2
V
j
+1
V
j
V
j
1
:
:
:
)
.
F
or
all
j
in
Z
,
V
j
+1
V
j
.
Let
W
j
+1
be
a
supplementary
of
V
j
+1
in
V
j
:
(
V
j
=
V
j
+1
W
j
+1
)
,
the
basis
of
F
aber
-Schauder
is
the
basis
of
W
j
+1
gi
v
en
by
the
f
amily
of
functions
j
n
n
2
Z
with:
j
n
=
'
j
2
n
+1
,
where:
'
j
n
(
t
)
=
2
j
'
2
j
t
n
;
and
'
(
t
)
=
8
<
:
1
+
t
if
1
t
0
1
t
if
0
t
1
0
if
t
=
2
[
1
;
1]
In
tw
o
dimensions,
L
2
(
R
2
)
is
approximated
by
using
the
tensor
product:
~
V
j
=
V
j
V
j
=
(
V
j
+1
W
j
+1
)
(
V
j
+1
W
j
+1
)
;
where:
~
V
j
+1
=
V
j
+1
V
j
+1
;
and
~
W
j
+1
=
(
V
j
+1
W
j
+1
)
+
(
W
j
+1
V
j
+1
)
+
(
W
j
+1
W
j
+1
)
Thus,
an
image
C
is
decomposed
into
four
blocks:
A,
H,
V
and
D
as
illustrated
in
Fig.
1.
A
corresponds
to
~
V
j
+1
,
while
H,
V
,
and
D
correspond
respecti
v
ely
to
the
three
subspaces
of
~
W
j
+1
.
The
decomposition
algorithm
of
F
aber
-Schauder
D
WT
is
gi
v
en
by
the
follo
wing
equations:
8
>
>
>
>
>
>
>
>
<
>
>
>
>
>
>
>
>
:
A
(
i;
j
)
=
C
(2
i;
2
j
)
H
(
i;
j
)
=
C
(2
i
+
1
;
2
j
)
C
(2
i;
2
j
)
+
C
(2
i
+
2
;
2
j
)
2
V
(
i;
j
)
=
C
(2
i;
2
j
+
1)
C
(2
i;
2
j
)
+
C
(2
i;
2
j
+
2)
2
D
(
i;
j
)
=
C
(2
i
+
1
;
2
j
+
1)
1
X
k
=0
1
X
r
=0
C
(2
i
+
2
k
;
2
j
+
2
r
)
4
The
reconstruction
algorithm
or
in
v
erse
F
aber
-Schauder
Discrete
W
a
v
elet
T
ransform
is
gi
v
en
by
the
Ste
gano
gr
aphic
Sc
heme
Based
on
Messa
g
e-Co
ver
matc
hing
(Y
oussef
T
aouil)
Evaluation Warning : The document was created with Spire.PDF for Python.
3596
ISSN:
2088-8708
Figure
1.
One
le
v
el
2D
F
aber
-Schauder
D
WT
of
the
image
Baboon
follo
wing
equations:
8
>
>
>
>
>
>
>
>
<
>
>
>
>
>
>
>
>
:
C
(2
i;
2
j
)
=
A
(
i;
j
)
C
(2
i
+
1
;
2
j
)
=
H
(
i;
j
)
A
(
i;
j
)
+
A
(
i
+
1
;
j
)
2
C
(2
i;
j
+
1)
=
V
(
i;
j
)
A
(
i;
j
)
+
A
(
i;
j
+
1)
2
C
(2
i
+
1
;
2
j
+
1)
=
D
(
i;
j
)
1
X
k
=0
1
X
r
=0
A
(
i
+
k
;
j
+
r
)
4
(1)
3.
PR
OPOSED
W
ORK
3.1.
Embedding
Pr
ocess
After
the
dissimulation
of
the
secret
message,
the
co
v
er
image
is
modified,
the
principal
objecti
v
e
of
ste
g
anograph
y
is
to
minimize
this
modification
so
that
the
hiding
does
not
arise
the
suspicion
of
ea
v
esdroppers.
The
proposed
method
is
based
on
F
aber
-Schauder
D
WT
.
The
block
A
represents
the
approximation
of
the
image
co
v
er
,
it
contains
the
lo
w
frequencies
where
the
human
e
ye
is
sensiti
v
e
to
slightest
modifications.
A
should
remain
unchanged.
Therefore,
data
is
hidden
in
the
three
remaining
blocks
H,
V
,
and
D
.
Let
m
be
the
binary
sequence
of
the
secret
message
m
=
f
m
1
;
:
:
:
;
m
L
g
m
k
2
f
0
;
1
g
,
and
let
Z
be
the
set
of
the
LSB
of
the
inte
ger
part
of
the
coef
ficients
of
the
blocks
H
,
V
and
D
.
W
e
di
vide
m
and
Z
into
pairs
m
=
S
m
k
and
Z
=
S
z
k
,
where
m
k
=
f
m
2
k
1
;
m
2
k
g
and
z
k
=
f
z
2
k
1
;
z
2
k
g
.
8
k
m
k
and
z
k
are
in
the
set
E
=
ff
0
;
0
g
;
f
0
;
1
g
;
f
1
;
0
g
;
f
1
;
1
gg
.
When
m
k
is
hidden
into
z
k
there
are
three
possibiliti
es:
the
y
are
identical
m
k
=
z
k
,
conjug
ate
m
k
+
z
k
=
f
1
;
1
g
or
the
y
ha
v
e
one
bit
dif
ferent.
T
o
visualize
all
these
possibilities,
we
introduce
the
matrix
G
whose
elements
denote
the
number
of
times
each
pair
m
k
from
E
encounters
a
pair
z
k
from
E
.
G
is
a
4
x
4
matrix,
because
car
d
(
E
)
=
4
,
its
elements
are
inte
ger
between
0
and
L=
2
,
G
2
M
4
;
4
(
f
0
;
:
:
:
;
L=
2
g
)
.
The
first
column
is
associated
to
f
0
;
0
g
,
the
second
column
to
f
0
;
1
g
,
the
third
column
to
f
1
;
0
g
and
the
last
column
to
f
1
;
1
g
.
The
same
thing
goes
for
the
ro
ws.
If
m
k
encounters
z
k
,
then
the
element
G
i;j
from
the
i
ro
w
and
j
column
is
incremented,
where
the
relation
between
the
pairs,
ro
ws
and
columns
is
gi
v
en
by
the
follo
wing
function
f
which
is
a
bijection
that
associates
each
pair
to
its
decimal
v
alue
plus
1:
IJECE
V
ol.
8,
No.
5,
October
2018:
3594
–
3603
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
3597
j
=
f
(
m
2
k
1
;
m
2
k
)
=
2
m
2
k
1
+
m
2
k
+
1
i
=
f
(
z
2
k
1
;
z
2
k
)
=
2
z
2
k
1
+
z
2
k
+
1
(2)
In
each
column,
the
diagonal
element
sho
w
ho
w
much
times
m
k
and
z
k
are
identical,
the
element
of
the
2
nd
diagonal
denotes
the
number
of
ti
mes
when
m
k
and
z
k
are
opposite
or
conjug
ate.
The
remaining
tw
o
elements
denote
ho
w
much
times
m
k
and
z
k
ha
v
e
on
bit
dif
ferent.
Example:
26
denotes
ho
w
man
y
times
f
0
;
1
g
of
the
message
encounters
f
1
;
0
g
in
t
he
the
coef
ficients
LSB
s.
G
=
0
B
B
B
B
@
f
0
;
0
g
f
0
;
1
g
f
1
;
0
g
f
1
;
1
g
f
0
;
0
g
64
36
87
51
f
0
;
1
g
38
57
72
93
f
1
;
0
g
19
26
18
17
f
1
;
1
g
29
16
27
21
1
C
C
C
C
A
The
error
generated
by
the
dissimulation
is
e
xpressed
by
the
follo
wing
e
xpression:
M
S
E
=
1
M
N
M
1
X
i
=0
N
1
X
j
=0
(
S
(
i;
j
)
C
(
i;
j
))
2
Let
H
0
(
i;
j
)
be
the
coef
ficient
produced
after
hiding
data
in
H
(
i;
j
)
,
and
h
(
i;
j
)
=
H
0
(
i;
j
)
H
(
i;
j
)
the
dif
ference
coming
from
this
dissimulation.
W
e
define
v
(
i;
j
)
and
d
(
i;
j
)
the
same
w
ay
.
Therefore,
using
the
reconstructions
equations
(1),
the
MSE
becomes:
M
S
E
=
1
M
N
M
=
2
1
X
i
=0
N
=
2
1
X
j
=0
h
(
i;
j
)
2
+
v
(
i;
j
)
2
+
d
(
i;
j
)
2
The
diagonal
elements
of
the
matrix
G
corresponds
to
when
data
is
hidden
with
zero
changes,
the
2nd
diagonal
elements
corresponds
to
when
2
changes
are
needed,
and
the
rest
corres
ponds
to
when
one
bit
is
changed
to
hide
2
bits,
as
described
in
the
follo
wing
matrix
W
G
.
W
G
=
0
B
B
@
0
1
1
2
1
0
2
1
1
2
0
1
2
1
1
0
1
C
C
A
Hence,
we
can
reformulate
the
MSE
based
on
the
matrix
G
as
follo
ws:
M
S
E
=
1
M
N
4
X
i
=1
4
X
j
=1
W
G
(
i;
j
)
G
(
i;
j
)
which
we
can
reformulate
as
follo
ws:
M
S
E
=
1
M
N
0
@
4
X
i
=1
4
X
j
=1
G
i;j
+
4
X
i
=1
G
5
i;i
tr
(
G
)
1
A
where
tr
(
G
)
is
the
trace
of
the
matrix
G
:
tr
(
G
)
=
4
X
i
=1
G
i;i
Since
4
X
i
=1
4
X
j
=1
G
i;j
is
unchanged
for
all
permutations,
then
we
define
the
function
#
which
associates
the
remaining
tw
o
terms
to
the
permutation:
#
:
S
4
!
Z
p
7
!
4
X
i
=1
G
5
i;i
tr
(
G
)
Ste
gano
gr
aphic
Sc
heme
Based
on
Messa
g
e-Co
ver
matc
hing
(Y
oussef
T
aouil)
Evaluation Warning : The document was created with Spire.PDF for Python.
3598
ISSN:
2088-8708
T
o
minimize
the
MSE
,
we
calculate
#
(
p
)
for
all
possible
p
in
S
4
(24
permutations).
Then,
we
search
for
the
permutation
p
corresponding
to
the
lo
west
v
alue
of
#
(
p
)
.
p
=
min
p
2
S
4
(
#
(
p
))
.
The
equation
p
(
j
)
=
j
0
signifies
that
the
column
j
is
permuted
into
j
0
,
which
means
that
the
pair
m
k
associated
to
j
by
the
function
f
introduced
in
(2)
is
consequently
changed
to
the
pair
associated
to
j
0
.
F
or
e
xample,
if
p
(3)
=
1
,
then
by
using
the
function
f
,
f
1
(3)
is
changed
int
o
f
1
(1)
i.e.
each
pair
f
1
;
0
g
in
the
secret
message
is
changed
into
f
0
;
0
g
.
Hence,
we
obtain
t
he
transformation
of
the
secret
message
m
0
that
allo
ws
us
to
reach
the
lo
west
MSE
calculated.
m
0
is
gi
v
en
by:
m
0
=
L=
2
[
k
=1
f
1
o
p
o
f
(
m
k
)
(3)
Example:
W
e
consider
the
message
”
H
E
L
L
O
”,
the
binary
sequence
of
this
message
is
m
=
0100100001100101011011000110110001101111
.
W
e
decompose
m
into
pairs:
m
=
01
j
00
j
10
j
00
j
01
j
10
j
01
j
01
j
01
j
10
j
11
j
00
j
01
j
10
j
11
j
00
j
01
j
10
j
11
j
11
.
Suppose
that
the
LSB
s
of
the
coef
ficients
are
:
Z
=
00
j
11
j
00
j
01
j
11
j
01
j
10
j
00
j
10
j
10
j
10
j
11
j
11
j
10
j
00
j
10
j
10
j
10
j
00
j
10
:
W
e
construct
the
matrix
G
:
G
=
0
B
B
@
0
2
1
2
1
0
1
0
1
3
3
2
2
2
0
0
1
C
C
A
The
error
no
w
is
25
,
which
means
that
there
is
25
among
the
40
message
bits
that
are
going
to
be
dissimulated
into
their
opposite
bits
of
the
coef
ficients.
No
w
,
we
calculate
the
errors
of
the
24
permutations
and
we
choose
the
permutation
p
associated
to
the
lo
west
error
.
p
and
its
associated
G
are
gi
v
en
by
p
=
1
2
3
4
4
3
2
1
;
G
=
0
B
B
@
2
1
2
0
0
1
0
1
2
3
3
1
0
0
0
2
1
C
C
A
The
error
becomes
15.
Hence,
we
construct
the
ne
w
binary
sequence
m
0
based
on
the
equation
(3)
as
follo
ws:
f
0
;
0
g
!
f
1
;
1
g
;
f
0
;
1
g
!
f
1
;
0
g
;
f
1
;
0
g
!
f
0
;
1
g
;
f
1
;
1
g
!
f
1
;
1
g
3.2.
Extraction
pr
ocess
In
the
e
xtraction,
we
retrie
v
e
the
message
m
0
from
the
LSB
of
the
coef
ficients’
inte
ger
part.
T
o
be
able
to
obtain
the
actual
mes
sage
m
,
the
permutation
p
is
needed.
Thus,
in
the
dissimulation
phase,
we
hide
an
identifier
in
the
first
coef
ficients.
p
(1)
,
p
(2)
,
p
(3)
and
p
(4)
are
hidden
int
the
first
eight
coef
ficients.
After
the
e
xtraction
of
m
0
,
we
use
the
p
(
i
)
to
retrie
v
e
the
message
m
as
follo
ws:
m
=
L=
2
[
k
=1
f
1
o
(
p
)
1
o
f
(
m
0
k
)
where
m
0
k
=
f
m
0
2
k
;
m
0
2
k
+1
g
IJECE
V
ol.
8,
No.
5,
October
2018:
3594
–
3603
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
3599
Embedding
algorithm
Read
the
co
v
er
image
as
tw
o
dimensional
file.
Perform
the
F
aber
-Schauder
D
WT
.
Construct
the
matrix
G
,
find
the
perm
u
t
ation
p
and
hide
p
(1)
,
p
(2)
,
p
(3)
and
p
(4)
in
the
first
eight
coef
ficients.
T
ransform
the
binary
sequence
of
the
message
m
into
m
0
using
p
and
f
and
hide
it
in
the
coef
ficients
starting
from
the
se
v
enteenth
one.
Apply
the
in
v
erse
F
aber
-Schauder
discrete
w
a
v
elet
transform
to
obtain
the
ste
go
image.
Extraction
algorithm
Read
the
ste
go
image
as
tw
o
dimensional
file.
Apply
the
F
aber
-Schauder
D
WT
to
the
ste
go
image.
Extract
the
permutation
p
from
the
first
eight
coef
ficients
and
the
identifier
of
the
the
k
e
y
from
the
second
eight
coef
ficients.
Extract
the
binary
sequence
m
0
from
the
coef
ficients,
and
reconstruct
m
using
the
function
f
and
permu-
tation
p
.
Re
group
the
binary
sequence
m
by
blocks
of
8
bits
to
obtain
the
hidden
message.
4.
EXPERIMENT
AL
RESUL
TS
AND
DISCUSSION
Experiments
were
accomplished
to
assess
the
performance
of
the
proposed
method
using
a
v
ariety
of
512x512
grayscale
images
of
the
SIPI
database,
containing
some
images
which
are
frequently
utilized
in
tests,
lik
e
”Baboon”,
”Peppers”,
”Lena”
and
”Elaine”
(see
Fig.
2).
Baboon
Elaine
Barbara
Lak
e
Peppers
Boat
Lena
F16
Figure
2.
Some
of
the
images
used
in
the
e
xperiment
The
proposed
w
ork
is
compared
with
the
methods
de
v
eloped
by
Amin
[13],
Miri
[16]
and
Al-Dmour
[17].
The
test
of
the
proposed
w
ork
and
the
comparison
are
based
on
the
follo
wing
metrics
[18]:
Ste
gano
gr
aphic
Sc
heme
Based
on
Messa
g
e-Co
ver
matc
hing
(Y
oussef
T
aouil)
Evaluation Warning : The document was created with Spire.PDF for Python.
3600
ISSN:
2088-8708
P
S
N
R
=
10
Log
255
2
M
S
E
;
N
AE
=
M
1
X
i
=0
N
1
X
j
=0
j
S
(
i;
j
)
C
(
i;
j
)
j
M
1
X
i
=0
N
X
j
=1
C
(
i;
j
)
I
F
=
1
M
1
X
i
=0
N
1
X
j
=0
(
S
(
i;
j
)
C
(
i;
j
))
2
M
1
X
i
=0
N
1
X
j
=0
C
(
i;
j
)
2
;
N
C
C
=
M
X
i
=1
N
X
j
=1
(
C
(
i;
j
)
C
)(
S
(
i;
j
)
S
)
v
u
u
t
M
X
i
=1
N
X
j
=1
(
C
(
i;
j
)
C
)
2
v
u
u
t
M
X
i
=1
N
X
j
=1
(
S
(
i;
j
)
S
)
2
The
PSNR
is
the
Peak
Signal
to
Noise
Ratio,
it
is
calculated
using
the
MSE
.
The
more
PSNR
increases,
the
more
the
ste
g
anographic
scheme
is
imperceptible.
The
N
AE
is
the
Normal
Absolute
Error
,
it
measures
the
absolute
v
alue
of
the
error
between
the
co
v
er
and
ste
go
images.
Small
v
alues
of
N
AE
(close
to
0)
are
a
sign
of
good
imperceptibility
.
IF
is
the
Image
Fidelity
,
the
quantity
1
I
F
measures
the
ratio
of
the
ener
gy
of
the
error
between
the
co
v
er
and
ste
go
images
to
the
ener
gy
of
the
co
v
er
image.
Ob
viously
,
good
imperceptibility
requires
that
1
I
F
is
v
ery
close
to
0,
which
means
that
IF
has
to
be
v
ery
close
to
1.
The
Normalized
Correlation
Coef
ficient
NCC
is
a
scalar
product
of
the
normalized
v
ectors
v
C
and
v
S
while
v
C
is
the
co
v
er
image
minus
its
mean
v
alue
C
and
v
S
is
the
ste
go
image
minus
its
mean
v
alue
S
,
so
it
tak
es
v
alues
between
1
and
1
.
The
closer
NCC
is
to
1
,
the
more
similar
are
the
images.
If
it
is
close
to
0
,
the
images
are
uncorrelated,
and
if
it
is
close
to
1
,
the
images
are
said
opposite.
4.1.
T
est
of
the
pr
oposed
method
T
o
test
the
proposed
method,
we
used
a
set
of
100
images
with
dif
ferent
modalities,
do
wnloaded
from
the
SIPI
image
database.
T
able
1.
Imperceptibility
for
the
proposed
method
Metrics
PSNR
N
AE
IF
NCC
PSNR
N
AE
IF
NCC
Data
3000
bytes
6000
bytes
Min
61.55
2.01e-4
0.999973
0.999654
58.53
4.01e-4
0.999964
0.999371
Max
62.31
1.38e-3
0.999999
0.999997
59.25
2.77e-3
0.999998
0.999994
Mean
61.71
3.69e-4
0.999997
0.999948
58.68
7.42e-4
0.999994
0.999893
Data
9000
bytes
12000
by
t
es
Min
56.76
6.02e-4
0.999921
0.999073
55.52
8.05e-4
0.999893
0.998526
Max
57.53
4.14e-3
0.999997
0.999987
56.25
5.51e-3
0.999996
0.999982
Mean
56.92
1.11e-3
0.999991
0.999842
55.67
1.48e-3
0.999988
0.999778
Data
18000
bytes
24000
bytes
Min
53.75
1.21e-3
0.999841
0.998147
52.51
1.61e-3
0.999787
0.997565
Max
54.49
8.29e-3
0.999994
0.999972
53.28
1.11e-2
0.999992
0.999962
Mean
53.91
2.22e-3
0.999982
0.999671
52.65
2.96e-3
0.999976
0.999554
T
able
1
presents
the
results
of
the
imperceptibility
test
for
the
proposed
method,
based
on
the
m
etrics
PSNR
,
N
AE
,
IF
and
NCC
.
In
this
simulation,
we
dissimulated
in
the
100
test
images
a
te
xt
of
3,
6,
9,
12,
18
and
24
Kilo
Bytes.
The
table
gi
v
es
the
minimum,
maximum
and
mean
v
alues.
A
ste
g
anograph
y
process
is
imperceptible
when
PSNR
is
be
yond
36
dB.
The
PSNR
v
alues
indicate
a
high
le
v
el
of
imperceptibility
,
N
AE
v
alues
are
v
ery
small
,
N
AE
<
10
2
,
and
IF
is
practically
1,
j
1
I
F
j
<
10
4
.
NCC
v
alues
are
v
ery
close
to
1,
j
1
N
C
C
j
<
10
3
,
which
pro
v
es
that
the
co
v
er
and
ste
go
images
are
practically
ident
ical.
Figure
3
e
xhibits
the
e
v
olution
of
the
PSNR
for
all
the
test
images
as
the
size
of
the
hidden
data
increases.
The
PSNR
diminishes,
because
when
we
hide
lar
ger
data,
the
error
becomes
important.
Ho
we
v
er
,
the
drop
of
the
imperceptibility
becomes
slo
wer
,
when
data
size
increas
es
from
12
Kilo
to
18
Kilo
and
from
18
Kilo
to
24
Kilo,
the
mean
PSNR
decreases
by
1
:
76
dB
and
1
:
26
dB
respecti
v
ely
.
IJECE
V
ol.
8,
No.
5,
October
2018:
3594
–
3603
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
3601
Figure
3.
Capacity-Imperceptibility
4.2.
Comparison
to
literatur
e
The
proposed
w
ork
is
compared
to
the
methods
de
v
eloped
by
Amin
[13],
Miri
[16]
and
Al-Dmour
[17].
The
tests
of
the
comparison
respects
the
same
conditions
(images,
size
of
hidden
data)
utilized
i
n
these
w
orks.
T
able
2
sho
ws
the
results
of
comparison
of
PSNR
to
Amin’
s
w
ork
for
the
four
images
used
in
his
w
ork,
and
table
3
compares
the
capaci
ty
of
hiding.
The
proposed
w
ork
pro
vides
a
lar
ger
capacity
3
4
M
N
8
bits,
about
2
:
3
times
the
one
of
Amin,
the
subtra
cted
8
bits
are
reserv
ed
to
hide
the
permutation
p
.
In
the
algorithm
he
proposed,
Amin
does
not
hide
data
in
all
the
w
a
v
elet
coef
ficients,
he
selects
the
location
where
to
hide
data
via
the
zero
tree
method,
hence
the
capacity
is
diminished.
On
another
hand,
e
v
en
concerning
the
imperceptibility
,
the
proposed
w
ork
still
has
better
results,
for
100
,
500
and
1
K
bytes,
the
dif
ference
is
approximati
v
ely
1
dB
.
But,
when
we
hide
5
K
,
10
K
and
15
K
bytes,
the
dif
ference
becomes
3
dB
.
T
able
2.
Comparison
of
PSNR
to
Amin
[13]
Image
Method
100
500
1000
5000
10000
15000
Barbara
Amin
73.98
66.61
63.64
65.55
53.64
52.02
Proposed
76.57
69.46
66.38
59.37
56.35
54.59
Peppers
Amin
74.12
66.61
63.78
56.54
53.58
51.89
Proposed
76.61
69.45
66.42
59.34
56.34
54.57
Baboon
Amin
75.62
68.18
62.89
56.06
53.32
51.75
Proposed
76.59
69.40
66.38
59.35
56.32
54.56
Lena
Amin
73.58
66.07
63.01
56.18
53.38
51.65
Proposed
76.57
69.42
66.41
59.37
56.37
54.59
T
able
4
sho
ws
the
results
of
the
comparison
of
the
PSNR
to
Miri
[16]
and
Al-Dmour
[17],
we
respected
the
size
of
hidden
data
used
in
[16].
The
proposed
w
ork
has
higher
v
alues.
F
or
Miri,
the
dif
ference
is
around
3
:
6
dB.
In
f
act,
Miri
may
hide
data
in
more
than
one
bit
on
a
w
a
v
elet
coef
ficient
depending
on
the
weight
(position)
of
the
most
significant
bit,
the
greater
is
the
position,
the
more
bits
of
the
coef
ficients
are
used
to
embed
data,
in
this
case,
the
error
generated
from
the
dissimulation
increases,
which
af
fected
his
PSNR
v
alues.
As
for
Al-Dmour
[17],
the
dif
ference
starts
with
3
dB
,
authors
hide
data
in
the
edge
coef
ficients
and
use
the
XOR
cording
in
order
to
minimize
the
error
of
the
dissimulation.
Ho
we
v
er
,
as
the
size
of
data
increased,
more
Ste
gano
gr
aphic
Sc
heme
Based
on
Messa
g
e-Co
ver
matc
hing
(Y
oussef
T
aouil)
Evaluation Warning : The document was created with Spire.PDF for Python.
3602
ISSN:
2088-8708
T
able
3.
Comparison
of
the
hiding
capacity
to
Amin
[13]
Image
Size
Amin
[13]
Proposed
Lena
128x128
5145
11891
Lena
256x256
20622
48371
Lena
512x512
82578
195059
Peppers
128x128
5223
11891
Peppers
256x256
20694
48371
Peppers
512x512
83846
195059
T
able
4.
Comparison
of
PSNR
to
Miri
[16]
and
Al-Dmour
[17].
Data
size
Al-Dmour
Miri
Proposed
6300
bits
64.76
63.80
67.44
12800
bits
61.50
60.66
64.32
28800
bits
56.91
56.79
60.78
51200
bits
52.62
54.78
58.28
67700
bits
50.28
53.68
57.06
bits
of
the
edge
coef
ficients
are
used
to
dissimulate
data
(and
depending
of
the
co
v
er
image
comple
xity
,
more
bits
of
the
coef
ficient
may
be
used),
which
decreases
significantly
the
PSNR
.
Hence,
the
dif
ference
enlar
ged
to
about
7
dB
since
in
our
case,
we
use
only
one
bit
in
each
coef
ficient,
and
the
optimal
permutation
p
transforms
the
message
into
the
best
match
for
the
co
v
er
image.
5.
CONCLUSION
In
this
paper
,
a
ste
g
anographic
method
based
on
F
aber
-Sc
hauder
D
WT
is
proposed.
Data
is
di
vided
into
pairs
of
2
bits,
the
same
is
done
to
the
LSB
of
the
details
in
the
transform
domain.
W
e
establish
a
matrix
that
c
alculates
the
number
of
times
where
data
and
the
coef
ficients
are
similar
or
opposite,
and
based
on
this
matrix
we
find
the
permutation
that
transforms
the
message
into
the
binary
sequence
that
pro
vides
the
most
match
possible
to
the
coef
ficients
LSB
s.
Results
sho
wed
good
trade-of
f
between
capacity
and
imperceptibility
,
and
higher
v
alues
in
both
of
them
compared
to
e
xisting
methods.
In
our
future
w
orks,
we
will
study
more
ho
w
to
minimize
the
error
generated
by
the
dissimulation
and
we
will
strengthen
the
security
through
the
analysis
of
the
hiding’
s
ef
fect
on
the
histogram.
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C.
K.
Chan
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M.
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Y
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Hsiao
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g
anogra-
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aouil,
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T
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Zeng,
X.
Chen,
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Hu
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.
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g
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Li,
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ersible
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g
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B.
Jahromi
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aez,
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ahab,
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v
ed
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Jung,
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data
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alue
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ferencing
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v
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IJECE
V
ol.
8,
No.
5,
October
2018:
3594
–
3603
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
3603
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v
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”
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2018.
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W
ang,
Z.
M.
Lub
and
Y
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J.
Hu,
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high
capacity
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”
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Qazanf
ari
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abakhsh,
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ste
g
anograph
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ano
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v
el
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g
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ree
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anced
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in
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&
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T
aouil,
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B.
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T
.
Belghiti,
”Ne
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g
anograph
y
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Based
on
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Discrete
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a
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elet
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2016.
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T
aouil,
E.
B.
Ameur
,
A.
Benhfid,
R.
Harba
and
R.
Jennane,
”A
Data
Hiding
Scheme
Based
on
the
Haar
Discrete
W
a
v
el
et
T
ransform
and
the
K-LSB,
”
International
Journal
of
Imaging
and
Roboti
cs
,
v
ol.
17,
pp.
41-53,
2017.
[16]
A.
Miri
and
K.
F
aez,
”An
image
ste
g
anograph
y
method
based
on
inte
ger
w
a
v
elet
transform,
”
Multimed
T
ools
Appl
,
2017,
doi:10.1007/s11042-017-4935-z
[17]
H.
Al-Dmour
and
A.
Al-Ani,
”A
ste
g
anograph
y
embedding
method
based
on
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identification
and
XOR
coding,
”
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ol.
46,
pp.
293306,
2016.
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S.
Subhedar
and
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.
H.
Mankar
,
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ste
g
anograph
y
using
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a
v
elet
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actorization,
”
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and
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Engineering
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54,
pp.
406-422,
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BIOGRAPHIES
OF
A
UTHORS
Y
oussef
T
aouil
is
a
PhD
Student
at
the
f
aculty
of
sciences
in
Ibn
T
of
ail
Uni
v
ersity
,
he
obtained
the
Engineering
diploma
in
electronics
and
embedded
systems
from
the
national
school
of
applied
sciences
at
the
sam
e
Uni
v
ersity
(2014).
His
researches
are
focused
on
ste
g
anograph
y
and
data
hiding.
El
Bachir
Ameur
is
a
full
Professor
of
computer
sciences
at
the
Uni
v
ersity
of
IbnT
of
ail,
F
aculty
of
science,
K
enitra
(Morocco),
where
he
is
af
filiated
to
t
he
LaRIT
Laboratory
.
In
2002
he
recei
v
ed
the
Ph.
D.
de
gree
in
numerical
analysis
and
computer
sciences
from
the
Uni
v
ersity
of
Mohamed
I
Oujda
(Morocco).
His
Ph.
D.
concerned
a
pproximation
and
reconstruction
of
2D/3D
data
by
spline
and
w
a
v
elet
functions.
His
research
interests
concerns
approximation
and
reconstruction
of
2D/3D
surf
aces
by
spline
and
w
a
v
elets,
signal
and
image
processing,
w
atermarking
and
ste
g
anograph
y
.
Ste
gano
gr
aphic
Sc
heme
Based
on
Messa
g
e-Co
ver
matc
hing
(Y
oussef
T
aouil)
Evaluation Warning : The document was created with Spire.PDF for Python.