Reversible Steganographic Scheme with High Embedding Capacity

using Dual Cover Images

Nagaraj V. Dharwadkar and B. B. Amberker

Department of Computer Science and Engg., National Institute of Technology, Warangal, 506004, India

Keywords:

Reversible, Steganography, Dual Cover Images, Embedding Capacity, Stegoimage, Stego-key, Secret

Communication.

Abstract:

The advances in Internet technology and digital image representation helped the user to easily exchange the

secret message. On Internet the transmission of the secret message is conducted using digital images which

created new needs, issues and opportunities to the researcher. The basic objective of secret message commu-

nication is to transmit a message securely by embedding it into a cover-image such that unintended observers

are unable to detect it. The image steganographic schemes are used in secret message communication. In

this paper, we have proposed reversible steganographic scheme for gray-scale images. This scheme uses dual

cover images to hide secret image and generates the perceptually similar dual stegoimages. Further, to extract

the secret image the knowledge of dual stegoimages and stego-key are necessary which improved the security

of this scheme. The experimental results show that the scheme provides a higher embedding capacity and

robustness with un-noticeable distortions in the stegoimages. The performance of the scheme is analyzed for

various types of image processing attacks on stegoimage. The proposed scheme was found rigid to the image

processing attacks.

1 INTRODUCTION

In many countries of the world the political dissent

is not tolerable and illegal. Hence, to exchange the

secret messages the dissident organization must exer-

cise extreme caution (Nagaraj V. Dharwadkar, 2010).

The dissidents always use the Internet to exchange

secret messages and face the security threats (Zou

et al., 2003). To conceal secret communications

the dissidents may use encryption or steganography

methods. Using encryption the dissidents will en-

sure the privacy of their communications. Unfortu-

nately, the very important fact is that two people are

exchanging encrypted messages indicates that they

have something to conceal. An alternate solution to

this problem is the use of steganography for secret

communication(Lee and Chen, 2000a; Katzenbesser

and Petitcolas, 2004; Artz, 2001). Steganography is

the art of hidden writing. First documented exam-

ple of steganography was found in the Histories of

Herodotus, where the father of history relates sev-

eral stories from the times of ancient Greece (Kahn,

1967). There are stories of secret messages written

in invisible ink or hidden in letters such that the ﬁrst

character of each sentence is used to spell a secret

message (Cox et al., 2008). In recent days, digital

steganographic schemes are widely used by prison-

ers, spies, terrorists and soldiers. Most of the recent

secret communications occurs electronically, where

the digital multimedia representations techniques are

used as the carrier for secret communication (W et al.,

1996). The Internet is increasingly becoming the pop-

ular communication channel for secret communica-

tion. The image Steganographic schemes are widely

used in the transmission of secret messages via the

Internet to provide secured communication (Artz.,

2001; Lee and Chen, 2000b).

In 2001, T. Sharp (Sharp, 2001) proposed one bit

LSB substitution scheme. In this scheme the secret

message is embedded into cover image by substitut-

ing the LSB of each pixel with encrypted secret bit

stream. Only the authorised receiver will extract the

secret bits by decrypting every LSB of pixel of the

cover image using a shared key. The embedding ca-

pacity of this scheme is 1 bit/pixel. This scheme gen-

erates visually imperceptible stegoimage which can

be statistically analyzed by unauthorised entity with-

out knowledge of the shared key. The random LSB

bit jumbling attack on stegoimage makes it difﬁcult

to extract the secret message. To address this prob-

15

V. Dharwadkar N. and B. Amberker B..

Reversible Steganographic Scheme with High Embedding Capacity using Dual Cover Images.

DOI: 10.5220/0003975700150024

In Proceedings of the International Conference on Security and Cryptography (SECRYPT-2012), pages 15-24

ISBN: 978-989-8565-24-2

Copyright

c

2012 SCITEPRESS (Science and Technology Publications, Lda.)

lem, A. Ker (Ker, 2005) proposed the LSB match-

ing scheme, but this scheme is vulnerable to detec-

tion algorithms. In order to minimize the effect of

detectability Rehab H. (Alwan et al., 2006) proposed

a novel scheme of image embedding which detects

the edge of the image using Sobel mask ﬁlters. On

the LSB of each edge pixels, a gray level connectiv-

ity is applied using fuzzy logic and the ASCII code

information is embedded into the edge pixels. The

well known steganographic scheme is Least Signiﬁ-

cant Bit (LSB) substitution scheme. This scheme di-

vides the secret message into n bit blocks and em-

beds each of these n bits by directly replacing the

n LSBs of a pixel of the cover image (Wang et al.,

2001; Thien and Lin, 2003). Using LSB substitution

schemes, more number of secret bits can be hidden

into cover image with low computational complex-

ity (Chan and Chen, 2004; Nagaraj V. Dharwadkar,

2010). Based on the ability of the steganographic

schemes to recover the cover images during extrac-

tion, the schemes are classiﬁed as reversible (Hon-

singer et al., 2001; Fridrich et al., 2002; Tian, 2003)

and irreversible(Chan and Cheng, 2004; Mielikainen,

2006). The reversible steganographic schemes are

able to recover the original cover image during ex-

traction of the secret message; where as in the irre-

versible steganographic scheme the secret message is

extracted from the stegoimages with no capability of

recovering the cover image into its original state.

The embedding capacity, visual quality and secu-

rity are three important issues concerned to a success-

ful steganographic schemes (Wang et al., 2001). The

crucial issue of the steganographic scheme is rigidity

of scheme to different types of attacks. To address is-

sues like embedding capacity, visual quality and secu-

rity of stegoimage, Chin-Feng et.al.(Lee et al., 2009).

In 2010, to address similar issues we have proposed

a scheme (Nagaraj V.Dharwadkar, 2010) which is an

improved reversible steganographic scheme based on

dual stegoimages. In Chin-Feng et.al. scheme, a max-

imum of two secret bits are embedded into a pair of

pixels which are originated from one original cover

image and its copy. This scheme achieves an embed-

ding capacity of 0.75 bpp. Where as the earlier pro-

posed our scheme embeds the three secret bits into

pair of pixels (Nagaraj V.Dharwadkar, 2010). This

scheme achieves an embedding capacity of 1.21 bpp.

This scheme is purely blind scheme and it will not use

any auxiliary array in extraction algorithm.

After analysing these schemes it was found that

the embedding capacity of these scheme can be pos-

sible to further increase using auxiliary array. To

achieve the high embedding capacity, in this paper

we propose an improved reversible steganographic

scheme using two cover images. In this scheme,

ﬁve bits of secret image are embedded into a pixel

pair which are alternatively selected from the orig-

inal cover image and its copy. We have used aux-

iliary array known as stego-key which increases the

embedding capacity and security of the scheme. This

scheme provides reversibility and high security with

less distortion in stegoimage. We have analyzed the

proposed scheme for its embedding capacity and its

robustness to different types of image processing at-

tacks.

The rest of the paper is organized as follows. The

proposed steganographic scheme is explained in Sec-

tion 2. Section 3 gives details of the experimental re-

sults. Section 4 gives the comparison of the proposed

scheme with the Chin-Feng Lee et. al and our own

earlier proposed scheme. The effect of image pro-

cessing attacks on dual stegoimages is discussed in

Section 5. Section 6 concludes the paper.

2 PROPOSED SCHEME

In the gray-scale image the intensity value of pixel

is represented by 8 bits value. The proposed scheme

relies on binary stream of intensity of pixel to de-

ﬁne space for embedding the secret bits. We con-

sider two identical cover images P and Q each of

size m × n. In Figure 1, the cover images P and Q

are represented as a matrices (P

i, j

)

1≤i≤m;1≤ j≤n

and

(Q

i, j

)

1≤i≤m;1≤ j≤n

. For embedding data we choose

a pair of pixels (P

i, j

,Q

i, j

) each from P and Q. If

P

i, j

is used for embedding secret, then P

i, j

is re-

ferred as the Embed pixel and Q

i, j

is referred as the

Ref pixel. For the next pair (P

i+1, j

,Q

i+1, j

), P

i+1, j

is Ref pixel and Q

i+1, j

is Embed pixel. Likewise,

pair of pixels are chosen row-wise from each cover

image P and Q. The proposed scheme embeds ﬁve

bits into a pair of pixels by maintaining the negligi-

ble difference between the original pixel and modi-

ﬁed pixel. To achieve negligible difference the mod-

iﬁed pixel is scaled up or down. The scale factors

which are used to preserve the difference narrow is

encoded in a location-map which is known as stego-

key. The hidden message is encoded in two places

: the image and the location-map. The secret bits

S

k

are selected and embedded into Embed pix

k

for

0 ≤ k ≤ 4 using look-up table as shown in Figure

2 to generate resultant Res pix.Later, the difference

d = Embed pix− Res pix is computed. If the differ-

ence |d| > 3 and d > 0 and to make Res pix equal

to Embed pix 4 is added count number of times and

stored in Res pix. Otherwise if d < 0 to make Res pix

equal to Embed pix 4 is subtracted count number of

SECRYPT2012-InternationalConferenceonSecurityandCryptography

16

times and stored into Res pix. Store the count in to

Stego− key element such that the LSB of Stego− key

element represents addition or subtraction operation.

The remaining bits represents the count value. The

embedding algorithm is given in Algorithm : 1 and

continued in Algorithm : 2.

(a) Cover image P. (b) Cover image Q.

Figure 1: Selection of alternate pixels from dual cover im-

ages P and Q where P = Q.

In extraction algorithm consider two embedded

images P

′

and Q

′

each of size m × n. From the em-

bedded image P

′

and Q

′

we choose a pair of pixels

(P

′

i, j

,Q

′

i, j

) each from P

′

and Q

′

. If P

′

i, j

is used for ex-

tracting secret, then P

′

i, j

is assigned to the Embed pix

and Q

′

i, j

is assigned to the Ref pixel. For the next

pair (P

′

i+1, j

,Q

′

i+1, j

), P

′

i+1, j

is Embed pixel and Q

′

i+1, j

is Ref pixel. Likewise, pair of pixels are chosen row-

wise from each stegoimage image P

′

and Q

′

. This

scheme extracts ﬁve bits from pair of pixels using the

location-map known as the stego-key. The stego-key

content is used to decide the scale factor by which the

embedded pixel values to be increased or decreased.

The altered embedded pixel and reference are used

to recover the hidden data.The original cover pixel is

recovered from the reference pixel. The extraction al-

gorithm is given in Algorithm: 3 and 4.

2.1 Illustration with Example

Let’s explain the scheme with a simple example.

Assume that we have two cover images I

1

, I

2

of size

3× 3, where I

1

= I

2

and secret image S of size 4× 4

I

1

= I

2

=

20 5 9

1 7 15

37 2 52

S =

0 0 0 0

1 1 1 0

1 0 1 1

0 0 1 0

The execution of embedding steps for cover image

I

1

,I

2

and secret image S will generate the following

output: Select the pixel p

1

1

= 20 = (00010100)

2

of cover image I

1

and 00001 the ﬁrst 5 bits of

S. Using look-up table as given in Figure 2 we

Figure 2: Look-up table used to map the cover image pixels

into stegoimages.

get r = (00011110) = 30 as modiﬁed pixel. The

difference |d| = |p

1

1

− r| = |20 − 30| = 10 is cal-

culated. As |d| > 3 r = r − 4 = 26 and set c

0

= 1.

Iteratively we calculate |d| = |p

1

1

− r| = |20− 26| = 6

until |d| > 3 therefore we get r = 26 − 4 = 22.

Then, we calculate |d| = |p

1

1

− r| = |20 − 22| = 2,

|d| < 3 therefore q

1

1

= r = 22. Thus, in this com-

plete iterations as 4 is subtracted 2 times we get

(c

3

,c

2

,c

1

) = (0,1,0) as the ﬁrst element of stego-

key. Consider next pixel p

2

2

= 5 = (00000101)

2

from I

2

and next 5 bits (11010)

2

of S. Us-

ing look-up table we get r = (00000101)

2

= 5,

|d| = |p

2

2

− r| = |5 − 5| = 0 and |d| < 3 therefore

c0 = 0 and (c

3

,c

2

,c

1

)=(0,0, 0) as the next element of

stego-key. Then the pixel p

1

3

= 9 = (00001001)

2

is

selected from I

1

, next 5 secret bits (11001)

2

from S.

We get r = (00000110)

2

= 6. Compute the difference

|d| = |p

1

3

− r| = |9 − 6| = 3 therefore c

0

= 0 and

(c

3

,c

2

,c

1

) = (0,0, 0) will be the next element of

stego-key. The remaining secret bit in S is 0 and pixel

p

2

4

= 1 = (00000001)

2

, using look-up table we get

r = (00000001)

2

= 1 and |d| = |p

2

4

− r| = |1− 1| = 0.

As |d| < 3 therefore append 0 to stego-key. The

resultant stegoimages are I

′

1

=

22 5 6

1 7 15

37 2 52

,

I

′

2

=

20 5 9

1 7 15

37 2 52

and Stego-

key=(0101,0000,0000,0)

2

The execution of extraction steps on dual stegoim-

ages I

′

1

, I

′

2

using Stego-keywill generate the following

output: I

′

1

=

22 5 6

1 7 15

37 2 52

,

I

′

2

=

20 5 9

1 7 15

37 2 52

and Stego-

key=(0101,0000,0000,0)

2

Select the ﬁrst pixel

from cover image p

1

1

= 22 from I

′

1

and ﬁrst 4 bits

of Stego-key (c

3

,c

2

,c

1

,c

0

) = (0,1,0,1). From

the bits of ﬁrst stego-key element we separate

c

0

bit to get (c

3

,c

2

,c

1

) = (0,1,0) = 2 & c

0

= 1.

As c

0

= 1 hence we need to add 4 twice to p

1

1

.

Thus, we get r

′

= 22 + 4 + 4 = 30 = (00011110)

2

.

ReversibleSteganographicSchemewithHighEmbeddingCapacityusingDualCoverImages

17

Matching the 5 LSB bits of the reference pixel

p

2

1

= 20 = (00010100)

2

and look-up table we get

(00001)

2

as the ﬁrst ﬁve secret bits. Select the next

pixel p

2

2

= 5 = (00000101) from I

′

2

and next 4 bits

of Stego-key element (c

3

,c

2

,c

1

,c

0

) = (0, 0,0,0).

We get (c

3

,c

2

,c

1

) = (0,0, 0) = 0 & c

0

= 0. Using

reference pixel p

1

2

= 5 = (00000101)

2

and look-up

table we get secret bits (11010)

2

. Select the next

pixel p

1

3

= 6 = (00000110)

2

from I

′

1

and 4 bits

of Stego-key element. Using the reference pixel

p

2

3

= 9 = (00001001)

2

we get secret bits (11001)

2

.

Select the last pixel p

2

4

= 1 = (00000001)

2

from I

′

2

and stego-key element value is c

0

= 0. using the

reference pixel p

1

4

= 1 = (00000001)

2

and look-up

table we get 0 as the secret bit.

3 RESULTS AND DISCUSSION

For the experimental analysis, we implemented the

proposed scheme using JAVA package. In the series

of experiments, the perceptual quality of stegoimage

is measured using Peak Signal to Noise (PSNR) and

Mean Square Error (MSE) between the two stegoim-

ages and cover image respectively. The experimental

values of PSNR and MSE between stegoimages and

cover image shows that both stegoimage are percep-

tually similar to cover image. In order to analyze the

embedding capacity of the proposed scheme, we con-

sidered different secret images for embedding on dif-

ferent cover images. The experimental setup used in

measuring perceptual quality and embeddingcapacity

are explained in the following sections. For the ex-

perimental determination of the embedding capacity,

we considered the Lena, Peppers, Baboon and Chess-

board images of size 300× 420, 225×225, 250×250

and 256×256 respectivelyas shown in Figure 3. Four

different monochrome secret images of different sizes

are used in the embedding algorithm. Figure 4 and

Figure 5 show the dual stegoimages generated by pro-

posed scheme. Figure 6 to Figure 9 show the orig-

inal monochrome secret image and extracted secret

images from Lena, Peppers, Baboon and Chessboard

cover images.

3.1 Perceptual Quality of Stegoimages

Table 1 shows the perceptual quality measures be-

tween cover image and the stegoimages. For each

cover image, the amount of noise added into the ste-

goimage is calculated by using PSNR and MSE be-

tween cover image and both stegoimages using fol-

lowing equation.

Algorithm 1: Embedding Algorithm.

Input : Grayscale image I

1

of size m× n and its

copy I

2

, where I

1

= {p

1

1

, p

1

2

,..., p

1

m×n

},

I

2

= {p

2

1

, p

2

2

,..., p

2

m×n

}, I

1

= I

2

and secret

image S of size h× w, where

S = {s

1

,s

2

,...,s

h×w

} and s

k

∈ {0,1}

Output: Dual stegoimages, I

′

1

= {q

1

1

,q

1

2

,...,q

1

m×n

}

and I

′

2

= {q

2

1

,q

2

2

,...,q

2

m×n

} such that I

′

1

6= I

′

2

and stegokey of size (4× h× w)/5, where

C = {C

0

,C

1

,...,C

(4×h×w)/5

− 1},

C

t

= {c

3

,c

2

,c

1

,c

0

} and c

k

∈ {0,1}

1. Set i=1; k=1; x = h× w; t=0; ;

2. Set Embed pixel = p

1

i

; Ref pixel = p

2

i

;

3. if (x < 5) then goto step 8

else Set x=x-5; Count=0; r = Embed pixel;

{b

7

,b

6

,b

5

,b

4

,b

3

,b

2

,b

1

,b

0

} = (Embed pixel)

2

.

Secret bits {s

k

,s

k+1

,s

k+2

,s

k+3

,s

k+4

} ∈ S are embed

into r using the following steps ;

4. for j ← 0 to 4 do

Switch(b

j

,s

k+4− j

)

Case(0,0) : r

j

= 1;break;

Case(0,1) : r

j

= 0;break;

Case(1,0) : r

j

= 1;break;

Case(1,1) : r

j

= 0;break;

5. Compute d = Ref pixel −r

6. if (|d| ≤ 3) then q

1

1

= r goto step 7

if (|d| > 3 & d > 0) then r = r+ 4;

Count = Count + 1; flag = 1; goto step 5

if (|d| > 3 & d < 0) then r = r − 4;

Count = Count + 1; flag = 0; goto step 5

7. Indicate the modiﬁcation of r into stego-key

C

t

= {c

3

,c

2

,c

1

,c

0

} using following steps.

(a) if ( f lag == 1) then c

0

= 0

(b) if ( f lag == 0) then c

0

= 1

(c) The remaining bits c

3

,c

2

,c

1

are assigned using

following cases: Switch(Count)

Case0 : (c

3

,c

2

,c

1

) = (0,0,0) break;

Case1 : (c

3

,c

2

,c

1

) = (0,0,1) break;

Case2 : (c

3

,c

2

,c

1

) = (0,1,0) break;

Case3 : (c

3

,c

2

,c

1

) = (0,1,1) break;

Case4 : (c

3

,c

2

,c

1

) = (1,0,0) break;

Case5 : (c

3

,c

2

,c

1

) = (1,0,1) break;

Case6 : (c

3

,c

2

,c

1

) = (1,1,0) break;

Case7 : (c3,c2,c1) = (1,1, 1) break;

8. Set i = i+ 1; k = k+ 5 x = x− 5;t = t +1;

9. if (i%2 == 1) then goto step 3;

else Set Embed pixel = p

2

i

and Ref pixel = p

1

i

,

Select next ﬁve secret bits (s

k

,s

k+1

,s

k+2

,s

k+3

,s

k+4

)

from S and repeat step 3 to step 7.

MSE =

∑

M

i=1

∑

N

j=1

(C[i, j] − I[i, j])

2

MN

(1)

Here, M and N are the height and width of image

respectively. C(i, j) is the (i, j)

th

pixel value of the

SECRYPT2012-InternationalConferenceonSecurityandCryptography

18

Algorithm 2: Embedding Algorithm continued.

10 if (x < 5) then Embed pixel = p

2

i

convert it into

binary stream {b

7

,b

6

,b

5

,b

4

,b

3

,b

2

,b

1

,b

0

} and

select x secret bits from S and Count1=0;

a for j ← 0 to x− 1 do

Switch(b

j

,s

k+4− j

)

Case(0,0) : r

j

= 1;break;

Case(0,1) : r

j

= 0;break;

Case(1,0) : r

j

= 1;break;

Case(1,1) : r

j

= 0;break;

b Compute d

′

= Ref pixel − r;

if (|d

′

| ≤ 3) then q

1

1

= r goto step c

if (|d

′

| > 3 & d

′

> 0) then r = r+ 4;

Count1 = Count1+ 1; flag = 1; goto step b

if (|d

′

| > 3 & d

′

< 0) then r = r− 4;

Count1 = Count1+ 1; flag = 0; goto step b

c Indicate the modiﬁcation of r into stegokey using

following steps.

if (x == 1) then C

t

= {c

0

};c

0

= 0;

if (x == 2) then C

t

= {c

0

};c

0

= 1;

if (x == 3)&( flag == 1) then

C

t

= {c

1

,c

0

};c

0

= 0;c

1

= 1;

if (x == 3)&( flag == 0) then

C

t

= {c

1

,c

0

};c

0

= 1;c

1

= 1;

if (x == 4)&( flag == 0) then c

0

= 1; if

(x == 4)&( flag == 1) then c

0

= 0;

Switch(Count1) Case0 : (c

2

,c

1

) = (0, 0)

Case1 : (c2, c1) = (0,1) Case2 : (c2,c1) = (1,0)

Case3 : (c2, c1) = (1,1)

(a) Lena. (b) Baboon. (c) Peppers. (d) Chessboard.

Figure 3: Cover Images.

(a) Lena. (b) Baboon. (c) Peppers. (d) Chessboard.

Figure 4: Stegoimage1 generated by proposed scheme.

cover image and I(i, j) is the (i, j)

th

pixel value of

stegoimage.

PSNR = 10log

(2

n

− 1)

2

MSE

(2)

Where n is the number of bits used for color represen-

(a) Lena. (b) Baboon. (c) Peppers. (d) Chessboard.

Figure 5: Stegoimage2 generated by proposed scheme.

(a) Original Secret

image.

(b) Extracted Secret

image.

Figure 6: Secret image used in Lena cover image.

(a) Original Secret

image.

(b) Extracted Secret

image.

Figure 7: Secret image used in Baboon cover image.

(a) Original Secret

image.

(b) Extracted Secret

image.

Figure 8: Secret image used in peppers cover image.

(a) Original Secret

image.

(b) Extracted Secret

image.

Figure 9: Secret image used in chessboard cover image.

tation. From these experimental results it was found

that the PSNR between the stegoimage and cover im-

age is in the range of 44 to 46 dB, which is the nearest

to the PSNR value of the perceptual images consider-

ing the Human Visual System.

The quality of extracted secret image is measured

by taking four different cover images. The qual-

ity measures like Normalized Cross Correlation (NC)

and Standard Correlation (SC) are calculated between

extracted image and secret image using following

equations.

(3)

SC =

∑

M

i=1

∑

N

j=1

(I[i, j] − I

′

)(J[i, j] − J

′

)

q

∑

M

i=1

∑

N

j=1

(I[i, j] − I

′

)

q

∑

M

i=1

∑

N

j=1

(J[i, j] − J

′

)

ReversibleSteganographicSchemewithHighEmbeddingCapacityusingDualCoverImages

19

Table 1: The PSNR and MSE between the cover image and stegoimage.

Properties Lena Baboon Peppers Chessboard

Size of cover image 300× 420 250× 250 225× 225 256 × 256

Size of secret image 1000× 630 625× 500 625× 405 1280× 256

MSE between 1.65 1.74 1.74 2.24

cover & stegoimage1

PSNR between 45.93 45.72 45.70 44.62

cover & stegoimage1 (dB)

MSE between 1.67 1.75 1.73 2.24

cover & stegoimage2

PSNR between 45.88 45.69 45.74 44.62

cover & stegoimage2 (dB)

Here, I(i, j) is original secret image, J(i, j) is ex-

tracted secret image, I

′

is the mean of original secret

image and J

′

is mean of extracted secret image.

NC =

∑

M

i=1

∑

N

j=1

(I[i, j]I

′

[i, j])

∑

M

i=1

∑

N

j=1

(I[i, j])

2

(4)

Where I(i, j) is original secret image and I

′

(i, j) is ex-

tracted secret image, M is height of image and N is

width of image. Table 2 shows the NC and SC be-

tween extracted and original secret images for differ-

ent cover images. The experimental results show that

the NC and SC for all images are equal to 1 which

show that the extracted secret image is completely

correlated to the original secret image.

3.2 Embedding Capacity

In steganography the most important issue is achiev-

ing higher embedding capacity. The embedding ca-

pacity of the cover image is the number of secret

bits that can be embedded into a cover image (Na-

garaj V.Dharwadkar, 2010). The embedding capacity

is measured as bits per pixel (bpp). The embedding

capacity of image of size m× n is calculated as

C =

|T|

mn

(5)

where |T| is the total number of secret bits embedded

into cover image of size m × n. Equation (5) is used

when the scheme uses only one cover image. Since

our proposed scheme uses dual cover images, each of

size m× n, we calculate the embedding capacity as

C =

|T|

2mn

(6)

To estimate the embedding capacity of proposed

scheme, consider two cover images C

1

and C

2

each of

size m× n such that C

2

is copy of C

1

. Assume hat all

distinct consecutive pairs of pixels are embeddable.

Under these assumptions we estimate the embedding

capacity achieved by proposed scheme. There are

(mn)/2 embeddable pairs of pixels in each cover im-

age C

1

and C

2

. So there are mn pairs of pixels among

two cover images. The proposed scheme embeds 5

secret bits into pair of pixels. Thus, the total number

of secret bits that can be embedded is 5mn. According

to (5), the embedding capacity is

C =

5mn

2mn

=

5

2

= 2.5 (7)

From the experimental results we found all pairs of

pixels are embeddable and proposed scheme achieves

on average an embedding capacity of 2.5 bpp.

4 COMPARISON

We can compare our proposed scheme with T Sharp,

Chin-Feng steganographic schemes and our own ear-

lier proposed scheme (Nagaraj V.Dharwadkar, 2010).

The steganographic schemes proposed by T. Sharp

and Chin-Feng achieve an embedding capacity of 1

bpp and 0.75 bpp respectively. Where as our earlier

proposed improved reversible steganographic scheme

using dual images can able to achieve an embedding

capacity of 1.12 bpp. The earlier proposed scheme is

entirely different scheme which will not use any aux-

iliary array information in embedding and extraction.

The earlier scheme is purely blind scheme. Where as

to achieve high embedding capacity the current pro-

posed scheme use an auxiliary array known as the

stego-key. Thus, the secret message is encoded in

both auxiliary array and stegoimage. Using stego-key

we can able to achieve an embedding capacity of 2.5

bpp. Thus, compared to T. Sharp scheme, proposed

scheme achieved150 % increase in the embeddingca-

pacity and compared to Chin-Feng scheme proposed

scheme achieves 233 % increase in embedding capac-

ity with high perceptible stegoimages. Table 3 shows

the comparisons of embedding capacity of proposed

scheme with references.

5 EFFECT OF IMAGE

PROCESSING ATTACKS

Secret image communication over insecure channel

may lead to intentional or unintentional tampering of

steganoimages. The alterations of steganoimage con-

tent is considered to be the attack on steganoimages.

SECRYPT2012-InternationalConferenceonSecurityandCryptography

20

Table 2: The NC and SC between the extracted and original secret images.

Properties Lena Baboon Peppers Chessboard

NC 1.00 1.00 1.00 1.00

SC 1.00 1.00 1.00 1.00

Table 3: Comparison of proposed scheme with Chin-Feng scheme (Lee et al., 2009) and our earlier scheme (Na-

garaj V.Dharwadkar, 2010) in terms of embedding capacity (bpp).

Lena Peppers Baboon Chessboard Security

/Barbara

Proposed 2.5 2.5 2.5 2.5 Dual stegoimages

scheme & stegokey

Our earlier scheme 1 1.12 1.1 1.20 Dual stegoimages

Chin-Feng 0.75 0.75 0.749 0.749 Dual stegoimages

scheme

(a) Gaussian

Noise density 30%

on stegoimage1.

(b) Gaussian

Noise density 30%

on stegoimage2.

(c) Gaussian ﬁlter

with 30 %stegoim-

age1.

(d) Gaussian ﬁlter

with 30 % on ste-

goimage2.

(e) Gaussian Blurr

radius of 30 pixels

on stegoimage1.

(f) Gaussian Blurr

radius of 30 pixels

on stegoimage2.

(g) Radial Blurr

radius of 30 pixels

on stegoimage1.

(h) Radial Blurr

radius of 30 pixels

on stegoimage2.

Figure 10: Effect of image processing attacks on Lena image.

In this section, we discuss the reasons for hostile and

coincidental attack on a steganoimage. The hostile

attack is an attempt to weaken, remove or alter the

hidden image. Where as the coincidental attack can

occur during common image processing and commu-

nication process. These attacks are not aimed at tam-

pering the secret image. In hostile or malicious attack,

the goal is to distort or add noise to the steganoim-

age in order to render the secret image unreadable (W

et al., 1996). The attack is successful if the secret im-

age cannot be extracted anymore. In coincidental at-

tacks, while transmission of image via Internet the im-

age is noise is added and ﬁltered which leads to fail-

ure in the extraction of secret image. We discuss the

effect of attacks on steganoimages. For experimen-

tal analysis we have considered the image processing

attacks like ﬁltration, adding noise and blurring. Fig-

ure 10 shows the effect of ﬁltration, adding noise and

blurring attacks on Lena image. Figure 11 shows the

extracted secret image from attacked Lena stegoim-

age with the NC between the extracted and original

secret image.

5.1 Effect of Gaussian Filter

The effect of ﬁltering attacks on steganoimage is an-

alyzed by applying Gaussian ﬁlter on steganoimage.

The two dimensional Gaussian ﬁlter is applied on

both stegoimage with standard deviation sigma (posi-

tive) varied from 10 to 100 %. The effect of Gaussian

ﬁlter is analyzed by calculating NC between extracted

and original secret image. Figure 12 shows the effect

of Gaussian ﬁlter on extraction algorithm. The results

show that the extraction of secret image from all im-

ages produce NC between extracted and secret orig-

inal images in the range of 0.8 to 0.7 for Gaussian

ﬁltered stegoimage with 100 % standard deviation.

From the results it was found that as the ﬁltration fac-

tor increases, the normalized correlation between ex-

tracted and original secret image decreases. To design

a robust steganography scheme against known group

of ﬁlters, the secret image should be hidden into high

energy components of the cover image for which ﬁl-

ters change the least.

ReversibleSteganographicSchemewithHighEmbeddingCapacityusingDualCoverImages

21

(a) Gaussian Noise

with NC= 0.68.

(b) Gaussian ﬁlter with

NC= 0.70.

(c) Gaussian Blurr with

NC=0.68.

(d) Radial Blurr with

NC= 0.70.

Figure 11: Extracted secret image from attacked Lena image.

(a) NC.

Figure 12: Effect of Gaussian ﬁlters on steganoimages.

(a) NC.

Figure 13: Effect of Gaussian noise on steganoimages.

5.2 Effect of Gaussian Noise

To analyze the effect of adding noise to stegoiamge, a

random signal with a given distribution (eg Gaussian,

uniform, Poisson, Bernoulli) is added to the image.

In certain applications the additive noise may origi-

nate from Digital-to Analog (D/A) and A/D convert-

ers, or as a consequence of transmission errors. How-

ever, an attacker may introduce perceptually shaped

noise (image-dependent mask) with maximum unno-

ticeable power. This will typically force the increase

of threshold at which the correlation of the detector

operates. The Gaussian noise is added to the stegoim-

ages with noise density d which affects approximately

d×(size(I)) pixels. The performance of extraction al-

gorithm is analyzed by increasing noise density start-

ing from 10 up to 100 pixels. The quality of ex-

tracted secret image is measured in terms of NC be-

tween original and extracted secret image. Figure 13

shows the effect of adding noise on both Stegoimage

by varying the noise density from 10 to 100 pixels.

In this experiment it is found that extraction of se-

cret image from stegoimages produces NC between

the extracted and the secret image is nearly equal to

0.80. These results show that the proposed scheme is

robust against the addition of noise.

(a) NC.

Figure 14: Effect of Gaussian blurring on steganoimages.

5.3 Effect of Gaussian Blurring

To analyze the effect of blurring on stegoiamges, a

Gaussian blurring is applied with varying blurring ra-

dius from 10 to 100 pixels. The disk radius is varied

from 10 to 100 pixels. The effect of blurring on ex-

traction algorithm is analyzed by calculating NC be-

tween secret image and extracted secret image. Figure

14 shows the effect of blurring on stegoimage in terms

of NC between secret image and extracted secret im-

age. Experimental results shows that extraction algo-

rithm produces an image which is highly correlated to

the secret image.

5.4 Effect of Radial Blurring

A Special type of circular averaging ﬁlter (pillbox ﬁl-

ter) is applied on the both stegoimage to analyze the

effect of blurring. This ﬁlter ﬁlters the stegoimage

within the square matrix of size 2×(DiskRadius)+1.

The disk radius is varied from 10 to 100 pixels. The

effect of blurring on extraction algorithm is analyzed

by calculating NC between secret image and extracted

secret image. Figure 15 shows the effect of blurring

on stegoimage in terms of NC between secret im-

age and extracted secret image. Experimental results

shows that even at DiskRadius = 100 pixels the ex-

traction algorithm produces an image which is highly

correlated to the secret image. Thus, the proposed

scheme is robust against the blurring attack.

6 CONCLUSIONS

We have proposed a reversible dual coverimage based

steganographic scheme. The proposed scheme produ-

SECRYPT2012-InternationalConferenceonSecurityandCryptography

22

Algorithm 3: Extraction Algorithm.

input : Dual stegoimages, I

′

1

= {q

1

1

,q

1

2

,...,q

1

m×n

}

and I

′

2

= {q

2

1

,q

2

2

,...,q

2

m×n

} such that I

′

1

6= I

′

2

and stego-key of size (4× h× w)/5, where

C = {C

0

,C

1

,...,C

(4×h×w)/5

},

C

o

= {c

3

,c

2

,c

1

,c

0

} and c

k

∈ {0,1}

output: Secret image S of size h× w where

S = {s

1

,s

2

,...,s

h×w)

} and two identical

grayscale images I

1

and I

2

of size m× n

1. Set i=1; l=0; k=1; x = h× w ;

2. if (numbe of bits(stego− key) < 4) then

goto step 7.

3. if (i%2 == 1) then Embedd pexel = p

1

i

and

Ref pixel = p

2

i

else Embedd pexel = p

2

i

and

Ref pixel = p

1

i

4. select two pixels Ref pixel and Embedd pexel

and four bits of key {c

k

,c

k+1

,c

k+2

,c

k+3

}.

Switch(c

k

,c

k+1

,c

k+2

)

Case(0,0,0) : count = 0;break;

Case(0,0,1) : count = 1;break;

Case(0,1,0) : count = 2;break;

Case(0,1,1) : count = 3;break;

Case(1,0,0) : count = 4;break;

Case(1,0,1) : count = 5;break;

Case(1,1,0) : count = 6;break;

Case(1,1,1) : count = 7;break;

if (c

k+3

== 1) then p

1

i

= p

1

i

+ 4× count. else

p

1

i

= p

1

i

− 4× count

5. Select Ref pixel = (b

1

7

,b

1

6

,...,b0

1

) and

Embedd pexel = (b

2

7

,b

2

6

,...,b0

2

) respectively and

apply the following operations.

6. for j ← 0 to 4 do

Switch(b

1

j

,b

2

j

) Case(0,0) : s

j

= 1;break;

Case(0,1) : s

j

= 0;break;

Case(1,0) : s

j

= 1;break;

Case(1,1) : s

j

= 0;break;

Thus, the extracted secret bits are

(s

j−4

,s

j−3

,s

j−2

,s

j−1

,s

j

) x = x− 5.

7. set i = i+ 1;k = k+ 4;

Repeat step 3 to step 6 until x < 4.

8. if (x == 1) then if (c

k

== 0) then p = 0;

goto step 12 if (x == 2)&(c

k

== 1) then p = 0;

goto step 12

if (x == 3) then p = 1 goto step 9 else p = 2

ces perceptual good quality stegoimages with an em-

bedding capacity of 2.5 bpp. The usage of dual ste-

gaoimages and stego-key enhances the security of the

secret image. Without complete knowledge of both

stegoimages and stego-key it is difﬁcult to determine

the secret image. From the experimental results it was

found that proposed scheme preserves the perceptual

quality of stegoimages. The proposed scheme has the

advantage of higher embedding capacity and good

Algorithm 4: Extraction Algorithm continued.

9 Select two pixels p

1

i

and p

2

i

and bits of stegokey

(c

k

,c

k+1

,c

k+2

). l = c

k+2

; Switch(c

k

,c

k+1

)

Case(0,0) : count = 0;break;

Case(0,1) : count = 1;break;

Case(1,0) : count = 2;break;

Case(1,1) : count = 3;break;

10 select two pixels p

1

i

and p

2

i

and stegokey bits

(c

k

,c

k+1

) if (c

k

== 1) then count = 1;l = c

k+1

else count = 0;

if (l == 1) then p

2

i

= p

2

i

+ 4× count else

p

2

i

= p

2

i

− 4× count

11 Select p

1

i

= (b

1

7

,b

1

6

,...,b

1

0

) and p

2

i

= (b

2

7

,b

2

6

,...,b

2

0

)

apply the following operations.

for j ← 0 to p do

Switch(b

1

j

,b

2

j

) Case(0,0) : s

j

= 1;break;

Case(0,1) : s

j

= 0;break;

Case(1,0) : s

j

= 1;break;

Case(1,1) : s

j

= 0;break;

The secret bits {s

0

,s

1

,...,s

p

} are extracted.

12 set i=1;

13 if (i%2 == 1) then p

1

i

= p

2

i

; else p

2

i

= p

1

i

;

14 i = i+ 1; Repeat step 12 to step 13

until i == m× n

aaa

(a) NC.

Figure 15: Effect of radial blurring on steganoimages.

visual quality of stegoimages. The performance of

the steganography scheme is analyzed by consider-

ing various types of image processing attacks and the

scheme was found robust to various types of image

processing attacks.

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