DCT-domain Robust Data Hiding Using Chaotic Sequence

Siddharth Singh1, Tanveer J Siddiqui 2, Rajiv Singh3,Harsh Vikram Singh4

1, 2, 3 Department of Electronics and Communication, University of Allahabad, Allahabad, India. 1 siddharthjnp@gmail.com

2 tjs@jkinstitute.org 3jkrajivsingh@gmail.com

4Department of Electronics Engineering, K.N.I.T..Sultanpur, India 4 harsh@knit.ac.in

Abstract— In this paper, we propose DCT-domain robust data hiding algorithm using chaotic sequence. The algorithm works by dividing the cover into blocks of equal sizes and then embeds the watermark in middle band of DCT coefficient. Performance evaluation for robustness and imperceptibility of proposed algorithm has been made using the bit error rate (BER) and the peak signal to noise ratio (PSNR) value for cover image and watermarked image. This algorithm is compared to PN sequence based DCT algorithm. The proposed algorithm provides more robustness against several common image processing attacks, such as JPEG compression, low-pass filtering and addition of noise. In case of JPEG compression attacks, for low quality compression (Q-60) it has been analyzed that more than 92% of the hidden data was recovered without any error and for same quality compression in PN sequence based DCT algorithm has more than 89% of the hidden data recovered without any error.

I. INTRODUCTION With the rapid growth of high speed computer networks

and that of internet reproduction and distribution of digital data has become easier than ever before. This also raises the issue of data protection. Digital watermarking is a kind of data hiding technology. It has been used for a variety of applications, including copyright protection, data hiding, and authentication and fingerprinting. Watermarking is a young field and it is growing exponentially [1, 2].

Based on the processing domain the data hiding schemes can be classified as spatial domain and transform domain [3, 4] techniques. The spatial domain is computationally simple and straight forward wherein host data is directly replaced by embedded data (watermark) using substitution techniques. However, these techniques are more fragile to external attacks and thus provide poor robustness of the watermark. On the other hand the transform domain techniques require more computations but they achieve more robustness against different filtering operations such as median, high-pass and low-pass, addition of noise etc[5].Therefore transform domain techniques more robust than spatial domain

techniques. Generally digital document distribution may consist of image, audio or text or their permutations distributed through open channel. The present study focuses on copyright protection on still image documents. Common transform domain techniques mainly are Discrete Cosine Transform (DCT) or Discrete Wavelet Transform (DWT) [6,7], Discrete Fourier Transform (DFT), but DCT is preferred because it is widely used in image and video compression [8,9]. Also it has been used in digital image watermarking using PN sequence [10].

In this paper, we propose a chaos-based DCT domain data hiding algorithm for still images. We use a chaotic map to generate a pseudo-random signal that behaves as embedding and detecting Key. The chaotic map is used for watermark signal spread in middle band of DCT coefficients of the cover image. The chaotic map can be used as pseudo-random generator [11], for digital data hiding, to increase security. The main aim of this algorithm is to design a secure data hiding technique by using chaotic sequence and compare our result with pseudo-random sequence based data hiding technique. We use a binary logo image as watermark.

The rest of paper is organized as follows. In Section II, the chaotic sequence is described. Section III describes Discrete Cosine Transform and Hiding in Mid-Frequency. Details of the proposed algorithm are presented in Section IV. Results are discussed in Section V. Finally, the conclusions have been made in Section VI.

II. CHAOTIC SEQUENCE Chaos theory describes the behavior of certain dynamical

system which is an unpredictable, deterministic and uncorrelated system that exhibits noise-like behavior through its sensitive dependence on its initial conditions which generates sequence similar to PN sequence [12].

A direct application of chaos theory to telecommunication system appears in conventional digital spread spectrum [13], where the information, is spread over a wide band by using a

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chaotic sequence instead of the traditional periodic PN sequences.

Various non-linear dynamic systems are used in order to generate the chaotic sequence, e.g. logistic map and tent map[14,15].The most commonly used function to generate chaotic sequence is logistic map:

1 (1 )k k kx r x x+ = ⋅ − , 0 < x <1 (1)

21 (1 2 )k kx x+ = − ) , -1< x <1 (2)

Where 0 < r ≤ 4 is bifurcation parameter. Research on chaos dynamic system show that when 3.569945< r ≤ 4,the logistic map is in chaotic state and sequence generated by logistic map is an non periodic and sensitive to initial value[16]. In this paper, we use the parameter ‘r’and initial values ‘x’ as key.

One major difference between chaotic sequence and PN sequences is that the generated chaotic sequences are not binary. Hence chaotic sequences must be converted into binary sequence by using threshold.

III. DISCRETE COSINE TRANSFORM The Discrete Cosine transform has been widely used for source coding in context of JPEG and MPEG and was later also considered for the use of embedding a message inside images and video. It possesses some other characteristics and advantages such as vector base good embodiment about image information, small computational complexity, high compression ratio, low error rate. So watermarking technique in DCT domain is more robust against compression attacks.

Two-dimensional discrete cosine transformation and its

inverse transform are defined as [17]: 1 1

0 0

(2 1) (2 1)( , ) ( ) ( ) ( , ) [ ] [ ]

2 2

N N

x y

x u y vC u v u v f x y Cos Cos

N Nα α

− −

= =

Π + Π += ∑∑

(3)

1 1

0 0

(2 1) (2 1)( , ) ( ) ( ) ( , ) [ ] [ ]

2 2

N N

u v

x u y vf x y u v c u v Cos Cos

N Nα α

− −

= =

Π + Π +=∑∑

(4)

Where u, v = 0, 1, 2……… N-1

x, y = 0,1,2………N-1

( )uα is defined as follows:

1( )uN

α = u=0;

2( )uN

α = u=1,2……N-1

The mid-frequency regions of the DCT coefficient blocks are used to embed the hidden data as shown in Figure-1, where fL, fM and fH represent the low, medium and high frequency bands respectively [18].

Fig 1: Mid-frequency DCT region used to embed the watermark

data The basic principle of digital data hiding algorithm

consists of two parts: Embedding and Recovery. In watermark embedding, original image is first divided into 8×8 sub blocks and then embed watermark bit is spread over middle frequency band DCT coefficient values in the image blocks. The spreading is done by two pseudo-random (PN) sequences, one for zero bit and other for one bit of watermark. At last, watermarked image comes from taking Inverse Discrete Cosine Transform (IDCT).In watermark recovery it is an inverse process of embedding which finds correlation between middle frequency band DCT coefficient values in the image and corresponding two PN sequences and recovery of watermark.

IV. PROPOSED ALGORITHM We propose a digital data hiding technique to produce a

secure algorithm using chaos. We use chaotic map to generate two pseudo-random (PN) sequences, one for zero bit and other for one bit of watermark with low correlation. Generally pseudo-random noise sequence is generated by using the rand function in MATLAB. This periodic pseudo-random sequence generator must be initialized using a predefined ‘key’. The proposed algorithm uses chaotic sequence which is highly sensitive to initial conditions. Use of chaotic sequence for spread spectrum entails robustness and its combination with DCT domain increases the robustness of this algorithm. The proposed algorithm provides robustness against a variety of image manipulation attacks.

A. EMBEDDING The algorithmic steps are discussed below: 1. Read Cover image and n-bit watermark signal. 2. Generate two PN sequences of length 22 (for 22 mid-band DCT coefficients) by using logistic map under an initial value as secret key. Then, we set a threshold ‘t’ to convert real valued chaotic sequence to binary sequence, it is defined as

{ 11

( )( )

1, if S1, if S( ) i t

i tp i ><−= (5)

3. Transform the original image using 8×8 block 2D-DCT. 4. Hide the ith watermark bit, with modulating the ith DCT block of the host using Equation-1(for a ‘0’ or a ‘1’ bit). For Mi=1 to n

{ ( , ), if ,, if ,

( , )( , )( , ) i M

M

u v u v fw u v f

I u v WI u vu vI α ∈

∉+ ∗= (6)

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Where fM is the mid-band frequency region, α is the gain factor (in present simulation α = 6) used to specify the strength of the embedded data, Wi is the appropriate pseudo random noise sequence, based on the ith watermark bit; I(u, v) represents the 8×8 DCT block of the original image IW(u,v) represents the corresponding waterarked DCT block. 5. Take the inverse transform each of the Watermarked DCT blocks, IW (u, v), using 8x8 blocks inverse 2D-DCT to get the final Watermarked image IW (x, y).

B. RECOVERY The watermark recovery procedure is based on correlation between the middle frequency band DCT coefficients of the image and corresponding PN sequences. Watermark recovery is the inverse process of the embedding. The steps involved in recovery are listed below:

1. Read watermarked image. 2. Generate the same pseudo-random (PN) sequences that were used in embedding process by using logistic map. 3. Transform the watermarked image using 8×8 block 2D-DCT. 4. Extract the middle band DCT coefficients which have recorded the location, determine the watermark information. 5. For Mi=1 to n Calculate the correlation between the mid-band DCT coefficients of block and PN-sequences. 6. Extract the jth watermark bit, bj using the following expression

{0, if corr(0) > corr(1)1, if corr(1) > corr(0)jb = (7)

Where corr (0) is the correlation between extracted coefficient of jth block and PN sequence generated for bit ‘0’.corr (1) is the correlation between extracted coefficient of jth block and PN sequence generated for bit ‘1’.

V. RESULTS AND DISCUSSIONS The proposed algorithm is tested with the 512×512 gray

Scale Lena, Girl and Tank images. The Watermark is binary logo of size (64×64) which is converted into a row vector of size 4096×1 as the watermarking signal, these watermark bits are embedded into the middle band DCT Coefficient of cover image. The keys of two chaotic sequences are parameter ‘r’and initial values. The value of ‘r’ is taken as 3.99996 and initial values are 0.1and 0.3. Performance metrics PSNR and BER are computed with and without attacks. Table1 shows PSNR and BER values for proposed algorithm and PN sequence based DCT algorithm. The results in Table 1 demonstrate that the performance of the proposed algorithm is more robust than traditional PN sequence based DCT algorithm due to low BER and greater than globally accepted PSNR value 35dB. The original and recovered watermarks using chaotic and PN sequence for Lena image are shown in figure 2, 3 and 4 respectively.

Table 1: Performance metrics of data hiding algorithm without attacks

(a) (b) Fig 2: (a).Original Lena Image and (b). Watermark Image

(a) (b)

Fig 3: Watermarked image without attacks using (a).Chaotic Sequence and (b). PN Sequence

(a) (b)

Fig 4: Recovered watermark without attacks using (a).Chaotic Sequence and (b). PN Sequence

The peak signal noise rate (PSNR) is used in this paper to evaluate the watermarked image quality. PSNR of a gray-level image is defined as:

2

1010 log ( )L

PSNRMSE

= (8)

where L is peak signal value of image. The mean square error (MSE) for an M×N gray-level image is defined as follows:

2, ,

1 1

1( )

M N

i j i ji j

MSE f gMN = =

= −⎡ ⎤⎢ ⎥⎣ ⎦∑ ∑ (9)

where M,N is no. of rows & column of original & watermarked image respectively, fi,j is pixel value of ith row and jth column of original image, gi,j is pixel value of ith row and jth column of watermarked image.

Peak Signal to Noise Ratio (PSNR) (dB)

Proposed Algorithm

PN Sequence based DCT Algorithm

37.09

40.91

Bit Error Rate (BER)

0.0237

0.0678

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The Bit error rate (BER) is used to evaluate the difference between watermark image and the recovered watermark. It is the ratio of the number of bits, elements, characters, or blocks incorrectly received to the total number.

BER = (No. of error bits) / (No. of transmitted bits) In Table-2, BER of the original watermark and the recovered watermark are calculated to demonstrate the robustness of proposed algorithm and PN sequence based DCT algorithm to several image processing attacks. It can be seen from Table-2, that the proposed algorithm is more robust than traditional PN sequence based DCT algorithm for every attack. In case of JPEG compression attacks, for quality compression (Q 80-60), the BER was 0.0308-0.0701 i.e. more than 92% of the hidden data was recovered without any errors. A Gaussian low–pass filtering attack does not affect the robustness of hidden data by a considerable amount. For different Gaussian variance (σ=0.5- 1.2), the BER was 0.0732-0.1582 i.e. more than 84% of embedded data was recovered without error. In the case of noise addition attack, for different variance (v=0.01-0.02), the BER were 0.2029-0.2744 for additive white Gaussian and 0.0715-0.1164 for salt & pepper noise. Table 2: BER at different attacks

Attack BER(max1) Proposed

Algorithm Traditional

PN Sequence based DCT Algorithm

JPEG(Q-90) 0.0237 0.0684 JPEG(Q-80) 0.0308 0.0708 JPEG(Q-60) 0.0701 0.1008

Gaussian low pass filtering σ=0.5

0.0732 0.1189

σ=1.0 0.1184 0.1777 σ=1.2 0.1582 0.2107 Gaussian noise addition v=0.01 0.2029 0.2908

v=0.02

0.2744 0.3481

Salt & Pepper noise addition v=0.01

0.0715 0.1536

v=0.02 0.1164 0.1953

VI. CONCLUSIONS In this paper we proposed DCT-domain robust data hiding

alogrithm using chaotic sequence. This algorithm uses chaotic sequence for spread spectrum and its combination with DCT domain increases the robustness.During watermark embedding,we use chaotic map to generate two pseudo-random (PN) sequences, one for zero bit and other for one bit of watermark. Experimental results show that the proposed alogrithm provides security and robustness against several common image processing attacks,such as JPEG compression,low-pass filtering and addition of noise. When compared to a traditional PN sequence based DCT algorithm, the proposed algorithm is more robust against various attacks. In case of JPEG compression attacks, for low quality compression (Q-60) it can be seen that more than 92% of the

hidden data was recovered without error and for same quality compression in PN sequence based DCT algorithm has more than 89% of the hidden data recovered without any error. According to result,we clearly find that this algorithm is more robust and secure than traditional PN sequence based DCT algorithm.

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