Steganography in image using discrete wavelet transform ation [600035]

Steganography in image using discrete wavelet transform ation
I. BADESCU , C. DUMITRESCU
University Politehnica of Bucharest, Independence Street, nr. 313, Bucharest,
Romania , [anonimizat] , [anonimizat].

Abstract : In this paper, we propose a new algorithm of steganography to allow simultaneous hiding secret
message and small -size image into an large- size image. To hide the secret message in small image we use the
Least Significant Bit (LSB) substitution, and the m ethod for hiding the image in the image cover use Discrete
Wavelet Transformation (DWT). The proposed method results in increasing the secret message capacity and
security level. The secret message won't be visible after embedding and can be extracted later.
Key-Words : LSB, wavel et, steganography, high capacity, pixel matrix, hide message.
1. Introduction
From Wikipedia, steganography is the art or practice
of concealing a message, image, or file within
another message, image, or file. The
word steganography is of Greek origin and means
"covered writing" or "concealed writing". Some implementations of steganography which lack
a shared secret are forms of security through
obscurity , whereas key -dependent steganographic
schemes adhere to Kerckhoffs's principle. It
combines the Greek words steganos (στεγα νός),
meaning "covered or protected", and graphei (γραφή) meaning "writing". The first
recorded use of the term was in 1499 by Johannes
Trithemius in his Steganographia, a treatise on
cryptography and steganography, disguised as a book on magic. Generally, the hidden messages will
appear to be (or be part of) somet hing else: images,
articles, shopping lists, or some other cover text . For
example, the hidden message may be in invisible
ink between the visible lines of a private letter.
Steganography includes the concealment of information within computer files. In digital steganography, electronic communications may include steganographic coding inside of a transport
layer, such as a document file, image file, program
or protocol. Media files are ideal for steganographic transmission because of their large size. For example, a sender might start with an innocuous image file and adjust the color of every 100th pixel to correspond to a letter in the alphabet,
a change so subtle that someone not specifically looking for it is unlikely to notice it.
The proposed algorithm has two stages of implementation. In the first stage the secret message (10,000 characters) is hidden in an image size 640 x 480 using LSB algorithm, and in the second stage
the stego -image resulting is hidden in an cover –
image size 1024×1024, using the decomposition of
multiresolution DWT. Thus simultaneous hiding the secret message and secret images in a single cover
image.
2. Wavelet
Many applications use the wavelet decomposition
taken as a whole. Some of these applications are
compression and denoising. Wavelet analysis allows
the use of long time intervals where we want mo re
precise low -frequency information, and shorter
regions where we want high-frequency information. The DWT [1][2] consists in splitting the signal x [n]
in low and high frequencies using a lowpass and a
highpass filter respectively (equation 1):

and
where H(ω) and G(ω) should be orthogonal:
(2)
Advances in Mathematical Models and Production Systems in Engineering
ISBN: 978-960-474-387-2
69

The signals obtained are down sampled by two, in
order to reduce their size. This process can be continued for each signal obtained from the lowpass filter for a number of arbitrary times (see Fig. 1). The
coefficients obtained are:

(3)

where j = 0,…,L is the resolution level (0 – high
resolution, L – the lowest resolution). The
coefficients aL[p] are the approximation of the
original signal and dj [p] are the detail coefficients of
x[n].

Fig. 1. The DWT (a) and the IDWT (b) of the 1D
signal x[n].
The reconstruction of the original signal x[n] is the
inverse process of the DWT (equation 4):

The DWT for two dimensional signals, like images,
is similar to the DWT for one dimensional signals.
The difference is that one has to implement separately for each dimension the DWT and IDWT respectively. The image will be decomposed for
each resolution l evel into a high -high (HH), high -low (HL), and low -high (LH) subband, and a low –
low (LL) subband for the coarsest resolution level.
The LL band is also known as as the approximation subimage because it contains most of the
information from the image. The HL, LH, HH sub
bands are the detail sub images containing the horizontal, vertical and diagonal details (see Fig. 2
and 3).

Fig.2. DWT pyramid decomposition of an image for two resolution levels.

Fig.3. W avelet transform, direct and inverse for two
levels of decomposition.
3. Implementation

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In Fig . 4 are presented the stages of implementation
of the proposed algorithm.

Fig.4. Stages of implementation of the proposed
algorithm.

3.1 LSB substitution based steganography
Here spatial features of image are used. This is a simplest steganographic technique that embeds the
bits of secret message directly into the least significant bit (LSB) plane of the cover image. In a gray-level image, every pixel consists of 8 bits [3] .
The basic concept of LSB substitution is to embed the confidential data at the rightmost bits (bits with the smallest weighting) so that the embedding procedure does not affect the original pixel value greatly. The mathematical representation for LSB is:
X
i’ = x i – x i mod 2k + m i (5)
The ith pixel value of the stego -image and x i
represents that of the original cover -image. M i
represents the decimal value of the ith block in the confidential data. The number of LSBs to be substituted is k. The extraction process is to copy
the k -rightmost bits directly. Mathematically the
extracted message is represented as in Equation ( 6).

m
i =x i mod 2k (6)

Hence, a simple permutation of the extracted mi
gives us the original confidential data. This method is easy and straightforward but this has low ability to bear some signal processing or noises. And secret
data can be easily stolen by extracting whole LSB
plane. In Fig . 5 shows the implementation of LSB algorithm used to hide secre t message in secret
image -cover image 1 (yellow blocks represented in
Figure 4).

Fig.5. LSB algorithm imp lementation used for
hiding the message.

3.2 Embedding process

Our information- hiding algorithm includes five
steps:
1) Perform LSB transformation secret messages on
the secret image (cover image 1) .
2) Perform single level Harr wavelet decomposition
both on the host image and the transformed secret
image, and four components (approximate,
horizontal, vertical, diagonal) of the host image and
the secret image are got respectively. Denote these
components as h i and s i, where i 2 a; h; v; d .
3) Quantize s i as qs i and encode qs i into bit stream A i
using Raw Binary Encoding , respectively. In order
to decrease additional information, more
specifically, quantization table to be shared between
the sender and the receiver, si is equally quantized.
Thus, only a quantization factor should be shared between the sender and the receiver before covert
communication. 4) Embed A
a into ha using the improved LSB
algorithm [4][5] [6], and embed A h, Av, Ad into the
relationship between hh and ha, hv and ha, hd and ha,
respectively.
Four secret keys are used to choose the set of DWT
coefficients for information embedding.
5) After information embedding, wavelet
reconstruction is performed on the host image using
modified h a, hh, hv and hd [7].
The whole embedding process is shown in Fig.4.
Advances in Mathematical Models and Production Systems in Engineering
ISBN: 978-960-474-387-2
71

4. Experimental results
For our experiment we introduced a message with a
length of 10,000 characters (can be encrypted by
AES), in a small 640 x 480 image gray scale, the result obtained being hidden in an image of size 1024×1024.
Thus was developed an application that can hide
text (secret) message and secret image at the same
time the same cover image.
Fig. 6. S tego image for a variable image quality : (a)
Q=20, (b) Q=50, (c) Q=75, (d) Q=85. Table 1 . Calculated result for above image
Calculation Result
Compression ratio 0.9715 db
SNR 23.98 db
PSNR 28.81 db
MSE 64.14 db

5. Conclusions In this paper , we propos e an algorithm to hide
information with robust and high capacity of hide.
The algorithm was tested for gray images, bu t can
be used for color images.
As a result of the experiments resulted as gray
images hide capacity can increase substantially.
Starting from these considerations can develop
steganography applications that allow hiding of gray
images in the color image.
Subsequent developments will focus for the development of an application to hide audio files in the cover image.
References:
[1]. S. Qian, D. Cheng, “Joint Time -Frequency
Analysis ”,Pretince Hall 1996;
[2].N. Corina, “ Digital watermarking in the wavelet
domain”,http://www.tc.etc.upt.ro/personal/corina/book05.pdf;
[3]. P. Nerkar,“ Steganography for colored images ”
International Journal of Electronics,
Communication & Soft Computing Science and
Engineering ISSN: 2277- 9477, Volume 2, Issue2 ,
2010; [4]. B. Yang, B. Deng , “Steganography in gray
images using wavelet” Technical Report 448, Departament of Statistics, Beijing University, 2011;
[5]. R. Gonzalez, R. Woods , “Digital Image
Processing ”, 3
rd Edition , 1995;
[6]. A. Jain, “ Fundamentals of Digital Image
Processing” Pretince/Hall International, 1987;
[7]. V. Strela , Multiwavelet: Theory and
Applications, PhD, Thesis, MIT, 1996.

Advances in Mathematical Models and Production Systems in Engineering
ISBN: 978-960-474-387-2
72