Implementation of Steganogrphy using Recursive Equation Approach

International Journal of Computer & Mathematical Sciences
ISSN 2347 – 8527
Volume 4, Special Issue
May 2015
Implementation of Steganogrphy using Recursive Equation
Ruchika Sharma
Assistant Professor, JaganNath Institute Of Management Sciences,
JIMS, New Delhi-110085
Dr. Vinay Kumar
Professor, Vivekananda School of IT, VIPS, GGSIPU, New Delhi 110 088, India
Abstract: The fast development of information transfer by way of internet has made it crucial to
provide security to information. The security of information can be achieved using the concept of
Steganography. Steganography is the process of hiding information in innocuous cover. It is used to
provide security to information by embedding secret information in digital cover. This paper focuses
on implementing steganography using a new approach “Recursive equation approach” for hiding
information in 24-bit BMP images. This approach is used to find bit positions in images to hide
Keywords: BMP, Steganography, Digital cover
This paper‟s focus is on introducing a new technique to hide information using
steganography. The growing need of information transfer on internet requires security to send
information especially on computer networks.To send information securely to destination,
steganography is used. Steganography word is derived from the Greek words “stegos” which means
“cover” and “grafia” which means “writing” and is defined as “covered writing”. Steganography is
the art and science of communicating in a way which hides the very existence of the communication
channel.The goal of steganography is to hide the presence of hidden communication in digital cover
With the advent of computer and its ever expanding application in different areas of life, the issue of
information security has become increasingly important. Different methods such as cryptography,
steganography, coding etc are used to provide security and privacy to digital data. Digital
Steganography has received attention of information scientist in recent years who are dealing with
information security and privacy.
A steganographic communication system consists of the following:
Embedding algorithm
Extraction algorithm
Optionally a key [6]
A secret message is embedded in a digital cover by slightly modifying the cover through embedding
algorithm. The resultant modified cover that contains the secret message is called stego-cover. The
digital cover used in steganography may be images, video clips, text, sounds etc [8,6].
Crucial requirement for a steganographic system is its detectability by an attacker with probability
not better than random guess, given the full knowledge of the embedding algorithm and statistical
properties of the original cover object. The stego key, if any, is not revealed [1,11].
Ruchika Sharma, Dr. Vinay Kumar
International Journal of Computer & Mathematical Sciences
ISSN 2347 – 8527
Volume 4, Special Issue
May 2015
Steganography is classified as follows:
Pure Steganography
Pure Steganpgraphy does not require prior exchange of any secret key. No information is required to
start the communication process, thus the security of the system depends entirely on its secrecy [7].
Pure Steganography can be defined as the quadruple (C, M, E, D), where
C: the set of possible covers.
M: the set of secret massage with |C| ≥ |M|.
E: C×M→C* the embedding function.
D: C*→M of the extraction function with the property that
D (E (c, m)) = m for all m  M and c  C
Symmetric steganography
Symmetric steganography is used where a private key would play vital role. Using Symmetric
Approach, a private key is created which is shared by the sender as well as receiver to embed and
extract hidden information respectively from the Digital file cover[8].
1.3 Public Key Steganography
In this type of steganography, two keys are required. It requires a public and private key. Public key
is used to embed hidden data whereas private key is used to reconstruct the original message[14].
2. Different Approaches of Steganography
2.1 LSB
Using LSB technique, the secret information is hidden at specific position of LSB of an image . The
LSB of every byte is replaced with a bit from secret information. Each 3-byte triplet in the bitmap
image represents relative intensities of blue, green and red color of a pixel.
For example:
Consider a 24-bit BMP image, the LSB of each Red, Green and Blue color can be considered to
hide secret information. A 24-bit BMP image which equals to 3 bytes are used for one pixel and in
each byte, one LSB bit of every byte can be replaced with a bit from secret information. So 3 bits of
secret information can be hidden in one pixel.
Consider the below three pixel grid which equals to nine bytes
11001100 10001101 10110011
Ruchika Sharma, Dr. Vinay Kumar
International Journal of Computer & Mathematical Sciences
ISSN 2347 – 8527
Volume 4, Special Issue
May 2015
10100011 11000111 10010001
10010001 10101011 10100111
If the number 234 whose binary equivalent is 11101010 to be hidden in above pixel grid then the
resultant grid after embedding this number is:
11001101 10001101 10110011
10100010 11000111 10010000
10010000 10101011 10100110
In the above example only five LSB bits need to be replaced with secret information because three
LSB bits of original pixel grid are same as that of the
secret information.
2.2 Enhanced LSB
In LSB approach, the secret information is embedded in LSB part of each Red, Green and Blue
color of the original pixel grid.
In Enhanced LSB approach, the secret information is embedded only in one out of the red, green or
blue color‟s LSB of original pixel grid. Using Enhanced LSB Approach, the possible distortion in the
digital cover due to embedding of secret information in it is much lesser than normal LSB technique
[9, 10].
2.3 Graph Theoretic approach
Graph Theoretic approach retains all bits in the color palette of 24-bit BMP image. This approach
does not replace or modify color bits of digital cover to avoid maximum distortion. In this approach,
the digital cover image is treated as data units. The approach is used to find relationship between
different data units and represent the relationship using graph. A digital image is treated as collection
of many data units. The approach is used to find maximum embedding space in digital cover and
then looking for relationship between data units that conveys the existence of message in digital
cover without either replacing or exchanging any color bits of cover[12].
3. Recursive Equation Approach
Recursion is the process of repeating itself in a self-similar way. Recursive equations are used to
create a multistage decision problem as a sequential process. Each recursive equation represents a
phase at which a decision is required. A series of equations are successively solved and each
equation is dependent on the output values of the previous equations[ ].This approach is used to find
bit locations in digital cover where bit value can be changed to hide a bit from information.
In this paper, symmetric key steganography is proposed to hide information in digital cover.
Recursive Equation approach is used to generate a secret key. Thereafter the key is used to find
appropriate place in digital cover to hide the secret message. This randomizes the location of
different bits of hidden information. The paper focus is on hiding secret information using secret key
which is generated through Recursive Equation Approach
The process used for generating key is as below.:
Consider a 24 bit BMP image of 300*300 pixels then we have total 90000*3 bytes (24bits) bit
positions in which we can manipulate and make changes in bits positions to hide a secret message. In
the proposed work, a symmetric key is created using recurrence equation. Let a recurrence equation
of first order be
an = an-1+2 , a0 = 3
This equation generates a sequence: a1 = 5, a2 = 7, a3 = 9 and so on. We may create a key here which
is combination of coefficient, constant in equation, initial position and initial value. i.e. (Coefficient,
Ruchika Sharma, Dr. Vinay Kumar
International Journal of Computer & Mathematical Sciences
ISSN 2347 – 8527
Volume 4, Special Issue
May 2015
Constant, Initial position, Initial Value) could be a1: (1,2,0,3), a2:(1,2,1,5), a3:(1,2,2,7), a4:(1,2,3,9)
and so on. Any one of this quadruplet can be used as secret key and the selected key will determine
from which position the embedding of hidden information starts.
4. Advantages of Recursive Equation Approach
It helps in improving the hidden communication techniques by randomizing the location of
hiding information in digital cover.
Digital watermarking is the technique of adding unique digital identity to digital artifacts
using steganographic principles i.e. hiding the digital identity cleverly so that whenever required, the
hidden data can be used to establish authenticity of the corresponding artifacts [13]. Watermarking
helps in establishing ownership of an artifact.
The confidentiality of secret information is ensured, even under the suspicion that Secret
information is being communicated.
The work can implementation of finger be used for printing of digital data. Watermarking
helps in identification of the origin of object whereas finger printing attempts to identify individual
copies of an object by means of embedding a unique marker in every copy that is distributed [4,5].
This proposed approach will help in a way that if at any stage, an illegal copy is found, the copyright
owner can identify the buyer by decoding the information.
The approach can also be used in maintaining Intellectual Property right (IPR).
5. Conclusion
In this paper, symmetric key which is generated using Recursive equation approach is proposed to
hide secret information. The key is used to find bit locations or position in digital cover where secret
information can be embedded. The hiding approach is symmetric key steganography. We propose to
use our algorithms to hide information in digital image stored in 24-bit BMP file format. The
proposed is useful in many real life applications wherein digital signature (unique identity of digital
data) need to be embedded to protect IPR. Also it is very good technique for hidden communication
where a lot of information are shared over public network.
Encouragement, support and suggestions for content improvement from all colleagues, peers and
seniors are gratefully acknowledged, which will remain essential for present and future scientific
thought processes beyond scheduled professional endeavors.
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International Journal of Computer & Mathematical Sciences
ISSN 2347 – 8527
Volume 4, Special Issue
May 2015
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Biographical Notes:
Ruchika Sharma is a Assistant Professor in JaganNath Institute of Management Sciences, Delhi.She
completed MBA(IT) From Symbiosis and M.Phill in Computer Science from Global Open
Vinay Kumar is a Professor in Vivekananda Institute of Professional Studies, Delhi. Earlier he
worked as Scientist in National Informatics Centre, MoCIT, Government of India. He completed his
Ph.D. in Computer Science from University of Delhi and MCA from Jawaharlal Nehru University,
Delhi. He has authored a book on Discrete Mathematics and has contributed many research papers to
refereed journals and conferences. His areas of interest are graph algorithm, information security &
privacy and e-governance. He is member of CSI and ACM.
Ruchika Sharma, Dr. Vinay Kumar