International Journal of Computer & Mathematical Sciences IJCMS ISSN 2347 – 8527 Volume 4, Special Issue May 2015 Implementation of Steganogrphy using Recursive Equation Approach 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 information. Keywords: BMP, Steganography, Digital cover 1.Introduction 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 [1,2]. 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: i) Embedding algorithm ii) Extraction algorithm iii) 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]. 15 Ruchika Sharma, Dr. Vinay Kumar International Journal of Computer & Mathematical Sciences IJCMS ISSN 2347 – 8527 Volume 4, Special Issue May 2015 Steganography is classified as follows: 1.1 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 1.2 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 16 Ruchika Sharma, Dr. Vinay Kumar International Journal of Computer & Mathematical Sciences IJCMS 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, 17 Ruchika Sharma, Dr. Vinay Kumar International Journal of Computer & Mathematical Sciences IJCMS 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 a) It helps in improving the hidden communication techniques by randomizing the location of hiding information in digital cover. b) 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. c) The confidentiality of secret information is ensured, even under the suspicion that Secret information is being communicated. d) 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. e) 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. Acknowledgement 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. References 1. Anderson, R. and Petit colas, F., (1998). „On the limits of steganography‟. IEEE Journal on Selected Areas in Communications, Vol. 16, No. 4, pp.474–481. 2. Aspert, N., Drelie, E., Maret, Y. and Ebrahimi, T., (2002). „Steganography for ThreeDimensional Polygonal Meshes‟. Proceedings of SPIE, 47th Annual Meeting, pp 705-708. 3. Bender, W., Gruhl, D., Morimoto, N. and Lu, A. (1996). „Techniques for data hiding‟. IBM Systems Journal, Vol. 35, Nos. 3–4, pp.313–336. 4. Birgit Pfitzmann and Matthias Schunter, Asymmetric fingerprinting, Advances in Cryptology: EUROCRYPT '96 (Ueli Maurer, ed.), Lecture Notes in Computer Science, vol.1233, Springer, 1996. 18 Ruchika Sharma, Dr. Vinay Kumar International Journal of Computer & Mathematical Sciences IJCMS ISSN 2347 – 8527 Volume 4, Special Issue May 2015 5. Birgit Pfitzmann and Michael Waidner, Anonymous fingerprinting, Advances in Cryptology: EUROCRYPT '97 (Walter Fumy, ed.), Lecture Notes in Computer Science, vol.1070, Springer, 1997. 6. Cole, E., (2003). Hiding in Plain Sight: Steganography and the Art of Covert Communication. USA: Wiley Publishing. 7. Hamid. A. Jalab, A. A Zaidan, B. B Zaidan, “New Design for Information Hiding with in Steganography Using Distortion Techniques”, International Journal of Engineering and Technology(IJET)), Vol 2, No. 1, ISSN: 1793-8236, Feb (2010), Singapore. 8. Ingemar J. Cox, Matthew L. Miller, Jeffrey A. Bloom, Jessica Fridrich and Ton Kalkar, s(2007). Digital Watermarking and Steganography. USA: Morgan Kaufmann Publishers. 9. Johnson, N.F. and Jajodia, S. (1998). „Exploring Steganography: Seeing the Unseen‟. IEEE Computer, February, pp. 26-34. 10. Johnson, N.F. and Jajodia, S., (1998a, April). „Steganalysis of Images Created Using Current Steganography Software‟. Proceedings of the Second Information Hiding Workshop, Portland, Oregon, USA, Vol. 1525, pp 273-289. 11. Katzenbeisser, S. and Petitcolas, F. A. P., (2000). Information Hiding Techniques for teganography and Digital Watermarking. Norwood, MA: Artech House. 12. kumar Vinay and Kumar Sunil, September(2011), „A Graph Theoretic Approach to Sustainable Steganography‟, MIS Review Vol. 17, No. 1, September (2011), pp. 19-37 13. Neil F. Johnson, Zoran Duric, Sushil Jajodia “Information Hiding-Steganography and Watermarking-Attacks and Countermeasures” Ed. III, Kluwer Academic Publisher, 2000 ISBN 0-7923-7204-2 14. Zaidoon Kh. AL-Ani, A.A.Zaidan, B.B.Zaidan and Hamdan.O.Alanazi,” Main Fundamentals for Steganography” JOURNAL OF COMPUTING, VOLUME 2, ISSUE 3, MARCH 2010, ISSN 2151-9617. 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 University. 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. 19 Ruchika Sharma, Dr. Vinay Kumar

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