Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31108
A Differential Calculus Based Image Steganography with Crossover

Authors: Srilekha Mukherjee, Subha Ash, Goutam Sanyal


Information security plays a major role in uplifting the standard of secured communications via global media. In this paper, we have suggested a technique of encryption followed by insertion before transmission. Here, we have implemented two different concepts to carry out the above-specified tasks. We have used a two-point crossover technique of the genetic algorithm to facilitate the encryption process. For each of the uniquely identified rows of pixels, different mathematical methodologies are applied for several conditions checking, in order to figure out all the parent pixels on which we perform the crossover operation. This is done by selecting two crossover points within the pixels thereby producing the newly encrypted child pixels, and hence the encrypted cover image. In the next lap, the first and second order derivative operators are evaluated to increase the security and robustness. The last lap further ensures reapplication of the crossover procedure to form the final stego-image. The complexity of this system as a whole is huge, thereby dissuading the third party interferences. Also, the embedding capacity is very high. Therefore, a larger amount of secret image information can be hidden. The imperceptible vision of the obtained stego-image clearly proves the proficiency of this approach.

Keywords: Steganography, Differential Calculus, crossover, peak signal to noise ratio, Cross-correlation Coefficient

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 944


[1] S. Bhattacharyya, G. Sanyal, “Hiding Data in Images Using Pixel Mapping Method (PMM)”, 'Security and Management', CSREA Press, pp. 683-689, 2010.
[2] R. Chandramouli, M. Kharrazi, N. Memon, “Image Steganography and Steganalysis Concepts and Practice”, Ton Kalker; Ingemar J. Cox & Yong Man Ro, ed., 'IWDW, Springer, pp. 35-49, 2003.
[3] T. Morkel, J. H. P. Eloff, M. S. Olivier, “An Overview of Image Steganography”, Paper presented at the meeting of the ISSA, Pretoria, South Africa, pp. 1-11, 2005.
[4] T. Kumar, A. Pareek, J. Kirori, M.S. Nehra, “Development of Crossover and Encryption based Text Steganography (CEBTS) Technique”, Emerging Trends in Computing and Communication, lecture notes in Electrical Engineering, vol 298, 2014 pp. 103-111.
[5] T. Apostol, Wiley, “Calculus.2. Multi-variable Calculus and Linear Algebra, with Applications to Differential Equations and Probability”, 1969.
[6] J. Fridrich, M. Goljan, and R. Du, “Detecting LSB Steganography in Color and Gray-Scale Images,” Magazine of IEEE Multimedia Special Issue on Security, pp. 22-28, Nov. 2001.
[7] BU Long, HU Bo. “An improved steganographic method by pixel value differencing,” Journal of circuits and systems, 11(3), pp. 9-13, 2006.
[8] Wang Chung-Ming, Wu Nan-i, Tsai Chwei-shyong, et al. “A High Quality Steganographic Method with Pixel Value Differencing and Modulus Function,” Journal of Systems and Software, pp. 150-158, 2008.
[9] P Huang. K.C. Chang., C.P Chang. and T.M Tu. “A Novel Image Steganography Method Using Tri-way Pixel Value Differencing”. Journal of Multimedia, 3, 2008.
[10] V. Potdar, E. Chang. “Gray Level Modification Steganography for Secret Communication”. IEEE International Conference on Industrial Informatics, Berlin, Germany, pp. 355–368, 2004.
[11] Ahmad T. Al-Taani., Abdullah M. AL-Issa, “A Novel Steganographic Method for Gray-Level Images”. International Journal of Computer, Information, and Systems Science, and Engineering, pp. 3, 2009.
[12] S. Bhattacharyya, A. Khan, A. Nandi, A. D. Malakar, S. Roy and G. Sanyal, “Pixel Mapping Method (PMM) Based Bit Plane Complexity Segmentation (BPCS) Steganography” at WICT (World Congress on Information and Communication Technologies), 2011.
[13] T.-H. Lan; M. F. Mansour, & A. H. Tewfik, Robust High Capacity Data Embedding, in 'ICIP', pp. 581-584, 2000.
[14] A. Almohammad, G. Ghinea., “Stego-image Quality and the Reliability of PSNR” Image Processing Theory, Tools and Applications, IEEE, 2010.
[15] S. Bhattacharyya, G. Sanyal, “Study and Analysis of Quality of Service in Different Image Based Steganography using Pixel Mapping Method”, International Journal of Applied Information Systems (UAIS)-ISSN: 2249-0868, pp. 42-57, 2012.
[16] N. Sai, R. C. Patil, “Image Retrieval using Equalized Histogram Image Bins Moments” International Journal on Signal & Image Processing 2 (1), 4, 2011.
[17] E. Verhulp, B. Rietbergen, R. Huiskes, “A Three-Dimensional Digital Image Correlation Technique for Strain Measurements in Microstructures”, Journal of Biomechanics 37 (9), 1313—1320, 2004.
[18] R. Lundin, S. Lindskog, “An investigation of entropy of selectively encrypted bitmap images” in 'CASoN', IEEE, pp. 238-243, 2012.
[19] S. Hemalatha, U. D. Acharya, A. Renuka, P. R. Kamath, “A Secure and High Capacity Image Steganography Technique”, CoRR abs/1304.3629, 2013.
[20] D. C. Rupa, B. Saijyothi, P. S. Avadhani, “A Novel Approach Text Steganography using cheating text by Genetic Operator Crossover”, IJARCS, Vol 2, 01/2011.
[21] C. Cachin, “An Information-Theoretic Model for Steganography”, IACR Cryptology ePrint Archive, pp. 28, 2000.
[22] A. Dermoune, “Differential calculus relative to some point processes”, Statistics & Probability Letters 24 (3), 233-242, 1995.
[23] G. A. K. Mahesh D. Pawar, V. P. Pawar, “Study and Performance Analysis of De-Blurring Techniques for Distorted Medical Images”, indian streams research journal 4 (4), 2014.
[24] E. N. Kirsanova, M. G. Sadovsky, “'Entropy Approach to Comparison of Images”, Open Syst. Inform. Dynam.8 (2), 183-200, 2001.
[25] Dr. V. Vijayalakshmi, Dr. G. Zayaraz, and V. Nagaraj, “A Modulo Based LSB Steganography Method”, international conference on control, automation, communication and energy conservation, 4th-6th June 2009, pp. 1 – 4, 2009.