A DIGITAL SCRAMBLING METHOD BASED ON BALANCING NUMBERS

Yıl 2019, Cilt: 9 Sayı: 2, 287 - 293, 01.06.2019

P. K. Ray B. K. Patel D. P. Chowdhury S. Kujur

Öz

In this article, a new approach to the study of image scrambling based on balancing numbers, balancing transformation is presented. The properties of the proposed transformation and its periodicity are studied in details. In order to reduce the periods of the balancing transformation, we separate the consecutive pixels as far as possible from each other in that domain of the digital images.

Anahtar Kelimeler

balancing numbers, Fibonacci transformation, Lucas transformation, balancing transformation, periodicity.

Kaynakça

• [1] Bai, S., Cao, C., (2002), A novel algorithm for scrambling the details of digital image, Proceeding of the 4-th world congress on Intelligent Control and Automation, pp. 1333-1336.
• [2] Behera, A., Panda, G. K., (1999), On the square roots of triangular numbers, The Fibo. Quart., 37 (2), pp. 98-105.
• [3] Bing, L., Jia-wei, X., (2005), Period of Arnold transformation and it’s application in image scrambling, J. Cent. South Univ. Tech., 12 (1), pp. 278-282.
• [4] Chang, C., Lin, I., YU, Y., (2006), A new stenographic method for color and gray scale image hiding, Computer Vision and Image Understanding, 20.
• [5] Dong-XU, Q., Jian-cheag, Z., Xiao-you, H., (2000), A new class of scrambling transformation and it’s application in the image information covering, Since in China(Series E), 43 (3), pp. 307-312.
• [6] Mishra, M., Mishra, P., Adhikary, M. C., Kumar, S., (2012), Image encryption using Fibonacci-Lucas transformation, Inter. Jour. On Cryptography and Information Security, 2(2), pp. 131-141.
• [7] Panda, G. K., (2009), Some fascinating properties of balancing numbers, Proc. of the eleventh Inter. Conf. on Fibo. Nos. and Their Applications., Congr. Numer., 194, pp. 185-189.
• [8] Panda, G. K., Ray, P. K., (2011), Some links of balancing and cobalancing numbers with Pell and associated Pell numbers, Bulletin of the Institute of Mathematics, Academia Sinica (New Series), 6(1), pp. 41-72.
• [9] Panda, G. K., Rout, S. S., (2014), Periodicity of Balancing numbers, Acta Math. Hungar., 143(2), pp. 274-286.
• [10] Patel, B. K., Ray, P. K., (2016), The Period, Rank and Order of the sequence of Balancing numbers Modulo m, Math. Reports, 18(68), pp. 395-401.
• [11] Qi, D. X., (1999), Matrix transformation and its applications to image hiding, J. North China univ. of tech., 11(1), pp. 24-28.
• [12] Wall, D. D., (1960), Fibonacci Series Modulo m, Amer. Math. Monthly, 67, pp. 525-532.
• [13] Zou, J. C., Ward, R. K., (2003), Introducing Two New Image Scrambling Methods, Proc. of IEEE Pac. Rim Conf. on Comm., Comp. and Sig. Proc., pp. 708-711.
• [14] Zou, J. C., Ward, R. K., (2003), Some novel image encryption methods based on chaotic dynamical systems, Proc. of the 9th Joint Inter. Computer Conf., Zhuhai, Chaina, pp. 188-191.
• [15] Zou, J. C., Ward, R. K., Qi, D. X., (2004), The generalized Fibonacci transformations and application to image scrambling, Proc. of the IEEE Inter. Conf. on Acoustic, Speech and Signal Proc., Canda, pp. 385-388.