Cohabitation of Fibonacci and Galois Modes in One Linear Feedback Shift Register

Öz

A linear feedback shift register (LFSR) is the basic element of the pseudo-random generators used to generate a sequence of pseudo-random values for a stream cipher. It consists of several cells; each cell is a flip-flop and a feedback function. The feedback function is a linear polynomial function; this function has a degree equal to the number of cells in the register. The basic elements of the register are connected to each other in two different ways, either in Fibonacci mode or in Galois mode. In this work, we propose the realization of a specific register which is cohabitation of these two modes (Fibonacci and Galois) in the same register and for the same feedback function, and which will be controlled by a random function for the selection of mode, which will be based on the chaotic logistics map. This specific register gave better results compared to registers with separate modes.

Anahtar Kelimeler

• LFSR
• cryptography
• stream cipher
• Pseudo-Random generation
• Fibonacci mode
• Galois mode
• logistic map

Kaynakça

1. [1] Schneier, B., “Applied cryptography-protocols, algorithms and source code in C”, John Wiley & Sounds, Inc, New York, Second Edition, (1996),.
2. [2] Menezes, A. J., Oorschot, P. C. V., Vanstone, S. A., “Handbook of applied cryptography” (1997) by CRC Press LLC.
3. [3] Gutub, A. A.-A., Al-Haidari, F., Al-Kahsah, K. M., Hamodi, J. “e-Text watermarking: utilizing “Kashida” extensions in Arabic language electronic writing”, J. Emerg. Technol. Web Intell. 2(1) (2010) : 48‑55.
4. [4] Gutub, A., Al-Qurashi, A., “Secure shares generation via m-blocks partitioning for counting-based secret sharing”, J. Eng. Res. 8(3) (2020) : 91‑117.
5. [5] George, M., Alfke, P., “Linear feedback shift registers in virtex devices (application note)”, http://www.xilinx.com/bvdocs/appnotes/xapp210.pdf.
6. [6] Goresky, M., Klapper, A., “Fibonacci and galois representations of feedback withcarry shift registers”, IEEE Transactions on Information Theory, 48(11) (2002) : 2826-2836.
7. [7] Stackoverflow, “Galois vs Fibonacci LFSR, more computer-friendly but what else?”, [online], nov 2011.
8. [8] Lv, Y., Tong, X., “A novel method of chaotic image encryption based on LFSR”, in 2009 International Conference on Management and Service Science, Beijing, China, sept. (2009) : 1‑4. doi: 10.1109/ICMSS.2009.5302775.

9. [9] Ayoup, A. M., Hussein, A. H., Attia, M. A. A., “Efficient selective image encryption”, Multimed. Tools Appl. 75(24) (2016): 17171‑17186.
10. [10] Kareem Jumaa, N., “Digital Image Encryption using AES and Random Number Generator”, Iraqi J. Electr. Electron. Eng. 14(1) (2018) : 80‑89.
11. [11] Naim, M., Ali Pacha, A., Serief, C., “A novel satellite image encryption algorithm based on hyperchaotic systems and Josephus problem”, Adv. Space Res. 67(7) (2021) : 2077‑2103.
12. [12] Golomb, S. W., “Shift register sequences”, Aegean Park Press, Laguna Hills, CA, (1982).
13. [13] Nyathi, J., Delgado-Frias, J. G., Lowe, J., “A high-performance, hybrid wave-pipelined linear feedback shift register with skew tolerant clocks,” 46th IEEE Midwest Symposium on Circuits and Systems, Cairo, Egypt, In Press, Dec. (2003).
14. [14] Mirella, A. M., Stratulat, M., “Study of software implementation for linear feedback shift register based on 8th degree irreducible polynomials”, International Journal Of Computers 8 (2014) : 46-55.
15. [15] Devaney, R. L., “A first course in chaotic dynamical systems theory and experiment”, New York: Westview Press, 1992. Aug 09, 2021. [online]: http://search.ebscohost.com/ login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=421133.
16. [16] Gleick, J., “Chaos: Making a New Science”, Albin Michel edition, (1987).
17. [17] Al-Roithy, B. O., Gutub, A. A., “Trustworthy image security via involving binary and chaotic gravitational searching within PRNG selections”, Int. J. Comput. Sci. Netw. Secur. 20(12) (2020) : 167‑176.
18. [18] Al-Qurashi, A., Gutub, A., “Reliable secret key generation for counting-based secret sharing”, J. Comput. Sci. Comput. Math. 8(4) (2018) 87‑101.
19. [19] Knuth, D.E., “The art of computer programming”, Addison-Wesley, Reading, MA, third edition, (1998).
20. [20] Berbain, C., “Analysis and design of stream algorithm Analysis and design of stream algorithm - in French language”, PhD thesis, University Paris 7. Diderot, supported on 10.2007, (2007).
21. [21] Gutub, A., Al-Shaarani, F., “Efficient implementation of multi-image secret hiding based on LSB and DWT steganography comparisons”, Arab. J. Sci. Eng. 45(4) (2020) : 2631‑2644.
22. [22] AlKhodaidi, T., Gutub, A., “Refining image steganography distribution for higher security multimedia counting-based secret-sharing”, Multimed. Tools Appl. 80(1) (2021) : 1143‑1173.
23. [23] Chen, G., Mao, Y., Chui, C. K., “A symmetric image encryption scheme based on 3D chaotic cat maps”, Chaos Solitons Fractals 21(3) (2004) : 749‑761.