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A New Application to Coding Theory via Fibonacci and Lucas Numbers

Year 2019, Volume: 7 Issue: 1, 62 - 70, 30.04.2019
https://doi.org/10.36753/mathenot.559251

Abstract

Coding/decoding algorithms are of great importance to help in improving information security since
information security is a more significant problem in recent years. In this paper we introduce two new
coding/decoding algorithms using Fibonacci Q-matrices and R-matrices. Our models are based on the
blocked message matrices and the encryption of each message matrix with different keys. These new
algorithms will not only increase the security of information but also has high correct ability.

References

  • [1] Basu, M. and Prasad, B., The generalized relations among the code elements for Fibonacci coding theory. Chaos Solitons Fractals 41 (2009), no. 5, 2517-2525.
  • [2] Bruggles I. D. and Jr Hoggatt, V. E., A Primer for the Fibonacci numbers-Part IV. Fibonacci Q. 1 (1963), no.4, 65-71.
  • [3] Gould, H.W., A history of the Fibonacci Q-matrix and a higher-dimensional problem. Fibonacci Quart. 19 (1981), no. 3, 250-257.
  • [4] Hoggat, V. E., Fibonacci and Lucas Numbers. Houghton-Mifflin. Palo Alto, 1969.
  • [5] Koshy, T., Fibonacci and Lucas numbers with applications. New York, NY: JohnWiley and Sons, 2001.
  • [6] Kuhapatanakul, K., The Lucas p-matrix. Internat. J. Math. Ed. Sci. Techn. (2015). http://dx.doi.org/10.1080/0020739X.2015.1026612
  • [7] Prajapat, S., Jain, A. and Thakur, R. S., A novel approach for information security with automatic variable key using Fibonacci Q-matrix. IJCCT 3 (2012), no. 3, 54-57.
  • [8] Prasad, B., Coding theory on Lucas p-numbers. Discrete Math. Algorithms Appl. 8 (2016), no.4, 17 pages.
  • [9] Stakhov, A. P., A generalizition of the Fibonacci Q-matrix. Rep. Natl. Acad. Sci. Ukraine 9 (1999), 46-49.
  • [10] Stakhov, A., Massingue, V. and Sluchenkov, A., Introduction into Fibonacci coding and cryptography. Osnova, Kharkov, 1999.
  • [11] Stakhov, A. P., Fibonacci matrices, a generalization of the Cassini formula and a new coding theory. Chaos Solitons Fractals 30 (2006), no. 1, 56-66.
  • [12] Tarle, B. S. and Prajapati, G. L., On the information security using Fibonacci series. International Conference and Workshop on Emerging Trends in Technology (ICWET 2011)-TCET, Mumbai, India.
  • [13] Taş, N., Uçar, S., Özgür, N. Y. and Kaymak, Ö. Ö., A new coding/decoding algorithm using Finonacci numbers. Discrete Math. Algorithms Appl. 10 (2018), no. 02, 1850028.
  • [14] Wang, F., Ding, J., Dai, Z. and Peng, Y., An application of mobile phone encryption based on Fibonacci structure of chaos. 2010 Second WRI World Congress on Software Engineering.
Year 2019, Volume: 7 Issue: 1, 62 - 70, 30.04.2019
https://doi.org/10.36753/mathenot.559251

Abstract

References

  • [1] Basu, M. and Prasad, B., The generalized relations among the code elements for Fibonacci coding theory. Chaos Solitons Fractals 41 (2009), no. 5, 2517-2525.
  • [2] Bruggles I. D. and Jr Hoggatt, V. E., A Primer for the Fibonacci numbers-Part IV. Fibonacci Q. 1 (1963), no.4, 65-71.
  • [3] Gould, H.W., A history of the Fibonacci Q-matrix and a higher-dimensional problem. Fibonacci Quart. 19 (1981), no. 3, 250-257.
  • [4] Hoggat, V. E., Fibonacci and Lucas Numbers. Houghton-Mifflin. Palo Alto, 1969.
  • [5] Koshy, T., Fibonacci and Lucas numbers with applications. New York, NY: JohnWiley and Sons, 2001.
  • [6] Kuhapatanakul, K., The Lucas p-matrix. Internat. J. Math. Ed. Sci. Techn. (2015). http://dx.doi.org/10.1080/0020739X.2015.1026612
  • [7] Prajapat, S., Jain, A. and Thakur, R. S., A novel approach for information security with automatic variable key using Fibonacci Q-matrix. IJCCT 3 (2012), no. 3, 54-57.
  • [8] Prasad, B., Coding theory on Lucas p-numbers. Discrete Math. Algorithms Appl. 8 (2016), no.4, 17 pages.
  • [9] Stakhov, A. P., A generalizition of the Fibonacci Q-matrix. Rep. Natl. Acad. Sci. Ukraine 9 (1999), 46-49.
  • [10] Stakhov, A., Massingue, V. and Sluchenkov, A., Introduction into Fibonacci coding and cryptography. Osnova, Kharkov, 1999.
  • [11] Stakhov, A. P., Fibonacci matrices, a generalization of the Cassini formula and a new coding theory. Chaos Solitons Fractals 30 (2006), no. 1, 56-66.
  • [12] Tarle, B. S. and Prajapati, G. L., On the information security using Fibonacci series. International Conference and Workshop on Emerging Trends in Technology (ICWET 2011)-TCET, Mumbai, India.
  • [13] Taş, N., Uçar, S., Özgür, N. Y. and Kaymak, Ö. Ö., A new coding/decoding algorithm using Finonacci numbers. Discrete Math. Algorithms Appl. 10 (2018), no. 02, 1850028.
  • [14] Wang, F., Ding, J., Dai, Z. and Peng, Y., An application of mobile phone encryption based on Fibonacci structure of chaos. 2010 Second WRI World Congress on Software Engineering.
There are 14 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Sümeyra Uçar

Nihal Taş This is me

Nihal Yılmaz Özgür This is me

Publication Date April 30, 2019
Submission Date January 18, 2018
Published in Issue Year 2019 Volume: 7 Issue: 1

Cite

APA Uçar, S., Taş, N., & Özgür, N. Y. (2019). A New Application to Coding Theory via Fibonacci and Lucas Numbers. Mathematical Sciences and Applications E-Notes, 7(1), 62-70. https://doi.org/10.36753/mathenot.559251
AMA Uçar S, Taş N, Özgür NY. A New Application to Coding Theory via Fibonacci and Lucas Numbers. Math. Sci. Appl. E-Notes. April 2019;7(1):62-70. doi:10.36753/mathenot.559251
Chicago Uçar, Sümeyra, Nihal Taş, and Nihal Yılmaz Özgür. “A New Application to Coding Theory via Fibonacci and Lucas Numbers”. Mathematical Sciences and Applications E-Notes 7, no. 1 (April 2019): 62-70. https://doi.org/10.36753/mathenot.559251.
EndNote Uçar S, Taş N, Özgür NY (April 1, 2019) A New Application to Coding Theory via Fibonacci and Lucas Numbers. Mathematical Sciences and Applications E-Notes 7 1 62–70.
IEEE S. Uçar, N. Taş, and N. Y. Özgür, “A New Application to Coding Theory via Fibonacci and Lucas Numbers”, Math. Sci. Appl. E-Notes, vol. 7, no. 1, pp. 62–70, 2019, doi: 10.36753/mathenot.559251.
ISNAD Uçar, Sümeyra et al. “A New Application to Coding Theory via Fibonacci and Lucas Numbers”. Mathematical Sciences and Applications E-Notes 7/1 (April 2019), 62-70. https://doi.org/10.36753/mathenot.559251.
JAMA Uçar S, Taş N, Özgür NY. A New Application to Coding Theory via Fibonacci and Lucas Numbers. Math. Sci. Appl. E-Notes. 2019;7:62–70.
MLA Uçar, Sümeyra et al. “A New Application to Coding Theory via Fibonacci and Lucas Numbers”. Mathematical Sciences and Applications E-Notes, vol. 7, no. 1, 2019, pp. 62-70, doi:10.36753/mathenot.559251.
Vancouver Uçar S, Taş N, Özgür NY. A New Application to Coding Theory via Fibonacci and Lucas Numbers. Math. Sci. Appl. E-Notes. 2019;7(1):62-70.

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