Transmission of Time and Position Variable Cryptology in Fibonacci and Lucas Number Series with Music

Year 2021, , 38 - 50, 30.04.2021

Cemil Karaçam , Firdevs Nur Algül , Daniel Tavit

https://doi.org/10.33187/jmsm.885876

Abstract

Since people existed, they have prioritized confidentiality in information sharing and communication. Although there are independent studies on encryption and music in literature, no study is seen on encryption methods that are created by using the properties of mathematical number strings and can be expressed with musical instruments. The purpose in this research is to develop ideas for an effective encryption method and to create a time and location variable encryption method considering this deficiency in the literature by getting advantage of the additive feature in Fibonacci and Lucas number sequences and moving from here to develop new perspectives on encryption science. In the research letters in alphabet, numbers and 10 of the most used symbols were selected and ASCII codes were determined. The objects to be encrypted are divided into 6 main groups (uppercase vowel, uppercase consonant, lowercase vowel, lowercase consonant letters, numbers, and symbols). ASCII codes are written with the additive property of the Fibonacci and Lucas numbers (Zeckendorf's Theorem) and matched with the corresponding notes. In addition to the first method in the study, the encryption system is encrypted by shifting depending on time. In addition to this method, the encryption system was encrypted by shifting depending on the location. In the last method, the text to be encrypted was encrypted by shifting depending on both location and time. The software of the first stage of the encryption system has been created. The encryption method we have created can be transmitted in both audio and text. Since encryption can be applied with various instruments, it offers variety in terms of data privacy. In the encryption system, people who have a musical ear can audibly decipher the password regardless of the written source. In the research, the same text differs as time and location change. This method allows multiple transformations of a character in a text. With these features, it differs from the encryption methods made until now.

Keywords

Cryptology, Music, Fibonacci number, Lucas number, Ascıı code

References

• [1] C. Ozyılmaz, Introduction to Cryptology, Master Thesis, Karabuk University, 2014.
• [2] M. Aghayev, On Cryptology and Data Encryption Techniques, Master Thesis, Ege University, 2017.
• [3] Z. H. Obaıd, Comparison of Cryptology Methods, Master Thesis, Erciyes University, 2016.
• [4] S. Bakım, Investigation of the Use of Fibonacci Sequence and Golden Ratio in Music, Master Thesis, Selc¸uk University, 2014.
• [5] A. Esi, Mathematics and music, J. Awareness, 2(3S) (2017), 631–642.
• [6] C. Orhan, Matematik ve m¨uzik, Matematik D¨unyası, 6(1995), 6–7.
• [7] A. Dikici, Investigation of the Effect of Music Education Provided with Orff Technique on Mathematical Ability, Ph.D. Thesis, Ankara University, 2002.
• [8] G. Kuzuoglu, Divisibility Properties of Some Sequences Related to Fibonacci Numbers, Master Thesis, Kocaeli University, 2019.
• [9] C. Bolat, Properties and Applications of K-Fibonacci, K-Lucas Numbers, Master Thesis, Selcuk University, 2008.
• [10] G.Karadeniz, Zeckendorf Representation of Fibonacci and Pell Numbers and Integers, Master Thesis, Gazi University, 2006.
• [11] S. Nasıbov, On Cryptology Systems and Applications, Master Thesis, Ege University, 2015.
• [12] D. Tymoczko, A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice, Oxford University Press, New York, 2011.
• [13] U. Bora, A key point where science and art cross: Mathematics and music relationship, J. Uluda˘g Univ. Fac. Educ., 15(1) (2002), 53–68.
• [14] E. Riedel, The Relationship Between Music Instruction and Academic Achievement in Mathematics by Nechelle Nipper Sharpe, Walden University, USA, 2013.
• [15] G. Gogus, The relation between musical and mathematical learning success, J. Uluda˘g Univ. Fac. Educ., 21(1) (2008), 79-89.
• [16] I. Kaya, Contributions of Pythagoras and Archytas to the Mathematical Music Theory, Master Thesis, Mimar Sinan Fine Arts University, 2009.
• [17] S. Beytekin, Mathematical Analysis of Jazz on Piano and Analysis of Its Relationship with Fractal Geometry, Master Thesis, 2015.
• [18] U. Bıcak, A New Harmony Theory With Solar Voyage For Orchestra In the Context of the Relationship Between Music and Mathematics, Master Thesis, Mimar Sinan Fine Arts University, 2018.
• [19] I. Kaya, The relation between monochord string splits and harmonics, Electron. J. Soc. Sci., 16(61) (2017), 636–646.
• [20] G. E. Roberts, From Music to Mathematics: Exploring the Connections, Johns Hoplinks University Press, Baltimore, 2016.
• [21] I. Lehmann, A. Posamentier, The Fabulous Fibonacci Numbers, Prometheus Books, New York, 2007.
• [22] A. Gokhan, ASCII Codes of Lowercase & Uppercase Letters, Accessed Date: 12.10.2019, available at http://www.phpservisi.com/ kucuk-buyuk-harflerin-ascii-kodlari/.