Generation of cryptographic keys with algorithm of polygon triangulation and catalan numbers

• Autorzy: Saracevic M. , Selimi A. , Selimovic F.

Identyfikatory

DOI

10.7494/csci.2018.19.3.2749

• Języki publikacji: EN

Abstrakty

EN

In this paper, a procedure for the application of one computational geometry algorithm in the process of generating hidden cryptographic keys from one segment of a 3D image is presented. The presented procedure consists of three phases. In the first phase, the separation of one segment from the 3D image and determination of the triangulation of the separated polygon are done. In the second phase, a conversion from the obtained triangulation of the polygon in the record that represents the Catalan key is done. In the third phase, the Catalan-key is applied in the encryption of the text based on the balanced parentheses combinatorial problem.

Słowa kluczowe

EN

computational geometry; polygon triangulation; Catalan numbers; cryptography; hidden cryptographic keys

• Wydawca: Wydawnictwa AGH
• Czasopismo: Computer Science
• Rocznik: 2018
• Tom: Vol. 19 (3)
• Strony: 243--256
• Opis fizyczny: Bibliogr. 13 poz., rys., tab.

Twórcy

autor

Saracevic M.

• University of Novi Pazar, Department of Computer Sciences, Serbia

autor

Selimi A.

• International Vision University, Faculty of Informatics, Macedonia

autor

Selimovic F.

• University of Novi Pazar, Department of Computer Sciences, Serbia

Bibliografia

• [1] Amounas F., El-Kinani E.H., Hajar M.: Novel Encryption Schemes Based on Catalan Numbers, International Journal of Information and Network Security, vol. 2(4), pp. 339-347, 2013.
• [2] Cohen E., Hansen T., Itzhaki N.: From entanglement witness to generalized Catalan numbers, Scientic Reports, 6:30232, pp. 1-10, 2016.
• [3] Higgins P.M.: Number Story: From Counting to Cryptography, Springer Science and Business Media, Berlin, Germany, 2008.
• [4] Horak P., Semaev I., Tuza I.Z.: An application of Combinatorics in Cryptography, Electronic Notes in Discrete Mathematics, vol. 49, pp. 31-35, 2015.
• [5] Koshy T.: Catalan Numbers with Applications. Oxford University Press, New York, 2009.
• [6] Kościelny C., Kurkowski M., Srebrny M.: Modern Cryptography Primer: Theoretical Foundations and Practical Applications, Springer Science and Business Media, Berlin, Germany, 2013.
• [7] Lachaud G., Ritzenthaler C., Tsfasman M.A.: Arithmetic, Geometry, Cryptography, and Coding Theory, American Mathematical Society, USA, 2009.
• [8] Saracevic M., Stanimirovic P., Masovic S., Bisevac E.: Implementation of the convex polygon trangulation algorithm. Facta Universitatis, Series Mathematics and Informatics, vol. 27(2), pp. 213-228, 2012.
• [9] Saracevic M.: Application of Catalan numbers and some combinatorial problems in cryptography (Bachelor's thesis), Faculty of Informatics and Computing, Singidunum University in Belgrade, 2017.
• [10] Saracevic M., Koricanin E., Bisevac E.: Encryption based on Ballot, Stack permutations and Balanced Parentheses using Catalan-keys, Journal of Information Technology and Applications, vol. 14(2), pp. 69-77, 2017.
• [11] Saracevic M.: Methods for solving the polygon triangulation problem and their implementation (PhD thesis), University of Nis, Serbia, 2013.
• [12] Stanimirovic P., Krtolica P., Saracevic M., Masovic S.: Decomposition of Catalan numbers and convex polygon triangulations, International Journal of Computer Mathematics, vol. 91(6), pp. 1315-1328, 2014.
• [13] Stanley R.P.: Catalan addendum to Enumerative Combinatorics, http://www-math.mit.edu/~rstan/ec/catadd.pdf [Available 24.05.2017.]

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).