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Polynomial Representation of Vernam Cipher

Year 2024, Volume: 45 Issue: 3, 557 - 561, 30.09.2024

Emin Aygun , İncinur Yılmaz

https://doi.org/10.17776/csj.1418207

Abstract

Storing information or data has been one of the basic needs of humans for many years and these needs have led to the existence of some systems throughout the years. In this paper, soft sets represented by polynomials will be encrypted and decrypted in line with their representations. We are going to use the Rijndael Algorithm for soft sets and then encrypt and decrypt the data in accordance with its algorithm. The Rijndael algorithm is an algorithm which carries out the cyclic process according to the keys it has. At the end of each loop, the key is renewed and is applied to the data. These data are firstly shown in strings. While enumerating, it starts with zero index and ends with one less than string length.

Keywords

Soft Sets Encryption Decryption Vernam Cipher Stream Cipher

References

  • [1] Aktaş H., Çağman N., Soft Sets and Soft Groups, Information Sciences, 177 (2007) 2726-2735.
  • [2] Aktaş H., Çağman N., Erratum to “Soft Sets and Soft Groups”, Information Sciences 3 (2009), 338. Information Sciences, 177 (2007) 272-2735.
  • [3] Atagün A.O., Sezgin A., Soft Substructures Of Rings, Fields and Modules, Computers & Mathematics With Applications, 61 (3) (2011) 592-601.
  • [4] Zadeh L.A., Fuzzy Sets, Information and Control, 8 (1965) 338-353.
  • [5] Zadeh L.A., Toward A Generalized Theory Of Uncertainty (GTU)-An Outline, Information Sciences, 172 (2005) 1-40.
  • [6] Gorzalzany M.B., A Method Of Inference In Approximate Reasoning Based On Interval-Valued Fuzzy Sets, Fuzzy Set and Systems, 21 (1987) 1-17.
  • [7] Dmitry M., Soft Sets Theory – First Results, Computers & Mathematics With Applications, 37 (1999) 19-31.
  • [8] Atagün A.O., Kamacı H., Oktay O., Reduced Soft Matrices and Generalized Products With Applications In Decision Making, Neural Computing and Applications, 29 (2018) 445-456.
  • [9] Aygün E., Soft Matrix Product and Soft Cryptosystem, Filomath, 32 (19) (2018) 6519-6530.
  • [10] Hashim H.R., Husain A.M., Vernem Cipher Over A Soft Set, Globakl Journal Of Mathematics, 5 (2) (2015) 2395-4760.
  • [11] Rosen K.H., Elementary Number Theory, and Its Applications. 5th Edn., United States of America, Boston, (2005) 363.
  • [12] Aygün E., Yılmaz İ., Esnek Kümeler Ve Vernam Şifreleme Üzerine, 3. Başkent International Conference On Multidisciplinary Studies Full Text Book, 3. Başkent International Conference On Multidisciplinary Studies, Ankara, 2022, 1108-1115.

Year 2024, Volume: 45 Issue: 3, 557 - 561, 30.09.2024

Emin Aygun , İncinur Yılmaz

https://doi.org/10.17776/csj.1418207

Abstract

References

  • [1] Aktaş H., Çağman N., Soft Sets and Soft Groups, Information Sciences, 177 (2007) 2726-2735.
  • [2] Aktaş H., Çağman N., Erratum to “Soft Sets and Soft Groups”, Information Sciences 3 (2009), 338. Information Sciences, 177 (2007) 272-2735.
  • [3] Atagün A.O., Sezgin A., Soft Substructures Of Rings, Fields and Modules, Computers & Mathematics With Applications, 61 (3) (2011) 592-601.
  • [4] Zadeh L.A., Fuzzy Sets, Information and Control, 8 (1965) 338-353.
  • [5] Zadeh L.A., Toward A Generalized Theory Of Uncertainty (GTU)-An Outline, Information Sciences, 172 (2005) 1-40.
  • [6] Gorzalzany M.B., A Method Of Inference In Approximate Reasoning Based On Interval-Valued Fuzzy Sets, Fuzzy Set and Systems, 21 (1987) 1-17.
  • [7] Dmitry M., Soft Sets Theory – First Results, Computers & Mathematics With Applications, 37 (1999) 19-31.
  • [8] Atagün A.O., Kamacı H., Oktay O., Reduced Soft Matrices and Generalized Products With Applications In Decision Making, Neural Computing and Applications, 29 (2018) 445-456.
  • [9] Aygün E., Soft Matrix Product and Soft Cryptosystem, Filomath, 32 (19) (2018) 6519-6530.
  • [10] Hashim H.R., Husain A.M., Vernem Cipher Over A Soft Set, Globakl Journal Of Mathematics, 5 (2) (2015) 2395-4760.
  • [11] Rosen K.H., Elementary Number Theory, and Its Applications. 5th Edn., United States of America, Boston, (2005) 363.
  • [12] Aygün E., Yılmaz İ., Esnek Kümeler Ve Vernam Şifreleme Üzerine, 3. Başkent International Conference On Multidisciplinary Studies Full Text Book, 3. Başkent International Conference On Multidisciplinary Studies, Ankara, 2022, 1108-1115.
There are 12 citations in total.

Details

Primary Language English
Subjects Quantitative Decision Methods , Numerical Analysis, Numerical and Computational Mathematics (Other)
Journal Section Natural Sciences
Authors

Emin Aygun 0000-0003-3503-0552

İncinur Yılmaz 0000-0001-6481-8918

Publication Date September 30, 2024
Submission Date January 11, 2024
Acceptance Date June 24, 2024
Published in Issue Year 2024Volume: 45 Issue: 3

Cite

APA Aygun, E., & Yılmaz, İ. (2024). Polynomial Representation of Vernam Cipher. Cumhuriyet Science Journal, 45(3), 557-561. https://doi.org/10.17776/csj.1418207
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