Text Encryption and Decryption using Mathematical Functions
Keywords:
Cryptographic Theorems, Ciphers, Playfair Cipher's
Abstract
One of the most important challenges that the world is still facing until now is the issue of information security and preservation From breach and change. Cryptography is the answer to this question. This science includes many ancient ciphers (classic), which was used to encrypt phrases and text messages. Among these ciphers are the Playfair cipher and the cipher cipher. Veginer of all kinds. These ciphers help secure the confidentiality of information, but they have the disadvantage that they are easy to break. That's because their algorithms rely on a single key for encryption and decryption. In order to increase the degree of security and confidentiality of the information, the complete VIGENER cipher has been developed in its numerical form to the matrix image to become more complex. And to obtain encrypted messages and phrases as well as re-decrypt them With the fastest time and the least effort, a program designed for the complete Visioner code was used on MATLAB.
References
1. T. Radożycki, Solving Problems in Mathematical Analysis, Part I: Sets, Functions, Limits, Derivatives, Integrals, Sequences and Series. books.google.com, 2020. [Online]. Available: https://books.google.com/books?hl=en&lr=&id=W-
7RDwAAQBAJ&oi=fnd&pg=PR5&dq=mathematical+functions&ots=aOaTlE3Obc&sig=r6DzaNC-WKA3ZVTcJBttrC_J3HQ
2. V. Innocente and P. Zimmermann, Accuracy of Mathematical Functions in Single, Double, Double Extended, and Quadruple Precision. homepages.loria.fr, 2021. [Online]. Available: https://homepages.loria.fr/PZimmermann/papers/glibc234-20210907.pdf
3. G. Urcid, R. Morales-Salgado, and M. Mares-Javier, “Analysis and Evaluation of Real-valued Functions in Mathematical Morphology,” academia.edu, [Online]. Available: https://www.academia.edu/download/97365813/E12013346.pdf
4. J. García-García, “Mathematical Understanding Based on the Mathematical Connections Made by Mexican High School Students Regarding Linear Equations and Functions,” The Mathematics Enthusiast, 2024, [Online]. Available: https://scholarworks.umt.edu/tme/vol21/iss3/7/
5. F. Mainardi, Special functions with applications to mathematical physics. mdpi.com, 2023. [Online]. Available: https://www.mdpi.com/books/reprint/7016
6. T. M. Gataullin and S. T. Gataullin, “Endpoint functions: mathematical apparatus and economic applications,” Mathematical Notes, 2022, doi: 10.1134/S0001434622110037.
7. N. E. Ndlovu, “Exploring learners’ understanding of mathematical concepts necessary in the learning of grade 11 algebraic functions: the case of three schools in ….” 2019.
8. O. Kryazhych and O. Kovalenko, “Examining a mathematical apparatus of Z-approximation of functions for the construction of an adaptive algorithm,” Восточно-Европейский журнал …, 2019, [Online]. Available: http://www.irbis-nbuv.gov.ua/cgi-bin/irbis_nbuv/cgiirbis_64.exe?I21DBN=LINK&P21DBN=UJRN&Z21ID=&S21REF=10&S21CNR=20&S21STN=1&S21FMT=ASP_meta&C21COM=S&2_S21P03=FILA=&2_S21STR=Vejpte_2019_3(4)__2
9. K. G. Campo-Meneses, V. Font, J. García-García, and ..., “Mathematical connections activated in high school students’ practice solving tasks on the exponential and logarithmic functions,” EURASIA Journal of …, 2021, [Online]. Available: https://www.ejmste.com/article/mathematical-connections-activated-in-high-school-students-practice-solving-tasks-on-the-exponential-11126
10. M. Hemery, F. Fages, and S. Soliman, “Compiling elementary mathematical functions into finite chemical reaction networks via a polynomialization algorithm for ODEs,” … September 22–24, 2021, Proceedings 19, 2021, doi: 10.1007/978-3-030-85633-5_5.
11. F. Mainardi and A. Consiglio, “The Wright functions of the second kind in Mathematical Physics,” Mathematics, 2020, [Online]. Available: https://www.mdpi.com/2227-7390/8/6/884
12. V. S. Ilkiv, Z. M. Nytrebych, P. Y. Pukach, and ..., “Analysis of measurement systems mathematical models by using the comparison of functions,” Mathematical …, 2019, [Online]. Available: http://jnas.nbuv.gov.ua/j-pdf/mmc_2019_6_2_12.pdf
A. Tabieh, “A teaching model impact of learning outcomes for mathematical content in functions,” Opción, 2020, [Online]. Available: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3685857
13. L. Siqing and L. Zhou, “AN EXPLORATION OF INTEGRATING MATHEMATICAL MODELING IDEAS IN TEACHING APPLICATION OF FUNCTIONS,” researchgate.net, [Online]. Available: https://www.researchgate.net/profile/Lili-Zhou-27/publication/375519330_AN_EXPLORATION_OF_INTEGRATING_MATHEMATICAL_MODELING_IDEAS_IN_TEACHING_APPLICATION_OF_FUNCTIONS/links/654d1c70ce88b87031d8b47e/AN-EXPLORATION-OF-INTEGRATING-MATHEMATICAL-MODELING-IDEAS-IN-TEACHING-APPLICATION-OF-FUNCTIONS.pdf
14. A. Firsova and G. Y. Chernyshova, “Mathematical models for evaluation of the higher education system functions with DEA approach,” … университета. Новая серия …, 2019, [Online]. Available: https://cyberleninka.ru/article/n/mathematical-models-for-evaluation-of-the-higher-education-system-functions-with-dea-approach
15. D. Cattaneo, M. Chiari, G. Magnani, N. Fossati, and ..., “FixM: Code generation of fixed point mathematical functions,” … Informatics and Systems, 2021, [Online]. Available: https://www.sciencedirect.com/science/article/pii/S2210537920302018
16. K. G. Campo-Meneses and ..., “Mathematical Connections Related to Exponential and Logarithmic Functions: A Literature Review,” RANGE: Jurnal …, 2023, [Online]. Available: http://jurnal.unimor.ac.id/index.php/JPM/article/view/4738
17. K. S. Sørensen, On some differential equations in mathematical-physics and singular functions in probability theory. vbn.aau.dk, 2022. [Online]. Available: https://vbn.aau.dk/files/549497701/PHD_KStudsgaardS_rensen.pdf
18. Kusmaryono, H. Suyitno, D. Dwijanto, and ..., “The Effect of Mathematical Disposition on Mathematical Power Formation: Review of Dispositional Mental Functions.,” International Journal of …, 2019, [Online]. Available: https://eric.ed.gov/?id=EJ1201186
19. Suklabaidya, M., Das, A., & Das, B. (2018). A cryptography model using hybrid encryption and decryption techniques. International Journal of Computational Intelligence & IoT, 2(4).
20. Agbedemnab, P. A. N., Baagyere, E. Y., & Daabo, M. I. (2019, October). A Novel Text Encryption and Decryption Scheme using the Genetic Algorithm and Residual Numbers. In ICICIS (pp. 20-31).
21. Singh, L. D., & Singh, K. M. (2015). Implementation of text encryption using elliptic curve cryptography. Procedia Computer Science, 54, 73-82.
22. Singh, J., Lata, K., & Ashraf, J. (2015). Image encryption & decryption with symmetric key cryptography using MATLAB. International Journal of Current Engineering and Technology, 5(1), 448-451.
23. Dhany, H. W., Izhari, F., Fahmi, H., Tulus, M., & Sutarman, M. (2017, October). Encryption and decryption using password based encryption, MD5, and DES. In International Conference on Public Policy, Social Computing and Development 2017 (ICOPOSDev 2017) (pp. 278-283). Atlantis Press.
24. Patil, P., & Bansode, R. (2020). Performance evaluation of hybrid cryptography algorithm for secure sharing of text & images. International Research Journal of Engineering and Technology, 7(9), 3773-3778.
25. Babaei, M. (2013). A novel text and image encryption method based on chaos theory and DNA computing. Natural computing, 12(1), 101-107.
26. Karudaiyar, G., Karthikeyan, S., & Sainath, B. (2014). Encryption and Decryption Scheme by Using Finite State Machine. Biosciences Biotechnology Research Asia, 11(3), 1867-1872.
27. Goyal, R., & Khurana, M. (2017). Cryptographic security using various encryption and decryption method. International Journal of Mathematical Sciences and Computing (IJMSC), 3(3), 1-11.
7RDwAAQBAJ&oi=fnd&pg=PR5&dq=mathematical+functions&ots=aOaTlE3Obc&sig=r6DzaNC-WKA3ZVTcJBttrC_J3HQ
2. V. Innocente and P. Zimmermann, Accuracy of Mathematical Functions in Single, Double, Double Extended, and Quadruple Precision. homepages.loria.fr, 2021. [Online]. Available: https://homepages.loria.fr/PZimmermann/papers/glibc234-20210907.pdf
3. G. Urcid, R. Morales-Salgado, and M. Mares-Javier, “Analysis and Evaluation of Real-valued Functions in Mathematical Morphology,” academia.edu, [Online]. Available: https://www.academia.edu/download/97365813/E12013346.pdf
4. J. García-García, “Mathematical Understanding Based on the Mathematical Connections Made by Mexican High School Students Regarding Linear Equations and Functions,” The Mathematics Enthusiast, 2024, [Online]. Available: https://scholarworks.umt.edu/tme/vol21/iss3/7/
5. F. Mainardi, Special functions with applications to mathematical physics. mdpi.com, 2023. [Online]. Available: https://www.mdpi.com/books/reprint/7016
6. T. M. Gataullin and S. T. Gataullin, “Endpoint functions: mathematical apparatus and economic applications,” Mathematical Notes, 2022, doi: 10.1134/S0001434622110037.
7. N. E. Ndlovu, “Exploring learners’ understanding of mathematical concepts necessary in the learning of grade 11 algebraic functions: the case of three schools in ….” 2019.
8. O. Kryazhych and O. Kovalenko, “Examining a mathematical apparatus of Z-approximation of functions for the construction of an adaptive algorithm,” Восточно-Европейский журнал …, 2019, [Online]. Available: http://www.irbis-nbuv.gov.ua/cgi-bin/irbis_nbuv/cgiirbis_64.exe?I21DBN=LINK&P21DBN=UJRN&Z21ID=&S21REF=10&S21CNR=20&S21STN=1&S21FMT=ASP_meta&C21COM=S&2_S21P03=FILA=&2_S21STR=Vejpte_2019_3(4)__2
9. K. G. Campo-Meneses, V. Font, J. García-García, and ..., “Mathematical connections activated in high school students’ practice solving tasks on the exponential and logarithmic functions,” EURASIA Journal of …, 2021, [Online]. Available: https://www.ejmste.com/article/mathematical-connections-activated-in-high-school-students-practice-solving-tasks-on-the-exponential-11126
10. M. Hemery, F. Fages, and S. Soliman, “Compiling elementary mathematical functions into finite chemical reaction networks via a polynomialization algorithm for ODEs,” … September 22–24, 2021, Proceedings 19, 2021, doi: 10.1007/978-3-030-85633-5_5.
11. F. Mainardi and A. Consiglio, “The Wright functions of the second kind in Mathematical Physics,” Mathematics, 2020, [Online]. Available: https://www.mdpi.com/2227-7390/8/6/884
12. V. S. Ilkiv, Z. M. Nytrebych, P. Y. Pukach, and ..., “Analysis of measurement systems mathematical models by using the comparison of functions,” Mathematical …, 2019, [Online]. Available: http://jnas.nbuv.gov.ua/j-pdf/mmc_2019_6_2_12.pdf
A. Tabieh, “A teaching model impact of learning outcomes for mathematical content in functions,” Opción, 2020, [Online]. Available: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3685857
13. L. Siqing and L. Zhou, “AN EXPLORATION OF INTEGRATING MATHEMATICAL MODELING IDEAS IN TEACHING APPLICATION OF FUNCTIONS,” researchgate.net, [Online]. Available: https://www.researchgate.net/profile/Lili-Zhou-27/publication/375519330_AN_EXPLORATION_OF_INTEGRATING_MATHEMATICAL_MODELING_IDEAS_IN_TEACHING_APPLICATION_OF_FUNCTIONS/links/654d1c70ce88b87031d8b47e/AN-EXPLORATION-OF-INTEGRATING-MATHEMATICAL-MODELING-IDEAS-IN-TEACHING-APPLICATION-OF-FUNCTIONS.pdf
14. A. Firsova and G. Y. Chernyshova, “Mathematical models for evaluation of the higher education system functions with DEA approach,” … университета. Новая серия …, 2019, [Online]. Available: https://cyberleninka.ru/article/n/mathematical-models-for-evaluation-of-the-higher-education-system-functions-with-dea-approach
15. D. Cattaneo, M. Chiari, G. Magnani, N. Fossati, and ..., “FixM: Code generation of fixed point mathematical functions,” … Informatics and Systems, 2021, [Online]. Available: https://www.sciencedirect.com/science/article/pii/S2210537920302018
16. K. G. Campo-Meneses and ..., “Mathematical Connections Related to Exponential and Logarithmic Functions: A Literature Review,” RANGE: Jurnal …, 2023, [Online]. Available: http://jurnal.unimor.ac.id/index.php/JPM/article/view/4738
17. K. S. Sørensen, On some differential equations in mathematical-physics and singular functions in probability theory. vbn.aau.dk, 2022. [Online]. Available: https://vbn.aau.dk/files/549497701/PHD_KStudsgaardS_rensen.pdf
18. Kusmaryono, H. Suyitno, D. Dwijanto, and ..., “The Effect of Mathematical Disposition on Mathematical Power Formation: Review of Dispositional Mental Functions.,” International Journal of …, 2019, [Online]. Available: https://eric.ed.gov/?id=EJ1201186
19. Suklabaidya, M., Das, A., & Das, B. (2018). A cryptography model using hybrid encryption and decryption techniques. International Journal of Computational Intelligence & IoT, 2(4).
20. Agbedemnab, P. A. N., Baagyere, E. Y., & Daabo, M. I. (2019, October). A Novel Text Encryption and Decryption Scheme using the Genetic Algorithm and Residual Numbers. In ICICIS (pp. 20-31).
21. Singh, L. D., & Singh, K. M. (2015). Implementation of text encryption using elliptic curve cryptography. Procedia Computer Science, 54, 73-82.
22. Singh, J., Lata, K., & Ashraf, J. (2015). Image encryption & decryption with symmetric key cryptography using MATLAB. International Journal of Current Engineering and Technology, 5(1), 448-451.
23. Dhany, H. W., Izhari, F., Fahmi, H., Tulus, M., & Sutarman, M. (2017, October). Encryption and decryption using password based encryption, MD5, and DES. In International Conference on Public Policy, Social Computing and Development 2017 (ICOPOSDev 2017) (pp. 278-283). Atlantis Press.
24. Patil, P., & Bansode, R. (2020). Performance evaluation of hybrid cryptography algorithm for secure sharing of text & images. International Research Journal of Engineering and Technology, 7(9), 3773-3778.
25. Babaei, M. (2013). A novel text and image encryption method based on chaos theory and DNA computing. Natural computing, 12(1), 101-107.
26. Karudaiyar, G., Karthikeyan, S., & Sainath, B. (2014). Encryption and Decryption Scheme by Using Finite State Machine. Biosciences Biotechnology Research Asia, 11(3), 1867-1872.
27. Goyal, R., & Khurana, M. (2017). Cryptographic security using various encryption and decryption method. International Journal of Mathematical Sciences and Computing (IJMSC), 3(3), 1-11.
Published
2024-07-01
How to Cite
Salman, H. M., H. O. Ajam, M., & Kadhim, H. I. (2024). Text Encryption and Decryption using Mathematical Functions. CENTRAL ASIAN JOURNAL OF MATHEMATICAL THEORY AND COMPUTER SCIENCES, 5(3), 121-131. Retrieved from https://cajmtcs.centralasianstudies.org/index.php/CAJMTCS/article/view/637
Section
Articles
