Abstract
References
- Uçar, S , Taş, N., and Özgür, N. (2019). "A New Application to Coding Theory via Fibonacci and Lucas Numbers". MSAEN 7: 62-70.
- Paar, C., and Pelzl, J. (2009). “Understanding cryptography: a textbook for students and practitioners.” Springer Science, Business Media.
- Koshy, T. (2018). “Fibonacci and Lucas Numbers with Applications.” Volume 1, John Wiley & Sons, New Jersey.
- Koshy, T. (2019). “Fibonacci and Lucas Numbers with Applications.” Volume 2, John Wiley & Sons, New Jersey.
- Stewart, I. (1990). “Galois theory.” Chapman and Hall/CRC.
- Klima, R. E., and Sigmon, N. P. (2012). “Cryptology: classical and modern with maplets.” Chapman and Hall/CRC.
- Daemen,, J., and Rijmen, V. (2003). "AES Proposal: Rijndael". National Institute of Standards and Technology. p. 1. Archived from the original on 5 March 2013. Retrieved 21 February 2013.
- Avaroğlu, E., Koyuncu, I., Özer, A. B., and Türk, M. (2015). “Hybrid pseudo-random number generator for cryptographic systems.” Nonlinear Dynamics, 82(1-2), 239-248.
Abstract
Galois field, has an important position in cryptology. Advanced Encryption Standard (AES) also used in polynomial operations. In this paper, we consider the polynomial operations on the Galois fields, the Fibonacci polynomial sequences. Using a certain irreducible polynomial, we redefine the elements of Fibonacci polynomial sequences to use in our cryptology algorithm. So, we find the classical AES-like cryptology via the Fibonacci polynomial matrix. Successful results were achieved with the method used.
Keywords
Fibonacci numbers Fibonacci polynomial numbers Cassini identity Fibonacci matrix Galois field
References
- Uçar, S , Taş, N., and Özgür, N. (2019). "A New Application to Coding Theory via Fibonacci and Lucas Numbers". MSAEN 7: 62-70.
- Paar, C., and Pelzl, J. (2009). “Understanding cryptography: a textbook for students and practitioners.” Springer Science, Business Media.
- Koshy, T. (2018). “Fibonacci and Lucas Numbers with Applications.” Volume 1, John Wiley & Sons, New Jersey.
- Koshy, T. (2019). “Fibonacci and Lucas Numbers with Applications.” Volume 2, John Wiley & Sons, New Jersey.
- Stewart, I. (1990). “Galois theory.” Chapman and Hall/CRC.
- Klima, R. E., and Sigmon, N. P. (2012). “Cryptology: classical and modern with maplets.” Chapman and Hall/CRC.
- Daemen,, J., and Rijmen, V. (2003). "AES Proposal: Rijndael". National Institute of Standards and Technology. p. 1. Archived from the original on 5 March 2013. Retrieved 21 February 2013.
- Avaroğlu, E., Koyuncu, I., Özer, A. B., and Türk, M. (2015). “Hybrid pseudo-random number generator for cryptographic systems.” Nonlinear Dynamics, 82(1-2), 239-248.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Articles |
| Authors | |
| Publication Date | July 1, 2020 |
| Published in Issue | Year 2020 Volume: 4 Issue: 3 |