Affiliation:
1. Department of Mathematics and Statistics, Sakon Nakhon Rajabhat University, Sakon Nakhon 47000, THAILAND
Abstract
In this paper, we define some n x n Hessenberg matrices and then we obtain determinants and permanents of their matrices that give the odd and even terms of bivariate complex Perrin polynomials. Moreover, we use our results to apply the application cryptology area. We discuss the Affine-Hill method over complex numbers by improving our matrix as the key matrix and present an experimental example to show that our method can work for cryptography.
Publisher
World Scientific and Engineering Academy and Society (WSEAS)
Reference18 articles.
1. R. P. M. Vieira, M. C. dos Santos Mangueira, F. R. V. Alves and P. M. M. C. Catarino, Perrin’s bivariate and complex polynomials, Notes on Number Theory and Discrete Mathematics, Vol.27, 2021, pp.70–78.
2. E. Kilic and D. Tasci, On the generalized Fibonacci and Pell sequences by Hessenberg matrices, Ars Combin, Vol.94, 2010, pp.161– 174.
3. K. Kaygısız and A. Sahin, Calculating terms of associated polynomials of Perrin and Cordonnier numbers, Notes on Number Theory and Discrete Mathematics, Vol.20, 2014, pp.10–18.
4. P. Kasempin, W. Vipismakul and A. Kaewsuy, Tridiagonal Matrices with Permanent Values Equal to k-Jacobsthal Sequence, Asian Journal of Applied Sciences, Vol.8, 2020, pp.269–274.
5. F. Yilmaz and D. Bozkurt, Hessenberg matrices and the Pell and Perrin numbers, Journal of Number Theory, Vol.131, 2011, pp.1390–1396.
Cited by
2 articles.
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