Dursun Tasci

Bio: Dursun Tasci is an academic researcher from Gazi University. The author has contributed to research in topics: Fibonacci number & Fibonacci polynomials. The author has an hindex of 12, co-authored 39 publications receiving 422 citations. Previous affiliations of Dursun Tasci include Selçuk University.

On the Generalized Order-$k$ Fibonacci and Lucas Numbers

Abstract: In this paper we consider the generalized order-k Fibonacci and Lucas numbers. We give the generalized Binet formula, combinatorial representation and some relations involving the generalized order-k Fibonacci and Lucas numbers.

The linear algebra of the pell matrix

Abstract: In this paper we consider the construction of the Pell and sym- metric Pell matrices. Also we discuss the linear algebra of these matrices. As applications, we derive some interesting relations which includes the Pell numbers by using the properties of these Pell matrices.

Hybrid threshold adaptable quantum secret sharing scheme with reverse Huffman-Fibonacci-tree coding

Abstract: With prevalent attacks in communication, sharing a secret between communicating parties is an ongoing challenge. Moreover, it is important to integrate quantum solutions with classical secret sharing schemes with low computational cost for the real world use. This paper proposes a novel hybrid threshold adaptable quantum secret sharing scheme, using an m-bonacci orbital angular momentum (OAM) pump, Lagrange interpolation polynomials, and reverse Huffman-Fibonacci-tree coding. To be exact, we employ entangled states prepared by m-bonacci sequences to detect eavesdropping. Meanwhile, we encode m-bonacci sequences in Lagrange interpolation polynomials to generate the shares of a secret with reverse Huffman-Fibonacci-tree coding. The advantages of the proposed scheme is that it can detect eavesdropping without joint quantum operations, and permits secret sharing for an arbitrary but no less than threshold-value number of classical participants with much lower bandwidth. Also, in comparison with existing quantum secret sharing schemes, it still works when there are dynamic changes, such as the unavailability of some quantum channel, the arrival of new participants and the departure of participants. Finally, we provide security analysis of the new hybrid quantum secret sharing scheme and discuss its useful features for modern applications.

Hybrid threshold adaptable quantum secret sharing scheme with reverse Huffman-Fibonacci-tree coding

Abstract: With prevalent attacks in communication, sharing a secret between communicating parties is an ongoing challenge. Moreover, it is important to integrate quantum solutions with classical secret sharing schemes with low computational cost for the real world use. This paper proposes a novel hybrid threshold adaptable quantum secret sharing scheme, using an m-bonacci orbital angular momentum (OAM) pump, Lagrange interpolation polynomials, and reverse Huffman-Fibonacci-tree coding. To be exact, we employ entangled states prepared by m -bonacci sequences to detect eavesdropping. Meanwhile, we encode m -bonacci sequences in Lagrange interpolation polynomials to generate the shares of a secret with reverse Huffman-Fibonacci-tree coding. The advantages of the proposed scheme is that it can detect eavesdropping without joint quantum operations, and permits secret sharing for an arbitrary but no less than threshold-value number of classical participants with much lower bandwidth. Also, in comparison with existing quantum secret sharing schemes, it still works when there are dynamic changes, such as the unavailability of some quantum channel, the arrival of new participants and the departure of participants. Finally, we provide security analysis of the new hybrid quantum secret sharing scheme and discuss its useful features for modern applications.

The Binet formula, sums and representations of generalized Fibonacci p-numbers

Abstract: In this paper, we consider the generalized Fibonacci p-numbers and then we give the generalized Binet formula, sums, combinatorial representations and generating function of the generalized Fibonacci p-numbers. Also, using matrix methods, we derive an explicit formula for the sums of the generalized Fibonacci p-numbers.

THE GENERALIZED BINET FORMULA, REPRESENTATION AND SUMS OF THE GENERALIZED ORDER-k PELL NUMBERS

Abstract: In this paper we give a new generalization of the Pell numbers in matrix representation. Also we extend the matrix representation and we show that the sums of the generalized order-k Pell numbers could be derived directly using this representation. Further we present some identities, the generalized Binet formula and combinatorial representation of the generalized order-k Pell numbers.