Ayse Nalli - Academia.edu (original) (raw)
Papers by Ayse Nalli
Abstract: In this paper, we obtain a generalization of [6]. We first construct the so-called circ... more Abstract: In this paper, we obtain a generalization of [6]. We first construct the so-called circulant matrix with the generalized Fibonacci numbers and then present lower and upper bounds for the Euclidean and spectral norms of this matrix.
Advances in computational intelligence and robotics book series, 2020
In this chapter, the authors have defined a new ElGamal cryptosystem by using the power Fibonacci... more In this chapter, the authors have defined a new ElGamal cryptosystem by using the power Fibonacci sequence module m. Then they have defined a new sequence module m and the other ElGamal cryptosystem by using the new sequence. In addition, they have compared that the new ElGamal cryptosystems and ElGamal cryptosystem in terms of cryptography. Then the authors have defined the third ElGamal cryptosystem.
In this paper, we have studied on adapting to asymmetric cryptography power Fibonacci sequence mo... more In this paper, we have studied on adapting to asymmetric cryptography power Fibonacci sequence module m. To do this, We have restructed Discreate Logarithm Problem which is one of mathematical difficult problems by using power Fibonacci sequence module m and by means of this sequences, we have made the mathematical difficult problem which is used only in prime modules is also useful for composite modules. Then we have constructed cryptographic system based on this more difficult problem which we have rearranged. Hence, we have obtained a new cryptosystem as ElGamal Cryptosystem. Lastly, we have compared that ElGamal Cryptosystem and a new cryptosystem which we constitute in terms of cryptography and we have obtained that a new cryptosystem is more advantageuos than ElGamal Cryptosystem.
Mathematical and computational applications, Dec 1, 2014
In this paper, we give recurrence relation obtained by using from [1] for Pentanacci sequence. Fu... more In this paper, we give recurrence relation obtained by using from [1] for Pentanacci sequence. Furthermore, we construct generating matrix for 6 , 6. Finally, we represent relationships between Pentanacci sequence and permanents of certain matrices.
Journal of Number Theory, Apr 1, 2015
In this paper, we have studied the third order variations on the Fibonacci universal code and we ... more In this paper, we have studied the third order variations on the Fibonacci universal code and we have defined (3) VF a
Methods, Implementation, and Application of Cyber Security Intelligence and Analytics
We all know that every positive integer has a unique Fibonacci representation, but some positive ... more We all know that every positive integer has a unique Fibonacci representation, but some positive integers have multiple Gopala Hemachandra (GH) representations, or some positive integers haven't any GH representation. Here, the authors found the first k-positive integer k=(3 2^((m-1))-1) for which there is no Zeckendorf's representation for Gopala Hemachandra sequence whose order m. Thus, the authors formulated the first positive integer whose Zeckendorf's representation can't be found in terms of its order. The authors also described the fourth, the fifth, and the sixth order GH representation of positive integers and obtained the fifth and the sixth order GH representations of the first 26 positive integers uniformly according to a certain rule with a table. Finally, the authors used these GH representations in symmetric cryptography, and the authors made some applications with a method which they construct similar to Nalli and Ozyilmaz.
Selcuk University Research Center of Applied Mathematics, 2006
In this paper we study the n n Hadamard exponential GCD matrix E = whose -entry is e(i,j). We giv... more In this paper we study the n n Hadamard exponential GCD matrix E = whose -entry is e(i,j). We give the structure theorem and calculate the determinant, the trace, inverse and determine upper bound for determinant of the Hadamard exponential GCD matrix. Furtermore determine lower bound for the Euclidean norm of the Hadamard exponential GCD matrix.
Selçuk Journal of Applied Mathematics
Abstract: In this paper, we obtain a generalization of [6]. We first construct the so-called circ... more Abstract: In this paper, we obtain a generalization of [6]. We first construct the so-called circulant matrix with the generalized Fibonacci numbers and then present lower and upper bounds for the Euclidean and spectral norms of this matrix.
Implementing Computational Intelligence Techniques for Security Systems Design, 2020
In this chapter, the authors have defined a new ElGamal cryptosystem by using the power Fibonacci... more In this chapter, the authors have defined a new ElGamal cryptosystem by using the power Fibonacci sequence module m. Then they have defined a new sequence module m and the other ElGamal cryptosystem by using the new sequence. In addition, they have compared that the new ElGamal cryptosystems and ElGamal cryptosystem in terms of cryptography. Then the authors have defined the third ElGamal cryptosystem. They have, particularly, called the new system as composite ElGamal cryptosystem. The authors made an application of composite ElGamal cryptosystem. Finally, the authors have compared that composite ElGamal cryptosystem and ElGamal cryptosystem in terms of cryptography and they have obtained that composite ElGamal cryptosystem is more advantageous than ElGamal cryptosystem.
ArXiv, 2018
In this paper, we have studied on adapting to asymmetric cryptography power Fibonacci sequence mo... more In this paper, we have studied on adapting to asymmetric cryptography power Fibonacci sequence module m . To do this, We have restructed Discreate Logarithm Problem which is one of mathematical difficult problems by using power Fibonacci sequence module m and by means of this sequences, we have made the mathematical difficult problem which is used only in prime modules is also useful for composite modules. Then we have constructed cryptographic system based on this more difficult problem which we have rearranged. Hence, we have obtained a new cryptosystem as ElGamal Cryptosystem. Lastly, we have compared that ElGamal Cryptosystem and a new cryptosystem which we constitute in terms of cryptography and we have obtained that a new cryptosystem is more advantageuos than ElGamal Cryptosystem.
International Journal of Contemporary Mathematical Sciences, 2007
In this paper we did a generalization of Hadamard product of Fibonacci Q n matrix and Fibonacci Q... more In this paper we did a generalization of Hadamard product of Fibonacci Q n matrix and Fibonacci Q −n matrix for continuous domain. We obtained Hadamard product of the golden matrices in the terms of the symmetrical hyperbolic Fibonacci functions and investigated some properties of Hadamard product of the golden matrices.
Mathematical and Computational Applications, 2014
Jp Journal of Algebra Number Theory and Applications, 2003
Ars Combinatoria Waterloo Then Winnipeg, 2012
Journal of Number Theory, 2015
In this paper, we have studied the third order variations on the Fibonacci universal code and we ... more In this paper, we have studied the third order variations on the Fibonacci universal code and we have defined (3) VF a
Linear and Multilinear Algebra, 2010
ABSTRACT A divisor d + of n + is said to be a unitary divisor of n if (d, n/d) = 1. In this artic... more ABSTRACT A divisor d + of n + is said to be a unitary divisor of n if (d, n/d) = 1. In this article we examine the greatest common unitary divisor (GCUD) reciprocal least common unitary multiple (LCUM) matrices. At first we concentrate on the difficulty of the non-existence of the LCUM and we present three different ways to overcome this difficulty. After that we calculate the determinant of the three GCUD reciprocal LCUM matrices with respect to certain types of functions arising from the LCUM problematics. We also analyse these classes of functions, which may be referred to as unitary analogs of the class of semimultiplicative functions, and find their connections to rational arithmetical functions. Our study shows that it does make a difference how to extend the concept of LCUM.
Chaos, Solitons & Fractals, 2009
Let hðxÞ be a polynomial with real coefficients. We introduce hðxÞ-Fibonacci polynomials that gen... more Let hðxÞ be a polynomial with real coefficients. We introduce hðxÞ-Fibonacci polynomials that generalize both Catalan's Fibonacci polynomials and Byrd's Fibonacci polynomials and also the k-Fibonacci numbers, and we provide properties for these hðxÞ-Fibonacci polynomials. We also introduce hðxÞ-Lucas polynomials that generalize the Lucas polynomials and present properties of these polynomials. In the last section we introduce the matrix Q h ðxÞ that generalizes the Q-matrix 1 1 1 0 whose powers generate the Fibonacci numbers.
![Research paper thumbnail of Erratum to “On the norms of circulant matrices with the Fibonacci and Lucas numbers” [Appl. Math. Comput. 160 (1) (2005) 125–132]](https://attachments.academia-assets.com/84562406/thumbnails/1.jpg)
](Applied Mathematics and Computation, 2007
The following correction for this paper should be noted. Theorem 2. Let the (n • n) matrix A be a... more The following correction for this paper should be noted. Theorem 2. Let the (n • n) matrix A be as A ¼ ba ij c such that a ij ¼ L ðmodðjÀi;nÞÞ. Then ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi F n Á F nÀ1 þ 4 Á F 2 nÀ1 þ F nÀ1 Á F nÀ2
Abstract: In this paper, we obtain a generalization of [6]. We first construct the so-called circ... more Abstract: In this paper, we obtain a generalization of [6]. We first construct the so-called circulant matrix with the generalized Fibonacci numbers and then present lower and upper bounds for the Euclidean and spectral norms of this matrix.
Advances in computational intelligence and robotics book series, 2020
In this chapter, the authors have defined a new ElGamal cryptosystem by using the power Fibonacci... more In this chapter, the authors have defined a new ElGamal cryptosystem by using the power Fibonacci sequence module m. Then they have defined a new sequence module m and the other ElGamal cryptosystem by using the new sequence. In addition, they have compared that the new ElGamal cryptosystems and ElGamal cryptosystem in terms of cryptography. Then the authors have defined the third ElGamal cryptosystem.
In this paper, we have studied on adapting to asymmetric cryptography power Fibonacci sequence mo... more In this paper, we have studied on adapting to asymmetric cryptography power Fibonacci sequence module m. To do this, We have restructed Discreate Logarithm Problem which is one of mathematical difficult problems by using power Fibonacci sequence module m and by means of this sequences, we have made the mathematical difficult problem which is used only in prime modules is also useful for composite modules. Then we have constructed cryptographic system based on this more difficult problem which we have rearranged. Hence, we have obtained a new cryptosystem as ElGamal Cryptosystem. Lastly, we have compared that ElGamal Cryptosystem and a new cryptosystem which we constitute in terms of cryptography and we have obtained that a new cryptosystem is more advantageuos than ElGamal Cryptosystem.
Mathematical and computational applications, Dec 1, 2014
In this paper, we give recurrence relation obtained by using from [1] for Pentanacci sequence. Fu... more In this paper, we give recurrence relation obtained by using from [1] for Pentanacci sequence. Furthermore, we construct generating matrix for 6 , 6. Finally, we represent relationships between Pentanacci sequence and permanents of certain matrices.
Journal of Number Theory, Apr 1, 2015
In this paper, we have studied the third order variations on the Fibonacci universal code and we ... more In this paper, we have studied the third order variations on the Fibonacci universal code and we have defined (3) VF a
Methods, Implementation, and Application of Cyber Security Intelligence and Analytics
We all know that every positive integer has a unique Fibonacci representation, but some positive ... more We all know that every positive integer has a unique Fibonacci representation, but some positive integers have multiple Gopala Hemachandra (GH) representations, or some positive integers haven't any GH representation. Here, the authors found the first k-positive integer k=(3 2^((m-1))-1) for which there is no Zeckendorf's representation for Gopala Hemachandra sequence whose order m. Thus, the authors formulated the first positive integer whose Zeckendorf's representation can't be found in terms of its order. The authors also described the fourth, the fifth, and the sixth order GH representation of positive integers and obtained the fifth and the sixth order GH representations of the first 26 positive integers uniformly according to a certain rule with a table. Finally, the authors used these GH representations in symmetric cryptography, and the authors made some applications with a method which they construct similar to Nalli and Ozyilmaz.
Selcuk University Research Center of Applied Mathematics, 2006
In this paper we study the n n Hadamard exponential GCD matrix E = whose -entry is e(i,j). We giv... more In this paper we study the n n Hadamard exponential GCD matrix E = whose -entry is e(i,j). We give the structure theorem and calculate the determinant, the trace, inverse and determine upper bound for determinant of the Hadamard exponential GCD matrix. Furtermore determine lower bound for the Euclidean norm of the Hadamard exponential GCD matrix.
Selçuk Journal of Applied Mathematics
Abstract: In this paper, we obtain a generalization of [6]. We first construct the so-called circ... more Abstract: In this paper, we obtain a generalization of [6]. We first construct the so-called circulant matrix with the generalized Fibonacci numbers and then present lower and upper bounds for the Euclidean and spectral norms of this matrix.
Implementing Computational Intelligence Techniques for Security Systems Design, 2020
In this chapter, the authors have defined a new ElGamal cryptosystem by using the power Fibonacci... more In this chapter, the authors have defined a new ElGamal cryptosystem by using the power Fibonacci sequence module m. Then they have defined a new sequence module m and the other ElGamal cryptosystem by using the new sequence. In addition, they have compared that the new ElGamal cryptosystems and ElGamal cryptosystem in terms of cryptography. Then the authors have defined the third ElGamal cryptosystem. They have, particularly, called the new system as composite ElGamal cryptosystem. The authors made an application of composite ElGamal cryptosystem. Finally, the authors have compared that composite ElGamal cryptosystem and ElGamal cryptosystem in terms of cryptography and they have obtained that composite ElGamal cryptosystem is more advantageous than ElGamal cryptosystem.
ArXiv, 2018
In this paper, we have studied on adapting to asymmetric cryptography power Fibonacci sequence mo... more In this paper, we have studied on adapting to asymmetric cryptography power Fibonacci sequence module m . To do this, We have restructed Discreate Logarithm Problem which is one of mathematical difficult problems by using power Fibonacci sequence module m and by means of this sequences, we have made the mathematical difficult problem which is used only in prime modules is also useful for composite modules. Then we have constructed cryptographic system based on this more difficult problem which we have rearranged. Hence, we have obtained a new cryptosystem as ElGamal Cryptosystem. Lastly, we have compared that ElGamal Cryptosystem and a new cryptosystem which we constitute in terms of cryptography and we have obtained that a new cryptosystem is more advantageuos than ElGamal Cryptosystem.
International Journal of Contemporary Mathematical Sciences, 2007
In this paper we did a generalization of Hadamard product of Fibonacci Q n matrix and Fibonacci Q... more In this paper we did a generalization of Hadamard product of Fibonacci Q n matrix and Fibonacci Q −n matrix for continuous domain. We obtained Hadamard product of the golden matrices in the terms of the symmetrical hyperbolic Fibonacci functions and investigated some properties of Hadamard product of the golden matrices.
Mathematical and Computational Applications, 2014
Jp Journal of Algebra Number Theory and Applications, 2003
Ars Combinatoria Waterloo Then Winnipeg, 2012
Journal of Number Theory, 2015
In this paper, we have studied the third order variations on the Fibonacci universal code and we ... more In this paper, we have studied the third order variations on the Fibonacci universal code and we have defined (3) VF a
Linear and Multilinear Algebra, 2010
ABSTRACT A divisor d + of n + is said to be a unitary divisor of n if (d, n/d) = 1. In this artic... more ABSTRACT A divisor d + of n + is said to be a unitary divisor of n if (d, n/d) = 1. In this article we examine the greatest common unitary divisor (GCUD) reciprocal least common unitary multiple (LCUM) matrices. At first we concentrate on the difficulty of the non-existence of the LCUM and we present three different ways to overcome this difficulty. After that we calculate the determinant of the three GCUD reciprocal LCUM matrices with respect to certain types of functions arising from the LCUM problematics. We also analyse these classes of functions, which may be referred to as unitary analogs of the class of semimultiplicative functions, and find their connections to rational arithmetical functions. Our study shows that it does make a difference how to extend the concept of LCUM.
Chaos, Solitons & Fractals, 2009
Let hðxÞ be a polynomial with real coefficients. We introduce hðxÞ-Fibonacci polynomials that gen... more Let hðxÞ be a polynomial with real coefficients. We introduce hðxÞ-Fibonacci polynomials that generalize both Catalan's Fibonacci polynomials and Byrd's Fibonacci polynomials and also the k-Fibonacci numbers, and we provide properties for these hðxÞ-Fibonacci polynomials. We also introduce hðxÞ-Lucas polynomials that generalize the Lucas polynomials and present properties of these polynomials. In the last section we introduce the matrix Q h ðxÞ that generalizes the Q-matrix 1 1 1 0 whose powers generate the Fibonacci numbers.
Applied Mathematics and Computation, 2007
The following correction for this paper should be noted. Theorem 2. Let the (n • n) matrix A be a... more The following correction for this paper should be noted. Theorem 2. Let the (n • n) matrix A be as A ¼ ba ij c such that a ij ¼ L ðmodðjÀi;nÞÞ. Then ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi F n Á F nÀ1 þ 4 Á F 2 nÀ1 þ F nÀ1 Á F nÀ2