The Advanced Encryption Standard(AES)is the most widely used symmetric cipher today.AES has an important place in cryptology.Finite field,also known as Galois Fields,are cornerstones for understanding any cryptography...The Advanced Encryption Standard(AES)is the most widely used symmetric cipher today.AES has an important place in cryptology.Finite field,also known as Galois Fields,are cornerstones for understanding any cryptography.This encryption method on AES is a method that uses polynomials on Galois fields.In this paper,we generalize the AES-like cryptology on 2×2 matrices.We redefine the elements of k-order Fibonacci polynomials sequences using a certain irreducible polynomial in our cryptology algorithm.So,this cryptology algorithm is called AES-like cryptology on the k-order Fibonacci polynomial matrix.展开更多
The main purpose of this paper is in using the generating function of generalized Fibonacci polynomials and its partial derivative to study the convolution evaluation of the second-kind Chebyshev polynomials, and give...The main purpose of this paper is in using the generating function of generalized Fibonacci polynomials and its partial derivative to study the convolution evaluation of the second-kind Chebyshev polynomials, and give an interesting formula.展开更多
Let H be a finite-dimensional pointed rank one Hopf algebra of nilpotent type over a finite group G.In this paper,we investigate the McKay matrix WV of H for tensoring with the 2-dimensional indecomposable H-module V:...Let H be a finite-dimensional pointed rank one Hopf algebra of nilpotent type over a finite group G.In this paper,we investigate the McKay matrix WV of H for tensoring with the 2-dimensional indecomposable H-module V:=M(2,0).It turns out that the characteristic polynomial,eigenvalues and eigenvectors of WV are related to the character table of the finite group G and a kind of generalized Fibonacci polynomial.Moreover,we construct some eigenvectors of each eigenvalue for WV by using the factorization of the generalized Fibonacci polynomial.As an example,we explicitly compute the characteristic polynomial and eigenvalues of WV and give all eigenvectors of each eigenvalue for WV when G is a dihedral group of order 4N+2.展开更多
基金This work is supported by the Scientific Research Project(BAP)2020FEBE009,Pamukkale University,Denizli,Turkey.
文摘The Advanced Encryption Standard(AES)is the most widely used symmetric cipher today.AES has an important place in cryptology.Finite field,also known as Galois Fields,are cornerstones for understanding any cryptography.This encryption method on AES is a method that uses polynomials on Galois fields.In this paper,we generalize the AES-like cryptology on 2×2 matrices.We redefine the elements of k-order Fibonacci polynomials sequences using a certain irreducible polynomial in our cryptology algorithm.So,this cryptology algorithm is called AES-like cryptology on the k-order Fibonacci polynomial matrix.
文摘The main purpose of this paper is in using the generating function of generalized Fibonacci polynomials and its partial derivative to study the convolution evaluation of the second-kind Chebyshev polynomials, and give an interesting formula.
文摘Let H be a finite-dimensional pointed rank one Hopf algebra of nilpotent type over a finite group G.In this paper,we investigate the McKay matrix WV of H for tensoring with the 2-dimensional indecomposable H-module V:=M(2,0).It turns out that the characteristic polynomial,eigenvalues and eigenvectors of WV are related to the character table of the finite group G and a kind of generalized Fibonacci polynomial.Moreover,we construct some eigenvectors of each eigenvalue for WV by using the factorization of the generalized Fibonacci polynomial.As an example,we explicitly compute the characteristic polynomial and eigenvalues of WV and give all eigenvectors of each eigenvalue for WV when G is a dihedral group of order 4N+2.
