Chebyshev action on finite fields
نویسنده
چکیده
Given a polynomial φ(x) and a finite field Fq one can construct a directed graph where the vertices are the values in the finite field, and emanating from each vertex is an edge joining the vertex to its image under φ. When φ is a Chebyshev polynomial of prime degree, the graphs display an unusual degree of symmetry. In this paper we provide a complete description of these graphs, and then use these graphs to determine the decomposition of primes in the Chebyshev radical extensions.
منابع مشابه
Post-buckling response of thin composite plates under end-shortening strain using Chebyshev techniques
In this paper, a method based on Chebyshev polynomials is developed for examination of geometrically nonlinear behaviour of thin rectangular composite laminated plates under end-shortening strain. Different boundary conditions and lay-up configurations are investigated and classical laminated plate theory is used for developing the equilibrium equations. The equilibrium equations are solved dir...
متن کاملChebyshev polynomials over finite fields and reversibility of -automata on square grids
Using number theory on function fields and algebraic number fields we prove results about Chebyshev polynomials over finite prime fields to investigate reversibility of two-dimensional additive cellular automata on finite square grids. For example, we show that there are infinitely many primitive irreversible additive cellular automata on square grids when the base field has order two or three.
متن کاملThe Graph Structure of Chebyshev Polynomials over Finite Fields and Applications
We completely describe the functional graph associated to iterations of Chebyshev polynomials over finite fields. Then, we use our structural results to obtain estimates for the average rho length, average number of connected components and the expected value for the period and preperiod of iterating Chebyshev polynomials.
متن کاملChebyshev finite difference method for solving a mathematical model arising in wastewater treatment plants
The Chebyshev finite difference method is applied to solve a system of two coupled nonlinear Lane-Emden differential equations arising in mathematical modelling of the excess sludge production from wastewater treatment plants. This method is based on a combination of the useful properties of Chebyshev polynomials approximation and finite difference method. The approach consists of reducing the ...
متن کاملAlgebraic Methods for Constructing One-way Trapdoor Functions
In this dissertation, we consider an extension of the discrete logarithm problem to the case of a semigroup acting on a finite set: the Semigroup Action Problem (SAP). New protocols and one-way trapdoor functions based on the difficulty of such problems are proposed. Several instances are studied both from a conceptual and cryptographic point of view. We discuss the application of existing gene...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discrete Mathematics
دوره 315-316 شماره
صفحات -
تاریخ انتشار 2014