In this paper, we investigate the generalized Tribonacci polynomials and deal with, in detail, two special cases which call them (r,s,t)-Tribonacci (r,s,t)-Tribonacci-Lucas polynomials. We also introduce a new sequence its namely co-Tribonacci, (r,s,t)-co-Tribonacci (r,s,t)-co-Tribonacci-Lucas polynomials, respectively. present Binet's formulas, generating functions, Simson summation formulas f...

Polynomial hashing as an instantiation of universal hashing is a widely employed method for the construction of MACs and authenticated encryption (AE) schemes, the ubiquitous GCM being a prominent example. It is also used in recent AE proposals within the CAESAR competition which aim at providing nonce misuse resistance, such as POET. The algebraic structure of polynomial hashing has given rise...

Extensive studies have been made of the public key cryptosystems based on multivariate polynomials over F2. However most of the proposed public key cryptosystems based on multivariate polynomials, are proved not secure. In this paper, we propose several types of new constructions of public key cryptosystems based on randomly generated singular simultaneous equations. One of the features of the ...

The generalized Stieltjes–Wigert polynomials depending on parameters 0 ≤ p < 1 and 0 < q < 1 are discussed. By removing the mass at zero of an N-extremal solution concentrated in the zeros of the D-function from the Nevanlinna parametrization, we obtain a discrete measure μM , which is uniquely determined by its moments. We calculate the coefficients of the corresponding orthonormal polynomials...

Here we present a new method to construct the explicit formula of a sequence of numbers and polynomials generated by a linear recurrence relation of order 2. The applications of the method to the Fibonacci and Lucas numbers, Chebyshev polynomials, the generalized Gegenbauer-Humbert polynomials are also discussed. The derived idea provides a general method to construct identities of number or po...

By using Dickson polynomials in several variables and Chebyshev polynomials of the second kind, we derive the explicit expression of the entries in the array defining the sequence A185905. As a result, we obtain a straightforward proof of some conjectures of Jeffery concerning this sequence and other related ones.

Abstract. In recent years classical polynomials of a real or complex variable and their generalizations to the case of several real or complex variables have been in a focus of increasing attention leading to new and interesting problems. In this paper we construct higher dimensional analogues to generalized Laguerre and Hermite polynomials as well as some based functions in the framework of Cl...