Applications of Pell Polynomials in Rings

Cryptographic Applications of Sparse Polynomials over Finite Rings

This paper gives new examples that exploit the idea of using sparse polynomials with restricted coefficients over a finite ring for designing fast, reliable cryptosystems and identification schemes.

Pell–Padovan-circulant sequences and their applications

This paper develops properties of recurrence sequences defined from circulant matrices obtained from the characteristic polynomial of the Pell–Padovan sequence. The study of these sequences modulo m yields cyclic groups and semigroups from the generating matrices. Finally, we obtain the lengths of the periods of the extended sequences in the extended triangle groups E(2, n, 2), E(2, 2, n) and E...

Some Constructions in Rings of Differential Polynomials

Some Constructions in Rings of Diierential Polynomials

Wedderburn Polynomials over Division Rings

A Wedderburn polynomial over a division ring K is a minimal polynomial of an algebraic subset of K. Special cases of such polynomials include, for instance, the minimal polynomials (over the center F = Z(K)) of elements of K that are algebraic over F . In this note, we give a survey on some of our ongoing work on the structure theory of Wedderburn polynomials. Throughout the note, we work in th...