An Effective S-box Construction Based on Linear Recurrences with Constant Co-Efficient

Construction of Equidistributed Generators based on linear recurrences modulo 2

Construction of Equidistributed Generators Based on Linear Recurrences Modulo 2

Random number generators based on linear recurrences modulo 2 are widely used and appear in different forms, such as the simple and combined Tausworthe generators, the GFSR, and the twisted GFSR generators. Low-discrepancy point sets for quasi-Monte Carlo integration can also be constructed based on these linear recurrences. The quality of these generators or point sets is usually measured by c...

Linear Recurrences with Constant Coeecients: the Multivariate Case

While in the univariate case solutions of linear recurrences with constant coeecients have rational generating functions, we show that the multivariate case is much richer: even though initial conditions have rational generating functions, the corresponding solutions can have generating functions which are algebraic but not rational, D-nite but not algebraic, and even non D-nite.

Linear recurrences with constant coefficients: the multivariate case

While in the univariate case solutions of linear recurrences with constant coe cients have rational generating functions we show that the multivariate case is much richer even though initial conditions have rational generating functions the corresponding solutions can have generating functions which are algebraic but not rational D nite but not algebraic and even non D nite Introduction The aim...

Diophantine Equations Related with Linear Binary Recurrences

In this paper we find all solutions of four kinds of the Diophantine equations begin{equation*} ~x^{2}pm V_{t}xy-y^{2}pm x=0text{ and}~x^{2}pm V_{t}xy-y^{2}pm y=0, end{equation*}% for an odd number $t$, and, begin{equation*} ~x^{2}pm V_{t}xy+y^{2}-x=0text{ and}text{ }x^{2}pm V_{t}xy+y^{2}-y=0, end{equation*}% for an even number $t$, where $V_{n}$ is a generalized Lucas number. This pape...