  We give a polynomial time algorithm for computing the Igusa local zeta
function $Z(s,f)$ attached to a polynomial $f(x)\in \QTR{Bbb}{Z}[x]$, in one
variable, with splitting field $\QTR{Bbb}{Q}$, and a prime number $p$. We also
propose a new class of Linear Feedback Shift Registers based on the computation
of Igusa's local zeta function.
