## Distribution of Inverses in Polynomial Rings

##### Abstract

Let IFp be the finite field with p elements, and let F(X) ∈ IFp[X] be a square-free polynomial. We show that in the ring R = IFp[X]/F(X), the inverses of polynomials of small height are uniformly distributed.
We also show that for any set L ⊂ R of very small cardinality, for almost all G ∈ R the set of inverses {(G+f)−1 | f ∈ L} are uniformly
distributed. These questions are motivated by applications to the NTRU cryptosystem.