Distribution of inverses in polynomial rings

William D. Banks, Igor E. Shparlinski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


Let Fp be the finite field with p elements, and let F(X) ε Fp[X] be a square-free polynomial. We show that in the ring R = Fp[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 ε R the set of inverses {(G + f)-1|f ε L} are uniformly distributed. These questions are motivated by applications to the NTRU cryptosystem.

Original languageEnglish
Pages (from-to)303-315
Number of pages13
JournalIndagationes Mathematicae
Issue number3
Publication statusPublished - 2001


Dive into the research topics of 'Distribution of inverses in polynomial rings'. Together they form a unique fingerprint.

Cite this