TY - JOUR

T1 - Distribution of inverses in polynomial rings

AU - Banks, William D.

AU - Shparlinski, Igor E.

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0035624728&partnerID=8YFLogxK

U2 - 10.1016/S0019-3577(01)80012-4

DO - 10.1016/S0019-3577(01)80012-4

M3 - Article

AN - SCOPUS:0035624728

SN - 0019-3577

VL - 12

SP - 303

EP - 315

JO - Indagationes Mathematicae

JF - Indagationes Mathematicae

IS - 3

ER -