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
VL - 12
SP - 303
EP - 315
JO - Indagationes Mathematicae
JF - Indagationes Mathematicae
SN - 0019-3577
IS - 3
ER -