Distribution of inverses in polynomial rings

William D. Banks; Igor E. Shparlinski

doi:10.1016/S0019-3577(01)80012-4

Distribution of inverses in polynomial rings

William D. Banks, Igor E. Shparlinski^*

^*Corresponding author for this work

School of Computing

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

Let F_p be the finite field with p elements, and let F(X) ε F_p[X] be a square-free polynomial. We show that in the ring R = F_p[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 language	English
Pages (from-to)	303-315
Number of pages	13
Journal	Indagationes Mathematicae
Volume	12
Issue number	3
DOIs	https://doi.org/10.1016/S0019-3577(01)80012-4
Publication status	Published - 2001

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abstract = "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.",

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AU - Banks, William D.

AU - Shparlinski, Igor E.

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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 - https://www.scopus.com/pages/publications/0035624728

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 -

Distribution of inverses in polynomial rings

Abstract

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