Double character sums over elliptic curves and finite fields

William D. Banks; John B. Friedlander; Moubariz Z. Garaev; Igor E. Shparlinski

Double character sums over elliptic curves and finite fields

William D. Banks^*
, John B. Friedlander
, Moubariz Z. Garaev
, Igor E. Shparlinski

^*Corresponding author for this work

School of Computing

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

Abstract

We estimate certain double character sums over points of an elliptic curve and in the multiplicative subgroup of a finite field. These bounds both improve and extend the scope of a series of previous results. We apply these results to estimate the related sums over primes, and to derive new uniformity of distribution results for the elliptic curve pseudorandom number power generator. We also mention some further applications, both to cryptography and to smooth number distribution.

Original language	English
Pages (from-to)	179-197
Number of pages	19
Journal	Pure and Applied Mathematics Quarterly
Volume	2
Issue number	1
Publication status	Published - Jan 2006

Keywords

DIFFIE-HELLMAN DISTRIBUTIONS
DOUBLE EXPONENTIAL-SUMS
GENERATORS

Cite this

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title = "Double character sums over elliptic curves and finite fields",

abstract = "We estimate certain double character sums over points of an elliptic curve and in the multiplicative subgroup of a finite field. These bounds both improve and extend the scope of a series of previous results. We apply these results to estimate the related sums over primes, and to derive new uniformity of distribution results for the elliptic curve pseudorandom number power generator. We also mention some further applications, both to cryptography and to smooth number distribution.",

keywords = "DIFFIE-HELLMAN DISTRIBUTIONS, DOUBLE EXPONENTIAL-SUMS, GENERATORS",

author = "Banks, \{William D.\} and Friedlander, \{John B.\} and Garaev, \{Moubariz Z.\} and Shparlinski, \{Igor E.\}",

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AU - Banks, William D.

AU - Friedlander, John B.

AU - Garaev, Moubariz Z.

AU - Shparlinski, Igor E.

PY - 2006/1

Y1 - 2006/1

N2 - We estimate certain double character sums over points of an elliptic curve and in the multiplicative subgroup of a finite field. These bounds both improve and extend the scope of a series of previous results. We apply these results to estimate the related sums over primes, and to derive new uniformity of distribution results for the elliptic curve pseudorandom number power generator. We also mention some further applications, both to cryptography and to smooth number distribution.

AB - We estimate certain double character sums over points of an elliptic curve and in the multiplicative subgroup of a finite field. These bounds both improve and extend the scope of a series of previous results. We apply these results to estimate the related sums over primes, and to derive new uniformity of distribution results for the elliptic curve pseudorandom number power generator. We also mention some further applications, both to cryptography and to smooth number distribution.

KW - DIFFIE-HELLMAN DISTRIBUTIONS

KW - DOUBLE EXPONENTIAL-SUMS

KW - GENERATORS

M3 - Article

SN - 1558-8599

VL - 2

SP - 179

EP - 197

JO - Pure and Applied Mathematics Quarterly

JF - Pure and Applied Mathematics Quarterly

IS - 1

ER -

Double character sums over elliptic curves and finite fields

Abstract

Keywords

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