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

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)179-197
Number of pages19
JournalPure and Applied Mathematics Quarterly
Volume2
Issue number1
Publication statusPublished - Jan 2006

Keywords

  • DIFFIE-HELLMAN DISTRIBUTIONS
  • DOUBLE EXPONENTIAL-SUMS
  • GENERATORS

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