Incomplete exponential sums and Diffie-Hellman triples

William D. Banks*, John B. Friedlander, Sergei V. Konyagin, Igor E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)
3 Downloads (Pure)

Abstract

Let $p$ be a prime and $\vartheta$ an integer of order $t$ in the multiplicative group modulo $p$. In this paper, we continue the study of the distribution of Diffie-Hellman triples $(θx, θy, θxy) $ by considering the closely related problem of estimating exponential sums formed from linear combinations of the entries in such triples. We show that the techniques developed earlier for complete sums can be combined, modified and developed further to treat incomplete sums as well. Our bounds imply uniformity of distribution results for Diffie-Hellman triples as the pair $(x,y)$ varies over small boxes.

Original languageEnglish
Pages (from-to)193-206
Number of pages14
JournalMathematical Proceedings of the Cambridge Philosophical Society
Volume140
Issue number2
DOIs
Publication statusPublished - Mar 2006

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