TY - JOUR

T1 - Incomplete exponential sums and Diffie-Hellman triples

AU - Banks, William D.

AU - Friedlander, John B.

AU - Konyagin, Sergei V.

AU - Shparlinski, Igor E.

PY - 2006/3

Y1 - 2006/3

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33244475850&partnerID=8YFLogxK

U2 - 10.1017/S0305004105008947

DO - 10.1017/S0305004105008947

M3 - Article

AN - SCOPUS:33244475850

VL - 140

SP - 193

EP - 206

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

SN - 0305-0041

IS - 2

ER -