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.
|Number of pages||14|
|Journal||Mathematical Proceedings of the Cambridge Philosophical Society|
|Publication status||Published - Mar 2006|