## Incomplete exponential sums and Diffie-Hellman triples

##### Abstract

Let p be a prime and 79 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 (V-x, V-y, V-xy) 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.

##### Part of

##### Citation

Incomplete character sums and Diffie-Hellman triples, Math. Proc. Cambridge Philos. Soc. 140 (2006), 193-206.