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.
|Number of pages||19|
|Journal||Pure and Applied Mathematics Quarterly|
|Publication status||Published - Jan 2006|
- DIFFIE-HELLMAN DISTRIBUTIONS
- DOUBLE EXPONENTIAL-SUMS