  In a former paper it has been shown that the elliptic Gau{\ss} sums, whose
use has been proposed in the context of counting points on elliptic curves and
primality tests, can be computed by using modular functions. In this work we
give detailed algorithms for the necessary computations, all of which have been
implemented in C. We analyse the relatively straightforward algorithms derived
from the theory and provide several improvements speeding up computations
considerably. In addition, slightly generalizing former results we describe how
(elliptic) Jacobi sums may be determined in a very similar way and show how
this can be used. We conclude by an analysis of space and run-time requirements
of the algorithms.
