  The purpose of Secure Multi-Party Computation is to enable protocol
participants to compute a public function of their private inputs while keeping
their inputs secret, without resorting to any trusted third party. However,
opening the public output of such computations inevitably reveals some
information about the private inputs. We propose a measure generalising both
Renyi entropy and g-entropy so as to quantify this information leakage. In
order to control and restrain such information flows, we introduce the notion
of function substitution which replaces the computation of a function that
reveals sensitive information with that of an approximate function. We exhibit
theoretical bounds for the privacy gains that this approach provides and
experimentally show that this enhances the confidentiality of the inputs while
controlling the distortion of computed output values. Finally, we investigate
the inherent compromise between accuracy of computation and privacy of inputs
and we demonstrate how to realise such optimal trade-offs.
