  Elaborate protocols in Secure Multi-party Computation enable several
participants to compute a public function of their own private inputs while
ensuring that no undesired information leaks about the private inputs, and
without resorting to any trusted third party. However, the public output of the
computation inevitably leaks some information about the private inputs. Recent
works have introduced a framework and proposed some techniques for quantifying
such information flow. Yet, owing to their complexity, those methods do not
scale to practical situations that may involve large input spaces. The main
contribution of the work reported here is to formally investigate the
information flow captured by the min-entropy in the particular case of secure
three-party computations of affine functions in order to make its
quantification scalable to realistic scenarios. To this end, we mathematically
derive an explicit formula for this entropy under uniform prior beliefs about
the inputs. We show that this closed-form expression can be computed in time
constant in the inputs sizes and logarithmic in the coefficients of the affine
function. Finally, we formulate some theoretical bounds for this privacy leak
in the presence of non-uniform prior beliefs.
