  In modern distributed computing applications, such as federated learning and
AIoT systems, protecting privacy is crucial to prevent adversarial parties from
colluding to steal others' private information. However, guaranteeing the
utility of computation outcomes while protecting all parties' data privacy can
be challenging, particularly when the parties' privacy requirements are highly
heterogeneous. In this paper, we propose a novel privacy framework for
multi-party computation called Threshold Personalized Multi-party Differential
Privacy (TPMDP), which addresses a limited number of semi-honest colluding
adversaries. Our framework enables each party to have a personalized privacy
budget. We design a multi-party Gaussian mechanism that is easy to implement
and satisfies TPMDP, wherein each party perturbs the computation outcome in a
secure multi-party computation protocol using Gaussian noise. To optimize the
utility of the mechanism, we cast the utility loss minimization problem into a
linear programming (LP) problem. We exploit the specific structure of this LP
problem to compute the optimal solution after O(n) computations, where n is the
number of parties, while a generic solver may require exponentially many
computations. Extensive experiments demonstrate the benefits of our approach in
terms of low utility loss and high efficiency compared to existing private
mechanisms that do not consider personalized privacy requirements or collusion
thresholds.
