Private Sum Computation: Trade-Offs between Communication, Randomness, and Privacy

Consider multiple users and a fusion center. Each user possesses a sequence of bits and can communicate with the fusion center through a one-way public channel. The fusion center’s task is to compute the sum of all the sequences under the privacy requirement that a set of colluding users, along with the fusion center, cannot gain more than a predetermined amount $δ$ of information, measured through mutual information, about the sequences of other users. Our first contribution is to characterize the minimum amount of necessary communication between the users and the fusion center, as well as the minimum amount of necessary randomness at the users. Our second contribution is to establish a connection between private sum computation and secret sharing by showing that secret sharing is necessary to generate the local randomness needed for private sum computation, and prove that it holds true for any $δ\geq 0$.

💡 Research Summary

This paper studies a distributed “private sum computation” problem in which L ≥ 2 users each hold an n‑bit binary sequence Sₗ and send a single‑shot, one‑way public message Xₗ to a fusion center. The fusion center must recover the exact sum ΣₗSₗ, while a coalition of up to T ≤ L − 2 colluding users together with the fusion center is allowed to learn at most a predetermined amount δ of information about the remaining users’ inputs. Information leakage is measured by the conditional mutual information I(S_