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 $δ\geq 0$.

翻译：考虑多个用户与一个融合中心。每个用户持有一个比特序列，并可通过单向公共信道与融合中心通信。融合中心的任务是在满足隐私要求的前提下计算所有序列的和：即一组共谋用户与融合中心通过互信息度量的关于其他用户序列的信息量不得超过预定阈值 $δ$。我们的首要贡献在于刻画了用户与融合中心之间所需的最小通信量，以及用户端所需的最小随机性量。我们的第二项贡献是建立了私有和计算与秘密共享之间的联系，通过证明秘密共享是生成私有和计算所需局部随机性的必要条件，并证明该结论对所有 $δ\geq 0$ 均成立。