In this paper, we study the problem of summation evaluation of secrets. The secrets are distributed over a network of nodes that form a ring graph. Privacy-preserving iterative protocols for computing the sum of the secrets are proposed, which are compatible with node join and leave situations. Theoretic bounds are derived regarding the utility and accuracy, and the proposed protocols are shown to comply with differential privacy requirements. Based on utility, accuracy and privacy, we also provide guidance on appropriate selections of random noise parameters. Additionally, a few numerical examples that demonstrate their effectiveness are provided.