One of the important streams of research in supply chain management is the coordination between suppliers and retailers by varying the lot-size and the purchase price and common replenishment epoch (CRE). But most of the CRE solutions either assume existence of a central planner who has all the information about the system, or assume that each participant of the computation shares all of his information with other participants. These solutions are problematic when the data is sensitive and the participants are reluctant to share their private information. The development and deployment of privacy preserving coordinating model in lot to lot supply chain based on common replenishment epoch could allow supply chain collaborations to take place without revealing any participant's data to the others, reaping the benefits of collaboration while avoiding the drawbacks. In this paper, we develop and apply secure minimum sum of multi-dimensional protocol to the problem of coordinating a single-vendor multi-retailer inventory system with a probabilistic demand which follows normal distribution, where the objective is to find a CRE policy for each facility in the system such that the total average ordering and inventory-related cost of the entire system is minimized.