Sharing and working on sensitive data in distributed settings from healthcare to finance is a major challenge due to security and privacy concerns. Secure multiparty computation (SMC) is a viable panacea for this, allowing distributed parties to make computations while the parties learn nothing about their data, but the final result. Although SMC is instrumental in such distributed settings, it does not provide any guarantees not to leak any information about individuals to adversaries. Differential privacy (DP) can be utilized to address this; however, achieving SMC with DP is not a trivial task, either. In this paper, we propose a novel Secure Multiparty Distributed Differentially Private (SM-DDP) protocol to achieve secure and private computations in a multiparty environment. Specifically, with our protocol, we simultaneously achieve SMC and DP in distributed settings focusing on linear regression on horizontally distributed data. That is, parties do not see each others' data and further, can not infer information about individuals from the final constructed statistical model. Any statistical model function that allows independent calculation of local statistics can be computed through our protocol. The protocol implements homomorphic encryption for SMC and functional mechanism for DP to achieve the desired security and privacy guarantees. In this work, we first introduce the theoretical foundation for the SM-DDP protocol and then evaluate its efficacy and performance on two different datasets. Our results show that one can achieve individual-level privacy through the proposed protocol with distributed DP, which is independently applied by each party in a distributed fashion. Moreover, our results also show that the SM-DDP protocol incurs minimal computational overhead, is scalable, and provides security and privacy guarantees.