Moving from a paper-based to electronic-based medical records has become recently a target for many medical institutions to increase efficiency and decrease costs. However, this makes patient's sensitive data – collected and stored in electronic medical records (EMRs) – more vulnerable and at the risk of privacy violations and breaches. For this sake, institutions try to protect the privacy of its patients' data. However, being a part of a bigger medical system may require that an institution be a part of a global query, such situation imposes new challenges for hospitals to preserve their data privacy while being able to participate in global analytical queries with other hospitals. Secure multi-party computation protocols (SMC) help in executing global analytical queries between a set of distrustful data owners who have no desire to share their confidential data, however they all need to cooperate to answer global queries about patients' medical history. The bulk of SMC protocols targets the ring topology execution environment in which query results at one node are passed to next node in the topology. In this paper, we propose a privacy preserving SMC technique to execute equality-test and range queries on EMRs. Our proposed technique uses bucketization to reduce computational cost. We replaced the conventional ring topology by start where each party can exchange messages directly over a private connection with the mediator. This too can improve management and improves the overall performance. Our experimental results show the effectiveness of our technique which provides better privacy without the need for trusted third party (TTP).