This paper appeared at the 8th Australasian Workshop on Health Informatics and Knowledge Management (HIKM 2015), Sydney, Australia, January 2015. Conferences in Research and Practice in Information Technology (CRPIT), Vol. 164, Anthony Maeder and Jim Warren, Ed. Reproduction for academic, not-for profit purposes permitted provided this text is includedIn an effort to reduce the risk of sensitive data exposure in untrusted networks such as the public cloud, increasing attention has recently been given to encryption schemes that allow specific computations to occur on encrypted data, without the need for decryption. This relies on the fact that some encryption algorithms display the property of homomorphism, which allows them to manipulate data in a meaningful way while still in encrypted form. Such a framework would find particular relevance in Clinical Decision Support (CDS) applications deployed in the public cloud. CDS applications have an important computational and analytical role over confidential healthcare information with the aim of supporting decision-making in clinical practice. This review paper examines the history and current status of homomoprhic encryption and its potential for preserving the privacy of patient data underpinning cloud-based CDS applications