Protecting the security and privacy of data is a paramount concern of enterprises in medical, educational, financial, and other highly regulated industries. While some industries have moved rapidly to take advantage of the cost savings, innovations in data analysis, and many benefits provided by cloud platforms, regulated enterprises with sensitive data have proceeded with caution. In this paper, we explore a fully public cloud-based architecture that is able to handle both service requirements and security requirements. In such a public cloud environment, the traditional notion of static perimeter-based reactive security can leave internal system components vulnerable to accidental data disclosures or malicious attacks originating from within the perimeter. Therefore, ensuring security and compliance of such a solution requires innovation and new approaches in several directions, including proactive log monitoring and analysis of virtually all parts of the cloud-based solution, full end-To-end data encryption from the client through Internet transmission to data storage and analytics in the solution, and robust firewall and network-intrusion detection systems. We discuss many of these techniques as applied to a specific real-world application known as the Watson Genomic Analytics Prototype.