Contact tracing is being widely employed to combat the spread of COVID-19. Many apps have been developed that allow for tracing to be done automatically based off location and interaction data generated by users. There are concerns, however, regarding the privacy and security of users data when using these apps. These concerns are paramount for users who contract the virus, as they are generally required to release all their data. Motivated by the need to protect users privacy we propose two solutions to this problem. Our first solution builds on current "message based" methods and our second leverages ideas from secret sharing and additively homomorphic encryption.