Encounter-based social networks and encounter-based systems link users who share a location at the same time, as opposed to the traditional social network paradigm of linking users who have an offline friendship. This new approach presents challenges that are fundamentally different from those tackled by previous social network designs. In this paper, we explore the functional and security requirements for these new systems, such as availability, security, and privacy, and present several design options for building secure encounter-based social networks. To highlight these challenges, we examine one recently proposed encounter-based social network design and compare it to a set of idealized security and functionality requirements. We show that it is vulnerable to several attacks, including impersonation, collusion, and privacy breaching, even though it was designed specifically for security. Mindful of the possible pitfalls, we construct a flexible framework for secure encounter-based social networks, which can be used to construct networks that offer different security, privacy, and availability guarantees. We describe two example constructions derived from this framework, and consider each in terms of the ideal requirements. Some of our new designs fulfill more requirements in terms of system security, reliability, and privacy than previous work. We also evaluate real-world performance of one of our designs by implementing a proof-of-concept iPhone application called MeetUp. Experiments highlight the potential of our system and hint at the deployability of our designs on a large scale.