The recent years have witnessed a rapid development of mobile devices and smart devices. As more and more people are getting involved in the online environment, privacy issues are becoming increasingly important. People’s privacy in the digital world is much easier to leak than in the real world, because every action people take online would leave a trail of information which could be recorded, collected and used by malicious attackers. Besides, service providers might collect users’ information and analyze them, which also leads to a privacy breach. Therefore, preserving people’s privacy is very important in the online environment.

In this dissertation, I study the problems of preserving people’s identity privacy and loca- tion privacy in the online environment. Specifically, I study four topics: identity privacy in online social networks (OSNs), identity privacy in anonymous message submission, lo- cation privacy in location based social networks (LBSNs), and location privacy in location based reminders. In the first topic, I propose a system which can hide users’ identity and data from untrusted storage site where the OSN provider puts users’ data. I also design a fine grained access control mechanism which prevents unauthorized users from accessing the data. Based on the secret sharing scheme, I construct a shuffle protocol that disconnects the relationship between members’ identities and their submitted messages in the topic of identity privacy in anonymous message submission. The message is encrypted on the mem- ber side and decrypted on the message collector side. The collector eventually gets all of the messages but does not know who submitted which message. In the third topic, I pro- pose a framework that hides users’ check-in information from the LBSN. Considering the limited computation resources on smart devices, I propose a delegatable pseudo random function to outsource computations to the much more powerful server while preserving privacy. I also implement efficient revocations. In the topic of location privacy in location based reminders, I propose a system to hide users’ reminder locations from an untrusted cloud server. I propose a cross based approach and an improved bar based approach, re- spectively, to represent a reminder area. The reminder location and reminder message are encrypted before uploading to the cloud server, which then can determine whether the dis- tance between the user’s current location and the reminder location is within the reminder distance without knowing anything about the user’s location information and the content of the reminder message.