This work is motivated by the emergence of participatory sensing applications, a new sensing paradigm that off-loads sensing responsibility from infrastructure sensors and professional sources to the crowd. This leads to unprecedented opportunities for sensory data collection and sharing. The privacy challenges in these applications arise naturally as personal data are shared among untrusted entities in the community. This dissertation develops mathematical foundations for optimal perturbation of both single-dimensional and multidimensional time-series data. The developed perturbation techniques allow users to effectively hide their original data while aggregated community statistics are still accurately reconstructed. Several real-world applications are also developed and successfully deployed that affirm the efficiency and accuracy of the perturbation and reconstruction techniques developed in this dissertation.