This thesis discusses the privacy issues in speech-based applications such as biometric authentication, surveillance, and external speech processing services. Author Manas A. Pathak presents solutions for privacy-preserving speech processing applications such as speaker verification, speaker identification and speech recognition. The author also introduces some of the tools from cryptography and machine learning and current techniques for improving the efficiency and scalability of the presented solutions. Experiments with prototype implementations of the solutions for execution time and accuracy on standardized speech datasets are also included in the text. Using the framework proposed  may now make it possible for a surveillance agency to listen for a known terrorist without being able to hear conversation from non-targeted, innocent civilians.