Speech is digitized, encrypted and sent between two parties in many situations. Digitized speech signals are generally considered as ordinary binary data streams as far as encryption is concerned. In this thesis, it is presented that the properties of speech signals are different from the text, image, video, and other non-speech signals and need special attention while being encrypted. These properties of speech signals have to be kept in mind, not only, while designing encryption algorithms for digitized speech signals but also during the implementation of these algorithms in software and hardware. It is presented that how the statistical properties of speech can be utilized to extract important information, from a cryptanalytic point of view, from the encrypted speech signals. Some of the published cryptanalysis techniques particularly used for text-based data are studied and then the effectiveness of these techniques on the underlying plaintext data if it is digitized and compressed speech is analyzed. In this work, the latest techniques of selective or partial speech encryption designed for mobile multimedia and voice over IP applications are analyzed.