Cryptography has become an important tool in data protection. Cryptosystems can be used to solve a large number of the data security problems. While cryptosystems have been used successfully in protection of messages, the discovery of many different types of cryptosystems has led to possible solutions for many other problems in data security that appeared to be either difficult to solve or were not suitable for "classical" types of cryptosystems. Most of the recent discoveries of cryptosystems have been in the digital domain. Digitizing data, however, is not always possible or economical. This research is intended to study new cryptosystems for protecting analog signals' privacy and authenticity. Public key analog cryptosystems will also be studied. In view of the relative scarcity of fast, secure digital public key cryptosystems, such cryptosystems might also be of interest in digital applications.