Abstract:  Cryptography and cryptanalysis have been studied throughout the ages and became a focus of research for the US government during World War II, primarily in terms of intelligence gathering.  Today, the importance of cryptography is even more evident as a result of the need for "secure" ways of transmitting sensitive data (e.g. safely sending credit card numbers over the Internet).  Basic examples will be presented that focus on the role of linear algebra in cryptography.  Encoding and decoding methods used today, such as RSA and PGP, will be discussed as they pertain to data encryption/decryption.  The discussion will focus on some of the number-theoretic aspects involved.  Cryptanalysis using the singular value decomposition (SVD) will be discussed if time permits.