The Rijndael cipher was chosen as the Advanced Encryption Standard (AES) in August 1999. Its internal structure exhibits unusual properties such as a clean and simple algebraic description for the S-box. In this research, we construct a scalable family of ciphers which behave very much like the original Rijndael. This approach gives us the opportunity to use computational complexity theory. In the main result, we generate a candidate one-way function family from the scalable Rijndael family. We note that, although reduction to one-way functions is a common theme in the theory of public-key cryptography, it is rare to have such a defense of security in the private-key theatre. In this thesis a plan of attack is introduced at the circuit level whose aim is not break the cryptosystem in any practical way, but simply to break the very bold Rijndael security claim. To achieve this goal, we are led to a formal understanding of the Rijndael security claim, juxtaposing it with rigorous security treatments. Several of the questions that arise in this regard are as follows: ``Do invertible functions represented by circuits with very small numbers of gates have better than worst case implementations for their inverses?' ``How many plaintext/ciphertext pairs are needed to uniquely determine the Rijndael key?'