Novel Cyclic and Algebraic Properties of AES

Rijndael, or the Advanced Encryption Standard, is an interesting cipher from a designer’s viewpoint. Over the last few decades, the most notable, and successful attacks against the best block ciphers were linear and differential cryptanalysis. On the other hand, Rijndael is designed from the ground up to resist these attacks, as well as many others, by employing special algebraic properties of its primitive operations. The byte inversion operation over finite field F256 was chosen by its designer to thwart all possibly useful linear and difference invariances, the basic ingredients of linear and differential cryptanalysis. However, by using simple algebraic operations with known properties, the combinations of them may possess many interesting, and unexpected, algebraic properties that were not known at design time. This paper presents such new unknown properties on the combinations of primitive operations of AES.