Commutative algebra and symmetric cryptography

In this thesis, I present a deeper relationship between symmetric cryptography and commutative algebra, which at first glace seems to be unrelated concepts. More specifically between the permutation of bits and modules over group algebras. This relationship provides a deeper mathematical understanding of linear functions which are constructed using these bit permutations. These functions are a popular choice for designing symmetric cryptographic schemes. This new connection helps us understand certain behaviour of these linear functions, and can be used to construct new functions which ommit certain cryptographic weaknesses.