  One of the major issues of cryptography is the cryptanalysis of cipher
algorithms. Cryptanalysis is the study of methods for obtaining the meaning of
encrypted information, without access to the secret information that is
normally required. Some mechanisms for breaking codes include differential
cryptanalysis, advanced statistics and brute-force.
  Recent works also attempt to use algebraic tools to reduce the cryptanalysis
of a block cipher algorithm to the resolution of a system of quadratic
equations describing the ciphering structure.
  In our study, we will also use algebraic tools but in a new way: by using
Boolean functions and their properties. A Boolean function is a function from
$F_2^n\to F_2$ with $n>1$, characterized by its truth table. The arguments of
Boolean functions are binary words of length $n$. Any Boolean function can be
represented, uniquely, by its algebraic normal form which is an equation which
only contains additions modulo 2 - the XOR function - and multiplications
modulo 2 - the AND function.
  Our aim is to describe the AES algorithm as a set of Boolean functions then
calculate their algebraic normal forms by using the M\"obius transforms. After,
we use a specific representation for these equations to facilitate their
analysis and particularly to try a combinatorial analysis. Through this
approach we obtain a new kind of equations system. This equations system is
more easily implementable and could open new ways to cryptanalysis.
