## Cryptology ePrint Archive: Report 2016/702

Mirror Theory and Cryptography

Jacques Patarin

Abstract: Mirror Theory'' is the theory that evaluates the number of solutions of affine systems of equalities (=) and non equalities ($\neq$) in finite groups. It is deeply related to the security and attacks of many generic cryptographic secret key schemes, for example random Feistel schemes (balanced or unbalanced), Misty schemes, Xor of two pseudo-random bijections to generate a pseudo-random function etc. In this paper we will assume that the groups are abelian. Most of time in cryptography the group is $((\mathbb{Z}/2\mathbb{Z})^n, \oplus)$ and we will concentrate this paper on these cases. We will present here general definitions, some theorems, and many examples and computer simulations.

Category / Keywords: secret-key cryptography / combinatorial cryptography