**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

**Date: **received 13 Jul 2016

**Contact author: **valerie nachef at u-cergy fr

**Available format(s): **PDF | BibTeX Citation

**Version: **20160713:140126 (All versions of this report)

**Short URL: **ia.cr/2016/702

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