Paper 2010/287
Introduction to Mirror Theory: Analysis of Systems of Linear Equalities and Linear Non Equalities for Cryptography
Jacques Patarin
Abstract
\begin{abstract} In this paper we will first study two closely related problems:\\ 1. The problem of distinguishing $f(x\Vert 0)\oplus f(x \Vert 1)$ where $f$ is a random permutation on $n$ bits. This problem was first studied by Bellare and Implagliazzo in~\cite{BI}.\\ 2. The so-called ``Theorem $P_i \oplus P_j$'' of Patarin (cf~\cite{P05}). Then, we will see many variants and generalizations of this ``Theorem $P_i \oplus P_j$'' useful in Cryptography. In fact all these results can be seen as part of the theory that analyzes the number of solutions of systems of linear equalities and linear non equalities in finite groups. We have nicknamed these analysis ``Mirror Theory'' due to the multiples induction properties that we have in it. \end{abstract}
Note: rectification of typos
Metadata
- Available format(s)
-
PDF
- Category
- Secret-key cryptography
- Publication info
- Preprint. MINOR revision.
- Keywords
- Xor of random permutationsSecurity proofs beyond the Birthday Bound
- Contact author(s)
- valerie nachef @ u-cergy fr
- History
- 2017-02-19: last of 2 revisions
- 2010-05-17: received
- See all versions
- Short URL
- https://ia.cr/2010/287
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2010/287,
author = {Jacques Patarin},
title = {Introduction to Mirror Theory: Analysis of Systems of Linear Equalities and Linear Non Equalities for Cryptography},
howpublished = {Cryptology {ePrint} Archive, Paper 2010/287},
year = {2010},
url = {https://eprint.iacr.org/2010/287}
}
