From 8f424b77532db5b13fac6d67a96fb052c3ab1dac Mon Sep 17 00:00:00 2001 From: Fabrice Mouhartem Date: Mon, 12 Feb 2018 15:22:23 +0100 Subject: [PATCH] Intro chap-structures --- chap-structures.tex | 7 +++++++ 1 file changed, 7 insertions(+) diff --git a/chap-structures.tex b/chap-structures.tex index fa9ec7f..37953f8 100644 --- a/chap-structures.tex +++ b/chap-structures.tex @@ -1,6 +1,13 @@ \chapter{Underlying Structures} \label{chap:structures} +In the previous chapter, we saw that theoretical cryptography has to rely on \emph{computational hardness assumptions}. +Beside \emph{information theory-base cryptography}, most hardness assumptions are built on top of algebraic structures. +For instance the discrete logarithm assumption (Definition~\ref{de:DLP}) is based on a cyclic group structure. +That is, in some groups it is assumed that computing the discrete logarithm is an intractable problem for any probabilistic polynomial time algorithms. + +In this chapter, we focus on describing the different structures on which the cryptography we build in this thesis are based on, namely bilinear groups and lattices. + \section{Pairing-Based Cryptography} \label{se:pairing}