20 lines
884 B
TeX
20 lines
884 B
TeX
\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}
|
|
|
|
\input sec-pairings
|
|
|
|
\section{Lattice-Based Cryptography}
|
|
\label{se:lattices}
|
|
|
|
\input sec-lattices
|