fmouhart/thesis
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

Add french TOC and ZK part

Browse Source
This commit is contained in:
Fabrice Mouhartem
2018-04-04 18:46:37 +02:00
parent 46d6a19111
commit 280d99008b
18 changed files with 203 additions and 11 deletions
Download Patch File Download Diff File Expand all files Collapse all files

8
chap-proofs.tex
View File

@ -1,4 +1,5 @@
\chapter{Security Proofs in Cryptography} \label{ch:proofs}
\addcontentsline{tof}{chapter}{\protect\numberline{\thechapter} Les preuves de sécurité en cryptographie}
Provable security is a subfield of cryptography where constructions are proven secure with regards to a security model.
To illustrate this notion, let us take the example of public-key encryption schemes.
@ -17,6 +18,7 @@ Then we will define these security models.
% Security Reductions %
%%%%%%%%%%%%%%%%%%%%%%%
\section{Security Reductions}
\addcontentsline{tof}{section}{\protect\numberline{\thesection} Réductions de sécurité}
Provable security providing constructions for which the security is guaranteed by a security proof, or \emph{security reduction}.
The name ``reduction'' comes from computational complexity.
@ -129,9 +131,9 @@ To illustrate this, let us consider the two following assumptions:
\end{definition}
\begin{restatable}[Decisional Diffie-Hellman]{definition}{defDDH}
\index{Discrete Logarithm!Decisional Diffie-Hellman} \label{de:DDH}
\index{Discrete Logarithm!Decisional Diffie-Hellman} \label{de:DDH}
Let $\GG$ be a cyclic group of order $p$. The \emph{decisional Diffie-Hellman} ($\DDH$) problem is the following.
Given the tuple $(g, g_1^{}, g_2^{}, g_3^{}) = (g, g^a_{}, g^b{}, g^c_{}) \in \GG^4_{}$, the goal is to decide whether $c = ab$ or $c$ is sampled uniformly in $\GG$.
Given the tuple $\bigl(g, g_1^{}, g_2^{}, g_3^{}\bigr) = \bigl(g, g^a_{}, g^b{}, g^c_{}\bigr) \in \GG^4_{}$, the goal is to decide whether $c = ab$ or $c$ is sampled uniformly in $\GG$.
The \textit{\DDH assumption} is the intractability of the problem for any $\ppt$ algorithm.
\end{restatable}
@ -157,6 +159,7 @@ In other words, the context in which the proofs are made.
This is the topic of the next section.
\section{Random-Oracle Model and Standard Model} \label{se:models}
\addcontentsline{tof}{section}{\protect\numberline{\thesection} Modèle de l'oracle aléatoire et modèle standard}
The most general model to do security proofs is the \textit{standard model}.
In this model, nothing special is assumed, and every assumptions are explicit.
@ -194,6 +197,7 @@ We now have defined the security structure on which we are working on and the ba
The following section explains how to define the security of a cryptographic primitive.
\section{Security Games and Simulation-Based Security} \label{se:games-sim}
\addcontentsline{tof}{section}{\protect\numberline{\thesection} Preuves par jeux et preuves par simulation}
Up to now, we defined the structure on which security proofs works. Let us now define what we are proving.
An example of what we are proving has been shown in Section~\ref{se:models} with cryptographic hash functions.