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\chapter{Security Proofs in Cryptography} \label{chap:proofs}
\chapter{Security Proofs in Cryptography} \label{ch:proofs}
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.
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Once that we define the notions related to the core of the proof, we have to define the objects on what we work on.
Namely, defining what we want to prove, and the hypotheses on which we rely, also called ``hardness assumption''.
The details of the hardness assumptions we use are given in Chapter~\ref{chap:structures}.
The details of the hardness assumptions we use are given in Chapter~\ref{ch:structures}.
Nevertheless, some notions are common to these and are evoked here.
The confidence one can put in a hardness assumption depends on many criteria.