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\chapter{Security Proofs in Cryptography} \label{chap:proofs}
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\chapter{Security Proofs in Cryptography} \label{ch:proofs}
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Provable security is a subfield of cryptography where constructions are proven secure with regards to a security model.
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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.
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Namely, defining what we want to prove, and the hypotheses on which we rely, also called ``hardness assumption''.
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The details of the hardness assumptions we use are given in Chapter~\ref{chap:structures}.
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The details of the hardness assumptions we use are given in Chapter~\ref{ch:structures}.
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Nevertheless, some notions are common to these and are evoked here.
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The confidence one can put in a hardness assumption depends on many criteria.
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