proof-reading
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Pairing-based cryptography was introduced by Antoine Joux~\cite{Jou00} to generalize Diffie-Hellman key exchange to three users in one round.
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Since then, many constructions have been proposed for cryptographic constructions, such as identity-based encryption~\cite{BF01,Wat05} or group signature~\cite{ACJT00,BBS04}.
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Since then, many constructions have been proposed for cryptographic constructions, such as identity-based encryption~\cite{BF01,Wat05} or group signature~\cite{BBS04}.
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Multiple constructions and parameter sets coexist for pairings.
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Real-world implementation are based on elliptic curves~\cite{BN06, KSS08}, but recent advances in cryptanalysis makes it hard to evaluate the security level of pairing-based cryptography~\cite{KB16,MSS17,BD18}.
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@ -50,5 +50,4 @@ In the aforementioned chapter, we also rely on the following assumption, which g
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where $a \sample \ZZ_p^{}$, computing $a \in \ZZ_p^{}$.
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\end{restatable}
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This assumption is still a static and non-interactive assumption.
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This assumption is also static and non-interactive.
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