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		@@ -7,7 +7,7 @@ Since then, many constructions have been proposed for cryptographic construction
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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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In the following, we rely on the black-box definition of cryptographic pairings as bilinear maps, and on the assumed hardness of classical assumptions over pairings, namely $\SXDH$ and $\SDL$.
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In the following, we rely on the black-box definition of cryptographic pairings as bilinear maps, and on the assumed hardness of classical constant-size assumptions over pairings, namely $\SXDH$ and $\SDL$.
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%\subsection{Bilinear maps}
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