SXDH

sec-pairings.tex

@@ -7,6 +7,8 @@ Since then, many constructions have been proposed for cryptographic construction
 Multiple constructions and parameter sets coexist for pairings.
 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,BD17}.
 
+In the following, we rely on the black-box definition of cryptographic pairings as bilinear maps, and on the assumed hardness of a classical assumption over pairings, namely $\SXDH$.
+
 
 %\subsection{Bilinear maps}
 \begin{definition}[Pairings~\cite{BSS05}] \label{de:pairings}
@@ -30,7 +32,7 @@ Most standard assumptions over pairings are derived from the equivalent of the D
 
 This hypothesis, from which the Diffie-Hellman key exchange relies its security on, is then used to defined the $\SXDH$ assumption.
 
-\begin{definition}[$\SXDH$]
+\begin{definition}[{$\SXDH$~\cite[As.~1]{BGdMM05}}]
   The \emph{Symmetric eXternal Diffie-Hellman} ($\SXDH$) assumption holds if the $\DDH$ assumption holds both in $\GG$ and $\Gh$.
 \end{definition}