sigmasig

sec-pairings.tex

@@ -33,6 +33,8 @@ This hypothesis, from which the Diffie-Hellman key exchange relies its security
   The \emph{Symmetric eXternal Diffie-Hellman} ($\SXDH$) assumption holds if the $\DDH$ assumption holds both in $\GG$ and $\Gh$.
 \end{restatable}
 
+The advantages of the best $\ppt$ adversary against $\DDH$ in group $\GG$ and $\Gh$ are written $\advantage{\DDH}{\GG}$ and $\advantage{\DDH}{\Gh}$ respectively. Both of those quantities are assumed negligible under the $\SXDH$ assumption.
+
 In \cref{ch:sigmasig}, the security of the group signature scheme relies on the $\SXDH$ assumption, which is a well-studied assumption.
 Moreover, this assumption is static, meaning that the size of the assumption is independent of any parameters, and is non-interactive, in the sense that it does not involve any oracle.