Uniformization of notations

sec-pairings.tex

@@ -8,9 +8,8 @@ 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,MSS17,BD18}.
 
 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 $\SDL$.
+The notations $1_{\GG}^{}$, $1_{\Gh}^{}$ and $1_{\GT}^{}$ denote the unit element in $\GG$, $\Gh$ and $\GT$ respectively.
 
-
-%\subsection{Bilinear maps}
 \begin{restatable}[Pairings~\cite{BSS05}]{definition}{defPairings} \label{de:pairings} \index{Pairings}
   A pairing is a map $e: \GG \times \Gh \to \GT$ over cyclic groups of order $p$ that verifies the following properties for any $g \in \GG, \hat{g} \in \Gh$:
   \begin{enumerate}[\quad (i)]