From 48b14956eb7f4353eb6ed866df539913b7b5a45c Mon Sep 17 00:00:00 2001 From: Fabrice Mouhartem Date: Thu, 19 Apr 2018 15:21:24 +0200 Subject: [PATCH] Uniformization of notations --- sec-pairings.tex | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/sec-pairings.tex b/sec-pairings.tex index 8fea2a1..a44b095 100644 --- a/sec-pairings.tex +++ b/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)]