From 680d223a8caad1a2e738e29126f35a1f632cdbf1 Mon Sep 17 00:00:00 2001 From: Fabrice Mouhartem Date: Tue, 20 Mar 2018 11:07:21 +0100 Subject: [PATCH] Symmetric Discrete Logarithm --- sec-pairings.tex | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/sec-pairings.tex b/sec-pairings.tex index 0061f94..179416b 100644 --- a/sec-pairings.tex +++ b/sec-pairings.tex @@ -7,7 +7,7 @@ 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,MSS17,BD18}. -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 $\SXDH$. +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 $\SDL$. %\subsection{Bilinear maps} @@ -41,9 +41,9 @@ For instance, Cheon gave an attack against $q$-Strong Diffie-Hellmann problem fo In the aforementioned chapter, we also rely on the following assumption, which generalizes the Discrete Logarithm problem to asymmetric groups. -\begin{definition}[SDL] +\begin{definition}[$\SDL$] \label{de:SDL} \index{Pairings!SDL} - In bilinear groups $(\GG,\hat{\GG},\GT^{})$ of prime order $p$, the \emph {Symmetric Discrete Logarithm} (SDL) problem consists in, given + In bilinear groups $(\GG,\hat{\GG},\GT^{})$ of prime order $p$, the \emph {Symmetric Discrete Logarithm} ($\SDL$) problem consists in, given $(g,\hat{g},g^a,\hat{g}^a) \in \GG \times \hat{\GG}$ where $a \sample \ZZ_p^{}$, computing $a \in \ZZ_p^{}$. \end{definition}