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Fabrice Mouhartem 2018-02-08 19:12:15 +01:00
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sec-pairings.tex
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@ -22,8 +22,8 @@ In the following, we rely on the black-box definition of cryptographic pairings
For cryptographic purpose, pairings are usually defined over elliptic curves, hence $\GT$ is a multiplicative subgroup of the multiplicative group of a finite field. For cryptographic purpose, pairings are usually defined over elliptic curves, hence $\GT$ is a multiplicative subgroup of the multiplicative group of a finite field.
Most standard assumptions over pairings are derived from the equivalent of the Diffie-Hellman assumptions from cyclic groups, The most standard assumptions over pairings are derived from the equivalent of the Diffie-Hellman assumptions from cyclic groups,
defined in Definition~\ref{de:DDH} and recalled here. described in Definition~\ref{de:DDH} and recalled here.
\begin{definition}[$\DDH$ (recall)] \index{Discrete Logarithm!Decisional Diffie-Hellman} \begin{definition}[$\DDH$ (recall)] \index{Discrete Logarithm!Decisional Diffie-Hellman}
Let $\GG$ be a cyclic group of order $p$. The \emph{decisional Diffie-Hellman} ($\DDH$) problem is the following. Let $\GG$ be a cyclic group of order $p$. The \emph{decisional Diffie-Hellman} ($\DDH$) problem is the following.