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\subsection{Zero Knowledge Proofs}
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\subsection{Zero Knowledge Proofs}
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\subsubsection{Proof 1: Knowledge of an ECDL}
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\subsubsection{Proof 1: Knowledge of an ECDL}
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Alice and Bob know $v$ and $g$ with $q = |g|$, but only Alice knows $x$, so that
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Alice and Bob know $v$, $g$ and $q = |g|$, but only Alice knows $x$, so that
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$v = xg$.
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$v = xg$.
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\begin{enumerate}
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\begin{enumerate}
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