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@ -9782,6 +9782,8 @@ Peter Newell's illustration of the Jubjub bird, from \cite{Carroll1902}. |
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\item Minor changes to avoid clashing notation for |
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Edwards curves $\Edwards{a,d}$, Montgomery curves $\Montgomery{A,B}$, and |
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extractors $\Extractor{\Adversary}$. |
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\item Correct a use of $\GroupJ$ that should have been $\MontCurve$ in the proof of |
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\theoremref{thmdistinctxcriterion}. |
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} %sapling |
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\end{itemize} |
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@ -11323,7 +11325,7 @@ $P_1 = \scalarmult{k_1}{Q}$, there can be only one other point $-P_1$ with |
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the same $x$-coordinate. (This follows from the fact that the curve equation |
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determines $\pm y$ as a function of $x$.) |
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But $-P_1 = \scalarmult{-1}{\scalarmult{k_1}{Q}} = \scalarmult{-k_1}{Q}$. |
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Since $\fun{k \typecolon \bigrange{-\halfs}{\halfs}}{\scalarmult{k}{Q} \typecolon \GroupJ}$ |
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Since $\fun{k \typecolon \bigrange{-\halfs}{\halfs}}{\scalarmult{k}{Q} \typecolon \MontCurve}$ |
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is injective and $k_\barerange{1}{2}$ are in $\bigrange{-\halfs}{\halfs}$, |
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then $k_2 = \pm k_1$ (contradiction). |
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\end{proof} |
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