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small update on notes_nova, fix typo on notes_halo

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arnaucube
2023-05-01 20:09:47 +02:00
parent 69baaa0137
commit ba6a51e768
4 changed files with 12 additions and 2 deletions
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notes_halo.tex
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@@ -112,7 +112,7 @@ Now, for $k$ rounds ($d=2^k$, from $j=k$ to $j=1$):
\item Prover sets random blinding factors: $l_j, r_j \in \mathbb{F}_p$
\item Prover computes
$$L_j = < \overrightarrow{a}_{lo}, \overrightarrow{G}_{hi}> + [l_j] H + [< \overrightarrow{a}_{lo}, \overrightarrow{b}_{hi}>] U$$
$$R_j = < \overrightarrow{a}_{lo}, \overrightarrow{G}_{hi}> + [l_j] H + [< \overrightarrow{a}_{lo}, \overrightarrow{b}_{hi}>] U$$
$$R_j = < \overrightarrow{a}_{hi}, \overrightarrow{G}_{lo}> + [r_j] H + [< \overrightarrow{a}_{hi}, \overrightarrow{b}_{lo}>] U$$
\item Verifier sends random challenge $u_j \in \mathbb{I}$
\item Prover computes the halved vectors for next round:
$$\overrightarrow{a} \leftarrow \overrightarrow{a}_{hi} \cdot u_j^{-1} + \overrightarrow{a}_{lo} \cdot u_j$$