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Add the missing ZKP to the theoretical solution

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Yiğit Kılıçoğlu
2023-05-01 20:27:55 -04:00
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parent 3a25cbba7e
commit d19f7e82d0
1 changed files with 2 additions and 2 deletions
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README.md
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@@ -50,7 +50,7 @@ Let Alice ($\mathcal{P}_A$) and Bob ($\mathcal{P}_B$) be the players of a ZheroT
**One-sided Board Update Protocol**:
1. Player $\mathcal{P}_1$ picks a uniform $\alpha \in \mathbb{Z}_p$ and sends $\mathcal{X}_1 = (H(\mathcal{N}_1^{'}))^\alpha$, where $H$ is a random oracle, to player $\mathcal{P}_2$ with a zero-knowledge proof that proves that (1) the move from $u$ to $u'$ is valid and that (2) the elements in $\mathcal{N}_1^{'}$ contain the neighbors of $u'$.
2. $\mathcal{P}_2$ picks a uniform $\beta \in \mathbb{Z}_p$ and sends back $\mathcal{X}_1^{'} = (\mathcal{X}_1)^\beta$ and $\mathcal{X}_2 = \{ (H(u_2))^\beta \}$. $\mathcal{P}_2$ sends along a zero-knowledge proof that proves that $\mathcal{X}_2$ was calculated correctly.
2. $\mathcal{P}_2$ picks a uniform $\beta \in \mathbb{Z}_p$ and sends back $\mathcal{X}_1^{'} = (\mathcal{X}_1)^\beta$ and $\mathcal{X}_2 = \{ (H(u_2))^\beta \}$. $\mathcal{P}_2$ sends along a zero-knowledge proof that proves that $\mathcal{X}_1^{'}$ and $\mathcal{X}_2$ were calculated correctly.
3. $\mathcal{P}_1$ calculates $\mathcal{X}_2^{'} = (\mathcal{X}_2)^{\alpha}$ and checks whether $\mathcal{X}_1^{'}$ and $\mathcal{X}_2^{'}$ intersect. If they intersect, then $\mathcal{P}_1$ is able to see $\mathcal{P}_2$. Otherwise, $\mathcal{P}_2$ is in the dark.
@@ -112,4 +112,4 @@ node index.js
[fogofwartutorial]: https://www.youtube.com/watch?v=_1F9LHuQFxc
[zherotag-slides]: https://docs.google.com/presentation/d/1OL8yg962QT-DHgDD-zecBKWVpN6b9eNND8x9Lz6F8Rc/edit?usp=sharing
[font]: http://www.patorjk.com/software/taag/
[language]: https://github.com/jonatasemidio/multilanguage-readme-pattern
[language]: https://github.com/jonatasemidio/multilanguage-readme-pattern