From fd810298c9b9d640c9ae81d265f77a6d80acdd87 Mon Sep 17 00:00:00 2001 From: arnaucube Date: Tue, 16 May 2023 00:32:59 +0200 Subject: [PATCH] add initial HyperNova notes --- README.md | 1 + notes_hypernova.pdf | Bin 0 -> 227741 bytes notes_hypernova.tex | 140 ++++++++++++++++++++++++++++++++++++++++++++ paper-notes.bib | 17 ++++++ 4 files changed, 158 insertions(+) create mode 100644 notes_hypernova.pdf create mode 100644 notes_hypernova.tex diff --git a/README.md b/README.md index 51951ee..7d74049 100644 --- a/README.md +++ b/README.md @@ -14,5 +14,6 @@ Notes, code and documents done while reading books and papers. - [Notes on FRI](notes_fri.pdf) - [Notes on Spartan](notes_spartan.pdf) - [Notes on Nova](notes_nova.pdf) +- [Notes on HyperNova](notes_hypernova.pdf) Also some Sage implementations can be found in the `*.sage` files of this repo. diff --git a/notes_hypernova.pdf b/notes_hypernova.pdf new file mode 100644 index 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\leftrightarrow P$: sum-check protocol:\\ + $$c \leftarrow (g, s, d+1, \sum_{j \in [t]} \gamma^j \cdot v_j)$$ + where:\\ + \begin{align*} + g(x) &:= \left( \sum_{j \in [t]} \gamma^j \cdot L_j(x) \right) + \gamma^{t+1} \cdot Q(x)\\ + L_j(x) &:= \widetilde{eq}(r_x, x) \cdot \left( \sum_{y \in \{0,1\}^{s'}} \widetilde{M}_j(x, y) \cdot \widetilde{z}_1(y) \right)\\ + Q(x) &:= \widetilde{eq}(\beta, x) \cdot \left( \sum_{i=1}^q c_i \cdot \prod_{j \in S_i} \left( \sum_{y \in \{0, 1\}^{s'}} \widetilde{M}_j(x, y) \cdot \widetilde{z}_2(y) \right) \right) + \end{align*} + \item $P \rightarrow V$: $\left( (\sigma_1, \ldots, \sigma_t), (\theta_1, \ldots, \theta_t) \right)$ + where + $$\sigma_j = \sum_{y \in \{0,1\}^{s'}} \widetilde{M}_j(x, y) \cdot \widetilde{z}_1(y)$$ + $$\theta_j = \sum_{y \in \{0, 1\}^{s'}} \widetilde{M}_j(x, y) \cdot \widetilde{z}_2(y)$$ + \item V: $e_1 \leftarrow \widetilde{eq}(r_x, r_x')$, $e_2 \leftarrow \widetilde{eq}(\beta, r_x')$\\ + check: + $$c = \left( \sum_{j \in [t]} \gamma^j e_1 \sigma_j + \gamma^{t+1} e_2 \left( \sum_{i=1}^q c_i \cdot \prod_{j \in S_i} \sigma \right) \right)$$ + \item $V \rightarrow P: \rho \in^R \mathbb{F}$ + \item $V, P$: output the folded LCCCS instance $(C', u', \mathsf{x}', r_x', v_1', \ldots, v_t')$, where $\forall i \in [t]$: + \begin{align*} + C' &\leftarrow C_1 + \rho \cdot C_2\\ + u' &\leftarrow u + \rho \cdot 1\\ + \mathsf{x}' &\leftarrow \mathsf{x}_1 + \rho \cdot \mathsf{x}_2\\ + v_i' &\leftarrow \sigma_i + \rho \cdot \theta_i + \end{align*} + \item $P$: output folded witness: $\widetilde{w}' \leftarrow \widetilde{w}_1 + \rho \cdot \widetilde{w}_2$. +\end{enumerate} + + +\bibliography{paper-notes.bib} +\bibliographystyle{unsrt} + +\end{document} diff --git a/paper-notes.bib b/paper-notes.bib index 0090122..91c271a 100644 --- a/paper-notes.bib +++ b/paper-notes.bib @@ -109,3 +109,20 @@ note = {\url{https://eprint.iacr.org/2019/550}}, url = {https://eprint.iacr.org/2019/550} } + +@misc{cryptoeprint:2023/552, + author = {Srinath Setty and Justin Thaler and Riad Wahby}, + title = {Customizable constraint systems for succinct arguments}, + howpublished = {Cryptology ePrint Archive, Paper 2023/552}, + year = {2023}, + note = {\url{https://eprint.iacr.org/2023/552}}, + url = {https://eprint.iacr.org/2023/552} +} +@misc{cryptoeprint:2023/573, + author = {Abhiram Kothapalli and Srinath Setty}, + title = {HyperNova: Recursive arguments for customizable constraint systems}, + howpublished = {Cryptology ePrint Archive, Paper 2023/573}, + year = {2023}, + note = {\url{https://eprint.iacr.org/2023/573}}, + url = {https://eprint.iacr.org/2023/573} +}