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update in offchain-decider commitmentscheme wording

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arnaucube
2024-10-01 09:59:10 +02:00
parent 94ea858c44
commit a1672876d6
1 changed files with 4 additions and 4 deletions
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src/design/nova-decider-offchain.md
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@@ -39,10 +39,10 @@ In the offchain case, since we can end up with proofs in both curves of the cycl
- 2: check that $u_n.\overline{E}=0$ and $u_n.u=1$ - 2: check that $u_n.\overline{E}=0$ and $u_n.u=1$
- 3: check that $u_n.x_0 = H(n, z_0, z_n, U_n)$ and $u_n.x_1 = H(U_{EC,n})$ - 3: check that $u_n.x_0 = H(n, z_0, z_n, U_n)$ and $u_n.x_1 = H(U_{EC,n})$
- 4: correct RelaxedR1CS relation of $U_{n+1}, W_{n+1}$ of the AugmentedFCircuit - 4: correct RelaxedR1CS relation of $U_{n+1}, W_{n+1}$ of the AugmentedFCircuit
- 5.1: Check correct computation of the KZG challenges for $U_{n+1}$ - 5.1: Check correct computation of the CommitmentScheme challenges for $U_{n+1}$
$$c_E = H(U_{n+1}.\overline{E}.\{x,y\}),~~c_W = H(U_{n+1}.\overline{W}.\{x,y\})$$ $$c_E = H(U_{n+1}.\overline{E}.\{x,y\}),~~c_W = H(U_{n+1}.\overline{W}.\{x,y\})$$
which we do through in-circuit Transcript. which we do through in-circuit Transcript.
- 5.2: check that the KZG evaluations for $U_{n+1}$ are correct - 5.2: check that the CommitmentScheme evaluations for $U_{n+1}$ are correct
- $eval_W == p_W(c_W)$ - $eval_W == p_W(c_W)$
- $eval_E == p_E(c_E)$ - $eval_E == p_E(c_E)$
<br>where $p_W, p_E \in \mathbb{F}[X]$ are the interpolated polynomials from $W_{i+1}.W,~ W_{i+1}.E$ respectively, <br>where $p_W, p_E \in \mathbb{F}[X]$ are the interpolated polynomials from $W_{i+1}.W,~ W_{i+1}.E$ respectively,
@@ -51,10 +51,10 @@ In the offchain case, since we can end up with proofs in both curves of the cycl
#### Circuit2 $\in Fq$ ($E_2.F_r$) #### Circuit2 $\in Fq$ ($E_2.F_r$)
- 6: correct RelaxedR1CS relation of $U_{EC,d}, W_{EC,d}$ - 6: correct RelaxedR1CS relation of $U_{EC,d}, W_{EC,d}$
- 7.1: Check correct computation of the KZG challenges for $U_{EC}$ - 7.1: Check correct computation of the CommitmentScheme challenges for $U_{EC}$
$$c_E = H(U_{EC}.\overline{E}.\{x,y\}),~~c_W = H(U_{EC}.\overline{W}.\{x,y\})$$ $$c_E = H(U_{EC}.\overline{E}.\{x,y\}),~~c_W = H(U_{EC}.\overline{W}.\{x,y\})$$
which we do through in-circuit Transcript. which we do through in-circuit Transcript.
- 7.2: check that the KZG evaluations for $U_{EC}$ are correct - 7.2: check that the CommitmentScheme evaluations for $U_{EC}$ are correct
- $eval_W == p_W(c_W)$ - $eval_W == p_W(c_W)$
- $eval_E == p_E(c_E)$ - $eval_E == p_E(c_E)$
<br>where $p_W, p_E \in \mathbb{F}[X]$ are the interpolated polynomials from $W_{i+1}.W,~ W_{i+1}.E$ respectively. <br>where $p_W, p_E \in \mathbb{F}[X]$ are the interpolated polynomials from $W_{i+1}.W,~ W_{i+1}.E$ respectively.