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[book] Sinsemilla: reintroduce fixed_y_q column. 

Loading fixed_y_q into an advice column introduces an additional
row. Instead, we load it into a fixed column.

Co-authored-by: Jack Grigg <jack@electriccoin.co>
This commit is contained in:
therealyingtong 2021-07-24 23:14:05 +08:00
parent 6c55e1a7e3
commit 78b0ec4e7b
1 changed files with 14 additions and 15 deletions
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29
book/src/design/circuit/gadgets/sinsemilla.md
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@ -96,25 +96,24 @@ $$
### Layout
$$
\begin{array}{|c|c|c|c|c|c|c|c|c|c|}
\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline
\text{Step} & x_A & x_P & bits & \lambda_1 & \lambda_2 & q_{S1} & q_{S2} & q_{S3} & q_{S4} \\\hline
-1 & y_Q & & & & & 0 & 0 & 0 & 1 \\\hline
0 & x_Q & x_{P[m_1]} & z_0 & \lambda_{1,0} & \lambda_{2,0} & 1 & 1 & 0 & 0 \\\hline
1 & x_{A,1} & x_{P[m_2]} & z_1 & \lambda_{1,1} & \lambda_{2,1} & 1 & 1 & 0 & 0 \\\hline
2 & x_{A,2} & x_{P[m_3]} & z_2 & \lambda_{1,2} & \lambda_{2,2} & 1 & 1 & 0 & 0 \\\hline
\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & 1 & 1 & 0 & 0 \\\hline
n-1 & x_{A,n-1} & x_{P[m_n]} & z_{n-1} & \lambda_{1,n-1} & \lambda_{2,n-1} & 1 & 0 & 0 & 0 \\\hline
0' & x'_{A,0} & x_{P[m'_1]} & z'_0 & \lambda'_{1,0} & \lambda'_{2,0} & 1 & 1 & 0 & 0 \\\hline
1' & x'_{A,1} & x_{P[m'_2]} & z'_1 & \lambda'_{1,1} & \lambda'_{2,1} & 1 & 1 & 0 & 0 \\\hline
2' & x'_{A,2} & x_{P[m'_3]} & z'_2 & \lambda'_{1,2} & \lambda'_{2,2} & 1 & 1 & 0 & 0 \\\hline
\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & 1 & 1 & 0 & 0 \\\hline
n-1' & x'_{A,n-1} & x_{P[m'_n]} & z'_{n-1} & \lambda'_{1,n-1} & \lambda'_{2,n-1} & 1 & 0 & 1 & 0 \\\hline
n' & x'_{A,n} & & & y_{A,n} & & 0 & 0 & 0 & 0 \\\hline
\text{Step} & x_A & x_P & bits & \lambda_1 & \lambda_2 & q_{S1} & q_{S2} & q_{S3} & q_{S4} & \textsf{fixed\_y\_Q}\\\hline
0 & x_Q & x_{P[m_1]} & z_0 & \lambda_{1,0} & \lambda_{2,0} & 1 & 1 & 0 & 1 & y_Q \\\hline
1 & x_{A,1} & x_{P[m_2]} & z_1 & \lambda_{1,1} & \lambda_{2,1} & 1 & 1 & 0 & 0 & 0 \\\hline
2 & x_{A,2} & x_{P[m_3]} & z_2 & \lambda_{1,2} & \lambda_{2,2} & 1 & 1 & 0 & 0 & 0 \\\hline
\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & 1 & 1 & 0 & 0 & 0 \\\hline
n-1 & x_{A,n-1} & x_{P[m_n]} & z_{n-1} & \lambda_{1,n-1} & \lambda_{2,n-1} & 1 & 0 & 0 & 0 & 0 \\\hline
0' & x'_{A,0} & x_{P[m'_1]} & z'_0 & \lambda'_{1,0} & \lambda'_{2,0} & 1 & 1 & 0 & 0 & 0 \\\hline
1' & x'_{A,1} & x_{P[m'_2]} & z'_1 & \lambda'_{1,1} & \lambda'_{2,1} & 1 & 1 & 0 & 0 & 0 \\\hline
2' & x'_{A,2} & x_{P[m'_3]} & z'_2 & \lambda'_{1,2} & \lambda'_{2,2} & 1 & 1 & 0 & 0 & 0 \\\hline
\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & 1 & 1 & 0 & 0 & 0 \\\hline
n-1' & x'_{A,n-1} & x_{P[m'_n]} & z'_{n-1} & \lambda'_{1,n-1} & \lambda'_{2,n-1} & 1 & 0 & 1 & 0 & 0 \\\hline
n' & x'_{A,n} & & & y_{A,n} & & 0 & 0 & 0 & 0 & 0 \\\hline
\end{array}
$$
$x_Q$, $y_Q$, $z_0$, $z'_0$, etc. would be copied in using equality constraints.
$x_Q$, $z_0$, $z'_0$, etc. would be copied in using equality constraints.
### Optimized Sinsemilla gate
$$