note_commit.md: make the descriptions of range checks for k_0 and k_2 consistent with other short range checks.

Signed-off-by: Daira Hopwood <daira@jacaranda.org>
This commit is contained in:
Daira Hopwood 2021-09-07 02:39:46 +01:00
parent 462550a26b
commit cc0ac1a744
1 changed files with 8 additions and 4 deletions

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@ -501,15 +501,14 @@ bits using a strict $25-$word [ten-bit lookup](../decomposition.md#lookup-decomp
The running sum outputs allow us to susbstitute $k_1 = z_{j, 1}.$
Recall that $b_2 = ỹ(\mathsf{g_d})$ and $d_1 = ỹ(\mathsf{pk_d})$ were pieces input to the
Sinsemilla hash and have already been boolean-constrained. To constrain the remaining
chunks, we use the following constraints:
Sinsemilla hash and have already been boolean-constrained. $k_0$ and $k_2$ are constrained
outside this gate to $9$ and $4$ bits respectively. To constrain the remaining chunks, we
use the following constraints:
$$
\begin{array}{|c|l|}
\hline
\text{Degree} & \text{Constraint} \\\hline
& \ShortLookupRangeCheck{k_0, 9} \\\hline
& \ShortLookupRangeCheck{k_2, 4} \\\hline
3 & q_{\NoteCommit,y} \cdot \BoolCheck{k_3} = 0 \\\hline
\end{array}
$$
@ -558,6 +557,7 @@ A_5 & A_6 & A_7 & A_8 & A_9 & q_{\NoteCommit,y} \\\hline
j & k_1 & z_{j,13} & j' & z_{j',13} & 0 \\\hline
\end{array}
$$
#### Constraints
$$
\begin{array}{|c|l|}
@ -570,6 +570,10 @@ $$
\end{array}
$$
Outside this gate, we have constrained:
- $\ShortLookupRangeCheck{k_0, 9}$
- $\ShortLookupRangeCheck{k_2, 4}$
### $y(\mathsf{pk_d})$
This can be checked in exactly the same way as $y(\mathsf{g_d})$, with $b_2$ replaced by
$d_1$.