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TomAFrench merged 1 commit into from
Jan 23, 2025
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chore: redo typo PR by savvar9991 #11412

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6 changes: 3 additions & 3 deletions docs/docs/aztec/concepts/storage/trees/indexed_merkle_tree.mdx
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Original file line number Diff line number Diff line change
Expand Up @@ -73,7 +73,7 @@ The insertion protocol is described below:
1. Look for a nullifier's corresponding low_nullifier where:

$$
low\_nullifier_{\textsf{next\_value}} > v
low\_nullifier_{\textsf{next\_value}} > new\_nullifier
$$

> if $new\_nullifier$ is the largest use the leaf:
Expand All @@ -86,7 +86,7 @@ The insertion protocol is described below:
3. Perform a range check on the low nullifier's value and next_value fields:

$$
new\_nullifier > low\_nullifier_{\textsf{value}} \: \&\& \: ( new\_nullifier < low\_nullifier_{\textsf{next\_value}} \: \| \: low\_nullifier_{\textsf{next\_value}} == 0 )
new\_nullifier > low\_nullifier_{\textsf{value}} \: \&\& \: ( new\_nullifier < low\_nullifier_{\textsf{next\_value}} \: || \: low\_nullifier_{\textsf{next\_value}} == 0 )
$$

4. Update the low nullifier pointers
Expand Down Expand Up @@ -217,7 +217,7 @@ In the following example we insert a subtree of size 4 into our tree at step 4.

<Image img={require("/img/indexed-merkle-tree/subtree-insert-7.png")} />

#### Performance gains from subtree insertion
### Performance gains from subtree insertion

Let's go back over the numbers:
Insertions into a sparse nullifier tree involve 1 non membership check (254 hashes) and 1 insertion (254 hashes). If we were performing insertion for 4 values that would entail 2032 hashes.
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