Suyash Bagad
Cryptography Engineer
Merkle Trees in Aztec
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Merkle Tree Basics
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\(\text{root}\)
\(\text{nodes}\)
\(\text{leaves}\)
\(\text{hash path}\)
\(\text{depth} = 4\)
Storage of Merkle Tree
- We store merkle trees using levelDB database
- Use of the dictionary data structureÂ
- For a depth \(d=3\) tree with all leaves non-empty:
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\(h^1_1\)
Storage of Merkle Tree
- Suppose we have depth \(d=3\) tree with only 5 filled leaves
- Right subtree at \(i=2\) is called as a stump as only one leaf is filled in it!
- For a stump, we only store the filled leaf value and its subtree index
- Note that we use \(65\) bytes to store a stump, \(64\) bytes for a usual node
- Provides optimised storage for sparse merkle trees
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Hash Path
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Hash Path
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Hash Path
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\(\text{Common Height} = 2\)
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Hash Path
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Hash Path
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Hash Path
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Hash Path
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Hash Path
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Hash Path
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Hash Path
Indexed Merkle Tree
\begin{aligned}
\textsf{val} = \\
\textsf{nextIdx} = \\
\textsf{nextVal} =
\end{aligned}
\begin{bmatrix}
0 \\
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0
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\begin{bmatrix}
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\begin{bmatrix}
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\end{bmatrix}
\begin{bmatrix}
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0
\end{bmatrix}
\begin{bmatrix}
0 \\
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0
\end{bmatrix}
Indexed Merkle Tree
\begin{aligned}
\textsf{val} = \\
\textsf{nextIdx} = \\
\textsf{nextVal} =
\end{aligned}
\begin{bmatrix}
0 \\
0 \\
0
\end{bmatrix}
\begin{bmatrix}
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0
\end{bmatrix}
\begin{bmatrix}
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\begin{bmatrix}
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0
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\begin{bmatrix}
0 \\
0 \\
0
\end{bmatrix}
\begin{bmatrix}
0 \\
0 \\
0
\end{bmatrix}
\begin{bmatrix}
0 \\
1 \\
30
\end{bmatrix}
\begin{bmatrix}
30 \\
0 \\
0
\end{bmatrix}
Indexed Merkle Tree
\begin{aligned}
\textsf{val} = \\
\textsf{nextIdx} = \\
\textsf{nextVal} =
\end{aligned}
\begin{bmatrix}
10 \\
1 \\
30
\end{bmatrix}
\begin{bmatrix}
0 \\
0 \\
0
\end{bmatrix}
\begin{bmatrix}
0 \\
0 \\
0
\end{bmatrix}
\begin{bmatrix}
0 \\
0 \\
0
\end{bmatrix}
\begin{bmatrix}
0 \\
0 \\
0
\end{bmatrix}
\begin{bmatrix}
0 \\
0 \\
0
\end{bmatrix}
\begin{bmatrix}
0 \\
2 \\
20
\end{bmatrix}
\begin{bmatrix}
30 \\
0 \\
0
\end{bmatrix}
Indexed Merkle Tree
\begin{aligned}
\textsf{val} = \\
\textsf{nextIdx} = \\
\textsf{nextVal} =
\end{aligned}
\begin{bmatrix}
10 \\
3 \\
20
\end{bmatrix}
\begin{bmatrix}
20 \\
1 \\
30
\end{bmatrix}
\begin{bmatrix}
0 \\
0 \\
0
\end{bmatrix}
\begin{bmatrix}
0 \\
0 \\
0
\end{bmatrix}
\begin{bmatrix}
0 \\
0 \\
0
\end{bmatrix}
\begin{bmatrix}
0 \\
0 \\
0
\end{bmatrix}
\begin{bmatrix}
0 \\
2 \\
20
\end{bmatrix}
\begin{bmatrix}
30 \\
0 \\
0
\end{bmatrix}
Indexed Merkle Tree
\begin{aligned}
\textsf{val} = \\
\textsf{nextIdx} = \\
\textsf{nextVal} =
\end{aligned}
\begin{bmatrix}
10 \\
3 \\
20
\end{bmatrix}
\begin{bmatrix}
20 \\
1 \\
30
\end{bmatrix}
\begin{bmatrix}
50 \\
0 \\
0
\end{bmatrix}
\begin{bmatrix}
0 \\
0 \\
0
\end{bmatrix}
\begin{bmatrix}
0 \\
0 \\
0
\end{bmatrix}
\begin{bmatrix}
0 \\
0 \\
0
\end{bmatrix}
\begin{bmatrix}
0 \\
2 \\
20
\end{bmatrix}
\begin{bmatrix}
30 \\
4 \\
50
\end{bmatrix}
Merkle Trees
By Suyash Bagad
Merkle Trees
How do Merkle trees work?
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