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merkletree: reduce gate amount (-23%) by custom poseidon to use flag as initial state (#472)

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* merkletree: custom poseidon to use flag as initial state.

This allows to do the merkletree related hashing in 1 gate instead of 2,
reducing ~23% of gates per merkle proof.

| tree levels   | 10 | 16 | 32  | 40  | 64  | 128 | 130 | 250  | 256  |
|---------------|----|----|-----|-----|-----|-----|-----|------|------|
| old num gates | 50 | 76 | 144 | 178 | 280 | 554 | 564 | 1076 | 1102 |
| new num gates | 39 | 59 | 111 | 137 | 215 | 425 | 433 | 825  | 845  |

* update docs with new tree hashing approach

* add inline comment stating clear how the flag is used in the state permutation
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arnaucube 2026-02-04 12:31:56 +01:00 • committed by GitHub
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book/src/merkletree.md
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@ -37,10 +37,12 @@ A Merkle tree with no entry at all is represented by the hash value
(With the Plonky2 backend, the hash function ```hash``` will output a 4-tuple of field elements.)
A Merkle tree with a single entry ```(key, value)``` is called a "leaf". It is represented by the hash value
```root = hash((key, value, 1)).```
```root = hash(1, (key, value))```, where `1` is a flag indicating that it is a leaf, and it's used as the initial state of the hash (Poseidon) permutation.
A Merkle tree ```tree``` with more than one entry is required to have two subtrees, ```left``` and ```right```. It is then represented by the hash value
```root = hash((left_root, right_root, 2)).```
```root = hash(2, (left_root, right_root))```, where `2` is a flag indicating that it is an intermediate node, and it's used as the initial state of the hash (Poseidon) permutation.
The flags are used as the initial state of the Poseidon permutation so that they don't account for extra inputs in the Poseidon gadget, needing only 1 gate for each node/leaf hash.
(The role of the constants 1 and 2 is to prevent collisions between leaves and non-leaf Merkle roots. If the constants were omitted, a large Merkle tree could be dishonestly interpreted as a leaf, leading to security vulnerabilities.)