Clarification about definition of O(T,l)

[Sidu28]

In the white paper, a function O(T,l) is described as the “the Merkle opening for leaf with index l” and “value of sister nodes on the way from
leaf l to the root, denoted by R”

To me, this seems kinda like the Merkle Proof, which is a sequence of all the sister nodes along the path to the leaf node. Is this correct?

In the description of the statement of Knowledge, O is referred to as the the opening of H2(k||r) at position l to R. Does this refer to the fact that H2 is used to determine the value of each node along the path in the tree? Thanks!

[poma]

@Sidu28

To me, this seems kinda like the Merkle Proof

That’s exactly what it is.

@Sidu28

In the description of the statement of Knowledge, O is referred to as the the opening of H2(k||r) at position l to R. Does this refer to the fact that H2 is used to determine the value of each node along the path in the tree?

Looks like there is a mistake in the whitepaper, should be H1(k||r) (Pedersen commitment and not MiMC). This is what we call a commitment, a hash of secret+nullifier that gets inserted into commitment tree as a leaf. H2 is indeed used to hash nodes of the merkle tree.

[Sidu28]

Ahh it is H1 not H2 - that makes more sense based on what I know. This is a lot more clear now, thanks!