doc: introduces short namespace absence proof in the NMT specs #209
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Closes #206 |
| - Compute the tree root `T'` using the leaves and the `proof.nodes`. | ||
| If the computed root `T'` is equal to the expected root `T` of the tree, then the `proof` is valid. | ||
| To compute the tree root `T'`, the [namespaced hash function](#namespaced-hash) should be utilized. | ||
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| ### Short Namespace Absence Proof |
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Can this eventually be combined as a single proof? Asked another way, is there anything different to the guarantees behind this proof to the standard absence proof?
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No, there is not. It has been expanded on in this forum post.
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Can this eventually be combined as a single proof?
Yes, they can. The reason they are not unified is twofold. Firstly, the current implementation does not support short-proof generation yet. And secondly, the original long version is more conventional and familiar to the readers, so discussing them separately can help to avoid confusion and potential questions.
| 1) `start` and `end` range: These represent the indices of the `SubtreeHash` within its respective level. | ||
| Nodes at each level are indexed from left to right starting at index `0`. |
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I don't understand why there are two indices. Don't you just need one, i.e. the index of that node. In the example you say start 1 and end 2 but afaiu it would just be index 1. Can you explain that to me?
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We use a general proof struct that applies to all namespace proofs. When there are multiple leaves that match the target namespace, start and end indicate a range of indices covering multiple nodes (end is always non-inclusive). However, in cases where only one matching leaf exists or for absence proofs, start and end represent the index of a single node. So, in this example with a single node, start is 1, and end is 2.
| It is important to note that there can be multiple candidates, each belonging to a different level of the tree, that satisfy this requirement for the `SubtreeHash`. | ||
| All such candidates are deemed valid from the verification perspective. | ||
| 2) The verification of Merkle inclusion proof of the returned `SubtreeHash` is valid. | ||
| 3) The `proof` satisfies the proof completeness as explained in the [Verification of NMT Inclusion Proof](#verification-of-nmt-inclusion-proof). |
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Thanks for the explanation yesterday. I think it's not so intuitive why you only need one SubTreeHash i.e. that the values in nodes which represent the proof path provides the other side necessary to prove that the namespace does not exist in the tree.
@cmwaters regarding this comment you made, I think you are referring to the completeness property, it should be verified on the verification side and is mentioned in here.
The nodes returned as part of the proof.nodes originally serve as normal Merkle inclusion proof for the proof range i.e., [proof.start, proof.end). Additionally, we perform a completeness check on them to ensure that no leaf matching the target namespace is left uncovered by the proof range. Does this address your question?
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The completeness property and the intuition behind it are explained earlier in the specs i.e., https://github.com/celestiaorg/nmt/blob/master/docs/spec/nmt.md#namespace-proof-verification
Completeness: There are no other leaves matching nID that do not belong to the returned range [start, end).
Proof inclusion can be verified via a regular Merkle range proof verification. However, completeness of the proof requires additional checks. Specifically, 1) the maximum namespace ID of the nodes in the proof that are on the left side of the branch connecting the start leaf to the root must be less than the provided namespace ID (nID), and 2) the minimum namespace ID of the nodes in the proof that are on the right side of the branch connecting the end-1 leaf to the root must be greater than the provided namespace ID (nID).
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Going to merge this PR, but will be monitoring this PR for addressing your questions and comments. |
Overview
Closes #205
Additionally, in line with this, to ensure consistency with how namespace ID and namespace (i.e., a combination of namespace ID and version) are utilized in the core-app, I have replaced all instances of words that refer to or imply namespace ID with the more accurate term "namespace".
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