Hash-based accumulators with quick insertion

Dear all,

I have been working on some constructions for cryptographic accumulators that optimise for quick insertion.

As a brief background, an accumulator is a data structure that maintains compact commitments to a potentially very large (and dynamic) set, while keeping proofs of membership short. Unsurprisingly, they are getting more popular, and one notable application in Bitcoin is to create light-weight full nodes that do not need to store the UTXO set (Utreexo accumulator[1]).

In this work, I focus on additive accumulators that supports adding new elements, but not removing them. My motivation is to support extending Script with access to an arbitrarily large portion of the blockchain history and state (e.g., past blocks, txids, or any more complex state obtained from them - with all due care). The additional storage and computation cost for nodes is small, and the cost (in additional bytesize) for any transaction that wishes to access state committed in the accumulator should be just slightly bigger than typical Merkle proofs.

I have focused on: - An accumulator with insertion time O(1) and proof size O(log^2 n) - A construction with insertion time O(log log n) and proof size O(log n log log n)

All the performance metrics above are in "number of hashes".

You can find: - draft writeup: https://github.com/bigspider/accumulator/blob/master/docs/paper-draft.pdf - sample python code (only for the first construction at this time): https://github.com/bigspider/accumulator

While this is still an unfinished work, the ideas in the draft are hopefully clear enough and easy to understand. I wanted to share it at this stage as it can benefit from comments to improve the constructions, to cover any related work or to find potential applications in Bitcoin (e.g. Script, layer2, side chains, etc).

Best, Salvatore Ingala

[1] - Thaddeus Dryja, Utreexo: A dynamic hash-based accumulator optimized for the Bitcoin UTXO set - https://eprint.iacr.org/2019/611.pdf

Interesting work! I should be fortunate to make time to read it.

I will point out, in case you'd not considered it, that you can support addition and removal indirectly by formulating it as a difference of sets. Similar to the collision-resistant replicated data types (CRDTs) concept. Checking for membership would simply become CheckMembershipInAdditionSet && !CheckMembershipInRemovalSet, assuming an item could only be added/removed once. You could also perhaps support multiple addition/removal by attaching a count of how many times it's been added though that might break some of the building blocks in the paper.