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The main problem of acculators is requiring witness updates for provers.

If I have a coin with mint A, the proof P will need to be updated every once in a while. The interval tends to be exponentially decaying, but existing.

This is the main challenge of building a bridgeless Utreexo network, wallets would need to download block proofs and update their proofs.

calle 2y ago

I see! I think the ecash case is a bit different though:

The accumulator is merely used by the mint to compress its database and elements never need to be removed. The accumulator can be shared with everyone (no privacy leak) but that's not the intent. In fact, there is nobody who needs to keep the "full database" to convince anyone else by proving membership. The accumulator is created and used only by the mint.

This is what an ecash accumulator needs to be able to do:

1) Check if incoming example is member of the accumulator

2) If not, add to accumulator

3) If member already, deny transaction (prevent double-spend)

In Utreexo, there is a global accumulator and everyone needs to prove membership of their utxo's in that accumulator to convince other users, right?

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Discussion

Erik 2y ago

Yes, there's a global accumulator, but just because there's a global utxo set. You can have purpose specific accumulators if you want.

However, all acculators I know need to update the witness on both add and del. I need to look at the paper again, but there's a provable tradeoff between update rate and size. You can't get a succinct acculator that also doesn't update the witness, so if you can't assume witness updates, IFAIK acculators won't do. (I might be wrong though, I'm not a cryptographer)