us VS minisketch

It might be easier to think about it as a stack, rather than a tree. Each element of the stack represents a subtree -- a perfect binary tree. If you ever have two subtrees of height k, you merge them together into one subtree of height k+1. Your stack might already have another subtree of height k+1; if so, you repeat the process, until there's at most one subtree of each height.

This process is isomorphic to binary addition. Worked example: let's start with a single leaf, i.e. a subtree of height 0. Then we "add" another leaf; since we now have a pair of two equally-sized leaves, we merge them into one subtree of height 1. Then we add a third leaf; now this one doesn't have a sibling to merge with, so we just keep it. Now our "stack" contains two subtrees: one of height 1, and one of height 0.

Now the isomorphism: we start with the binary integer 1, i.e. a single bit at index 0. We add another 1 to it, and the 1s "merge" into a single 1 bit at index 1. Then we add another 1, resulting in two 1 bits at different indices: 11. If we add one more bit, we'll get 100; likewise, if we add another leaf to our BNT, we'll get a single subtree of height 2. Thus, the binary representation of the number of leaves "encodes" the structure of the BNT.

This isomorphism allows you to do some neat tricks, like calculating the size of a Merkle proof in 3 asm instructions. There's some code here if that helps: https://github.com/lukechampine/us/blob/master/merkle/stack....

You could also check out section 5.1 of the BLAKE3 paper: https://github.com/BLAKE3-team/BLAKE3-specs/blob/master/blak...

This isn't what I'm asking for - I don't care if it's baked into us, exists as a backend for minio, uses PseudoKV https://github.com/lukechampine/us/issues/67, or whatever the case may be. I see no value in sending any third party my private data in an unencrypted form (uploading to your server, even if over HTTPS, you got my data).

Anyone interested in IBLT with low failure probablity should also be aware of pinsketch and, particularly, our implementation of it: minisketch ( https://github.com/sipa/minisketch/ ).

Our implementation communicates a difference of N b-bit entries with exactly N*b bits with 100% success. The cost for this communications efficiency and reliability is that the decoder takes CPU time quadratic in N, instead of IBLT's linear decoder. However, when N is usually small, if the implementation is fast this can be fine -- especially since you wouldn't normally want to use set recon unless you were communications limited.

Pinsketches and iblt can also be combined-- one can use pinsketches as the cells of an iblt and one can also use a small pinsketch to improve the failure rate of an iblt (since when a correctly sized IBLT fails, it's usually just due to a single undecodable cycle).

Since the protocol appears to use adhoc synchronization, the authors might be interested in https://github.com/sipa/minisketch/ which is a library that implements a data structure (pinsketch) that allows two parties to synchronize their sets of m b-bit elements which differ by c entries using only b*c bits. A naive protocol would use m*b bits instead, which is potentially much larger.

I'd guess that under normal usage the message densities probably don't justify such efficient means-- we developed this library for use in bitcoin targeting rates on the order of a dozen new messages per second and where every participant has many peers with potentially differing sets--, but it's still probably worth being aware of. The pinsketch is always equal or more efficient than a naive approach, but may not be worth the complexity.

The somewhat better known IBLT data structure has constant overheads that make it less efficient than even naive synchronization until the set differences are fairly large (particular when the element hashes are small); so some applications that evaluated and eschewed IBLT might find pinsketch applicable.

I love the set reconciliation structures like the IBLT (Iterative Bloom Lookup Table) and BCH set digests like minisketch.

https://github.com/sipa/minisketch

Lets say you have a set of a billion items. Someone else has mostly the same set but they differ by 10 items. These let you exchange messages that would fit in one UDP packet to reconcile the sets.

Sipa is working on a better version of that for a while. The technical term is a "set reconciliation protocol", but Bitcoin Core been doing a more basic version of this for a while. Note that the "BCH" there isn't the same as Bcash

I'd also have to say that Zig is a pretty neat library for this. In order to implement PBS I needed the MiniSketch-library (written in C/C++) and I'll have to say that integrating with it has been a breeze. Some fiddling in build.zig so that I can avoid Makefile, and after that everything has worked amazingly.

Networks that need to constrain themselves to limited typologies to avoid traffic magnification do so at the expense of robustness, especially against active attackers that grind their identifiers to gain privileged positions.

Maybe this is a space where efficient reconciliation ( https://github.com/sipa/minisketch/ ) could help-- certainly if the goal were to flood messages to participants reconciliation can give almost optimal communication without compromising robustness.