us VS lnd

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).

Install LND: https://github.com/lightningnetwork/lnd/blob/master/docs/INSTALL.md#install-lnd Install Bitcoin Core: https://github.com/bitcoin/bitcoin/blob/master/doc/build-windows.md#building-with-mingw-w64-cross-tools

To be able to follow along, you must have both bitcoind and lnd installed.

If you want multiple users, you'll need multiple node instances. LNbits (mentioned by /u/sos755) does not implement this. Rather, it simply abstracts the funds associated with a single node into multiple logical accounts. This means that the node administrator still has underlying control of all funds associated with the node. See this GitHub discussion for a bit more info: https://github.com/lightningnetwork/lnd/issues/2652

LND doesn’t use BIP39 mnemonics. https://github.com/lightningnetwork/lnd/blob/master/aezeed/README.md

Both Bitcoin Core and LND have binaries available for macOS, for example. I have not seen an actual guide to set everything up on macOS tho. It's quite similar to Linux honestly.

As for taproot change addresses, this has been the default behaviour since version 0.15.5. Just update your lnd and you're all set.