> We present Verkle Trees, which are constructed similarly to Merkle Trees, but using Vector Commitments rather than cryptographic hash functions. In a Merkle Tree, a parent node is the hash of its children. In a Verkle Tree, a parent node is the Vector Commitment of its children. A Verkle Tree with branching factor k achieves O(kn) construction time and O(logk n) membership proof-size. This means that the branching factor, k, offers a tradeoff between computational power and bandwidth. The bandwidth reduction is independent of the depth of the tree; it depends only on the branching factor. We find experimentally that with a branching factor of k = 1024, which provides a factor of 10 reduction in bandwidth, it takes 110.1 milliseconds on average per leaf to construct a Verkle Tree with 214 leaves. A branching factor of k = 32, which provides a bandwidth reduction factor of 5, yields a construction time of 8.4 milliseconds on average per leaf for a tree with 214 leaves.

Thanks for posting the abstract. It's $2^{14}$ leaves in the original LaTeX rather than 214, just in case anyone is confused. (It's also $O(\log_k n)$ = O(log n / log k).)

Thanks! I actually wasn't aware of the intellectual history. I added a link to your paper at the start of my post.

Vitalik should really give you proper attribution.

Yeah :/. I was sent the Vitalik article by someone, and (despite other people liking it) found it somewhat poorly written (as did another friend of mine in the same group chat, who was left with similar questions) and then searched around trying to find more information and came across the original paper--the abstract for which was way way better than Vitalik's article :D--that hadn't been linked anywhere in the various internal cluster of references and documentation by any of the Ethereum people, near far as I could tell :(.

How did you get so proficient at math/CS while only in high school?