Paper 2026/2098 Original: eprint.iacr.org/2026/2098 ↗

Faster Incremental Authenticated Dictionaries: Removing the Query Bottleneck

Abstract

Known lower bounds prohibit the construction of very-efficient authenticated dictionaries that support both insertions and deletions. It remains an open question, however, whether it may be possible to construct very efficient authenticated dictionaries that are \emph{insertion-only}. The current paper answers this question in the affirmative, providing the constructions that strictly dominate the classic Merkle tree in the incremental setting. Our first result is an authenticated incremental dictionary, called the exponential Verkle forest, that supports retrieval queries with time and proof size $O(\log \log n)$ and that supports insertions with time and proof size $O(\log \log \log n)$. The data structure also offers an \emph{amortized} bound of $O(1)$ for insertions. Building on this, we also present a full-query version of the dictionary, supporting both retrieval and exclusion queries. This data structure continues to support retrieval queries in time and proof size $O(\log \log n)$, while supporting all other operations in time and proof size $O(\log n)$. Our results take a purely data-structural perspective on authenticated data structures, seeking to achieve the best bounds possible with the cryptographic primitives (collision-resistant hashing and position-binding vector commitments) that already exist. We also give partial evidence, in the form of a lower bound that applies to a natural class of data structures, that our $O(\log \log n)$ query bound is optimal for any solution with linear construction time.