Paper 2025/1160

Black-box Approaches to Authenticated Dictionaries: New Constructions and Lower Bounds

Abstract

Authenticated dictionaries (ADs) enable secure lookups to a dictionary hosted by an untrusted server and are a key component of various real-world applications, including transparency systems and cryptocurrencies. Despite significant overlap in techniques for building ADs and related primitives, such as memory checkers and accumulators (i.e., authenticated sets), these relationships have yet to be formalized. In this work, we give a rigorous treatment of ADs and prove their precise connection to the latter two cornerstone primitives. We start by laying out the minimal algorithms and security properties needed in practice and introduce a new security notion for ADs called write-committing, which requires update proofs to guarantee an exact count of changes. We prove that any AD built from a black-box authenticated set (AS) makes at least $\Omega(\log n)$ AS calls per lookup and obeys a trade-off between lookups and updates. With optimal lookups, such a scheme requires at least $\Omega(\log n/\log\log n)$ AS calls per update. We also resolve the open question of constructing a secure AD from only black-box access to an AS and present two schemes adhering to the trade-off: one with optimal lookup overhead and the other with higher lookup complexity, but which only requires two AS calls for an update. Finally, we make strides towards unifying memory checkers and ADs. To this end, we present two constructions for memory checkers with black-box access to an AD: one that incurs constant overhead (but needs write-committing) and a second that only requires the AD to be lookup-secure but incurs logarithmic overhead. We then give a simple AD construction using a memory checker as a black-box, with $\mathcal{O}(1)$ overhead. Our results demonstrate the inherent limitations of ADs built from accumulators but lay the foundation for extending existing results on memory checkers and other primitives, such as vector commitments, to ADs.