A survey of set accumulators for blockchain systems

Set accumulators are cryptographic primitives used to represent arbitrarily large sets of elements with a single constant-size value and to efficiently verify whether a value belongs to that set. Accumulators support the generation of membership proofs, meaning that they can certify the presence of a given value among the elements of a set. In this paper we present an overview of the theoretical concepts underlying set accumulators, we compare the most popular constructions from a complexity perspective, and we survey a number of their applications related to blockchain technology. In particular, we focus on four different use cases: query authentication, stateless transactions validation, anonymity enhancement, and identity management. For each of these scenarios, we examine the main problems they introduce and discuss the most relevant accumulator-based solutions proposed in the literature. Finally, we point out the common approaches between the proposals and highlight the currently open problems in each field.