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.

集合累加器是加密原语，用于表示具有单个恒定大小值的任意大元素集，并有效地验证一个值是否属于该集合。累加器支持成员资格证明的生成，这意味着它们可以证明给定值在集合元素中的存在。在本文中，我们概述了集合累加器的理论概念，我们从复杂性的角度比较了最流行的结构，并调查了它们与区块链技术相关的一些应用。特别是，我们关注四种不同的用例：查询身份验证、无状态交易验证、匿名增强和身份管理。对于这些场景中的每一个，我们研究了它们引入的主要问题，并讨论了文献中提出的最相关的基于累加器的解决方案。最后，我们指出了提案之间的共同方法，并强调了每个领域当前未解决的问题。