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Cryptographic accumulators are a common solution to proving information about a large set S. They allow one to compute a short digest of S and short certificates of some of its basic properties, notably membership of an element. Accumulators also allow one to track set updates: a new accumulator is obtained by inserting/deleting a given element. In this work we consider the problem of generating membership and update proofs for \em batches of elements so that we can succinctly prove additional properties of the elements (i.e., proofs are of constant size regardless of the batch size), and we can preserve privacy. Solving this problem would allow obtaining blockchain systems with improved privacy and scalability.

The state-of-the-art approach to achieve this goal is to combine accumulators (typically Merkle trees) with zkSNARKs. This solution is however expensive for provers and does not scale for large …