Paper 2018/1188

Batching Techniques for Accumulators with Applications to IOPs and Stateless Blockchains

Dan Boneh, Benedikt Bünz, and Ben Fisch


We present batching techniques for cryptographic accumulators and vector commitments in groups of unknown order. Our techniques are tailored for distributed settings where no trusted accumulator manager exists and updates to the accumulator are processed in batches. We develop techniques for non-interactively aggregating membership proofs that can be verified with a constant number of group operations. We also provide a constant sized batch non-membership proof for a large number of elements. These proofs can be used to build the first positional vector commitment (VC) with constant sized openings and constant sized public parameters. As a core building block for our batching techniques we develop several succinct proof systems in groups of unknown order. These extend a recent construction of a succinct proof of correct exponentiation, and include a succinct proof of knowledge of an integer discrete logarithm between two group elements. We use these new constructions to design a stateless blockchain, where nodes only need a constant amount of storage in order to participate in consensus. Further, we show how to use these techniques to reduce the size of IOP instantiations, such as STARKs.

Note: Removed use of fractional root assumption in favor of strong RSA assumption

Available format(s)
Cryptographic protocols
Publication info
Preprint. MINOR revision.
accumulatorszero knowledgecommitmentsRSA
Contact author(s)
benedikt @ cs stanford edu
2021-05-20: last of 9 revisions
2018-12-10: received
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Creative Commons Attribution


      author = {Dan Boneh and Benedikt Bünz and Ben Fisch},
      title = {Batching Techniques for Accumulators with Applications to IOPs and Stateless Blockchains},
      howpublished = {Cryptology ePrint Archive, Paper 2018/1188},
      year = {2018},
      note = {\url{}},
      url = {}
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