Cryptology ePrint Archive: Report 2018/1188

Batching Techniques for Accumulators with Applications to IOPs and Stateless Blockchains

Dan Boneh and Benedikt Bünz and Ben Fisch

Abstract: 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.

Category / Keywords: cryptographic protocols / accumulators, zero knowledge, commitments, RSA

Date: received 7 Dec 2018, last revised 20 May 2021

Contact author: benedikt at cs stanford edu

Available format(s): PDF | BibTeX Citation

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

Version: 20210520:233145 (All versions of this report)

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