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Accumulation Without Homomorphism

Authors Benedikt Bünz , Pratyush Mishra , Wilson Nguyen, William Wang

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Author Details

Benedikt Bünz
  • New York University, NY, USA
Pratyush Mishra
  • University of Pennsylvania, Philadelphia, PA, USA
Wilson Nguyen
  • Stanford University, CA, USA
William Wang
  • New York University, NY, USA

Funding

  • Bünz, Benedikt: Supported by Alpen Labs, Chaincode Labs, and the Sui Foundation.
  • Nguyen, Wilson: Supported by NSF, DARPA, the Simons Foundation, UBRI, NTT Research, and the Stanford Future of Digital Currency Initiative (FDCI). Opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of DARPA.

Cite As Get BibTex

Benedikt Bünz, Pratyush Mishra, Wilson Nguyen, and William Wang. Accumulation Without Homomorphism. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 23:1-23:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ITCS.2025.23

Abstract

Accumulation schemes are a simple yet powerful primitive that enable highly efficient constructions of incrementally verifiable computation (IVC). Unfortunately, all prior accumulation schemes rely on homomorphic vector commitments whose security is based on public-key assumptions. It is an interesting open question to construct efficient accumulation schemes that avoid the need for such assumptions.
In this paper, we answer this question affirmatively by constructing an accumulation scheme from non-homomorphic vector commitments which can be realized from solely symmetric-key assumptions (e.g., Merkle trees). We overcome the need for homomorphisms by instead performing spot-checks over error-correcting encodings of the committed vectors.
Unlike prior accumulation schemes, our scheme only supports a bounded number of accumulation steps. We show that such bounded-depth accumulation still suffices to construct proof-carrying data (a generalization of IVC). We also demonstrate several optimizations to our PCD construction which greatly improve concrete efficiency.

Subject Classification

ACM Subject Classification
  • Theory of computation → Cryptographic protocols
Keywords
  • Proof-carrying data
  • incrementally verifiable computation
  • accumulation schemes

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