Cryptology ePrint Archive: Report 2021/599

Hyperproofs: Aggregating and Maintaining Proofs in Vector Commitments

Shravan Srinivasan and Alex Chepurnoy and Charalampos Papamanthou and Alin Tomescu and Yupeng Zhang

Abstract: We present Hyperproofs, the first vector commitment (VC) scheme that is efficiently maintainable and aggregatable. Similar to Merkle proofs, our proofs form a tree that can be efficiently maintained: updating all $n$ proofs in the tree after a single leaf change only requires $O(\log{n})$ time. Importantly, unlike Merkle proofs, Hyperproofs are efficiently aggregatable, anywhere from 10$\times$ to 100$\times$ faster than SNARK-based aggregation of Merkle proofs. At the same time, an individual Hyperproof consists of only $\log{n}$ algebraic hashes (e.g., 32-byte elliptic curve points) and an aggregation of $b$ such proofs is only $O(\log{(b\log{n})})$-sized. Hyperproofs are also reasonably fast to update when compared to Merkle trees with SNARK-friendly hash functions.

As another added benefit over Merkle trees, Hyperproofs are homomorphic: digests (and proofs) for two vectors can be homomorphically combined into a digest (and proofs) for their sum. Homomorphism is very useful in emerging applications such as stateless cryptocurrencies. First, it enables unstealability, a novel property that incentivizes proof computation. Second, it makes digests and proofs much more convenient to update.

Finally, Hyperproofs have certain limitations: they are not transparent, have linear-sized public parameters, are slower to verify, and have larger aggregated proofs than SNARK-based approaches. Nonetheless, end-to-end, aggregation and verification in Hyperproofs is 10$\times$ to 100$\times$ faster than SNARK-based Merkle trees.

Category / Keywords: vector commitments; aggregation; proof updates; unstealability; homomorphism; polynomial commitments;

Date: received 7 May 2021

Contact author: tomescu alin at gmail com

Available format(s): PDF | BibTeX Citation

Version: 20210510:083346 (All versions of this report)

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