CryptoDB
Non-malleable Vector Commitments via Local Equivocability
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| Abstract: | Vector commitments (VCs), enabling to commit to a vector and locally reveal any of its entries, play a key role in a variety of both classic and recently evolving applications. However, security notions for VCs have so far focused on passive attacks, and non-malleability notions considering active attacks have not been explored. Moreover, existing frameworks that may enable to capture the non-malleability of VCs seem either too weak (non-malleable non-interactive commitments that do not account for the security implications of local openings) or too strong (non-malleable zero-knowledge sets that support both membership and non-membership proofs). We put forward a rigorous framework capturing the non-malleability of VCs, striking a careful balance between the existing weaker and stronger frameworks: We strengthen the framework of non-malleable non-interactive commitments by considering attackers that may be exposed to local openings, and we relax the framework of non-malleable zero-knowledge sets by focusing on membership proofs. In addition, we strengthen both frameworks by supporting (inherently private) updates to entries of committed vectors, and discuss the benefits of non-malleable VCs in the context of both UTXO-based and account-based stateless blockchains, and in the context of simultaneous multi-round auctions (that have been adopted by the US Federal Communications Commission as the standard auction format for selling spectrum ranges). Within our framework, we present a direct approach for constructing non-malleable VCs whose efficiency essentially matches that of the existing standard VCs. Specifically, we show that any VC can be transformed into a non-malleable one, relying on a new primitive that we put forth. Our new primitive, locally equivocable commitments with all-but-one binding , is evidently both conceptually and technically simpler compared to multi-trapdoor mercurial trapdoor commitments (the main building block underlying existing non-malleable zero-knowledge sets), and admits more efficient instantiations based on the same number-theoretic assumptions. |
BibTeX
@article{jofc-2023-33823,
title={Non-malleable Vector Commitments via Local Equivocability},
journal={Journal of Cryptology},
publisher={Springer},
volume={36},
doi={10.1007/s00145-023-09480-4},
author={Lior Rotem and Gil Segev},
year=2023
}