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.