We build quantum cryptosystems that support publicly-verifiable deletion from standard cryptographic assumptions. We introduce target-collapsing as a weakening of collapsing for hash functions, analogous to how second preimage resistance weakens collision resistance; that is, target-collapsing requires indistinguishability between superpositions and mixtures of preimages of an honestly sampled image.
We show that target-collapsing hashes enable publicly-verifiable deletion (PVD), proving conjectures from [Poremba, ITCS’23] and demonstrating that the Dual-Regev encryption (and corresponding fully homomorphic encryption) schemes support PVD under the LWE assumption. We further build on this framework to obtain a variety of primitives supporting publicly-verifiable deletion from weak cryptographic assumptions, including:
– Commitments with PVD assuming the existence of injective one-way functions, or more generally, almost-regular one-way functions. Along the way, we demonstrate that (variants of) target-collapsing hashes can be built from almost-regular one-way functions.
– Public-key encryption with PVD assuming trapdoored variants of injective (or almost-regular) one-way functions. We also demonstrate that the encryption scheme of [Hhan, Morimae, and Yamakawa, Eurocrypt’23] based on pseudorandom group actions has PVD.
– $X$ with PVD for $X in {$attribute-based encryption, quantum fully-homomorphic encryption, witness encryption, time-revocable encryption$}$, assuming $X$ and trapdoored variants of injective (or almost-regular) one-way functions.

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Author Of this post: James Bartusek

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