Publicly-Verifiable Deletion via Target-Collapsing Functions. (arXiv:2303.08676v1 [quant-ph])

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. …

build collision deletion enable encryption fully homomorphic encryption functions hash hashes hash functions homomorphic encryption quantum standard support target