# Contributed Talks 1c: Theory Talks

Mon, 14 Aug
, 15:50 - 16:30

- Publicly-Verifiable Deletion via Target-Collapsing FunctionsJames Bartusek (UC Berkeley); Dakshita Khurana (UIUC); Alexander Poremba (Caltech)[Abstract]
**Abstract:**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, {\em 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. - Simple Tests of Quantumness Also Certify QubitsZvika Brakerski (Weizmann Institute of Science); Alexandru Gheorghiu (Chalmers University of Technology); Gregory D. Kahanamoku-Meyer (Lawrence Berkeley National Laboratory & UC Berkeley); Eitan Porat (Weizmann Institute of Science); Thomas Vidick (Weizmann Institute of Science)[Abstract]
**Abstract:**A test of quantumness is a protocol that allows a classical verifier to certify (only) that a prover is not classical. We show that tests of quantumness that follow a certain template, which captures recent proposals such as (Kalai et al., 2022), can in fact do much more. Namely, the same protocols can be used for certifying a qubit, a building-block that stands at the heart of applications such as certifiable randomness and classical delegation of quantum computation. Certifying qubits was previously only known to be possible based on the hardness of the Learning with Errors problem and the use of adaptive hardcore (Brakerski et al., 2018). Our framework allows certification of qubits based only on the existence of post-quantum trapdoor claw-free functions, or on quantum fully homomorphic encryption. These can be instantiated, for example, from Ring Learning with Errors. On the technical side, we show that the quantum soundness of any such protocol can be reduced to proving a bound on a simple algorithmic task: informally, answering "two challenges simultaneously'' in the protocol. Our reduction formalizes the intuition that these protocols demonstrate quantumness by leveraging the impossibility of rewinding a general quantum prover. This allows us to prove tight bounds on the quantum soundness of (Kahanamoku-Meyer et al., 2021) and (Kalai et al., 2022), showing that no quantum polynomial-time prover can succeed with probability larger than cos^2(π/8)≈0.853. Previously, only an upper bound on the success probability of classical provers, and a lower bound on the success probability of quantum provers, were known. We then extend this proof of quantum soundness to show that provers that approach the quantum soundness bound must perform almost anti-commuting measurements. This certifies that the prover holds a qubit.