On the Power of Oblivious State Preparation

• URL: http://arxiv.org/abs/2411.04234v1
• Date: Wed, 06 Nov 2024 19:58:53 GMT
• Title: On the Power of Oblivious State Preparation
• Authors: James Bartusek, Dakshita Khurana,
• Abstract summary: Oblivious State Preparation (OSP) is a cryptographic primitive that unifies techniques developed in the context of a quantum server interacting with a classical client. Results help to ''explain'' the use of public-key cryptography in approaches to establishing a ''classical leash'' on a quantum server.
• Score: 14.520515990983897
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• Abstract: We put forth Oblivious State Preparation (OSP) as a cryptographic primitive that unifies techniques developed in the context of a quantum server interacting with a classical client. OSP allows a classical polynomial-time sender to input a choice of one out of two public observables, and a quantum polynomial-time receiver to recover an eigenstate of the corresponding observable -- while keeping the sender's choice hidden from any malicious receiver. We obtain the following results: - The existence of (plain) trapdoor claw-free functions implies OSP, and the existence of dual-mode trapdoor claw-free functions implies round-optimal (two-round) OSP. - OSP implies the existence of proofs of quantumness, test of a qubit, blind classical delegation of quantum computation, and classical verification of quantum computation. - Two-round OSP implies quantum money with classical communication, classically-verifiable position verification, and (additionally assuming classical FHE with log-depth decryption) quantum FHE. Several of these applications were previously only known via tailored LWE-based constructions, whereas our OSP-based constructions yield new results from a wider variety of assumptions, including hard problems on cryptographic group actions. Finally, towards understanding the minimal hardness assumptions required to realize OSP, we prove the following: - OSP implies oblivious transfer between one classical and one quantum party. - Two-round OSP implies public-key encryption with classical keys and ciphertexts. In particular, these results help to ''explain'' the use of public-key cryptography in the known approaches to establishing a ''classical leash'' on a quantum server. For example, combined with a result of Austrin et al. (CRYPTO 22), we conclude that perfectly-correct OSP cannot exist unconditionally in the (quantum) random oracle model.

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