Verifiable Quantum Advantage without Structure
Abstract
We show the following hold, unconditionally unless otherwise stated, relative to a random oracle:By replacing the random oracle with a concrete cryptographic hash function such as SHA2, we obtain plausible Minicrypt instantiations of the above results. Previous analogous results all required substantial structure, either in terms of highly structured oracles and/or algebraic assumptions in Cryptomania and beyond.
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There are NP search problems solvable by quantum polynomial-time (QPT) machines but not classical probabilistic polynomial-time (PPT) machines.
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There exist functions that are one-way, and even collision resistant, against classical adversaries but are easily inverted quantumly. Similar counterexamples exist for digital signatures and CPA-secure public key encryption (the latter requiring the assumption of a classically CPA-secure encryption scheme). Interestingly, the counterexample does not necessarily extend to the case of other cryptographic objects such as PRGs.
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There are unconditional publicly verifiable proofs of quantumness with the minimal rounds of interaction: for uniform adversaries, the proofs are non-interactive, whereas for non-uniform adversaries the proofs are two message public coin.
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Our results do not appear to contradict the Aaronson-Ambanis conjecture. Assuming this conjecture, there exist publicly verifiable certifiable randomness, again with the minimal rounds of interaction.
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Index Terms
- Verifiable Quantum Advantage without Structure
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Published In
June 2024
323 pages
ISSN:0004-5411
EISSN:1557-735X
DOI:10.1145/3613558
- Editor:
- Venkatesan Guruswami
Copyright © 2024 Copyright held by the owner/author(s).
This work is licensed under a Creative Commons Attribution International 4.0 License.
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New York, NY, United States
Publication History
Published: 11 June 2024
Online AM: 22 April 2024
Accepted: 09 April 2024
Revised: 19 March 2024
Received: 23 February 2023
Published in JACM Volume 71, Issue 3
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