Code-routing: A New Attack On Position Verification

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Abstract

The cryptographic task of position verification attempts to verify one party’s location in spacetime by exploiting constraints on quantum information and relativistic causality. A popular verification scheme known as $f$-routing involves requiring the prover to redirect a quantum system based on the value of a Boolean function $f$. Cheating strategies for the $f$-routing scheme require the prover use pre-shared entanglement, and security of the scheme rests on assumptions about how much entanglement a prover can manipulate. Here, we give a new cheating strategy in which the quantum system is encoded into a secret-sharing scheme, and the authorization structure of the secret-sharing scheme is exploited to direct the system appropriately. This strategy completes the $f$-routing task using $O(SP_p(f))$ EPR pairs, where $SP_p(f)$ is the minimal size of a span program over the field $mathbb{Z}_p$ computing $f$. This shows we can efficiently attack $f$-routing schemes whenever $f$ is in the complexity class $text{Mod}_ptext{L}$, after allowing for local pre-processing. The best earlier construction achieved the class L, which is believed to be strictly inside of $text{Mod}_ptext{L}$. We also show that the size of a quantum secret sharing scheme with indicator function $f_I$ upper bounds entanglement cost of $f$-routing on the function $f_I$.

► BibTeX data

@article{Cree2023coderoutingnew, doi = {10.22331/q-2023-08-09-1079}, url = {https://doi.org/10.22331/q-2023-08-09-1079}, title = {Code-routing: a new attack on position verification}, author = {Cree, Joy and May, Alex}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {7}, pages = {1079}, month = aug, year = {2023}<br /> }

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Cited by

[1] Alex May, “Complexity and entanglement in non-local computation and holography”, Quantum 6, 864 (2022).

[2] Alex May, Jonathan Sorce, and Beni Yoshida, “The connected wedge theorem and its consequences”, Journal of High Energy Physics 2022 11, 153 (2022).

[3] Kfir Dolev and Sam Cree, “Holography as a resource for non-local quantum computation”, arXiv:2210.13500, (2022).

[4] Kfir Dolev and Sam Cree, “Non-local computation of quantum circuits with small light cones”, arXiv:2203.10106, (2022).

[5] Rene Allerstorfer, Harry Buhrman, Alex May, Florian Speelman, and Philip Verduyn Lunel, “Relating non-local quantum computation to information theoretic cryptography”, arXiv:2306.16462, (2023).

[6] Llorenç Escolà-Farràs and Florian Speelman, “Single-qubit loss-tolerant quantum position verification protocol secure against entangled attackers”, arXiv:2212.03674, (2022).

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This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.

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Source: https://quantum-journal.org/papers/q-2023-08-09-1079/

Time Stamp: August 9, 2023

Time Stamp: May 15, 2023

Republished By Plato

Abstract

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