Paper 2024/716

Unclonable Secret Sharing

Prabhanjan Ananth, University of California, Santa Barbara
Vipul Goyal, NTT Research, Carnegie Mellon University
Jiahui Liu, Massachusetts Institute of Technology
Qipeng Liu, University of California, San Diego
Abstract

Unclonable cryptography utilizes the principles of quantum mechanics to addresses cryptographic tasks that are impossible classically. We introduce a novel unclonable primitive in the context of secret sharing, called unclonable secret sharing (USS). In a USS scheme, there are $n$ shareholders, each holding a share of a classical secret represented as a quantum state. They can recover the secret once all parties (or at least $t$ parties) come together with their shares. Importantly, it should be infeasible to copy their own shares and send the copies to two non-communicating parties, enabling both of them to recover the secret. Our work initiates a formal investigation into the realm of unclonable secret sharing, shedding light on its implications, constructions, and inherent limitations. ** Connections: We explore the connections between USS and other quantum cryptographic primitives such as unclonable encryption and position verification, showing the difficulties to achieve USS in different scenarios. **Limited Entanglement: In the case where the adversarial shareholders do not share any entanglement or limited entanglement, we demonstrate information-theoretic constructions for USS. **Large Entanglement: If we allow the adversarial shareholders to have unbounded entanglement resources (and unbounded computation), we prove that unclonable secret sharing is impossible. On the other hand, in the quantum random oracle model where the adversary can only make a bounded polynomial number of queries, we show a construction secure even with unbounded entanglement. Furthermore, even when these adversaries possess only a polynomial amount of entanglement resources, we establish that any unclonable secret sharing scheme with a reconstruction function implementable using Cliffords and logarithmically many T-gates is also unattainable.

Note: added discussions on relations to secret sharing of quantum states (page 8)

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Preprint.
Keywords
quantum cryptographysecret sharingunclonable cryptography
Contact author(s)
prabhanjan @ cs ucsb edu
vipul @ cmu edu
jiahuiliu @ csail mit edu
qipengliu0 @ gmail com
History
2024-06-16: revised
2024-05-09: received
See all versions
Short URL
https://ia.cr/2024/716
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2024/716,
      author = {Prabhanjan Ananth and Vipul Goyal and Jiahui Liu and Qipeng Liu},
      title = {Unclonable Secret Sharing},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/716},
      year = {2024},
      url = {https://eprint.iacr.org/2024/716}
}
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