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Computational Quantum Secret Sharing

Authors Alper Çakan , Vipul Goyal, Chen-Da Liu-Zhang, João Ribeiro

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Author Details

Alper Çakan
  • Carnegie Mellon University, Pittsburgh, PA, USA
Vipul Goyal
  • NTT Research, Sunnyvale, CA, USA
  • Carnegie Mellon University, Pittsburgh, PA, USA
Chen-Da Liu-Zhang
  • NTT Research, Sunnyvale, CA, USA
João Ribeiro
  • NOVA LINCS and NOVA School of Science and Technology, Caparica, Portugal

Funding

Research supported by the following grants of Vipul Goyal: NSF award 1916939, DARPA SIEVE program, a gift from Ripple, a DoE NETL award, a JP Morgan Faculty Fellowship, a PNC center for financial services innovation award, and a Cylab seed funding award.
  • Liu-Zhang, Chen-Da: Part of the work was done while at Carnegie Mellon University.
  • Ribeiro, João: Part of the work was done while at Carnegie Mellon University. Research also supported by NOVA LINCS (UIDB/04516/2020) with the financial support of FCT.IP.

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Alper Çakan, Vipul Goyal, Chen-Da Liu-Zhang, and João Ribeiro. Computational Quantum Secret Sharing. In 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 266, pp. 4:1-4:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.TQC.2023.4

Abstract

Quantum secret sharing (QSS) allows a dealer to distribute a secret quantum state among a set of parties in such a way that certain authorized subsets can reconstruct the secret, while unauthorized subsets obtain no information about it. Previous works on QSS for general access structures focused solely on the existence of perfectly secure schemes, and the share size of the known schemes is necessarily exponential even in cases where the access structure is computed by polynomial size monotone circuits. This stands in stark contrast to the classical setting, where polynomial-time computationally-secure secret sharing schemes have been long known for all access structures computed by polynomial-size monotone circuits under standard hardness assumptions, and one can even obtain shares which are much shorter than the secret (which is impossible with perfect security).
While QSS was introduced over twenty years ago, previous works only considered information-theoretic privacy. In this work, we initiate the study of computationally-secure QSS and show that computational assumptions help significantly in building QSS schemes, just as in the classical case. We present a simple compiler and use it to obtain a large variety results: We construct polynomial-time computationally-secure QSS schemes under standard hardness assumptions for a rich class of access structures. This includes many access structures for which previous results in QSS necessarily required exponential share size. In fact, we can go even further: We construct QSS schemes for which the size of the quantum shares is significantly smaller than the size of the secret. As in the classical setting, this is impossible with perfect security.
We also apply our compiler to obtain results beyond computational QSS. In the information-theoretic setting, we improve the share size of perfect QSS schemes for a large class of n-party access structures to 1.5^{n+o(n)}, improving upon best known schemes and matching the best known result for general access structures in the classical setting. Finally, among other things, we study the class of access structures which can be efficiently implemented when the quantum secret sharing scheme has access to a given number of copies of the secret, including all such functions in 𝖯 and NP.

Subject Classification

ACM Subject Classification
  • Theory of computation → Cryptographic primitives
  • Theory of computation → Quantum computation theory
Keywords
  • Quantum secret sharing
  • quantum cryptography

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