Message randomization and strong security in quantum stabilizer-based secret sharing for classical secrets

Ryutaroh Matsumoto*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

We improve the flexibility in designing access structures of quantum stabilizer-based secret sharing schemes for classical secrets, by introducing message randomization in their encoding procedures. We generalize the Gilbert–Varshamov bound for deterministic encoding to randomized encoding of classical secrets. We also provide an explicit example of a ramp secret sharing scheme with which multiple symbols in its classical secret are revealed to an intermediate set, and justify the necessity of incorporating strong security criterion of conventional secret sharing. Finally, we propose an explicit construction of strongly secure ramp secret sharing scheme by quantum stabilizers, which can support twice as large classical secrets as the McEliece–Sarwate strongly secure ramp secret sharing scheme of the same share size and the access structure.

Original languageEnglish
JournalDesigns, Codes, and Cryptography
Volume88
Issue number9
Pages (from-to)1893-1907
Number of pages15
ISSN0925-1022
DOIs
Publication statusPublished - 2020

Keywords

  • Gilbert–Varshamove bound
  • Quantum error-correcting code
  • Secret sharing
  • Strong security

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