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.
Originalsprog | Engelsk |
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Tidsskrift | Designs, Codes, and Cryptography |
Vol/bind | 88 |
Udgave nummer | 9 |
Sider (fra-til) | 1893-1907 |
Antal sider | 15 |
ISSN | 0925-1022 |
DOI | |
Status | Udgivet - 2020 |
Bibliografisk note
Funding Information:Orally presented at the unrefereed poster session in 2019 IEEE ISIT, Paris, France . This research is partly supported by JSPS Grant No. 17K06419.
Publisher Copyright:
© 2020, The Author(s).