Quantum strongly secure ramp secret sharing
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Quantum secret sharing is a scheme for encoding a quantum state (the secret) into multiple shares and distributing them among several participants. If a sufficient number of shares are put together, then the secret can be fully reconstructed. If an insufficient number of shares are put together however, no information about the secret can be revealed. In quantum ramp secret sharing, partial information about the secret is allowed to leak to a set of participants, called an unqualified set, that cannot fully reconstruct the secret. By allowing this, the size of a share can be drastically reduced. This paper introduces a quantum analog of classical strong security in ramp secret sharing schemes. While the ramp secret sharing scheme still leaks partial information about the secret to unqualified sets of participants, the strong security condition ensures that qudits with critical information can no longer be leaked.
KeywordsQuantum secret sharing Non-perfect secret sharing Ramp secret sharing Strong security
Mathematics Subject Classification81P94 94A62
The authors would like to thank the reviewers for their careful reading that improved the presentation. This research was conducted as part of Tokyo Institute of Technology International Research Opportunities Program under Re-Inventing Japan Project funded by Ministry of Education, Culture, Sports, Science and Technology. This research is partly supported by the National Institute of Information and Communications Technology, Japan, and by the Japan Society for the Promotion of Science Grant Nos. 23246071 and 26289116, and the Villum Foundation through their VELUX Visiting Professor Programme 2013–2014.
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