Quantum Strongly Secure Ramp Secret Sharing

Abstract

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.

svjour3.cls, 14 pages, 1 figure. Versions 1&2 were wrong. V3 is mathematically correct. The first author was moved to the second

References in corpus (3)

• How to share a quantum secret
• On the Theory of Quantum Secret Sharing
• Quantum Secret Sharing Schemes and Reversibility of Quantum Operations

Cited by in corpus (7)

• Communication Efficient Quantum Secret Sharing
• Unitary Reconstruction of Secret for Stabilizer Based Quantum Secret Sharing
• Unified Approach to Secret Sharing and Symmetric Private Information Retrieval with Colluding Servers in Quantum Systems
• Coding Theoretic Construction of Quantum Ramp Secret Sharing
• Message Randomization and Strong Security in Quantum Stabilizer-Based Secret Sharing for Classical Secrets
• Measurement-free reconstruction circuit of quantum secrets in quantum secret sharing
• Advance Sharing Procedures for the Ramp Quantum Secret Sharing Schemes With the Highest Coding Rate