Quantum Strongly Secure Ramp Secret Sharing

TL;DR

This paper introduces a quantum analog of classical strong security in ramp secret sharing schemes, ensuring critical information remains secure even when partial data leaks occur, and reduces share size.

Contribution

It proposes a novel quantum strong security model for ramp secret sharing, enhancing security guarantees while maintaining reduced share sizes.

Findings

Quantum strong security prevents leakage of critical information.

The scheme reduces share size compared to traditional quantum secret sharing.

It extends classical security concepts to quantum 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.