Message Randomization and Strong Security in Quantum Stabilizer-Based Secret Sharing for Classical Secrets

TL;DR

This paper enhances quantum stabilizer-based secret sharing for classical secrets by introducing message randomization, generalizing bounds, and constructing strongly secure schemes with larger secret capacity.

Contribution

It introduces message randomization into quantum secret sharing, generalizes bounds for randomized encoding, and constructs a strongly secure scheme supporting larger secrets.

Findings

Supports twice as large classical secrets compared to previous schemes.

Provides an explicit construction of strongly secure ramp secret sharing.

Justifies the necessity of strong security criteria in secret sharing.

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.