Message Randomization and Strong Security in Quantum Stabilizer-Based Secret Sharing for Classical Secrets
This work addresses the need for more efficient and secure secret sharing schemes in cryptography, offering a significant improvement over existing methods.
The paper tackles the problem of designing flexible access structures in quantum stabilizer-based secret sharing for classical secrets by introducing message randomization, resulting in a scheme that supports twice as large classical secrets as the previous best method with the same share size and access structure.
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.