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.

中文翻译：

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基于量子稳定器的经典秘密秘密共享中的消息随机化和强安全性

我们通过在编码过程中引入消息随机化，提高了为经典秘密设计基于量子稳定器的秘密共享方案的访问结构的灵活性。我们将确定性编码的 Gilbert-Varshamov 界限推广到经典秘密的随机编码。我们还提供了一个斜坡秘密共享方案的明确示例，该方案将其经典秘密中的多个符号透露给一个中间集合，并证明了结合传统秘密共享的强安全标准的必要性。最后，我们提出了一种由量子稳定器显式构建的强安全斜坡秘密共享方案，它可以支持两倍于相同共享大小和访问结构的 McEliece-Sarwate 强安全斜坡秘密共享方案的经典秘密。