基于RS码生成机制的(k,n)门限量子秘密共享方案

(k,n) Threshold Quantum Secret Sharing Scheme Based on the Generation of Reed Solomon Code

文章利用生成矩阵分割法提出了(k,n)量子门限秘密共享方案。与以往经典方案相比,它具有更好的安全性和可靠性。从量子方案的角度看,编码多样性提高了密钥破译难度。针对生成矩阵的循环周期问题和因某些元素不存在本原根而不能构造生成矩阵的问题,文章也提出了解决方案。本文方案的核心思想是参照量子信息与经典信息的对应关系,利用有限域中的本原根构造生成矩阵来实现经典秘密的分割,生成矩阵满足任意k列列向量线性独立;传输采用了基于超密集编码的量子安全直接通信。

A（k,n） quantum threshold secret sharing scheme based on generator matrix segmentation is proposed in this paper. Compared with the previous classical schemes, our scheme has better security and reliability, and it also has the diversity of encoding with the quantum system, which can improve the diffi culty of deciphering. A solution for the issue of matrix cycle period and the problem that some numbers without the primitive element can＇t construct generation matrix is derived. The core idea of our scheme is to achieve the secret division by applying the primitive element in the fi nite domain for generation matrix based on the correspondence between the quantum and classical information, where the generation matrix satisfi es that any k column vectors are linearly independent. The transmission process involves quantum secure direct communication（QSDC） based on superdense coding.