Volume 2,Issue 3
秘密共享中的双陪集结构
线性秘密共享方案（LSSS）为现代密码协议提供了计算高效的基石，而代数结构的引入能极大地丰富其理论与应用内涵。本文旨在将群论中的双陪集结构系统性地嵌入秘密共享框架，构建一个兼具代数严谨性与密码学实用性的新模型。首先，形式化定义了基于双陪集的秘密共享方案，阐明其如何将秘密编码为群中的双陪集，并将份额生成与恢复过程转化为群元素运算。其次，深入探讨了该方案的核心代数基础，即群作用下的轨道空间与访问结构的群论表征。并通过基于矩阵群的具体实例，展示了该模型在实现多级秘密共享方面的独特优势。双陪集结构所提供的代数工具，不仅能够自然地支持多级秘密共享，其内在的对偶性也使得设计高效安全的协议成为可能。这一框架在安全多方计算、分布式存储以及量子密码学等多个前沿领域展现出重要的应用潜力。
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