HerA 方案：通过 Hermitian 码实现安全分布式矩阵乘法
HerA Scheme: Secure Distributed Matrix Multiplication via Hermitian Codes
AI总结：
提出HerA方案，利用Hermitian码及其对偶码编码矩阵，在更小有限域上实现安全分布式矩阵乘法，并提升安全性能。
摘要：
我们考虑安全分布式矩阵乘法（SDMM）问题，其中用户拥有两个矩阵，并希望在 N 个诚实但好奇的服务器帮助下计算它们的乘积，同时满足安全约束：任何关于矩阵 A 或 B 的信息都不会泄露给任何服务器。本文提出了一种新方案，该方案考虑了矩阵 A 和 B 的内积划分。我们的核心技术依赖于分别用 Hermitian 码及其对偶码对矩阵 A 和 B 进行编码。我们提出了 Hermitian 代数（HerA）方案，该方案采用 Hermitian 码，并刻画了在矩阵元素属于含有 q^2 个元素的有限域时，划分能力与安全能力。我们展示了该方案在显著更小的有限域上执行安全分布式矩阵乘法，并且与现有文献中的结果相比，扩大了安全允许范围。
英文摘要：
We consider the problem of secure distributed matrix multiplication (SDMM), where a user has two matrices and wishes to compute their product with the help of $N$ honest but curious servers under the security constraint that any information about either $A$ or $B$ is not leaked to any server. This paper presents a \emph{new scheme} that considers the inner product partition for matrices $A$ and $B$. Our central technique relies on encoding matrices $A$ and $B$ in a Hermitian code and its dual code, respectively. We present the Hermitian Algebraic (HerA) scheme, which employs Hermitian codes and characterizes the partitioning and security capacities given entries of matrices belonging to a finite field with $q^2$ elements. We showcase that this scheme performs the secure distributed matrix multiplication in a significantly smaller finite field and expands security allowances compared to the existing results in the literature.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
