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 anew 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 this scheme performs the secure distributed matrix multiplication in a significantly smaller finite field than the existing results in the literature.

翻译：本文考虑安全的分布式矩阵乘法（SDMM）问题，在该问题中，用户有两个矩阵并希望在$N$个诚实但好奇的服务器的帮助下计算其乘积，同时任何关于矩阵$A$或$B$的信息都不泄漏给任何服务器。本文提出了一个新的方案，该方案考虑了矩阵$A$和$B$的内积分区。我们的核心技术依赖于使用Hermitian编码对矩阵$A$和$B$进行编码。我们提出了Hermitian代数（HerA）方案，利用Hermitian编码并表征了分区和安全容量，给出属于有$q^2$个元素的有限域的矩阵项。我们展示了该方案在比文献中现有结果更小的有限域中进行安全分布式矩阵乘法的性能。