论文标题
带有噪声对齐的GCSA代码，用于安全编码的多方批次矩阵乘法
GCSA Codes with Noise Alignment for Secure Coded Multi-Party Batch Matrix Multiplication
论文作者
论文摘要
考虑了安全的多方批次矩阵乘法问题（SMBMM），其目标是通过在S服务器上分发计算，使主能够有效地计算两个大型矩阵的成对产品。任何X勾结服务器都不会获得有关输入的信息，并且主人没有获得有关产品以外的输入的其他信息。基于跨空间比对代码，提出了一种称为具有噪声比对（GCSA-NA）（GCSA-NA）（GCSA-NA）的通用交叉子空间比对代码的解决方案。对SMBMM的最先进的解决方案是Nodehi和Maddah-Ali提出的称为多项式共享（PS）的编码方案。 GCSA-NA在几个关键方面都优于PS代码 - 更高效，更安全的服务器间通信，较低的延迟，灵活的服务器间网络拓扑，有效的批处理处理以及对Stragglers的耐受性。噪声比对的概念也可以与N源交叉子空间对齐（N-CSA）代码和快速矩阵乘法算法（如Strassen的构造）结合使用。此外，噪声对准可以应用于对称安全的私人信息检索中以实现渐近能力。
A secure multi-party batch matrix multiplication problem (SMBMM) is considered, where the goal is to allow a master to efficiently compute the pairwise products of two batches of massive matrices, by distributing the computation across S servers. Any X colluding servers gain no information about the input, and the master gains no additional information about the input beyond the product. A solution called Generalized Cross Subspace Alignment codes with Noise Alignment (GCSA-NA) is proposed in this work, based on cross-subspace alignment codes. The state of art solution to SMBMM is a coding scheme called polynomial sharing (PS) that was proposed by Nodehi and Maddah-Ali. GCSA-NA outperforms PS codes in several key aspects - more efficient and secure inter-server communication, lower latency, flexible inter-server network topology, efficient batch processing, and tolerance to stragglers. The idea of noise alignment can also be combined with N-source Cross Subspace Alignment (N-CSA) codes and fast matrix multiplication algorithms like Strassen's construction. Moreover, noise alignment can be applied to symmetric secure private information retrieval to achieve the asymptotic capacity.
