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arXiv · 2002.07750

GCSA Codes with Noise Alignment for Secure Coded Multi-Party Batch Matrix Multiplication

Zhen Chen·Zhuqing Jia·Zhiying Wang·Syed A. Jafar
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Abstract

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.

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Zhen Chen, Zhuqing Jia, Zhiying Wang, Syed A. Jafar. 2020-02-18. GCSA Codes with Noise Alignment for Secure Coded Multi-Party Batch Matrix Multiplication. https://arxiv.org/abs/2002.07750

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