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

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.

References in corpus (7)

• Speeding Up Distributed Machine Learning Using Codes
• Polynomial Codes: an Optimal Design for High-Dimensional Coded Matrix Multiplication
• Coded Sparse Matrix Multiplication
• Fundamental Limits of Coded Linear Transform
• Secure Degrees of Freedom of Wireless X Networks Using Artificial Noise Alignment
• Entangled Polynomial Codes for Secure, Private, and Batch Distributed Matrix Multiplication: Breaking the "Cubic" Barrier
• Cross Subspace Alignment Codes for Coded Distributed Batch Computation