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

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...

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Vydáno v:IEEE journal on selected areas in information theory Ročník 2; číslo 1; s. 306 - 316
Hlavní autoři: Chen, Zhen, Jia, Zhuqing, Wang, Zhiying, Jafar, Syed Ali
Médium: Journal Article
Jazyk:angličtina
Vydáno: Piscataway IEEE 01.03.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Algorithms
Alignment
Batch processing
coded computing
Distributed computing
Encoding
Information retrieval
Interference
Matrices (mathematics)
matrix multiplication
Multiplication
Network topologies
Network topology
Noise
noise alignment
Polynomials
Privacy
secure multi-party computation
Servers
Subspaces
ISSN:2641-8770, 2641-8770
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Shrnutí: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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ISSN:2641-8770
2641-8770
DOI:10.1109/JSAIT.2021.3052934