Improved Constructions for Secure Multi-Party Batch Matrix Multiplication

This paper investigates the problem of Secure Multi-party Batch Matrix Multiplication (SMBMM), where a user aims to compute the pairwise products \mathbf {A}\divideontimes \mathbf {B}\triangleq (\mathbf {A}^{(1)}\mathbf {B}^{(1)},\ldots,\mathbf {A}^{(M)}\mathbf {B}^{(M)}) of two batch of massive m...

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Bibliographic Details
Published in:IEEE transactions on communications 2021-11, Vol.69 (11), p.7673-7690
Main Authors: Zhu, Jinbao, Yan, Qifa, Tang, Xiaohu
Format: Article
Language:English
Subjects:
Complexity
Complexity theory
cross subspace alignment
Decoding
Distributed databases
Distributed matrix multiplication
Downloading
Encoding
multi-party computation
Multiplication
Randomness
Recovery
Redundancy
security
Servers
Task analysis
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Summary:This paper investigates the problem of Secure Multi-party Batch Matrix Multiplication (SMBMM), where a user aims to compute the pairwise products \mathbf {A}\divideontimes \mathbf {B}\triangleq (\mathbf {A}^{(1)}\mathbf {B}^{(1)},\ldots,\mathbf {A}^{(M)}\mathbf {B}^{(M)}) of two batch of massive matrices \mathbf {A} and \mathbf {B} that are generated from two sources, through N honest but curious servers which share some common randomness. The matrices \mathbf {A} (resp. \mathbf {B} ) must be kept secure from any subset of up to X_{\mathbf {A}} (resp. X_{\mathbf {B}} ) servers even if they collude, and the user must not obtain any information about (\mathbf {A},\mathbf {B}) beyond the products \mathbf {A}\divideontimes \mathbf {B} . A novel computation strategy for single secure matrix multiplication problem (i.e., the case M=1 ) is first proposed, and then is generalized to the strategy for SMBMM by means of cross subspace alignment. The SMBMM strategy focuses on the tradeoff between recovery threshold (the number of successful computing servers that the user needs to wait for), system cost (upload cost, the amount of common randomness, and download cost) and system complexity (encoding, computing, and decoding complexities). Notably, compared with the known result by Chen et al. , the strategy for the degraded case X= X_{\mathbf {A}}=X_{\mathbf {B}} achieves better recovery threshold, amount of common randomness, download cost and decoding complexity when X is less than some parameter threshold, while the performance with respe
ISSN:0090-6778
1558-0857
DOI:10.1109/TCOMM.2021.3107942