2021/03/17 by Jinbao Zhu, Zhu, Jinbao, Qifa Yan +3 · 1 citation
Computer Science · #Complexity and Algorithms in Graphs #Cryptography and Data Security #FOS: Computer and information sciences #Information Theory (cs.IT) #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2103.09592
openalex publication_date 2021/03/17 · openalex created_date 2021/03/29 · openalex updated_date 2026/07/28
This paper investigates the problem of Secure Multi-party Batch Matrix Multiplication (SMBMM), where a user aims to compute the pairwise products A\divideontimesB\triangleq(A(1)B(1),…,A(M)B(M)) of two batch of massive matrices A and B that are generated from two sources, through N honest but curious servers which share some common randomness. The matrices A (resp. B) must be kept secure from any subset of up to XA (resp. XB) servers even if they collude, and the user must not obtain any information about (A,B) beyond the products A\divideontimesB. 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= XA=XB 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 respect to other measures remain identical.