GASP Codes for Secure Distributed Matrix Multiplication

D’Oliveira, Rafael G. L.; Rouayheb, Salim El; Karpuk, David

doi:10.1109/isit.2019.8849446

Cited by 36 publications

(78 citation statements)

References 7 publications

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“…Remark 1 (J -Sided Matrix Multiplication): In analogy to the construction of the achievable scheme applicable only to the product of two matrices, the scheme can be extended to the computation of J j=1 M j , where M j is the j-th matrix from the left. Choosing the first J − 1 matrices similarly to (11) and M J according to (12), we can attain a rate of R N , = 1 − J N . The achievable recovery threshold, on the other hand, becomes ω N , = min{r + J , N } with r representing the partition level of M J .…”

Section: Secure Cross Subspace Alignment-based Matrix Multiplicationmentioning

confidence: 99%

“…By comparing with the converse, their proposed scheme for the second model seems to be loose in terms of communication rate and the maximum number of tolerable colluding servers supporting a non-zero rate. Very recently, gap additive secure polynomial (GASP) and PolyDot codes have been proposed for the two-sided model focusing on optimizing the downlink rate [12] and balancing recovery threshold with communication load [13].…”

Section: Introductionmentioning

confidence: 99%

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On the Capacity and Straggler-Robustness of Distributed Secure Matrix Multiplication

2019

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Computationally efficient matrix multiplication is a fundamental requirement in various fields, including and particularly in data analytics. To do so, the computation task of large-scale matrix multiplication is typically outsourced to multiple servers. However, due to data misusage at the servers, security is typical of concern. In this paper, we first study the two-sided secure matrix multiplication problem, where a user is interested in the matrix product AB of two finite field private matrices A and B from an information-theoretic perspective. In this problem, the user exploits the computational resources of N servers to compute the matrix product but simultaneously tries to conceal the private matrices from the servers. Our goal is twofold: (i) to maximize the downlink communication rate, and (ii) to minimize the effective number of server observations needed to determine AB, while preserving security, where we allow for up to ≤ N servers to collude. To this end, we propose two schemes -an aligned secret sharing scheme (A3S) and a secure cross subspace alignment (SCSA) scheme. For A3S, we optimize the partitioning of matrices A and B in order to either optimize objective (i) or (ii) as a function of the system parameters (e.g., N and ). A proposed inductive approach gives us analytical, close-to-optimal solutions for both (i) and (ii). The SCSA, on the other hand, is shown to be (rate) capacity-optimal for the general J -sided distributed secure matrix multiplication problem J j=1 M j . We show this by developing a recursive information-theoretic upper bound (converse) on the downlink rate for the J -sided secure matrix multiplication problem. With respect to (i), both A3S and SCSA, significantly outperform the state-of-the-art in terms of (a) communication rate, (b) maximum tolerable number of colluding servers, and (c) computational complexity. Overall SCSA (A3S) is the preferred choice when the focus is on the downlink (uplink).

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Section: Secure Cross Subspace Alignment-based Matrix Multiplicationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Capacity and Straggler-Robustness of Distributed Secure Matrix Multiplication

2019

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“…As the computations are scaling out across many distributed servers, besides stragglers, security is also a concern as the servers might be curious about the matrix contents. A typical assumption is that any X of them may collude to deduce information about the matrices possessed by the user [7]. This raises the problem of secure distributed matrix multiplication (SDMM), which has recently received a lot of attention from an information-theoretic perspective [7]- [14].…”

Section: Introductionmentioning

confidence: 99%

“…A typical assumption is that any X of them may collude to deduce information about the matrices possessed by the user [7]. This raises the problem of secure distributed matrix multiplication (SDMM), which has recently received a lot of attention from an information-theoretic perspective [7]- [14].…”

Section: Introductionmentioning

confidence: 99%

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Improved Private and Secure Distributed Matrix Multiplication

Hollanti

2021

2021 IEEE International Symposium on Information Theory (ISIT)

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Consider the problem of a user having a private matrix A and N non-colluding servers sharing a library of L (L > 1) matrices B (0) , B (1) , . . . , B (L−1) , for which the user wishes to compute AB (θ) for some θ ∈ [0, L) without revealing any information of the matrix A to the servers, and keeping the index θ private to the servers. This problem is known as private and secure distributed matrix multiplication (PSDMM) and is supposed to have wide application potential. However, studies of PSDMM are still scarce in the literature. In this paper, we propose a new efficient private and secure distributed matrix multiplication coding scheme, which has a better performance than state-of-the-art schemes in that it achieves a smaller recovery threshold and download cost as well as providing a more flexible tradeoff between the upload and download costs.

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