Distributed and Private Coded Matrix Computation with Flexible Communication Load

Aliasgari, Malihe; Simeone, Osvaldo; Kliewer, Joerg

doi:10.1109/isit.2019.8849606

Cited by 36 publications

(34 citation statements)

References 29 publications

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“…Some other configurations are also considered in [25], where the master should not know which part of some external data set has been used for computation. In [26], the authors propose a code for private matrix multiplication that is flexible to achieve a trade-off between number of servers needed and communication load.…”

Section: A Concurrent and Follow-up Resultsmentioning

confidence: 99%

Limited-Sharing Multi-Party Computation for Massive Matrix Operations

Nodehi

Maddah-Ali

2018

2018 IEEE International Symposium on Information Theory (ISIT)

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In this paper, we consider a secure multi-party computation problem (MPC), where the goal is to offload the computation of an arbitrary polynomial function of some massive private matrices to a network of workers. The workers are not reliable, some may collude to gain information about the input data. The system is initialized by sharing a (randomized) function of each input matrix to each server. Since the input matrices are massive, the size of each share is assumed to be at most 1/k fraction of the input matrix, for some k ∈ N. The objective is to minimize the number of workers needed to perform the computation task correctly, such that even if an arbitrary subset of t − 1 workers, for some t ∈ N, collude, they cannot gain any information about the input matrices. We propose a sharing scheme, called polynomial sharing, and show that it admits basic operations such as adding and multiplication of matrices, and transposing a matrix. By concatenating the procedures for basic operations, we show that any polynomial function of the input matrices can be calculated, subject to the problem constraints. We show that the proposed scheme can offer order-wise gain, in terms of number of workers needed, compared to the approaches formed by concatenation of job splitting and conventional MPC approaches.

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Section: A Concurrent and Follow-up Resultsmentioning

confidence: 99%

Limited-Sharing Multi-Party Computation for Massive Matrix Operations

Nodehi

Maddah-Ali

2018

2018 IEEE International Symposium on Information Theory (ISIT)

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“…In the process, we also introduce a novel perspective on distributed computing codes based on the signal processing concepts of convolution and ztransform. SGPD codes were first introduced in the conference version of this paper [1]. Then, SGPD codes are modified to offer a novel solution for the scenario in Fig.…”

Section: Main Contributionmentioning

confidence: 99%

“…The master server must be able to decode the product C (κ) from the output of a subset of P R servers, which defines the recovery threshold. of a confidential input matrix A with a matrix B (κ) from a set of public matrices {B (1) , . .…”

Section: Private and Secure Matrix Multiplicationmentioning

confidence: 99%

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Private and Secure Distributed Matrix Multiplication With Flexible Communication Load

Aliasgari

Simeone

Kliewer

2020

IEEE Trans.Inform.Forensic Secur.

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Large matrix multiplications are central to largescale machine learning applications. These operations are often carried out on a distributed computing platform with a master server and multiple workers in the cloud operating in parallel. For such distributed platforms, it has been recently shown that coding over the input data matrices can reduce the computational delay, yielding a trade-off between recovery threshold, i.e., the number of workers required to recover the matrix product, and communication load, i.e., the total amount of data to be downloaded from the workers. In this paper, in addition to exact recovery requirements, we impose security and privacy constraints on the data matrices, and study the recovery threshold as a function of the communication load. We first assume that both matrices contain private information and that workers can collude to eavesdrop on the content of these data matrices. For this problem, we introduce a novel class of secure codes, referred to as secure generalized PolyDot (SGPD) codes, that generalize state-of-the-art non-secure codes for matrix multiplication. SGPD codes allow a flexible trade-off between recovery threshold and communication load for a fixed maximum number of colluding workers while providing perfect secrecy for the two data matrices. We then assume that one of the data matrices is taken from a public set known to all the workers. In this setup, the identity of the matrix of interest should be kept private from the workers. For this model, we present a variant of generalized PolyDot codes that can guarantee both secrecy of one matrix and privacy for the identity of the other matrix for the case of no colluding servers.

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“…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%

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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Distributed and Private Coded Matrix Computation with Flexible Communication Load

Cited by 36 publications

References 29 publications

Limited-Sharing Multi-Party Computation for Massive Matrix Operations

Limited-Sharing Multi-Party Computation for Massive Matrix Operations

Private and Secure Distributed Matrix Multiplication With Flexible Communication Load

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

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