GASP Codes for Secure Distributed Matrix Multiplication

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

doi:10.1109/tit.2020.2975021

Cited by 75 publications

(48 citation statements)

References 16 publications

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“…In [23], the authors improve the communication and computation cost of the scheme of [22]. In [24], the authors rely on arithmetic progressions to improve the sharing scheme to further reduce the number of servers needed.…”

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 [18], [25], coded schemes have been used to develop multi-party computation techniques to calculate arbitrary polynomials of massive matrices, preserving security of the data matrices. In [20], [21], [23] a reduction of the communication load is obtained by extending polynomial codes. While these works focus on either minimizing recovery threshold or communication load, the trade-off between these two fundamental quantities has not been addressed in the open literature to the best of our knowledge.…”

Section: B Related Workmentioning

confidence: 99%

“…As we will discuss, the projection of this set onto the plane defined by the condition P C = 0 includes the set of pairs (P R , C L ) in (15) and (16) obtained by the GPD code [14]. The proposed secure GPD (SGPD) code augments matrices A and B by adding P C random block matrices to the input matrices A and B, in a manner similar to prior works [18]- [21], [23], yielding augmented matrices A * and B * . As we will see, a direct application of the GPD codes to these matrices is suboptimal.…”

Section: Secure Polydot Codementioning

confidence: 99%

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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“…More generally, coding is able to control the tradeoff between computational delay and communication load between workers and master server [7]- [11]. Furthermore, stochastic coding can help keeping both input and output data secure from the workers, assuming that the latter are honest by carrying out the prescribed protocol, but curious [12]- [17]. This paper contributes to this line of work by investigating the trade-off between computational delay and communication This work was supported in part by the European Research Council (ERC) under the European Union Horizon 2020 research and innovative programme (grant agreement No 725731) and by U.S. NSF grants CNS-1526547, CCF-1525629.…”

Section: Introductionmentioning

confidence: 99%

“…In [13] Lagrange coding is presented which achieves the minimum recovery threshold for multilinear functions by generalizing MatDot codes. In [14], [15], [17] a reduction of the communication load is addressed by extending polynomial codes. While these works focus on either minimizing recovery threshold or communication load, the trade-off between these two fundamental quantities has not been addressed in the open literature to the best of our knowledge.…”

Section: Introductionmentioning

confidence: 99%

Distributed and Private Coded Matrix Computation with Flexible Communication Load

Aliasgari

Simeone

Kliewer

2019

2019 IEEE International Symposium on Information Theory (ISIT)

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Tensor operations, such as matrix multiplication, are central to large-scale machine learning applications. For user-driven tasks these operations can be carried out on a distributed computing platform with a master server at the user side and multiple workers in the cloud operating in parallel. For 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 and communication load. In this paper we impose an additional security constraint on the data matrices and assume that workers can collude to eavesdrop on the content of these data matrices. Specifically, we introduce a novel class of secure codes, referred to as secure generalized PolyDot codes, that generalizes previously published non-secure versions of these codes for matrix multiplication. These codes extend the state-of-the-art by allowing a flexible trade-off between recovery threshold and communication load for a fixed maximum number of colluding workers.

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GASP Codes for Secure Distributed Matrix Multiplication

Cited by 75 publications

References 16 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

Distributed and Private Coded Matrix Computation with Flexible Communication Load

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