Degree Tables for Secure Distributed Matrix Multiplication

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

doi:10.1109/jsait.2021.3102882

Cited by 16 publications

(17 citation statements)

References 21 publications

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“…In this paper we present two SDMM schemes that work over the complex numbers and show that they can achieve information leakage that is arbitrarily small by a suitable choice of the parameters. These schemes have been previously considered in the context of SDMM over finite fields in [5], [6], [22], but this paper provides a more practical way of using them in the real world. A similar idea of using roots of unity as evaluation points was recently considered in [26], [27] in the context of coded distributed polynomial evaluation.…”

Section: B Motivation and Contributionmentioning

confidence: 99%

“…The following scheme follows the construction of the GASP big code presented in [5]. We use this special case of the more general GASP code presented in [6], since the GASP big code is a subcode of a Generalized Reed-Solomon code with a small dimension. Therefore, it is possible to use a Vandermonde matrix as the generator matrix, which makes it simple to choose the evaluation points of the scheme.…”

Section: B Gasp Code Over Complex Numbersmentioning

confidence: 99%

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Analog Secure Distributed Matrix Multiplication over Complex Numbers

Okko¹,

Hollanti²

2022

Preprint

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This work considers the problem of distributing matrix multiplication over the real or complex numbers to helper servers, such that the information leakage to these servers is close to being information-theoretically secure. These servers are assumed to be honest-but-curious, i.e., they work according to the protocol, but try to deduce information about the data. The problem of secure distributed matrix multiplication (SDMM) has been considered in the context of matrix multiplication over finite fields, which is not always feasible in real world applications. We present two schemes, which allow for variable degree of security based on the use case and allow for colluding and straggling servers. We analyze the security and the numerical accuracy of the schemes and observe a trade-off between accuracy and security.

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Section: B Motivation and Contributionmentioning

confidence: 99%

Section: B Gasp Code Over Complex Numbersmentioning

confidence: 99%

Analog Secure Distributed Matrix Multiplication over Complex Numbers

Okko¹,

Hollanti²

2022

Preprint

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“…However, in the setting of matrix-matrix multiplication no known scheme achieves this rate. When restricting the encoding to polynomials, better bounds can be obtained by replacing the ideal rate with the lower bounds provided in [42]. We use the ideal scheme to keep our lower bound theoretical and independent from the encoding strategy.…”

Section: A Theoretical Lower Boundmentioning

confidence: 99%

Adaptive Private Distributed Matrix Multiplication

Bitar¹,

Xhemrishi²,

Wachter-Zeh³

2021

Preprint

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We consider the problem of designing codes with flexible rate (referred to as rateless codes), for private distributed matrixmatrix multiplication. A master server owns two private matrices A and B and hires worker nodes to help computing their multiplication. The matrices should remain information-theoretically private from the workers. Codes with fixed rate require the master to assign tasks to the workers and then wait for a predetermined number of workers to finish their assigned tasks. The size of the tasks, hence the rate of the scheme, depends on the number of workers that the master waits for.We design a rateless private matrix-matrix multiplication scheme, called RPM3. In contrast to fixed-rate schemes, our scheme fixes the size of the tasks and allows the master to send multiple tasks to the workers. The master keeps sending tasks and receiving results until it can decode the multiplication; rendering the scheme flexible and adaptive to heterogeneous environments.Despite resulting in a smaller rate than known straggler-tolerant schemes, RPM3 provides a smaller mean waiting time of the master by leveraging the heterogeneity of the workers. The waiting time is studied under two different models for the workers' service time. We provide upper bounds for the mean waiting time under both models. In addition, we provide lower bounds on the mean waiting time under the worker-dependent fixed service time model.

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“…• We analyze the time complexity trade-off between the user and the servers when using GASP codes, introduced in [3] and improved on in [4]. They are currently the best polynomial codes in terms of total communication cost.…”

Section: A Main Contributionsmentioning

confidence: 99%

Notes on Communication and Computation in Secure Distributed Matrix Multiplication

D’Oliveira

Rouayheb

Heinlein

et al. 2020

2020 IEEE Conference on Communications and Network Security (CNS)

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We consider the problem of secure distributed matrix multiplication in which a user wishes to compute the product of two matrices with the assistance of honest but curious servers.We show that if the user is only concerned in optimizing the download rate, a common assumption in the literature, then the problem can be converted into a simple private information retrieval problem by means of a scheme we call Private Oracle Querying. However, this comes at large upload and computational costs for both the user and the servers.In contrast, we show that for the right choice of parameters, polynomial codes can lower the computational time of the system, e.g. if the computational time complexity of an operation in Fq is at most Zq and the computational time complexity of multiplying two n × n matrices is O(n ω Zq) then the user together with the servers can compute the multiplication in O(n 4− 6 ω+1 Zq) time.

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Degree Tables for Secure Distributed Matrix Multiplication

Cited by 16 publications

References 21 publications

Analog Secure Distributed Matrix Multiplication over Complex Numbers

Analog Secure Distributed Matrix Multiplication over Complex Numbers

Adaptive Private Distributed Matrix Multiplication

Notes on Communication and Computation in Secure Distributed Matrix Multiplication

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