Rate-Efficiency and Straggler-Robustness through Partition in Distributed Two-Sided Secure Matrix Computation

Kakar, Jaber; Ebadifar, Seyedhamed; Sezgin, Aydin

doi:10.48550/arxiv.1810.13006

Cited by 10 publications

(45 citation statements)

References 11 publications

(21 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…State of the art schemes in secure distributed matrix multiplication [12], [13] are combined and improved in [14], referred to as GASP codes. Originally, GASP codes are designed for the single-message scenario, in which each worker is assigned a single computation task.…”

Section: Extension Of Gasp Codes To Multi-message Settingmentioning

confidence: 99%

See 1 more Smart Citation

Bivariate Polynomial Codes for Secure Distributed Matrix Multiplication

Hasircioglu,

Gomez-Vilardebo,

Gunduz

2021

Preprint

View full text Add to dashboard Cite

We consider the problem of secure distributed matrix multiplication. Coded computation has been shown to be an effective solution in distributed matrix multiplication, both providing privacy against workers and boosting the computation speed by efficiently mitigating stragglers. In this work, we present a non-direct secure extension of the recently introduced bivariate polynomial codes. Bivariate polynomial codes have been shown to be able to further speed up distributed matrix multiplication by exploiting the partial work done by the stragglers rather than completely ignoring them while reducing the upload communication cost and/or the workers' storage's capacity needs. We show that, especially for upload communication or storage constrained settings, the proposed approach reduces the average computation time of secure distributed matrix multiplication compared to its competitors in the literature. I. INTRODUCTIONMatrix multiplication is a fundamental building block of many applications in signal processing and machine learning. For some applications, especially those involving massive matrices and stringent latency requirements, matrix multiplication in a single computer is infeasible, and distributed solutions need to be adopted. In such scenarios, the full multiplication task is first partitioned into smaller sub-tasks, which are then distributed across dedicated workers.

show abstract

Section: Extension Of Gasp Codes To Multi-message Settingmentioning

confidence: 99%

“…This requires increasing the degree of the encoding polynomial and thus increasing the recovery threshold. The recovery threshold has been improved in subsequent works [13], [14], by carefully choosing the degrees of the encoding monomials so that the resultant decoding polynomial contains the minimum number of additional coefficients.…”

mentioning

confidence: 99%

Bivariate Polynomial Codes for Secure Distributed Matrix Multiplication

Hasircioglu,

Gomez-Vilardebo,

Gunduz

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…is satisfied for any |T | ≤ T , for uniformly randomly generated A and B. Secure distributed matrix multiplication has been studied in [11]- [14], [17]- [19], [43]- [50]. In particular, [17]- [19] presented coded computing designs for general block-wise partitioning of the input matrices, all requiring at least pmn workers' computation.…”

Section: A Secure Distributed Matrix Multiplicationmentioning

confidence: 99%

Entangled Polynomial Codes for Secure, Private, and Batch Distributed Matrix Multiplication: Breaking the "Cubic" Barrier

Avestimehr

2020

Preprint

View full text Add to dashboard Cite

In distributed matrix multiplication, a common scenario is to assign each worker a fraction of the multiplication task, by partition the input matrices into smaller submatrices. In particular, by dividing two input matrices into m-by-p and p-by-n subblocks, a single multiplication task can be viewed as computing linear combinations of pmn submatrix products, which can be assigned to pmn workers. Such block-partitioning based designs have been widely studied under the topics of secure, private, and batch computation, where the state of the arts all require computing at least "cubic" (pmn) number of submatrix multiplications. Entangled polynomial codes, first presented for straggler mitigation, provides a powerful method for breaking the cubic barrier. It achieves a subcubic recovery threshold, meaning that the final product can be recovered from any subset of multiplication results with a size order-wise smaller than pmn. In this work, we show that entangled polynomial codes can be further extended to also include these three important settings, and provide a unified framework that order-wise reduces the total computational costs upon the state of the arts by achieving subcubic recovery thresholds. I. INTRODUCTIONLarge scale distributed computing faces several modern challenges, in particular, to provide resiliency against stragglers, robustness against computing errors, security against Byzantine and eavesdropping adversaries, privacy of sensitive information, and to efficiently handle repetitive computation [1]- [7]. Coded computing is an emerging field that resolves these issues by introducing and developing new coding theoretic concepts, started focusing on straggler mitigation [8]-[10], then later extended to secure and private computation [6], [7], [11]- [14].Coding for straggler mitigation is first studied in [8] for linear computation, where classical linear codes can be directly applied to achieve same performances. For computation beyond linear functions, new classes of coding designs are needed to achieve optimality. In [10], we studied matrix-by-matrix multiplication and introduced the polynomial coded computing (PCC) framework. The main coding idea is to jointly encode the input variables into single variate polynomials where the coefficients are functions of the inputs. By assigning each worker evaluations of these polynomials as coded variables, they essentially evaluate a new polynomial composed by each worker's computation and the encoding functions at the same point. As long as the needed final results can be recovered from the coefficients of the composed polynomial, the master can decode the final output when sufficiently many workers complete their computation. PCC significantly reduces the design problem of coded computation to finding polynomials satisfying the above decodability constraint while minimizing the degree of the decomposed polynomial. It has been shown that PCC achieves a great success in providing exact optimal coding constructions for large classes of computation tasks includi...

show abstract

“…To hide the matrices from the workers, random matrix partitions are created, and linearly encoded together with the true matrix partitions using polynomial codes. The recovery threshold has been improved in subsequent works [12], [13], by carefully choosing the degrees of the encoding monomials so that the resultant decoding polynomial contains the minimum number of additional coefficients.…”

Section: Introductionmentioning

confidence: 99%

Speeding Up Private Distributed Matrix Multiplication via Bivariate Polynomial Codes

Hasırcıoglu¹,

Gómez-Vilardebó²,

Gündüz³

2021

Preprint

View full text Add to dashboard Cite

We consider the problem of private distributed matrix multiplication under limited resources. Coded computation has been shown to be an effective solution in distributed matrix multiplication, both providing privacy against the workers and boosting the computation speed by efficiently mitigating stragglers. In this work, we propose the use of recently-introduced bivariate polynomial codes to further speed up private distributed matrix multiplication by exploiting the partial work done by the stragglers rather than completely ignoring them. We show that the proposed approach significantly reduces the average computation time of private distributed matrix multiplication compared to its competitors in the literature, while improving the upload communication cost and the workers' storage efficiency.

show abstract

Rate-Efficiency and Straggler-Robustness through Partition in Distributed Two-Sided Secure Matrix Computation

Cited by 10 publications

References 11 publications

Bivariate Polynomial Codes for Secure Distributed Matrix Multiplication

Bivariate Polynomial Codes for Secure Distributed Matrix Multiplication

Entangled Polynomial Codes for Secure, Private, and Batch Distributed Matrix Multiplication: Breaking the "Cubic" Barrier

Speeding Up Private Distributed Matrix Multiplication via Bivariate Polynomial Codes

Contact Info

Product

Resources

About