Entangled Polynomial Coding in Limited-Sharing Multi-Party Computation

Nodehi, Hanzaleh Akbari; Najarkolaei, Seyed Reza Hoseini; Maddah-Ali, Mohammad Ali

doi:10.1109/itw.2018.8613446

Cited by 34 publications

(65 citation statements)

References 4 publications

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“…In addition, it was presented in CTW 2018 in May 2018. We also presented a generalized version of [1] in [21].…”

Section: A Concurrent and Follow-up Resultsmentioning

confidence: 99%

“…In addition, overall, the min{2pmn + 2t − 3, mpn + 2mp + np + nt − 2n − 2p + 1} coefficients in this polynomial is not zero. Thus if the number of workers is at least min{2pmn + 2t − 3, mpn + 2mp + np + nt − 2n − 2p + 1}, similar to Theorem 3, we can calculate C. Similar procedures in Section VII, we can calculate any polynomial function G, satisfying constraints (1), (2), and (3) (see [21]).…”

Section: Extensionmentioning

confidence: 97%

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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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“…In addition, it was presented in CTW 2018 in May 2018. We also presented a generalized version of [1] in [21].…”

Section: A Concurrent and Follow-up Resultsmentioning

confidence: 99%

Section: Extensionmentioning

confidence: 97%

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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“…Coded computing has recently emerged as a technique of utilizing information/coding theoretical tools to inject redundant data and computations into distributed computing systems, to mitigate communication and straggler bottlenecks, and provide security and privacy for various computation tasks (see, e.g., [5], [10], [11], [15], [16], [19], [20], [22]- [30]). Privately retrieving a message from a distributed storage system without revealing the index of the message has been studied extensively in the problem of Private Information Retrieval (PIR) [31]- [37] in recent years.…”

Section: A Related Workmentioning

confidence: 99%

“…To the best of our knowledge, the state-of-the-art strategies for SMM with arbitrary partitioning of matrices above can be divided into two categories in terms of coding techniques, i.e., SMM based on polynomial codes [11], [15] and SMM based on Lagrange codes [16]. The essential components behind these coded strategies lie in constructing the encoding functions of matrices A and B, denoted by f (x) and h(x) respectively, such that the desired products of sub-matrices…”

Section: I(y(αmentioning

confidence: 99%

“…An essential component behind these coded strategies is to construct appropriate encoding functions of A and B, such that the desired product AB can be recovered by interpolating a polynomial from worker responses. The state-of-the-art strategies for SMM based on polynomial codes and Lagrange codes are reflected in [11], [15] and [16], respectively. Having observed the similarities between PSMM/FPMM and SMM in requiring privacy-preserving matrix multiplication, and their key difference that whether or not queries for the workers are needed, we are interested in the question:…”

Section: Introductionmentioning

confidence: 99%

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A Systematic Approach towards Efficient Private Matrix Multiplication

Zhu,

2022

Preprint

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We consider the problems of Private and Secure Matrix Multiplication (PSMM) and Fully Private Matrix Multiplication (FPMM), for which matrices privately selected by a master node are multiplied at distributed worker nodes without revealing the indices of the selected matrices, even when a certain number of workers collude with each other. We propose a novel systematic approach to solve PSMM and FPMM with colluding workers, which leverages solutions to a related Secure Matrix Multiplication (SMM) problem where the data (rather than the indices) of the multiplied matrices are kept private from colluding workers. Specifically, given an SMM strategy based on polynomial codes or Lagrange codes, one can exploit the special structure inspired by the matrix encoding function to design private coded queries for PSMM/FPMM, such that the algebraic structure of the computation result at each worker resembles that of the underlying SMM strategy. Adopting this systematic approach provides novel insights in private query designs for private matrix multiplication, substantially simplifying the processes of designing PSMM and FPMM strategies. Furthermore, the PSMM and FPMM strategies constructed following the proposed approach outperform the state-of-the-art strategies in one or more performance metrics including recovery threshold (minimal number of workers the master needs to wait for before correctly recovering the multiplication result), communication cost, and computation complexity, demonstrating a more flexible tradeoff in optimizing system efficiency.

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An FPGA based Method of Polynomial Multiplication

Xiao

Diao

et al. 2022

2022 Asia Conference on Algorithms, Computing and Machine Learning (CACML)

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Entangled Polynomial Coding in Limited-Sharing Multi-Party Computation

Cited by 34 publications

References 4 publications

Limited-Sharing Multi-Party Computation for Massive Matrix Operations

Limited-Sharing Multi-Party Computation for Massive Matrix Operations

A Systematic Approach towards Efficient Private Matrix Multiplication

An FPGA based Method of Polynomial Multiplication

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