Uplink-Downlink Tradeoff in Secure Distributed Matrix Multiplication

Kakar, Jaber; Khristoforov, Anton; Ebadifar, Seyedhamed; Sezgin, Aydin

doi:10.48550/arxiv.1910.13849

Cited by 6 publications

(6 citation statements)

References 21 publications

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“…Hence, now we only need to focus on the first stage where we aim to minimize the number of totally transmitted linearly independent combinations (i.e., λ) for the (N, N, N r , 1, M ) non-secure distributed linearly separable computation problem (for the sake of simplicity, we will call it (N, M ) non-secure problem since N r = N − M + 1). Notice that if in the first stage F is chosen as that in (15) where all elements outside the first line are chosen i.i.d. over F q , the computing scheme becomes the scheme with the cyclic assignment for Theorem 5.…”

Section: Is Proved Inmentioning

confidence: 99%

On Secure Distributed Linearly Separable Computation

Wan¹,

Sun²,

Ji³

et al. 2021

Preprint

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Distributed linearly separable computation, where a user asks some distributed servers to compute a linearly separable function, was recently formulated by the same authors and aims to alleviate the bottlenecks of stragglers and communication cost in distributed computation. For this purpose, the data center assigns a subset of input datasets to each server, and each server computes some coded packets on the assigned datasets, which are then sent to the user. The user should recover the task function from the answers of a subset of servers, such the effect of stragglers could be tolerated.In this paper, we formulate a novel secure framework for this distributed linearly separable computation, where we aim to let the user only retrieve the desired task function without obtaining any other information about the input datasets, even if it receives the answers of all servers. In order to preserve the security of the input datasets, some common randomness variable independent of the datasets should be introduced into the transmission.We show that any non-secure linear-coding based computing scheme for the original distributed linearly separable computation problem, can be made secure without increasing the communication cost (number of symbols the user should receive). Then we focus on the case where the computation cost of each server (number of datasets assigned to each server) is minimum and aim to minimize the size of the randomness variable (i.e., randomness size) introduced in the system while achieving the optimal communication cost. We first propose an information theoretic converse bound on the randomness size. We then propose secure computing schemes based on two well-known data assignments, namely K. Wan and G. Caire are with the Electrical Engineering and

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Section: Is Proved Inmentioning

confidence: 99%

On Secure Distributed Linearly Separable Computation

Wan¹,

Sun²,

Ji³

et al. 2021

Preprint

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“…Remark 4 (Uplink and downlink loads). Besides downlink load, uplink load is also considered in the distributed matrix-matrix multiplication problem [16]- [18]. In this work, the communication cost of uploading the demand matrix to the server is not a focus, i..e, we assume that each user communicates the whole demand matrix to the server and all other users on a separate channel that is not the bottleneck in the system.…”

Section: System Modelmentioning

confidence: 99%

Cache-Aided General Linear Function Retrieval

Wan

Sun

et al. 2020

Entropy

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Coded Caching, proposed by Maddah-Ali and Niesen (MAN), has the potential to reduce network traffic by pre-storing content in the users’ local memories when the network is underutilized and transmitting coded multicast messages that simultaneously benefit many users at once during peak-hour times. This paper considers the linear function retrieval version of the original coded caching setting, where users are interested in retrieving a number of linear combinations of the data points stored at the server, as opposed to a single file. This extends the scope of the authors’ past work that only considered the class of linear functions that operate element-wise over the files. On observing that the existing cache-aided scalar linear function retrieval scheme does not work in the proposed setting, this paper designs a novel coded caching scheme that outperforms uncoded caching schemes that either use unicast transmissions or let each user recover all files in the library.

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“…The information theft by the distributed computing nodes can be modeled by the collusion pattern, which has also been studied in problems of secret sharing [12] and private information retrieval [13,14]. Some of the existing literature has studied the SDMM problem under homogeneous collusion patterns, where up to l computing nodes may collude to obtain the information of the two input matrices [9,[15][16][17][18]. To balance the tradeoff between the uplink and downlink cost, the works proposed two schemes based on the secure cross subspace alignment [15].…”

Section: Introductionmentioning

confidence: 99%

Minimizing Computation and Communication Costs of Two-Sided Secure Distributed Matrix Multiplication under Arbitrary Collusion Pattern

Li,

Liu,

Kang

2024

Entropy

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This paper studies the problem of minimizing the total cost, including computation cost and communication cost, in the system of two-sided secure distributed matrix multiplication (SDMM) under an arbitrary collusion pattern. In order to perform SDMM, the two input matrices are split into some blocks, blocks of random matrices are appended to protect the security of the two input matrices, and encoded copies of the blocks are distributed to all computing nodes for matrix multiplication calculation. Our aim is to minimize the total cost, overall matrix splitting factors, number of appended random matrices, and distribution vector, while satisfying the security constraint of the two input matrices, the decodability constraint of the desired result of the multiplication, the storage capacity of the computing nodes, and the delay constraint. First, a strategy of appending zeros to the input matrices is proposed to overcome the divisibility problem of matrix splitting. Next, the optimization problem is divided into two subproblems with the aid of alternating optimization (AO), where a feasible solution can be obtained. In addition, some necessary conditions for the problem to be feasible are provided. Simulation results demonstrate the superiority of our proposed scheme compared to the scheme without appending zeros and the scheme with no alternating optimization.

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Uplink-Downlink Tradeoff in Secure Distributed Matrix Multiplication

Cited by 6 publications

References 21 publications

On Secure Distributed Linearly Separable Computation

On Secure Distributed Linearly Separable Computation

Cache-Aided General Linear Function Retrieval

Minimizing Computation and Communication Costs of Two-Sided Secure Distributed Matrix Multiplication under Arbitrary Collusion Pattern

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