The Need for Alignment in Rate-Efficient Distributed Two-Sided Secure Matrix Computation

Ebadifar, Seyedhamed; Kakar, Jaber; Sezgin, Aydin

doi:10.1109/icc.2019.8761275

Cited by 11 publications

(7 citation statements)

References 12 publications

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“…Remark 1. The case of s is different from the cases of t and d. When (l ∆ , t, d) is fixed, from security constraint (10) and decodability constraint (11), we see that on one hand, increasing s increases the number of blocks, but on the other hand, it also relaxes the security constraint. When computing nodes are heterogeneous, i.e., computing nodes have different computation cost, upload transmission cost and download transmission cost, the increase in s does not necessarily increase the total cost, because due to the more relaxed security constraint, we can distribute more blocks to computing nodes with lower costs.…”

Section: The Feasible Set Of (T S D)mentioning

confidence: 84%

“…In this work, we would like to jointly optimize the distribution vector J, and the matrix split parameter (t, s, d, l ∆ ) such that the cost of the user, defined in (17), is minimized. At the same time, the security constraint (10), the decodability constraint (11), the storage constraint (13), and the delay constraint ( 16) must be satisfied.…”

Section: Problem Formulationmentioning

confidence: 99%

“…• • • }, the only decodability constraint (11) becomes relaxed, and other constraints are unchanged. In this case, we can prove that the optimal cost will increase compared to t ∈ [1 : T] and d ∈ [1 : D].…”

Section: The Feasible Set Of (T S D)mentioning

confidence: 99%

“…In the first case, the user only wants to protect the information security of matrix A, and B is a public matrix known to all computing nodes [10]. In the second case, we need to consider the information security of both matrices A and B [9,11]. 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].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: The Feasible Set Of (T S D)mentioning

confidence: 84%

Section: Problem Formulationmentioning

confidence: 99%

Section: The Feasible Set Of (T S D)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…Initially, the research focused on minimizing the download costs for cases where either only one matrix (e.g. A) is private [6] 2 or both matrices A, B ought to be secured [7]- [10], [14]. For the first scenario, the capacity is fully characterized while for the latter scenario only the asymptotic capacity where the ratio of matrix dimensions satisfy n /min(m,p) → ∞ is known.…”

Section: Introductionmentioning

confidence: 99%

Uplink-Downlink Tradeoff in Secure Distributed Matrix Multiplication

Kakar¹,

Khristoforov²,

Ebadifar³

et al. 2019

Preprint

Self Cite

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In secure distributed matrix multiplication (SDMM) the multiplication AB from two private matrices A and B is outsourced by a user to N distributed servers. In -SDMM, the goal is to a design a joint communication-computation procedure that optimally balances conflicting communication and computation metrics without leaking any information on both A and B to any set of ≤ N servers. To this end, the user applies coding with Ãi and Bi representing encoded versions of A and B destined to the i-th server. Now, SDMM involves multiple tradeoffs. One such tradeoff is the tradeoff between uplink (UL) and downlink (DL) costs. To find a good balance between these two metrics, we propose two schemes which we term USCSA and GSCSA that are based on secure cross subspace alignment (SCSA). We show that there are various scenarios where they outperform existing SDMM schemes from the literature with respect to UL-DL efficiency.Next, we implement schemes from the literature, including USCSA and GSCSA, and test their performance on Amazon EC2. Our numerical results show that USCSA and GSCSA establish a good balance between the time spend on the communication and computation in SDMMs. This is because they combine advantages of polynomial codes, namely low time for the upload of Ãi , Bi N i=1 and the computation of O i = Ãi Bi , with those of SCSA, being a low timing overhead for the download of (O i ) N i=1 and the decoding of AB.

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

Avestimehr

2020

2020 IEEE International Symposium on Information Theory (ISIT)

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The Need for Alignment in Rate-Efficient Distributed Two-Sided Secure Matrix Computation

Cited by 11 publications

References 12 publications

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

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

Uplink-Downlink Tradeoff in Secure Distributed Matrix Multiplication

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

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