Uplink Cost Adjustable Schemes in Secure Distributed Matrix Multiplication

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

doi:10.1109/isit44484.2020.9174509

Cited by 13 publications

(29 citation statements)

References 13 publications

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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: Notation Conventionmentioning

confidence: 99%

Cache-Aided Scalar Linear Function Retrieval

Wan

Sun

et al. 2020

2020 IEEE International Symposium on Information Theory (ISIT)

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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 peakhour 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. Index Terms Coded caching; linear function retrieval; uncoded cache placement I. INTRODUCTION Content caching is an efficient technique to handle the increase of requests for massive amounts of data and content over communication networks. By leveraging low-cost memory components K. Wan and G. Caire are with the Electrical Engineering and

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Section: Notation Conventionmentioning

confidence: 99%

Cache-Aided Scalar Linear Function Retrieval

Wan

Sun

et al. 2020

2020 IEEE International Symposium on Information Theory (ISIT)

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“…(Uplink and downlink loads) . Besides downlink load, uplink load is also considered in the distributed matrix-matrix multiplication problem [ 17 , 18 , 19 ]. 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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“…For a relatively recent survey on coded computing we refer the reader to [25]. Information-theoretic privacy and straggler mitigation in coded computing (for polynomial evaluation, matrix-matrix and matrix-vector multiplication) is achieved by using secret sharing [26]- [39]. For a very recent survey on private distributed computing and its connections we refer the reader to [40].…”

Section: Introductionmentioning

confidence: 99%

Secure Private and Adaptive Matrix Multiplication Beyond the Singleton Bound

Hofmeister¹,

Bitar²,

Xhemrishi³

et al. 2021

Preprint

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Consider the problem of designing secure and private codes for distributed matrix-matrix 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. Some of the workers are malicious and return corrupted results to the master. This work is motivated by the literature on myopic adversaries in network coding and distributed storage. Security beyond the Singleton bound is possible when the adversary has limited knowledge about the master's data and probabilistic decoding is acceptable. The key observation in this setting is that the master is the sender and the receiver. Therefore, the master enjoys a plethora of advantages that enable coding for security beyond the Singleton bound.We design a framework for security against malicious adversaries in private matrix-matrix multiplication. Our main goal is to apply this security framework to schemes with adaptive rates previously introduced by a subset of the authors. Adaptive schemes divide the workers into clusters and thus provide flexibility in trading decoding complexity for efficiency. Checking the integrity of the computation per cluster has low complexity but costs deleting the results of a whole cluster with at least one malicious worker. Checking the integrity of the results per worker is more complex but allows an efficient use of the non-malicious workers. Our scheme, called SRPM3, provides a computationally efficient security check that detects malicious workers with high probability and can tolerate the presence of an arbitrary number of malicious workers. We provide simulation results that validate our theoretical findings.

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Uplink Cost Adjustable Schemes in Secure Distributed Matrix Multiplication

Cited by 13 publications

References 13 publications

Cache-Aided Scalar Linear Function Retrieval

Cache-Aided Scalar Linear Function Retrieval

Cache-Aided General Linear Function Retrieval

Secure Private and Adaptive Matrix Multiplication Beyond the Singleton Bound

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