Secure Distributed Gram Matrix Multiplication

Okko Makkonen; Camilla Hollanti

doi:10.1109/ITW55543.2023.10161614

Secure Distributed Gram Matrix Multiplication

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

2 Citations (Scopus)

Abstract

The Gram matrix of a matrix A is defined as AAT (or ATA). Computing the Gram matrix is an important operation in many applications, such as linear regression with the least squares method, where the explicit solution formula includes the Gram matrix of the data matrix. Secure distributed matrix multiplication (SDMM) can be used to compute the product of two matrices using the help of worker servers. If a Gram matrix were computed using SDMM, the data matrix would need to be encoded twice, which causes an unnecessary overhead in the communication cost. We propose a new scheme for this purpose called secure distributed Gram matrix multiplication (SDGMM). It can leverage the advantages of computing a Gram matrix instead of a regular matrix product.

Original language	English
Title of host publication	2023 IEEE Information Theory Workshop, ITW 2023
Publisher	IEEE
Pages	192-197
Number of pages	6
ISBN (Electronic)	979-8-3503-0149-6
DOIs	https://doi.org/10.1109/ITW55543.2023.10161614
Publication status	Published - 2023
MoE publication type	A4 Conference publication
Event	IEEE Information Theory Workshop - Saint-Malo, France Duration: 23 Apr 2023 → 28 Apr 2023

Publication series

Name	Proceedings : information theory workshop
ISSN (Electronic)	2475-4218

Conference

Conference	IEEE Information Theory Workshop
Abbreviated title	ITW
Country/Territory	France
City	Saint-Malo
Period	23/04/2023 → 28/04/2023

Access to Document

10.1109/ITW55543.2023.10161614

https://arxiv.org/abs/2211.14213

Cite this

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title = "Secure Distributed Gram Matrix Multiplication",

abstract = "The Gram matrix of a matrix A is defined as AAT (or ATA). Computing the Gram matrix is an important operation in many applications, such as linear regression with the least squares method, where the explicit solution formula includes the Gram matrix of the data matrix. Secure distributed matrix multiplication (SDMM) can be used to compute the product of two matrices using the help of worker servers. If a Gram matrix were computed using SDMM, the data matrix would need to be encoded twice, which causes an unnecessary overhead in the communication cost. We propose a new scheme for this purpose called secure distributed Gram matrix multiplication (SDGMM). It can leverage the advantages of computing a Gram matrix instead of a regular matrix product.",

author = "Okko Makkonen and Camilla Hollanti",

note = "Funding Information: ACKNOWLEDGEMENTS This work has been supported by the Academy of Finland under Grant No. 336005 and by the Vilho, Yrj{\"o} and Kalle V{\"a}is{\"a}l{\"a} Foundation of the Finnish Academy of Science and Letters. Publisher Copyright: {\textcopyright} 2023 IEEE.; IEEE Information Theory Workshop, ITW ; Conference date: 23-04-2023 Through 28-04-2023",

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doi = "10.1109/ITW55543.2023.10161614",

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booktitle = "2023 IEEE Information Theory Workshop, ITW 2023",

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AU - Makkonen, Okko

AU - Hollanti, Camilla

N1 - Funding Information: ACKNOWLEDGEMENTS This work has been supported by the Academy of Finland under Grant No. 336005 and by the Vilho, Yrjö and Kalle Väisälä Foundation of the Finnish Academy of Science and Letters. Publisher Copyright: © 2023 IEEE.

PY - 2023

Y1 - 2023

N2 - The Gram matrix of a matrix A is defined as AAT (or ATA). Computing the Gram matrix is an important operation in many applications, such as linear regression with the least squares method, where the explicit solution formula includes the Gram matrix of the data matrix. Secure distributed matrix multiplication (SDMM) can be used to compute the product of two matrices using the help of worker servers. If a Gram matrix were computed using SDMM, the data matrix would need to be encoded twice, which causes an unnecessary overhead in the communication cost. We propose a new scheme for this purpose called secure distributed Gram matrix multiplication (SDGMM). It can leverage the advantages of computing a Gram matrix instead of a regular matrix product.

AB - The Gram matrix of a matrix A is defined as AAT (or ATA). Computing the Gram matrix is an important operation in many applications, such as linear regression with the least squares method, where the explicit solution formula includes the Gram matrix of the data matrix. Secure distributed matrix multiplication (SDMM) can be used to compute the product of two matrices using the help of worker servers. If a Gram matrix were computed using SDMM, the data matrix would need to be encoded twice, which causes an unnecessary overhead in the communication cost. We propose a new scheme for this purpose called secure distributed Gram matrix multiplication (SDGMM). It can leverage the advantages of computing a Gram matrix instead of a regular matrix product.

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U2 - 10.1109/ITW55543.2023.10161614

DO - 10.1109/ITW55543.2023.10161614

M3 - Conference article in proceedings

AN - SCOPUS:85165071442

T3 - Proceedings : information theory workshop

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EP - 197

BT - 2023 IEEE Information Theory Workshop, ITW 2023

PB - IEEE

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Secure Distributed Gram Matrix Multiplication

Abstract

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Conference

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Hollanti_ICT: Secure Distributed Computation Schemes with Applications to Digitalized Remote Healthcare

Cite this

Secure Distributed Gram Matrix Multiplication

Abstract

Publication series

Conference

Access to Document

Other files and links

Fingerprint

Projects

Hollanti_ICT: Secure Distributed Computation Schemes with Applications to Digitalized Remote Healthcare

Cite this