General Framework for Linear Secure Distributed Matrix Multiplication with Byzantine Servers

Okko Makkonen; Camilla Hollanti

doi:10.1109/ITW54588.2022.9965828

General Framework for Linear Secure Distributed Matrix Multiplication with Byzantine Servers

Okko Makkonen
, Camilla Hollanti

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

6 Citations (Scopus)

Abstract

In this paper, a general framework for linear secure distributed matrix multiplication (SDMM) is introduced. The model allows for a neat treatment of straggling and Byzantine servers via a star product interpretation as well as simplified security proofs. Known properties of star products also immediately yield a lower bound for the recovery threshold, as well as an upper bound for the number of colluding workers the system can tolerate. It produces many of the known SDMM schemes as special cases, hence providing unification for the previous literature on the topic. Furthermore, error behavior specific to SDMM is discussed and interleaved codes are proposed as a suitable means for efficient error correction in the proposed model. Analysis of the error correction capability is also provided, largely based on well-known results on interleaved codes.

Original language	English
Title of host publication	2022 IEEE Information Theory Workshop, ITW 2022
Publisher	IEEE
Pages	143-148
Number of pages	6
ISBN (Electronic)	978-1-6654-8341-4
DOIs	https://doi.org/10.1109/ITW54588.2022.9965828
Publication status	Published - 2022
MoE publication type	A4 Conference publication
Event	IEEE Information Theory Workshop - Mumbai, India Duration: 1 Nov 2022 → 9 Nov 2022

Workshop

Workshop	IEEE Information Theory Workshop
Abbreviated title	ITW
Country/Territory	India
City	Mumbai
Period	01/11/2022 → 09/11/2022

Funding

This work has been supported by the Academy of Finland under Grant No. 336005.

Access to Document

10.1109/ITW54588.2022.9965828

https://arxiv.org/abs/2205.07052v2

Cite this

@inproceedings{cac70982d6e74aff9ce001eccbc91850,

title = "General Framework for Linear Secure Distributed Matrix Multiplication with Byzantine Servers",

abstract = "In this paper, a general framework for linear secure distributed matrix multiplication (SDMM) is introduced. The model allows for a neat treatment of straggling and Byzantine servers via a star product interpretation as well as simplified security proofs. Known properties of star products also immediately yield a lower bound for the recovery threshold, as well as an upper bound for the number of colluding workers the system can tolerate. It produces many of the known SDMM schemes as special cases, hence providing unification for the previous literature on the topic. Furthermore, error behavior specific to SDMM is discussed and interleaved codes are proposed as a suitable means for efficient error correction in the proposed model. Analysis of the error correction capability is also provided, largely based on well-known results on interleaved codes.",

author = "Okko Makkonen and Camilla Hollanti",

note = "Funding Information: This work has been supported by the Academy of Finland under Grant No. 336005. Publisher Copyright: {\textcopyright} 2022 IEEE.; IEEE Information Theory Workshop, ITW ; Conference date: 01-11-2022 Through 09-11-2022",

year = "2022",

doi = "10.1109/ITW54588.2022.9965828",

language = "English",

pages = "143--148",

booktitle = "2022 IEEE Information Theory Workshop, ITW 2022",

publisher = "IEEE",

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T1 - General Framework for Linear Secure Distributed Matrix Multiplication with Byzantine Servers

AU - Makkonen, Okko

AU - Hollanti, Camilla

PY - 2022

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N2 - In this paper, a general framework for linear secure distributed matrix multiplication (SDMM) is introduced. The model allows for a neat treatment of straggling and Byzantine servers via a star product interpretation as well as simplified security proofs. Known properties of star products also immediately yield a lower bound for the recovery threshold, as well as an upper bound for the number of colluding workers the system can tolerate. It produces many of the known SDMM schemes as special cases, hence providing unification for the previous literature on the topic. Furthermore, error behavior specific to SDMM is discussed and interleaved codes are proposed as a suitable means for efficient error correction in the proposed model. Analysis of the error correction capability is also provided, largely based on well-known results on interleaved codes.

AB - In this paper, a general framework for linear secure distributed matrix multiplication (SDMM) is introduced. The model allows for a neat treatment of straggling and Byzantine servers via a star product interpretation as well as simplified security proofs. Known properties of star products also immediately yield a lower bound for the recovery threshold, as well as an upper bound for the number of colluding workers the system can tolerate. It produces many of the known SDMM schemes as special cases, hence providing unification for the previous literature on the topic. Furthermore, error behavior specific to SDMM is discussed and interleaved codes are proposed as a suitable means for efficient error correction in the proposed model. Analysis of the error correction capability is also provided, largely based on well-known results on interleaved codes.

UR - https://www.scopus.com/pages/publications/85144591272

U2 - 10.1109/ITW54588.2022.9965828

DO - 10.1109/ITW54588.2022.9965828

M3 - Conference article in proceedings

AN - SCOPUS:85144591272

SP - 143

EP - 148

BT - 2022 IEEE Information Theory Workshop, ITW 2022

PB - IEEE

T2 - IEEE Information Theory Workshop

Y2 - 1 November 2022 through 9 November 2022

ER -

General Framework for Linear Secure Distributed Matrix Multiplication with Byzantine Servers

Abstract

Workshop

Funding

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