General Framework for Linear Secure Distributed Matrix Multiplication with Byzantine Servers

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2024-06-01
Major/Subject
Mcode
Degree programme
Language
en
Pages
14
Series
IEEE Transactions on Information Theory, Volume 70, issue 6, pp. 3864-3877
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. Another bound on the recovery threshold is given by the decodability condition, which generalizes a bound for GASP codes. The framework produces many of the known SDMM schemes as special cases, thereby 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 under natural assumptions about the error distribution is also provided, largely based on well-known results on interleaved codes. Error detection and other error distributions are also discussed.
Description
Publisher Copyright: IEEE
Keywords
Codes, Geometry, Interleaved codes, Linear codes, Product codes, Reed– Solomon codes, Secure distributed matrix multiplication, Stars, Symbols, informationtheoretic security, interleaved codes, star product codes
Other note
Citation
Makkonen, O & Hollanti, C 2024, ' General Framework for Linear Secure Distributed Matrix Multiplication with Byzantine Servers ', IEEE Transactions on Information Theory, vol. 70, no. 6, pp. 3864-3877 . https://doi.org/10.1109/TIT.2024.3359355