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We consider the problem of secure distributed matrix multiplication (SDMM) in which a user wishes to compute the product of two matrices with the assistance of honest but curious servers. We construct polynomial codes for SDMM by studying a recently introduced combinatorial tool called the degree table. Maximizing the download rate of a polynomial code for SDMM is equivalent to minimizing N, the number of distinct elements in the corresponding degree table. We propose new constructions of degree tables with a low number of distinct elements. These new constructions lead to a general family of polynomial codes for SDMM, which we call GASPr (Gap Additive Secure Polynomial codes) parametrized by an integer r. GASPr outperforms all previously known polynomial codes for SDMM. We also present lower bounds on N and show that GASPr achieves the lower bounds in the case of no server collusion.
|Title of host publication||2019 IEEE Information Theory Workshop, ITW 2019|
|Publication status||Published - 1 Aug 2019|
|MoE publication type||A4 Article in a conference publication|
|Event||IEEE Information Theory Workshop - Visby, Sweden|
Duration: 25 Aug 2019 → 28 Aug 2019
|Workshop||IEEE Information Theory Workshop|
|Period||25/08/2019 → 28/08/2019|
- additive combinatorics
- degree table
- polynomial codes
- Secure distributed matrix multiplication
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- 1 Finished
Construction and Classification of Discrete Mathematic Structures
Kokkala, J., Laaksonen, A., Östergård, P., Szollosi, F., Pöllänen, A., Ganzhinov, M. & Heinlein, D.
01/09/2015 → 31/08/2019
Project: Academy of Finland: Other research funding