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Abstract
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 GASP_{r} (Gap Additive Secure Polynomial codes) parametrized by an integer r. GASP_{r} outperforms all previously known polynomial codes for SDMM. We also present lower bounds on N and show that GASP_{r} achieves the lower bounds in the case of no server collusion.
Original language  English 

Title of host publication  2019 IEEE Information Theory Workshop, ITW 2019 
Publisher  IEEE 
Pages  414418 
ISBN (Electronic)  9781538669006 
DOIs  
Publication status  Published  1 Aug 2019 
MoE publication type  A4 Conference publication 
Event  IEEE Information Theory Workshop  Visby, Sweden Duration: 25 Aug 2019 → 28 Aug 2019 
Workshop
Workshop  IEEE Information Theory Workshop 

Abbreviated title  ITW 
Country/Territory  Sweden 
City  Visby 
Period  25/08/2019 → 28/08/2019 
Keywords
 additive combinatorics
 degree table
 polynomial codes
 Secure distributed matrix multiplication
 sumsets.
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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