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Straggler- and Adversary-Tolerant Secure Distributed Matrix Multiplication Using Polynomial Codes.

Eimear Byrne1, Oliver W Gnilke2, Jörg Kliewer3

  • 1School of Mathematics and Statistics, University College Dublin, D04 V1W8 Dublin, Ireland.

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This study introduces novel polynomial codes for secure distributed matrix multiplication, enhancing efficiency and security in large-scale machine learning by tolerating slow workers and protecting data from collusion.

Keywords:
distributed computationdistributed learninginformation theoretic securitymatrix multiplicationpolynomial codes

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Area of Science:

  • Distributed Computing
  • Machine Learning
  • Coding Theory
  • Information Security

Background:

  • Large-scale machine learning relies on distributed platforms for matrix multiplication due to data size limitations on single servers.
  • Straggling workers (those with significantly slower execution times) introduce computational delays in distributed systems.
  • Existing coding techniques can mitigate delays but often lack robust security against data eavesdropping and collusion.

Purpose of the Study:

  • To develop a new coding scheme for distributed matrix multiplication that addresses both computational delay and data security.
  • To enhance tolerance against straggling workers while preventing collusion and eavesdropping by worker nodes.
  • To improve the recovery threshold compared to existing methods, especially for large matrices and numerous colluding workers.

Main Methods:

  • Introduction of a novel class of polynomial codes with a reduced number of non-zero coefficients.
  • Development of a distributed framework for matrix multiplication incorporating these secure coding techniques.
  • Derivation of closed-form expressions for the recovery threshold to analyze scheme performance.

Main Results:

  • The proposed polynomial codes achieve a lower recovery threshold than existing schemes for secure distributed matrix multiplication.
  • Performance improvements are particularly significant for larger matrix dimensions and a moderate to large number of colluding workers.
  • In scenarios without security constraints, the proposed construction is shown to be optimal in terms of recovery threshold.

Conclusions:

  • The novel polynomial coding scheme effectively reduces computational delay and enhances data security in distributed matrix multiplication.
  • This approach offers a superior solution for large-scale machine learning applications requiring both efficiency and confidentiality.
  • The findings advance the state-of-the-art in secure and efficient distributed data processing.