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Minimizing Computation and Communication Costs of Two-Sided Secure Distributed Matrix Multiplication under Arbitrary

Jin Li1, Nan Liu1, Wei Kang2

  • 1National Mobile Communications Research Laboratory, Southeast University, Nanjing 211189, China.

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Summary
This summary is machine-generated.

This study minimizes costs for secure distributed matrix multiplication (SDMM) by optimizing matrix splitting and random matrix usage. A novel zero-appending strategy and alternating optimization significantly improve efficiency and security.

Keywords:
arbitrary collusion patterninteger geometric programminginteger linear programmingsecure distributed matrix multiplication

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Area of Science:

  • Distributed computing
  • Information security
  • Matrix computation

Background:

  • Secure Distributed Matrix Multiplication (SDMM) is crucial for privacy-preserving computations.
  • Existing SDMM schemes face challenges in minimizing combined computation and communication costs under arbitrary collusion.
  • The divisibility problem in matrix splitting and storage constraints also impact system efficiency.

Purpose of the Study:

  • To minimize the total cost (computation and communication) in two-sided SDMM systems.
  • To optimize matrix splitting factors, random matrix quantities, and distribution vectors.
  • To satisfy security, decodability, storage, and delay constraints under arbitrary collusion.

Main Methods:

  • A strategy of appending zeros to input matrices is introduced to resolve matrix splitting divisibility issues.
  • Alternating Optimization (AO) is employed to divide the main problem into two solvable subproblems.
  • Analysis includes deriving necessary conditions for problem feasibility.

Main Results:

  • The proposed scheme, incorporating zero appending and AO, yields a feasible solution for SDMM cost minimization.
  • Simulation results validate the superiority of the proposed method over schemes lacking zero appending or AO.
  • The optimized scheme effectively balances security, decodability, storage, and delay constraints.

Conclusions:

  • The novel zero-appending strategy and AO-based optimization effectively reduce total costs in two-sided SDMM.
  • The proposed approach enhances SDMM efficiency and security, particularly under arbitrary collusion patterns.
  • This work provides a robust framework for practical and secure distributed matrix multiplication.