For secure gradient coding with each dataset stored on M=N−Nr+m servers, the minimum source key size is claimed to be at least ceil(mN/M)/m−1, with a recursive scheme achieving this bound for several parameter regimes.
Multiparty unconditionally secure protocols,
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On the Optimal Source Key Size of Secure Gradient Coding
For secure gradient coding with each dataset stored on M=N−Nr+m servers, the minimum source key size is claimed to be at least ceil(mN/M)/m−1, with a recursive scheme achieving this bound for several parameter regimes.