For decentralized secure aggregation with at least U surviving users and at most T colluders, the optimal two-round rates are R1 ≥ 1 and R2 ≥ 1/(U-T-1) when U > T+1, and the task is impossible otherwise.
The Capacity of Symmetric Private Information Retrieval
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For any demand family in SPSSR, the maximum retrieval rate is 1-1/N, achieved with shared-randomness ratio D/(N-1) and subpacketization (N-1)/gcd(D,N-1) for balanced linear schemes.
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Information-Theoretic Decentralized Secure Aggregation with User Dropouts
For decentralized secure aggregation with at least U surviving users and at most T colluders, the optimal two-round rates are R1 ≥ 1 and R2 ≥ 1/(U-T-1) when U > T+1, and the task is impossible otherwise.
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Secure and Private Structured-Subset Retrieval: Fundamental Limits and Achievable Schemes
For any demand family in SPSSR, the maximum retrieval rate is 1-1/N, achieved with shared-randomness ratio D/(N-1) and subpacketization (N-1)/gcd(D,N-1) for balanced linear schemes.