Fundamental Limits of Information-Theoretic Secure Aggregation with User Dropouts in Federated Learning
Year: 2026
Type: preprint
Abstract: Secure aggregation enables a server to compute the sum of users' gradients or model updates without revealing individual values. With user dropouts, correlated random keys protect local gradients while allowing recovery of the desired gradient sum. We consider three phases: key distribution, masked-gradient upload, and mask elimination. Users establish correlated keys, upload masked gradients, and provide additional messages to eliminate residual aggregate masks. Existing information-theoretic schemes typically design mask-elimination communication for a prescribed dropout threshold and evaluate its cost under worst-case dropouts across the masked-gradient upload and mask-elimination phases. Such designs cannot adjust communication to actual dropout scenarios. Moreover, the randomness and communication costs of establishing correlated keys remain largely unexplored. To address these limitations, we formulate an adaptive secure aggregation framework under the T-colluding security constraint and construct a single scheme that supports all feasible dropout scenarios by adapting its communication to the actual number of dropouts. We establish converse bounds on four resources: key randomness, key-distribution communication, masked-gradient communication, and mask-elimination communication. The latter two bounds are characterized for each realized dropout set in the masked-gradient upload phase. The proposed scheme achieves the optimal masked-gradient communication rate for every feasible dropout scenario and the optimal mask-elimination communication rate in almost all feasible regimes. Its key rate and key-distribution communication rate are each optimal or within a factor of two of their respective information-theoretic optima. These results characterize the fundamental randomness and communication costs of secure aggregation with user dropouts.
Source: arXiv (Cornell University)
Authors: Zhu, Jinbao, Wan, Kai, Caire, Giuseppe
Institution: Southwest Jiaotong University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223036447