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Fundamental Limits of Information-Theoretic Secure Aggregation with User Dropouts in Federated Learning

Jinbao Zhu, Kai Wan, Giuseppe Caire · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.25743 · cited by 0 works (OpenAlex) · open-access PDF

Korean

보안 속도 마스크 커뮤니케이션은 서버가 개별 값을 공개하지 않고 사용자의 gradients 또는 모델 업데이트의 합계를 계산할 수 있도록 해줍니다. 사용자 속도 마스크 커뮤니케이션과 관련된 무작위 키는 원하는 gradient 합계의 복구를 허용하는 동안 로컬 gradients를 보호합니다.우리는 세 단계를 고려합니다: 키 분포, 마스크-gradient 업로드 및 마스크 제거.사용자는 최적의 마스크-gradient 업로드 및 마스크 제거 단계를 통해 최악의 droppouts에서 비용을 평가합니다.사용자는 나머지 무작위 집계 마스크 내에서 통신을 제거하기 위해 추가 메시지를 제공합니다.현재 정보 이론적 계획은 일반적으로 지정된 지정된 droppo

Machine translation (Meta M2M100); the English original follows.

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.

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Topics: Randomness, Computer science, Converse, Upload, Key (lock), Secure communication

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