# The Capacity of Information-Theoretic Secure Aggregation in Federated Learning

arXiv: https://arxiv.org/abs/2606.07277 · HTML: https://mlsanity.com/paper/2606.07277/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 38 references that are in the map.
- First posted on arXiv 5 Jun 2026.

## Builds on (most cited first, 19 of 19)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [Deep Leakage from Gradients](https://mlsanity.com/paper/1906.08935/) (2019)
- [Inverting Gradients -- How easy is it to break privacy in federated learning?](https://mlsanity.com/paper/2003.14053/) (2020)
- [Turbo-Aggregate: Breaking the Quadratic Aggregation Barrier in Secure Federated Learning](https://mlsanity.com/paper/2002.04156/) (2020)
- [LightSecAgg: a Lightweight and Versatile Design for Secure Aggregation in Federated Learning](https://mlsanity.com/paper/2109.14236/) (2021)
- [FastSecAgg: Scalable Secure Aggregation for Privacy-Preserving Federated Learning](https://mlsanity.com/paper/2009.11248/) (2020)
- [Privacy-Preserving Aggregation in Federated Learning: A Survey](https://mlsanity.com/paper/2203.17005/) (2022)
- [Federated Learning with Autotuned Communication-Efficient Secure Aggregation](https://mlsanity.com/paper/1912.00131/) (2019)
- [Efficient Dropout-resilient Aggregation for Privacy-preserving Machine Learning](https://mlsanity.com/paper/2203.17044/) (2022)
- [Information Theoretic Secure Aggregation with User Dropouts](https://mlsanity.com/paper/2101.07750/) (2021)
- [Aggregation Service for Federated Learning: An Efficient, Secure, and More Resilient Realization](https://mlsanity.com/paper/2202.01971/) (2022)
- [Communication-Computation Efficient Secure Aggregation for Federated Learning](https://mlsanity.com/paper/2012.05433/) (2020)
- [SwiftAgg+: Achieving Asymptotically Optimal Communication Loads in Secure Aggregation for Federated Learning](https://mlsanity.com/paper/2203.13060/) (2022)
- [Sparsified Secure Aggregation for Privacy-Preserving Federated Learning](https://mlsanity.com/paper/2112.12872/) (2021)
- [Hierarchical Secure Aggregation with Heterogeneous Security Constraints and Arbitrary User Collusion](https://mlsanity.com/paper/2507.14768/) (2025)
- [Information-Theoretic Decentralized Secure Aggregation with Passive Collusion Resilience](https://mlsanity.com/paper/2508.00596/) (2025)
- [On the Capacity Region of Individual Key Rates in Vector Linear Secure Aggregation](https://mlsanity.com/paper/2601.03241/) (2026)

## Abstract (arXiv)

Secure aggregation allows a server to aggregate users' local updates while preserving update privacy. Existing information-theoretic problems typically assume that correlated random keys are provided by a trusted third party (TTP) or generated via prescribed groupwise structures, while the communication cost for establishing such correlated keys is often ignored. Consequently, the fundamental limits under general key-distribution mechanisms remain unknown. In this paper, we study the T-colluding information-theoretic secure aggregation problem with N users under a general two-phase framework consisting of a key distribution phase and an update aggregation phase. Unlike prior work, we model key distribution through user-to-user communication and allow arbitrary user-generated key-distribution mechanisms, eliminating TTP or prescribed structures. This enables a joint characterization of three resources: randomness for security, key-distribution communication, and aggregation communication. We completely characterize the capacity region among these three resources by constructing a novel secure aggregation scheme together with a matching information-theoretic converse. In particular, we develop an explicit deterministic capacity-achieving construction over any finite field of size at least N, whereas most existing schemes either rely on TTP or employ randomized or existential constructions over sufficiently large finite fields. We further show that the optimal performance can be achieved using only pairwise shared keys, enabling implementation via Diffie--Hellman key exchange. Compared with Google's seminal secure aggregation scheme, the proposed scheme requires fewer random masking keys while preserving the same aggregation communication overhead.