# On the Communication Complexity of Secure Computation

arXiv: https://arxiv.org/abs/1311.7584 · HTML: https://mlsanity.com/paper/1311.7584/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Nov 2013.

## Built on by (most cited first, 4 of 4)

- [RFLPA: A Robust Federated Learning Framework against Poisoning Attacks with Secure Aggregation](https://mlsanity.com/paper/2405.15182/) (2024)
- [Fairness-Driven Private Collaborative Machine Learning](https://mlsanity.com/paper/2109.14376/) (2021)
- [Privacy-Preserving, Dropout-Resilient Aggregation in Decentralized Learning](https://mlsanity.com/paper/2404.17984/) (2024)
- [SoK: Enhancing Cryptographic Collaborative Learning with Differential Privacy](https://mlsanity.com/paper/2601.09460/) (2026)

## Abstract (arXiv)

Information theoretically secure multi-party computation (MPC) is a central primitive of modern cryptography. However, relatively little is known about the communication complexity of this primitive. In this work, we develop powerful information theoretic tools to prove lower bounds on the communication complexity of MPC. We restrict ourselves to a 3-party setting in order to bring out the power of these tools without introducing too many complications. Our techniques include the use of a data processing inequality for residual information - i.e., the gap between mutual information and G'acs-K"orner common information, a new information inequality for 3-party protocols, and the idea of distribution switching by which lower bounds computed under certain worst-case scenarios can be shown to apply for the general case. Using these techniques we obtain tight bounds on communication complexity by MPC protocols for various interesting functions. In particular, we show concrete functions that have "communication-ideal" protocols, which achieve the minimum communication simultaneously on all links in the network. Also, we obtain the first explicit example of a function that incurs a higher communication cost than the input length in the secure computation model of Feige, Kilian and Naor (1994), who had shown that such functions exist. We also show that our communication bounds imply tight lower bounds on the amount of randomness required by MPC protocols for many interesting functions.