# Interactive Secure Function Computation

## TL;DR

This paper investigates the fundamental limits of interactive and non-interactive secure function computation between two users, providing characterizations of feasibility, optimal communication rates, and the role of randomness under various privacy constraints.

## Contribution

It introduces single-letter characterizations for the feasibility and optimal rates of secure interactive computation, and analyzes the impact of common randomness and interaction.

## Key findings

- Single-letter expressions for feasibility and optimal rates.
- Characterization of functions securely computable with one message.
- Bounds on message lengths in non-interactive secure computation.

## Abstract

We consider interactive computation of randomized functions between two users with the following privacy requirement: the interaction should not reveal to either user any extra information about the other user's input and output other than what can be inferred from the user's own input and output. We also consider the case where privacy is required against only one of the users. For both cases, we give single-letter expressions for feasibility and optimal rates of communication. Then we discuss the role of common randomness and interaction in both privacy settings. We also study perfectly secure non-interactive computation when only one of the users computes a randomized function based on a single transmission from the other user. We characterize randomized functions which can be perfectly securely computed in this model and obtain tight bounds on the optimal message lengths in all the privacy settings.