# Security in Asynchronous Interactive Systems

## TL;DR

This paper extends secure computation techniques to asynchronous interactive systems, ensuring bidirectional simulation of protocols with optimal security conditions, even under adversarial scheduling influences.

## Contribution

It introduces a novel secure simulation construction for asynchronous systems that guarantees bidirectional output consistency, achieving optimal security bounds.

## Key findings

- Construction secure if n > 4t, the best possible bound.
- Satisfies additional security properties for 3t < n ≤ 4t.
- Addresses challenges posed by asynchronous scheduler influence.

## Abstract

Secure function computation has been thoroughly studied and optimized in the past decades. We extend techniques used for secure computation to simulate arbitrary protocols involving a mediator. The key feature of our notion of simulation is that it is bidirectional: not only does the simulation produce only outputs that could happen in the original protocol, but the simulation produces all such outputs. In a synchronous system, it can be shown that this requirement can already be achieved by the standard notion of secure computation. However, in an asynchronous system, new subtleties arise because the scheduler can influence the output. We provide a construction that is secure if $n > 4t$, where $t$ is the number malicious agents, which is provably the best possible. We also show that our construction satisfies additional security properties even if $3t < n \le 4t$.