# Towards Attack-Tolerant Networks: Concurrent Multipath Routing and the Butterfly Network

## TL;DR

This paper investigates how network structure, specifically the butterfly topology, can be leveraged to enhance attack-tolerance through concurrent multipath routing, providing a formal framework for evaluating adversarial fault resilience.

## Contribution

It introduces a novel formalism for assessing network attack-tolerance based on trust transitivity and demonstrates exponential redundancy in butterfly networks, along with a new routing algorithm.

## Key findings

- Redundancy in butterfly networks grows exponentially with trust transitivity.
- A new concurrent multipath routing algorithm improves attack-tolerance.
- The formalism quantifies how network structure impacts adversarial fault resilience.

## Abstract

Targeted attacks against network infrastructure are notoriously difficult to guard against. In the case of communication networks, such attacks can leave users vulnerable to censorship and surveillance, even when cryptography is used. Much of the existing work on network fault-tolerance focuses on random faults and does not apply to adversarial faults (attacks). Centralized networks have single points of failure by definition, leading to a growing popularity in decentralized architectures and protocols for greater fault-tolerance. However, centralized network structure can arise even when protocols are decentralized. Despite their decentralized protocols, the Internet and World-Wide Web have been shown both theoretically and historically to be highly susceptible to attack, in part due to emergent structural centralization. When single points of failure exist, they are potentially vulnerable to non-technological (i.e., coercive) attacks, suggesting the importance of a structural approach to attack-tolerance. We show how the assumption of partial trust transitivity, while more realistic than the assumption underlying webs of trust, can be used to quantify the effective redundancy of a network as a function of trust transitivity. We also prove that the effective redundancy of the wrap-around butterfly topology increases exponentially with trust transitivity and describe a novel concurrent multipath routing algorithm for constructing paths to utilize that redundancy. When portions of network structure can be dictated our results can be used to create scalable, attack-tolerant infrastructures. More generally, our results provide a theoretical formalism for evaluating the effects of network structure on adversarial fault-tolerance.