# Building a Sybil-Resilient Digital Community Utilizing Trust-Graph Connectivity

## TL;DR

This paper proposes trust-graph connectivity methods to prevent sybil identities from infiltrating digital communities, enabling indefinite growth while maintaining security against malicious actors.

## Contribution

It introduces two novel tools, graph conductance and vertex expansion, to limit sybil penetration and ensure secure, indefinite community growth.

## Key findings

- Trust-graph connectivity can prevent sybil infiltration
- High conductance or vertex expansion ensures safe community growth
- Maintaining less than one-third byzantines enables Byzantine Agreement

## Abstract

Preventing fake or duplicate digital identities (aka sybils) from joining a digital community may be crucial to its survival, especially if it utilizes a consensus protocol among its members or employs democratic governance, where sybils can undermine consensus, tilt decisions, or even take over. Here, we explore the use of a trust-graph of identities, with edges representing trust among identity owners, to allow a community to grow indefinitely without increasing its sybil penetration. Since identities are admitted to the digital community based on their trust by existing digital community members, corrupt identities, which may trust sybils, also pose a threat to the digital community. Sybils and their corrupt perpetrators are together referred to as byzantines, and the overarching aim is to limit their penetration into a digital community. We propose two alternative tools to achieve this goal. One is graph conductance, which works under the assumption that honest people are averse to corrupt ones and tend to distrust them. The second is vertex expansion, which relies on the assumption that there are not too many corrupt identities in the community. Of particular interest is keeping the fraction of byzantines below one third, as it would allow the use of Byzantine Agreement [15] for consensus as well as for sybil-resilient social choice [19]. This paper considers incrementally growing a trust graph and shows that, under its key assumptions and additional requirements, including keeping the conductance or vertex expansion of the community trust graph sufficiently high, a community may grow safely, indefinitely.