Bridging the Epistemic Gap in the Invisible Internet: Extended Mathematical Modeling and Empirical Characterization of I2P Topology

2026-07-26

AI Summary

Existing protocol-document-based models struggle to accurately capture the topology and behavior of the I2P network in real-world environments. This work proposes an extended mathematical model (EMM) that, for the first time, integrates I2P’s production code logic into its formalism. The model is empirically validated through a 30-day experiment on a six-node geographically distributed testbed. The study reveals topology asymmetry arising from autonomous node selection, quantifies the resources required by adversaries to compromise privacy, and demonstrates that node visibility is limited to approximately 25%. Furthermore, it identifies oversampling in Fast-tier tunnel preferences and High Capacity-tier exploratory tunnels. The EMM effectively predicts the actual I2P network topology, offering a more accurate representation than prior approaches.

Abstract

The Invisible Internet Project (I2P) is a decentralized, peer-to-peer network underpinning secure and adversarial communications with major implications for cybersecurity and national security. Its global topology emerges from thousands of independent peer-selection decisions, producing a hub-dominated, complex structure that resists external observation. Prior models based on protocol documentation failed to capture real-world behavior. We close this gap with an Extended Mathematical Model (EMM) derived from production code and validated on a six-router, geographically distributed testbed over thirty days. Results reveal limited router visibility (~25% of nodes), relativistic tier allocations, strong Fast-tier tunnel preference, and overrepresented High Capacity-tier exploratory tunnels. The model accurately predicts emergent topological asymmetries and defines the adversarial resources required to compromise privacy, providing a principled foundation for cyber deterrence and secure decentralized network design.

Problem

• I2P
• network topology
• epistemic gap
• decentralized network
• adversarial communications

Innovation

• Extended Mathematical Model
• I2P topology
• peer-to-peer network
• empirical characterization
• cyber deterrence