Keyed Gauge Laplacians: Active Deception and Cryptographic Flow Routing in Adversarial Networks

Abstract

Static perimeter firewalls and conventional intrusion detection systems struggle to contain automated adversarial reconnaissance. Once an internal subnet is compromised, graph-based algorithms can identify structural routes toward mission-critical assets. Conventional honeypots offer passive deception but may be bypassed after their topology is discovered. We introduce Keyed Gauge Laplacians (Lₖ), a topological framework that integrates cryptographic keying into network routing through discrete gauge transformations and complex edge phases. By controlling edge conductances and gauge holonomies with a secret key K, the framework creates distinct routing landscapes for authorized and unauthorized entities. Authorized traffic uses an inverse gauge transformation to recover a harmonic potential field that guides packets through designated high-conductance corridors toward protected assets. In contrast, adversaries using the unkeyed network model encounter altered flow patterns that redirect their exploration toward engineered decoy sinks and honeypots. We establish a theoretical relationship between adversarial entrapment and the effective resistances of decoy and genuine asset pathways. Simulations across multilayer enterprise network architectures demonstrate the potential of this approach to distinguish authorized navigation from unkeyed reconnaissance, directing legitimate traffic efficiently while steering adversarial exploration toward deceptive endpoints. These findings introduce a topological deception paradigm in which network structure itself becomes a cryptographically controlled defense mechanism. By combining harmonic navigation, spectral interference, and keyed routing, the framework offers a mathematical foundation for adaptive network defense and protected asset isolation. Cryptographic Laplacians, Gauge Theory on Graphs, Active Cyber-Deception, Honeynets, Zero Trust Architecture, Moore-Penrose Pseudoinverse, Aharonov-Bohm Effect