Tracing the Man in the Middle in Monoidal Categories

TL;DR

This paper explores how traced monoidal categories can model Man-in-the-Middle attacks and network interactions, introducing a normal trace property to analyze what is hidden during computation.

Contribution

It introduces a model of network computation using pomsets and normal traces, connecting monoidal trace structures with coalgebraic and monadic frameworks.

Findings

Normal trace structures can be derived from coalgebraic models.

Monoidal trace structures effectively model network interactions.

The framework provides insights into detecting and analyzing MM-attacks.

Abstract

Man-in-the-Middle (MM) is not only a ubiquitous attack pattern in security, but also an important paradigm of network computation and economics. Recognizing ongoing MM-attacks is an important security task; modeling MM-interactions is an interesting task for semantics of computation. Traced monoidal categories are a natural framework for MM-modelling, as the trace structure provides a tool to hide what happens *in the middle*. An effective analysis of what has been traced out seems to require an additional property of traces, called *normality*. We describe a modest model of network computation, based on partially ordered multisets (pomsets), where basic network interactions arise from the monoidal trace structure, and a normal trace structure arises from an iterative, i.e. coalgebraic structure over terms and messages used in computation and communication. The correspondence is established using a convenient monadic description of normally traced monoidal categories.