Modelling Trust and Trusted Systems: A Category Theoretic Approach

2026-02-11

AI Summary

This work addresses the limitations of traditional binary trust models in trusted computing by proposing a formal trust framework grounded in category theory and Heyting algebras. Trust elements, assertions, outcomes, and decisions are modeled as objects, while proofs, verification, and decision processes are treated as morphisms. The framework introduces exponential objects to capture the compositional nature of proof operations. Notably, it is the first to integrate category theory with Heyting algebras, enabling fine-grained representation of trust levels and providing a novel metric to quantify the expressive power of proof environments. Experimental evaluations demonstrate the model’s expressiveness and scalability in scenarios including boot-run-shutdown sequences, Evil Maid attack analysis, and multi-component dynamic systems.

Technology Category

• Data Mining & Knowledge Management: Representing, Reasoning, and Using Provenance, Trust
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Semantics and Knowledge: Provenance, trust, security and privacy, and ethical issues in managing semantic data
• Security and Privacy: Data transparency and provenance
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

We introduces a category-theoretic framework for modelling trust as applied to trusted computation systems and remote attestation. By formalizing elements, claims, results, and decisions as objects within a category, and the processes of attestation, verification, and decision-making as morphisms, the framework provides a rigorous approach to understanding trust establishment and provides a well-defined semantics for terms such as `trustworthiness'and'justification'/forensics. The trust decision space is formalized using a Heyting Algebra, allowing nuanced trust levels that extend beyond binary trusted/untrusted states. We then present additional structures and in particular utilise exponentiation in a category theoretic sense to define compositions of attestation operations and provide the basis of a measurement for the expressibility of an attestation environment. We present a number of worked examples including boot-run-shutdown sequences, Evil Maid attacks and the specification of an attestation environment based upon this model. We then address challenges in modelling dynamic and larger systems made of multiple compositions.

Problem

• trust
• trusted systems
• remote attestation
• category theory
• Heyting algebra

Innovation

• category theory
• trust modeling
• Heyting algebra
• remote attestation
• exponentiation in categories