Category Theory in Identity Systems

Exploring categorical foundations for identity resolution and compositional verification frameworks.

Dr. Tove Lindqvist - 2024

Abstract

This research presents a categorical framework for modeling identity resolution and verification systems. We demonstrate how category-theoretic abstractions enable compositional semantics and verification consistency in distributed identity protocols.

Key Contributions

Categorical models for identity composition
Functorial mappings for verification consistency
Natural transformations for identity resolution
Category-theoretic cryptography for identity verification

Methodology

Our approach combines:

Category Theory: Functors between identity systems
Algebraic Topology: Homotopic identity mappings
Formal Verification: Coq-based categorical proofs

Verification Scope

Cryptographic Primitives

Verified: Bilinear pairings, hash functions, and elliptic curve operations

Identity Resolution

Formal proofs for DIDs and Verifiable Credentials

Security Properties

Non-repudiation, freshness, and forward secrecy verification

// Coq proof snippet
Theorem resolve_did_secure:
  forall (ctx : verification_context) (did : did_uri),
    verified_resolution ctx did -> valid_cryptographic_signature did.
Proof.
  unfold verified_resolution.
  apply resolution_lemma.
Qed.

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