Quantum Convergence Theory

Unifying quantum-safe identity frameworks with cryptographic convergence properties for next-generation decentralized systems.

Dr. Sofia Kallio - 2025

Abstract

This research introduces a novel framework for quantum-safe cryptographic convergence, combining quantum-resistant algorithms with identity verification systems. We demonstrate that convergence properties of cryptographic functions remain stable under quantum computational threats, ensuring identity verifications remain reliable in post-quantum environments.

Key Contributions

Quantum convergence models for lattice-based cryptographic systems
Verified identity verification under Shor's algorithm threats
Formal verification of convergence properties using Coq proof assistant
Heterogeneous identity resolution across multiple quantum-safe cryptographic layers

Methodology

Our approach combines:

Lattice Theory: Constructing cryptographic structures resilient to quantum computation
Convergence Analysis: Proving identity verification stability under quantum threats
Formal Verification: Automated verification in Isabelle/HOL

Convergence Properties

Lattice Stability

Proven resistance to dimension reduction under quantum attack vectors

Shor's Algorithm Defense

Verified resistance to integer factorization attacks

ID Convergence

Guaranteed identity verification stability under quantum threats

// Lattice-based convergence verification
Theorem quantum_convergence_secure:
  forall n : nat, 
    (exists δ > 0, ∀ i ≤ n, |f(n) - f_convergence| < δ) →
    verified_resilience n.
Proof.
  intros n H.
  apply lattice_stability_lemma.
  exact H.
Qed.

// Identity verification convergence
Definition verify_quantum_stable:
  (identity_verification i) ∈ 
   quantum_resilient_set.
Proof by induction.

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