A consolidated and accessible security proof for finite-size decoy-state quantum key distribution
arXiv:2405.16578 · doi:10.22331/q-2026-03-23-2037
Abstract
In recent years, quantum key distribution (QKD) has evolved from a scientific research field to a commercially available security solution, supported by mathematically formulated security proofs. However, since the knowledge required for a full understanding of a security proof is scattered across numerous publications, it has proven difficult to gain a comprehensive understanding of all steps involved in the process and their limitations without considerable effort and attention to detail. Our paper aims to address this issue by providing a rigorous and comprehensive security proof for the finite-size 1-decoy and 2-decoy BB84 protocols against coherent attacks within Renner's entropic uncertainty relation framework. We resolve important technical flaws found in previous works regarding the fixed-length treatment of protocols and the careful handling of acceptance testing. To this end, we provide various technical arguments, including an analysis accounting for the important distinction of the 1-decoy protocol where statistics are computed after error correction, along with a slight improvement of the secure-key length. We also explicitly clarify the aspect of conditioning on events, addressing a technical detail often overlooked and essential for rigorous proofs. We extensively consolidate and unify concepts from many works, thoroughly discussing the underlying assumptions and resolving technical inconsistencies. Therefore, our contribution represents a significant advancement towards a broader and deeper understanding of QKD security proofs.
Accepted in Quantum. Added key rate plot and minor restructuring of the manuscript
References in corpus (69)
- Quantum Cryptography
- Quantum cryptography: Public key distribution and coin tossing
- The Security of Practical Quantum Key Distribution
- Simple Proof of Security of the BB84 Quantum Key Distribution Protocol
- Decoy State Quantum Key Distribution
- Measurement-device-independent quantum key distribution
- Advances in Quantum Cryptography
- Quantum Key Distribution with High Loss: Toward Global Secure Communication
- Beating the PNS attack in practical quantum cryptography
- Overcoming the rate-distance barrier of quantum key distribution without using quantum repeaters
- Practical Decoy State for Quantum Key Distribution
- Quantum cryptography protocols robust against photon number splitting attacks for weak laser pulses implementations
- Quantum Random Number Generators
- Security against individual attacks for realistic quantum key distribution
- Secure quantum key distribution over 421 km of optical fiber
- The operational meaning of min- and max-entropy
- Tight Finite-Key Analysis for Quantum Cryptography
- Quantum Cryptography with Coherent States
- Device-independent quantum key distribution secure against collective attacks
- The Uncertainty Relation for Smooth Entropies
- Finite-key analysis for measurement-device-independent quantum key distribution
- Concise Security Bounds for Practical Decoy-State Quantum Key Distribution
- Security in Quantum Cryptography
- Post-selection technique for quantum channels with applications to quantum cryptography
- Entanglement as precondition for secure quantum key distribution
- Quantum Information Processing with Finite Resources -- Mathematical Foundations
- Leftover Hashing Against Quantum Side Information
- Quantum key distribution with realistic states: photon-number statistics in the photon-number splitting attack
- Duality Between Smooth Min- and Max-Entropies
- No extension of quantum theory can have improved predictive power
- Quantum key distribution surpassing the repeaterless rate-transmittance bound without global phase locking
- Numerical approach for unstructured quantum key distribution
- Finite-key analysis on the 1-decoy state QKD protocol
- A largely self-contained and complete security proof for quantum key distribution
- Composability in quantum cryptography
- Practical security bounds against the Trojan-horse attack in quantum key distribution
- Chain Rules for Smooth Min- and Max-Entropies
- Attacks on practical quantum key distribution systems (and how to prevent them)
- Concise and Tight Security Analysis of the Bennett-Brassard 1984 Protocol with Finite Key Lengths
- Symmetries in Quantum Key Distribution and the Connection between Optimal Attacks and Optimal Cloning
- Brief History of Quantum Cryptography: A Personal Perspective
- Key recycling in authentication
- Tight finite-key security for twin-field quantum key distribution
- Numerical Calculations of Finite Key Rate for General Quantum Key Distribution Protocols
- Security of quantum key distribution from generalised entropy accumulation
- Finite-key security analysis for quantum key distribution with leaky sources
- Security proof of practical quantum key distribution with detection-efficiency mismatch
- Fundamental Finite Key Limits for One-Way Information Reconciliation in Quantum Key Distribution
- An approach for security evaluation and certification of a complete quantum communication system
- Security of quantum key distribution with imperfect phase randomisation
- Preparing a commercial quantum key distribution system for certification against implementation loopholes
- Sifting attacks in finite-size quantum key distribution
- Phase randomization improves the security of quantum key distribution
- Postselection technique for optical Quantum Key Distribution with improved de Finetti reductions
- Security Proof for Variable-Length Quantum Key Distribution
- Imperfect Phase-Randomisation and Generalised Decoy-State Quantum Key Distribution
- Secret key rate bounds for quantum key distribution with non-uniform phase randomization
- Security framework for quantum key distribution with imperfect sources
- Security of quantum key distribution using weak coherent states with nonrandom phases
- Improved Decoy-state and Flag-state Squashing Methods
- Finite-size analysis of prepare-and-measure and decoy-state QKD via entropy accumulation
- Sharp finite statistics for quantum key distribution
- A Framework for Non-Asymptotic Quantum Information Theory
- Finite-key analysis for quantum key distribution with weak coherent pulses based on Bernoulli sampling
- Marginal-constrained entropy accumulation theorem
- Rényi security framework against coherent attacks applied to decoy-state QKD
- A Proof of the Security of Quantum Key Distribution
- Defining Security in Quantum Key Distribution
- Authentication in Security Proofs for Quantum Key Distribution