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Security Independent Submission quantum cryptography QKD CPF quantum key distribution This document specifies an enhanced Collapse Purity Filter (CPF) algorithm for Quantum Key Distribution (QKD) systems. The enhanced CPF algorithm improves key generation efficiency by 100% compared to conventional CPF implementations while maintaining quantum security guarantees. The algorithm uses adaptive filter verification instead of fixed threshold filtering, achieving near-zero Quantum Bit Error Rate (QBER) in ideal conditions and accurate eavesdropping detection in adversarial scenarios. This specification is compatible with BB84 protocol and complies with Korean Internet Security Agency (KISA) standards TTAK.KO-12.0281 for quantum key distribution protocols.

Introduction Quantum Key Distribution (QKD) provides information-theoretic security based on the laws of quantum mechanics. The BB84 protocol established the foundation for QKD systems. The Collapse Purity Filter (CPF) algorithm is a quantum circuit-based approach for generating cryptographic keys using quantum entanglement and measurement collapse properties. Conventional CPF implementations suffer from a critical inefficiency: they accept only filter qubit measurements of '0', rejecting approximately 50% of valid quantum states. This document presents an enhanced CPF algorithm that uses adaptive verification, comparing measured filter values against expected values rather than using fixed thresholds. This work complies with Korean Internet Security Agency (KISA) standards and considers post-quantum cryptography guidelines . The reference implementation uses the Qiskit framework for quantum circuit execution.

Terminology The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in BCP 14 when, and only when, they appear in all capitals, as shown here. This document uses the following terms:

• CPF: Collapse Purity Filter
• QKD: Quantum Key Distribution
• QBER: Quantum Bit Error Rate
• CNOT: Controlled-NOT quantum gate
• Qubit: Quantum bit

Enhanced CPF Algorithm Specification

Quantum Circuit Construction The enhanced CPF algorithm uses a two-qubit quantum circuit where:

• q0: Data qubit (encodes Alice's secret bit)
• q1: Filter qubit (verifies quantum state purity)

Circuit construction procedure:

1. Initialize two qubits in |0⟩ state
2. If alice_bit = 1, apply X gate to q0
3. Apply CNOT(q0, q1) to create entanglement
4. If basis_flip = true, apply H gate to q0 (BB84 compatibility)
5. Measure both qubits

The CNOT gate creates a correlation where q1 becomes a copy of q0 in the computational basis. In ideal conditions, q1 MUST equal the initial value of q0 (alice_bit).

Adaptive Filter Verification The key innovation of the enhanced CPF algorithm is adaptive filter verification. Instead of accepting only q1='0' measurements, the algorithm compares the measured filter value against the expected value. Verification procedure: Where expected_filter = alice_bit (the initial value encoded in q0). This approach achieves 100% acceptance rate in ideal conditions, compared to 50% in conventional CPF implementations.

QBER Analysis and Eavesdropping Detection The Quantum Bit Error Rate (QBER) is calculated as: QBER thresholds (based on KISA TTAK.KO-12.0281):

• QBER ≤ 5%: Safe (continue communication)
• 5% < QBER ≤ 8%: Warning (increased monitoring)
• 8% < QBER ≤ 11%: Critical (eavesdropping suspected)
• QBER > 11%: Abort (session termination required)

The enhanced CPF algorithm provides accurate QBER measurements:

• No eavesdropping: QBER ≈ 0% (hardware noise only)
• 20% bit tampering: QBER ≈ 20% (accurate detection)

In contrast, conventional CPF shows QBER ≈ 50% even without eavesdropping, making attack detection ambiguous.

Protocol Flow

Key Generation Phase (Alice)

1. Generate random bit: alice_bit ∈ {0, 1}
2. Generate random basis: basis_flip ∈ {true, false}
3. Construct CPF quantum circuit
4. Execute circuit on quantum hardware (50 shots)
5. Measure qubits and obtain result: (q1, q0)
6. Verify: if q1 == alice_bit, accept q0 as key bit
7. Repeat until target key length achieved
8. Monitor QBER; abort if QBER > 11%

Key Verification Phase (Bob)

1. Receive quantum key bits and sample indices from Alice
2. Calculate QBER using sample bits (public channel)
3. If QBER > 11%, abort session
4. Verify HMAC-SHA256 integrity tag
5. Apply Privacy Amplification
6. Derive encryption key using HKDF-SHA256
7. Decrypt ciphertext using AES-256-GCM

Performance Analysis

Efficiency Improvements Comparison with conventional CPF:

Metric	Conventional CPF	Enhanced CPF	Improvement
Bit acceptance rate	~50%	~100%	+100%
Circuit executions (256-bit key)	~512	~256	-50%
QBER (no eavesdropping)	~50%	~0%	Accurate
QBER (20% tampering)	~60%	~20%	Accurate

Security Analysis The enhanced CPF algorithm maintains the same security guarantees as conventional CPF while improving efficiency:

• Quantum security: Based on no-cloning theorem and measurement collapse
• Eavesdropping detection: QBER analysis with 11% threshold
• BB84 compatibility: Basis randomization prevents intercept-resend attacks
• Multi-layer defense: CPF filtering + QBER analysis + HMAC verification

Implementation Considerations

Quantum Hardware Requirements The algorithm can be implemented on any quantum computing platform supporting:

• Minimum 2 qubits
• Single-qubit gates: X, H
• Two-qubit gate: CNOT
• Measurement in computational basis

Tested platforms: IBM Quantum (real hardware and Aer simulator), compatible with Qiskit 1.0+.

Classical Post-Processing Required classical cryptographic primitives:

• Privacy Amplification: Universal hash functions
• Key Derivation: HKDF-SHA256
• Encryption: AES-256-GCM (NIST FIPS 197)
• Authentication: HMAC-SHA256

Security Considerations

Quantum Attacks The enhanced CPF algorithm is resistant to known quantum attacks:

• Intercept-resend attack: Detected via QBER increase
• Photon number splitting: Mitigated by decoy states (future work)
• Trojan horse attack: Requires physical security measures

Classical Attacks Classical security is provided by:

• AES-256-GCM: Quantum-resistant symmetric encryption
• HMAC-SHA256: Prevents packet tampering
• HKDF: Ensures key independence

Side-Channel Considerations Implementations MUST protect against:

• Timing attacks: Use constant-time cryptographic operations
• Power analysis: Implement countermeasures in hardware
• Electromagnetic leakage: Shield sensitive components

QBER Threshold Selection The 11% QBER threshold is based on BB84 theoretical limits. Implementations MAY use lower thresholds (e.g., 8%) for higher security margins, at the cost of increased false positive rates in noisy environments.

IANA Considerations This document has no IANA actions. Future versions may request registration of:

• QKD protocol identifiers
• Cryptographic algorithm identifiers for CPF

References Normative References Informative References Korea Internet and Security Agency (KISA) Telecommunications Technology Association (TTA) National Institute of Standards and Technology IBM Quantum Available at: https://qiskit.org

Acknowledgments The author thanks the IBM Quantum team for providing access to quantum hardware and the Qiskit framework. This work was developed in compliance with KISA (Korea Internet & Security Agency) standards for quantum cryptography.

Example Implementation A reference implementation in Python using Qiskit is available at: https://github.com/your-repo/kisa-qkd Example quantum circuit construction: Example filter verification: