Enhanced Collapse Purity Filter Algorithm for Quantum Key Distribution

1.1. 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 [RFC2119] [RFC8174] 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¶

2.1. 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).¶

2.2. 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:¶

function verify_quantum_state(measured_filter, expected_filter):
    if measured_filter == expected_filter:
        return ACCEPT  // Pure quantum state
    else:
        return REJECT  // Contaminated by noise or eavesdropping

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.¶

2.3. QBER Analysis and Eavesdropping Detection

The Quantum Bit Error Rate (QBER) is calculated as:¶

QBER = error_count / (confirmed_bits + error_count)

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.¶

3.1. 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%¶

3.2. 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¶

4.1. Efficiency Improvements

Comparison with conventional CPF:¶

4.2. 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¶

5.1. 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+.¶

5.2. Classical Post-Processing

Required classical cryptographic primitives:¶

• Privacy Amplification: Universal hash functions¶
• Key Derivation: HKDF-SHA256 [RFC5869]¶
• Encryption: AES-256-GCM (NIST FIPS 197)¶
• Authentication: HMAC-SHA256 [RFC2104]¶

6.1. 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¶

6.2. Classical Attacks

Classical security is provided by:¶

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

6.3. 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¶

6.4. 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.¶