Overview

Teaching: 150 min
Exercises: 0 min

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Quantum Cryptography and the Physics of Secure Communication

1. Introduction

Quantum cryptography leverages the laws of quantum mechanics to achieve unbreakable encryption and secure communication. Unlike classical cryptography, which relies on mathematical complexity, quantum cryptography is rooted in the fundamental principles of physics, making it resistant to computational attacks, including those from quantum computers.

🚀 Key Concept: Quantum Key Distribution (QKD) is the most well-known quantum cryptographic technique, ensuring that eavesdropping is physically detectable.

2. Physics Principles Behind Quantum Cryptography

2.1 The Heisenberg Uncertainty Principle

🔹 States that measuring a quantum system inevitably disturbs it.
🔹 If an eavesdropper (Eve) tries to intercept a quantum transmission, the system will change, alerting legitimate users.

🔹 Mathematical Formulation:
[ \Delta x \cdot \Delta p \geq \frac{\hbar}{2} ]

• Any attempt to measure quantum states introduces uncertainty, which can be detected in secure communication.

2.2 Quantum Superposition and Qubits

🔹 Qubits (Quantum Bits) can exist in multiple states simultaneously (unlike classical bits, which are 0 or 1).
🔹 Encoding information in qubits enables new forms of cryptographic protocols.

🔹 Example: Quantum Bit Representation
[ |\psi\rangle = \alpha |0\rangle + \beta |1\rangle ] where ( \alpha ) and ( \beta ) are probability amplitudes.

🚀 Benefit: Impossible to clone an unknown quantum state (No-Cloning Theorem), preventing attackers from copying qubits undetected.

2.3 Quantum Entanglement

🔹 When two particles are entangled, their states are instantaneously correlated, no matter the distance.
🔹 This enables secure key exchanges over long distances.

🔹 Mathematical Formulation (Bell States Example):
[ |\Phi^+\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle) ]

• If one qubit is measured, the other’s state is instantly determined.

🚀 Benefit: Eavesdropping disrupts entanglement, making detection possible.

3. Quantum Cryptographic Techniques

3.1 Quantum Key Distribution (QKD)

QKD allows two parties (Alice & Bob) to securely exchange cryptographic keys using quantum mechanics.

🔹 BB84 Protocol (Bennett & Brassard, 1984) – Uses quantum states to encode bits:

1. Alice sends randomly polarized photons to Bob.
2. Bob measures them using a random basis.
3. If Eve intercepts, the measurement changes, exposing eavesdropping.

🔹 Ekert91 Protocol – Uses quantum entanglement to detect eavesdropping via Bell’s Theorem.

🚀 Security Advantage: QKD is information-theoretically secure—even quantum computers cannot break it.

3.2 Post-Quantum Cryptography (PQC)

🔹 While QKD relies on quantum mechanics, post-quantum cryptography (PQC) is based on mathematically hard problems that even quantum computers struggle with (e.g., lattice-based encryption).
🔹 Examples: CRYSTALS-Kyber, NTRUEncrypt.

🚀 Future-Proofing Security: PQC ensures classical networks remain secure even against quantum attacks.

4. Real-World Applications of Quantum Cryptography

🔹 Government & Military: Quantum-secured networks for classified communications.
🔹 Financial Institutions: Quantum-safe transactions to prevent future hacking.
🔹 Satellite-Based QKD: China’s Micius satellite demonstrated global quantum encryption.

5. Conclusion

Quantum cryptography fundamentally changes cybersecurity by using laws of physics rather than computational difficulty.

✅ Key Takeaways:

• Heisenberg’s Uncertainty Principle & No-Cloning Theorem ensure undetectable eavesdropping.
• Quantum Key Distribution (QKD) enables unbreakable encryption.
• Quantum entanglement & superposition provide unique cryptographic advantages.
• Post-Quantum Cryptography (PQC) is crucial for protecting classical networks from future quantum threats.

📡 Next Steps: Would you like a deeper dive into quantum-resistant encryption algorithms or real-world QKD implementations? 🚀

Key Points

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