Quantum Cryptography Basics

Table of Contents

1. Introduction
2. What Is Quantum Cryptography?
3. Classical Cryptography: A Brief Recap
4. Quantum vs Classical Security
5. Core Principles Behind Quantum Cryptography
6. Quantum Superposition and Measurement
7. The Role of Entanglement
8. Heisenberg Uncertainty and Security
9. No-Cloning Theorem in Cryptography
10. Key Distribution vs Encryption
11. Quantum Key Distribution (QKD)
12. The BB84 Protocol
13. The E91 Protocol
14. Differences Between BB84 and E91
15. Security of QKD
16. Error Rates and Eavesdropping Detection
17. Privacy Amplification
18. Authentication in Quantum Channels
19. Post-Quantum Cryptography vs Quantum Cryptography
20. Quantum Cryptographic Devices
21. Experimental Demonstrations
22. Current Challenges and Limitations
23. Integration with Classical Systems
24. Applications and Future Directions
25. Conclusion

1. Introduction

Quantum cryptography uses the laws of quantum mechanics to enable secure communication. It guarantees unconditional security, something impossible with classical methods relying on computational assumptions.

2. What Is Quantum Cryptography?

It is the science of using quantum properties (like superposition and entanglement) to:

• Detect eavesdropping
• Securely distribute cryptographic keys
• Build fundamentally secure systems

3. Classical Cryptography: A Brief Recap

Classical cryptography relies on:

• RSA (factoring-based)
• ECC (elliptic curves)
• AES (symmetric key)

Their security is based on computational difficulty, not physics.

4. Quantum vs Classical Security

5. Core Principles Behind Quantum Cryptography

Quantum cryptography is built on:

• Superposition
• Entanglement
• Measurement disturbance
• No-cloning theorem

6. Quantum Superposition and Measurement

Measuring a quantum state collapses it:

\[
|\psi\rangle = \alpha|0\rangle + \beta|1\rangle \Rightarrow \text{collapse to } |0\rangle \text{ or } |1\rangle
\]

This property is exploited to detect eavesdropping.

7. The Role of Entanglement

Entanglement creates strong correlations between distant particles. These correlations can be used to:

• Verify secure channels
• Detect tampering

8. Heisenberg Uncertainty and Security

Uncertainty principle prevents simultaneous knowledge of complementary observables:

\[
\Delta x \cdot \Delta p \geq \frac{\hbar}{2}
\]

This ensures tampering can’t go undetected.

9. No-Cloning Theorem in Cryptography

No one can copy unknown quantum states:

\[
|\psi\rangle \nrightarrow |\psi\rangle \otimes |\psi\rangle
\]

This guarantees eavesdroppers cannot clone the transmitted qubits.

10. Key Distribution vs Encryption

Quantum cryptography mostly focuses on Quantum Key Distribution (QKD), not encryption itself. Encryption is done classically using the secret key.

11. Quantum Key Distribution (QKD)

QKD allows two parties to:

• Establish a shared secret key
• Detect any third-party attempts to observe the exchange
• Use that key in classical encryption (e.g., one-time pad)

12. The BB84 Protocol

Proposed by Bennett and Brassard in 1984, it uses:

• Polarization states in two bases: rectilinear and diagonal
• Random bit and basis selection

Steps:

1. Alice sends qubits encoded in random bases
2. Bob measures in random bases
3. They compare bases and keep matching bits

13. The E91 Protocol

Proposed by Ekert in 1991:

• Uses entangled particles
• Verifies quantum correlations using Bell inequality tests
• Offers security proofs based on entanglement

14. Differences Between BB84 and E91

15. Security of QKD

QKD is provably secure against all computational attacks, even from quantum computers, as long as physical assumptions hold.

16. Error Rates and Eavesdropping Detection

Eavesdropping introduces errors. If error rate > threshold (usually ~11%), communication is aborted.

17. Privacy Amplification

After key generation, Alice and Bob perform:

• Error correction
• Privacy amplification to remove eavesdropper’s partial knowledge

18. Authentication in Quantum Channels

QKD requires authenticated classical channels to prevent man-in-the-middle attacks. Authentication is done using classical cryptographic hashes or pre-shared keys.

19. Post-Quantum Cryptography vs Quantum Cryptography

• Post-quantum: Classical protocols safe from quantum attacks
• Quantum cryptography: Uses quantum mechanics for security

They are complementary, not exclusive.

20. Quantum Cryptographic Devices

• Single-photon sources
• Polarization filters
• Avalanche photodiodes
• Quantum random number generators (QRNGs)

21. Experimental Demonstrations

QKD has been demonstrated over:

• Optical fibers (>500 km)
• Free-space and satellite links (e.g., China’s Micius satellite)

22. Current Challenges and Limitations

• Cost and complexity of equipment
• Photon loss and noise in channels
• Scalability to large networks
• Authentication and key management

23. Integration with Classical Systems

Quantum keys are often used with:

• Classical one-time pads
• AES encryption with frequent key refresh
• Hybrid classical-quantum secure systems

24. Applications and Future Directions

• Secure government and military communication
• Banking and finance
• Long-distance secure communication via quantum repeaters
• Building a quantum internet

25. Conclusion

Quantum cryptography marks a revolutionary step in secure communication. By leveraging the fundamental principles of quantum mechanics, it provides security guarantees that classical systems cannot match. As technology matures, QKD and related techniques will play a crucial role in safeguarding data in the quantum era.