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Computer Science
Cybersecurity
Quantum Cryptography and Post-Quantum Cryptography
1. Foundations of Modern Cryptography
2. Quantum Computing Fundamentals
3. Quantum Cryptography Principles
4. Quantum Key Distribution
5. QKD Implementation and Technology
6. QKD Security Analysis
7. Advanced Quantum Cryptographic Protocols
8. Post-Quantum Cryptography Foundations
9. Lattice-Based Cryptography
10. Code-Based Cryptography
11. Hash-Based Cryptography
12. Multivariate Cryptography
13. Isogeny-Based Cryptography
14. NIST Post-Quantum Cryptography Standardization
15. PQC Implementation and Deployment
16. Cryptanalysis of Post-Quantum Schemes
17. Quantum-Classical Cryptographic Integration
18. Quantum Networks and Infrastructure
19. Future Directions and Emerging Technologies
10.
Code-Based Cryptography
10.1.
Mathematical Foundations
10.1.1.
Linear Error-Correcting Codes
10.1.1.1.
Code Parameters
10.1.1.2.
Generator and Parity-Check Matrices
10.1.1.3.
Syndrome Decoding
10.1.2.
Decoding Problem Hardness
10.1.2.1.
General Linear Code Decoding
10.1.2.2.
NP-Completeness Results
10.1.2.3.
Average-Case Hardness
10.1.3.
Specific Code Families
10.1.3.1.
Goppa Codes
10.1.3.2.
Reed-Solomon Codes
10.1.3.3.
LDPC Codes
10.1.3.4.
Polar Codes
10.2.
Cryptographic Constructions
10.2.1.
McEliece Cryptosystem
10.2.1.1.
Original Construction
10.2.1.2.
Goppa Code Implementation
10.2.1.3.
Security Analysis
10.2.1.4.
Key Size Challenges
10.2.2.
Niederreiter Cryptosystem
10.2.2.1.
Dual Construction
10.2.2.2.
Advantages over McEliece
10.2.2.3.
Implementation Considerations
10.2.3.
Code-Based Signatures
10.2.3.1.
CFS Signatures
10.2.3.2.
Wave Signatures
10.2.3.3.
Security Properties
10.3.
Modern Developments
10.3.1.
Structured Codes
10.3.1.1.
Quasi-Cyclic Codes
10.3.1.2.
Key Size Reduction
10.3.1.3.
Security Trade-offs
10.3.2.
Rank-Based Cryptography
10.3.2.1.
Rank Metric Codes
10.3.2.2.
LRPC Codes
10.3.2.3.
Security Analysis
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9. Lattice-Based Cryptography
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11. Hash-Based Cryptography