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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
12.
Multivariate Cryptography
12.1.
Mathematical Foundations
12.1.1.
Multivariate Polynomial Systems
12.1.2.
NP-Hardness of MQ Problem
12.1.3.
Finite Field Arithmetic
12.1.4.
Gröbner Basis Attacks
12.2.
Signature Schemes
12.2.1.
Oil and Vinegar Schemes
12.2.1.1.
Unbalanced Oil and Vinegar
12.2.1.2.
Security Analysis
12.2.1.3.
Parameter Selection
12.2.2.
HFE Signatures
12.2.2.1.
Hidden Field Equations
12.2.2.2.
Trapdoor Construction
12.2.2.3.
Security Considerations
12.2.3.
Rainbow Signatures
12.2.3.1.
Multi-Layer Construction
12.2.3.2.
Efficiency Improvements
12.2.3.3.
Cryptanalysis Results
12.3.
Encryption Schemes
12.3.1.
Challenges in Multivariate Encryption
12.3.2.
ABC Encryption
12.3.3.
Security Limitations
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11. Hash-Based Cryptography
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13. Isogeny-Based Cryptography