Quantum Cryptography and Post-Quantum Cryptography

  1. Hash-Based Cryptography
    1. Theoretical Foundations
      1. One-Way Functions
        1. Hash Function Security Properties
          1. Merkle Tree Structures
            1. Security Reductions
            2. One-Time Signatures
              1. Lamport Signatures
                1. Construction and Security
                  1. Key and Signature Sizes
                    1. Implementation Details
                    2. Winternitz Signatures
                      1. Parameter Trade-offs
                        1. Security Analysis
                          1. Optimization Techniques
                        2. Few-Time Signatures
                          1. HORS Signatures
                            1. Security Degradation
                              1. Parameter Selection
                              2. Many-Time Signatures
                                1. Merkle Signature Scheme
                                  1. Tree-Based Construction
                                    1. State Management
                                      1. Security Properties
                                      2. XMSS
                                        1. Stateful Design
                                          1. Forward Security
                                            1. Implementation Standards
                                            2. SPHINCS+
                                              1. Stateless Construction
                                                1. FORS and WOTS+ Integration
                                                  1. NIST Standardization
                                                    1. Performance Analysis

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                                                10. Code-Based Cryptography

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                                                12. Multivariate Cryptography