Quantum Cryptography and Post-Quantum Cryptography

  1. Code-Based Cryptography
    1. Mathematical Foundations
      1. Linear Error-Correcting Codes
        1. Code Parameters
          1. Generator and Parity-Check Matrices
            1. Syndrome Decoding
            2. Decoding Problem Hardness
              1. General Linear Code Decoding
                1. NP-Completeness Results
                  1. Average-Case Hardness
                  2. Specific Code Families
                    1. Goppa Codes
                      1. Reed-Solomon Codes
                        1. LDPC Codes
                          1. Polar Codes
                        2. Cryptographic Constructions
                          1. McEliece Cryptosystem
                            1. Original Construction
                              1. Goppa Code Implementation
                                1. Security Analysis
                                  1. Key Size Challenges
                                  2. Niederreiter Cryptosystem
                                    1. Dual Construction
                                      1. Advantages over McEliece
                                        1. Implementation Considerations
                                        2. Code-Based Signatures
                                          1. CFS Signatures
                                            1. Wave Signatures
                                              1. Security Properties
                                            2. Modern Developments
                                              1. Structured Codes
                                                1. Quasi-Cyclic Codes
                                                  1. Key Size Reduction
                                                    1. Security Trade-offs
                                                    2. Rank-Based Cryptography
                                                      1. Rank Metric Codes
                                                        1. LRPC Codes
                                                          1. Security Analysis

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                                                      9. Lattice-Based Cryptography

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                                                      11. Hash-Based Cryptography