Quantum Cryptography and Post-Quantum Cryptography

  1. Quantum Computing Fundamentals
    1. Basic Quantum Mechanics for Cryptography
      1. Quantum States and Qubits
        1. Qubit Representation
          1. Bloch Sphere Visualization
            1. Superposition Principle
              1. Measurement and Collapse
              2. Quantum Entanglement
                1. Definition and Properties
                  1. Bell States
                    1. EPR Paradox
                      1. Implications for Information Processing
                      2. Quantum Measurement
                        1. Measurement Postulates
                          1. Observable and Measurement Operators
                            1. Measurement Disturbance
                              1. Quantum Non-Demolition Measurements
                              2. No-Cloning Theorem
                                1. Statement and Proof Outline
                                  1. Implications for Quantum Information
                                    1. Security Implications
                                    2. Heisenberg Uncertainty Principle
                                      1. Mathematical Formulation
                                        1. Relevance to Quantum Cryptography
                                          1. Information Extraction Limitations
                                        2. Quantum Computing Model
                                          1. Quantum Gates and Circuits
                                            1. Single-Qubit Gates
                                              1. Pauli Gates
                                                1. Hadamard Gate
                                                  1. Phase Gates
                                                    1. Rotation Gates
                                                    2. Two-Qubit Gates
                                                      1. CNOT Gate
                                                        1. Controlled-Z Gate
                                                          1. SWAP Gate
                                                          2. Multi-Qubit Gates
                                                            1. Quantum Circuit Model
                                                              1. Quantum Parallelism
                                                              2. Quantum Algorithms
                                                                1. Deutsch-Jozsa Algorithm
                                                                  1. Bernstein-Vazirani Algorithm
                                                                    1. Simon's Algorithm
                                                                      1. Quantum Fourier Transform
                                                                    2. Quantum Algorithms Threatening Classical Cryptography
                                                                      1. Shor's Algorithm
                                                                        1. Algorithm Overview
                                                                          1. Period Finding Problem
                                                                            1. Quantum Fourier Transform Application
                                                                              1. Integer Factorization
                                                                                1. Impact on RSA
                                                                                  1. Required Quantum Resources
                                                                                  2. Discrete Logarithm Solution
                                                                                    1. Impact on Diffie-Hellman
                                                                                      1. Impact on ECC
                                                                                      2. Implementation Requirements
                                                                                        1. Timeline Estimates
                                                                                        2. Grover's Algorithm
                                                                                          1. Algorithm Overview
                                                                                            1. Quadratic Speedup Mechanism
                                                                                              1. Oracle Function Model
                                                                                                1. Threat to Symmetric Cryptography
                                                                                                  1. Effective Key Length Reduction
                                                                                                    1. Impact on AES
                                                                                                    2. Threat to Hash Functions
                                                                                                      1. Collision Finding Speedup
                                                                                                        1. Preimage Attack Speedup
                                                                                                        2. Implementation Requirements

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                                                                                                    1. Foundations of Modern Cryptography

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                                                                                                    3. Quantum Cryptography Principles