Number Theory

  1. Cryptographic Applications
    1. Classical Cryptography
      1. Caesar Cipher
        1. Affine Cipher
          1. Hill Cipher
            1. Cryptanalysis Methods
            2. Modern Public Key Cryptography
              1. Basic Principles
                1. One-Way Functions
                  1. Trapdoor Functions
                  2. RSA Cryptosystem
                    1. Mathematical Foundation
                      1. Key Generation Algorithm
                        1. Encryption Process
                          1. Decryption Process
                            1. Security Analysis
                              1. Attacks and Countermeasures
                              2. Diffie-Hellman Key Exchange
                                1. Discrete Logarithm Problem
                                  1. Protocol Description
                                    1. Security Considerations
                                      1. Variants and Extensions
                                      2. Primality Testing
                                        1. Deterministic Tests
                                          1. Probabilistic Tests
                                            1. Fermat Test
                                              1. Miller-Rabin Test
                                              2. Practical Considerations
                                              3. Integer Factorization
                                                1. Trial Division
                                                  1. Pollard's Rho Method
                                                    1. Quadratic Sieve
                                                      1. Elliptic Curve Method
                                                        1. Cryptographic Implications

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                                                      12. Elementary Analytic Number Theory

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                                                      14. Advanced Topics and Connections