Cryptography

  1. Mathematical Foundations
    1. Number Theory Basics
      1. Prime Numbers
        1. Definition and Properties
          1. Prime Factorization
            1. Primality Testing
              1. Prime Generation
              2. Modular Arithmetic
                1. Congruence Relations
                  1. Modular Addition and Multiplication
                    1. Modular Inverses
                      1. Extended Euclidean Algorithm
                      2. Greatest Common Divisor
                        1. Euclidean Algorithm
                          1. Bézout's Identity
                          2. Chinese Remainder Theorem
                            1. Statement and Applications
                              1. Constructive Proof
                              2. Euler's Theorem
                                1. Euler's Totient Function
                                  1. Applications in Cryptography
                                  2. Fermat's Little Theorem
                                    1. Statement and Proof
                                      1. Cryptographic Applications
                                    2. Group Theory
                                      1. Groups
                                        1. Definition and Properties
                                          1. Cyclic Groups
                                            1. Group Orders
                                            2. Finite Fields
                                              1. Field Properties
                                                1. Galois Fields
                                                  1. Polynomial Arithmetic
                                                  2. Discrete Logarithm Problem
                                                    1. Computational Difficulty
                                                  3. Elliptic Curve Mathematics
                                                    1. Elliptic Curve Definition
                                                      1. Point Addition
                                                        1. Scalar Multiplication
                                                          1. Elliptic Curve Groups
                                                            1. Elliptic Curve Discrete Logarithm Problem
                                                            2. Probability and Information Theory
                                                              1. Basic Probability
                                                                1. Random Variables
                                                                  1. Entropy
                                                                    1. Perfect Secrecy
                                                                      1. Computational Indistinguishability

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                                                                    1. Foundations of Cryptography

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                                                                    3. Symmetric Key Cryptography