UsefulLinks
Mathematics
Number Theory
1. Foundations of Number Theory
2. Divisibility Theory
3. Prime Numbers and Factorization
4. Greatest Common Divisor and Least Common Multiple
5. Modular Arithmetic and Congruences
6. Classical Theorems in Number Theory
7. Arithmetic Functions
8. Diophantine Equations
9. Quadratic Residues and Reciprocity
10. Prime Number Theory
11. Continued Fractions
12. Elementary Analytic Number Theory
13. Cryptographic Applications
14. Advanced Topics and Connections
13.
Cryptographic Applications
13.1.
Classical Cryptography
13.1.1.
Caesar Cipher
13.1.2.
Affine Cipher
13.1.3.
Hill Cipher
13.1.4.
Cryptanalysis Methods
13.2.
Modern Public Key Cryptography
13.2.1.
Basic Principles
13.2.2.
One-Way Functions
13.2.3.
Trapdoor Functions
13.3.
RSA Cryptosystem
13.3.1.
Mathematical Foundation
13.3.2.
Key Generation Algorithm
13.3.3.
Encryption Process
13.3.4.
Decryption Process
13.3.5.
Security Analysis
13.3.6.
Attacks and Countermeasures
13.4.
Diffie-Hellman Key Exchange
13.4.1.
Discrete Logarithm Problem
13.4.2.
Protocol Description
13.4.3.
Security Considerations
13.4.4.
Variants and Extensions
13.5.
Primality Testing
13.5.1.
Deterministic Tests
13.5.2.
Probabilistic Tests
13.5.2.1.
Fermat Test
13.5.2.2.
Miller-Rabin Test
13.5.3.
Practical Considerations
13.6.
Integer Factorization
13.6.1.
Trial Division
13.6.2.
Pollard's Rho Method
13.6.3.
Quadratic Sieve
13.6.4.
Elliptic Curve Method
13.6.5.
Cryptographic Implications
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12. Elementary Analytic Number Theory
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14. Advanced Topics and Connections