Number Theory

Euclidean Algorithm
Modular Arithmetic
Modular Inverse
Chinese Remainder Theorem
Factorization
Euler Totient Function
Primality Tests
Quadratic Residue
Legendre Symbol
Jacobi Symbol

Cryptography

Primitive Roots
Modular Exponentiation
Elliptic Curves
Pohlig Hellman
Diffie Hellman
elGamal
Vigenere Cipher
Pollard's p-1
Alphabet Frequency
n-gram Frequency