Summary of Number-theoretic Preliminaries
Modular Arithmetic:
- Speed up calculations by reducing modulo n
- Exponentiation is fast.
Two numbers relatively prime when share no common factors.
a -1 (mod n) is the number x such that ax (mod n) = 1.
- has unique solution if a and n are relatively prime.
- has no solution otherwise.
Extended Euclidean Algorithm
- to calculate gcd(a,b)
- to calculate a -1 (mod n)