Finite Field

A set of Integers that will be Modulus by $n$ Oftentimes, $n$ is a Prime Number or number to the power of two.

${\mathbb{Z}}_n$ or $GF(n)$

$\{x|x=a\mathrm{mod}n,a\in Z\}$ or alternatively, ${\mathbb{Z}}_n=\{0,\dots ,n-1\}$ Has two operations:

• +_{\mod_{n}} ($a{+}_{\mathrm{mod}n}b=(a+b)\mathrm{mod}n$)
• ${\times }_{\mathrm{mod}n}$ $(a{\times }_{\mathrm{mod}n}b=(ab)\mathrm{mod}n)$

Concepts

• Euclidean Metric for Real Numbers
• Trivial Absolute Value
• Galois Field Multiplication

Theorems

• Trivial Absolute Value is the only Absolute value for Finite Fields