Finite Fields
A finite field is a set with finite elements. We are interested in the set of integers modulo p, where p is a prime number.
E.g. if p=7, then
Note: p being prime is necessary for the multiplicative inverse to be defined i.e. 3*5mod7 = 1
This is also written as
That's also how we define modulo division
The great thing about finite fields on elliptic curves is that they have the same geometric properties as for the continuous case. Proof by Stefan Friedel
Visit our git project to see explore finite elliptic curves!
https://github.com/asher-pembroke/elliptic