Finite Field

Multiplicative Inverse

For $a \in \mathbb{F}_{p}$, the inverse is the solution of $ax \cong 1 (\mathrm{mod}\ p)$. $x \cong a^{p - 2} (\mathrm{mod}\ p)$.

For example, $a := 3 \in GF(7) = \mathbb{F}_{7}$. $3^{5} = 243 \cong 5 (\mathrm{mod}\ 7)$.

Reference

• https://en.wikipedia.org/wiki/Finite_field_arithmetic